QUANTA - ESI€¦ · QUANTA CHARMm Principles Release 2000 December 2000 9685 Scranton Road San Diego, CA 92121-3752 858/799-5000 Fax: 858/799-5100

QUANTACHARMm Principles

Release 2000December 2000

9685 Scranton RoadSan Diego, CA 92121-3752

858/799-5000 Fax: 858/799-5100

Copyright*

This document is copyright © 2001, Accelrys Incorporated. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or dis-tributed in any form or by any means or stored in a database retrieval system without the prior written permission of Molecular Simulations Inc.The software described in this document is furnished under a license and may be used or copied only in accordance with the terms of such license.

Restricted Rights LegendUse, duplication, or disclosure by the Government is subject to restrictions as in subparagraph (c)(1)(ii) of the Rights in Technical Data and Computer Software clause at DFAR 252.227–7013 or subpara-graphs (c)(1) and (2) of the Commercial Computer Software—Restricted Rights clause at FAR 52.227-19, as applicable, and any successor rules and regulations.

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Contents

How to Use This Book vWho should use this book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viHow to find information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiUsing this book with QUANTA books . . . . . . . . . . . . . . . . . . . . viiTypographical conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .viii

1. Introduction to CHARMm 1Getting started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Understanding CHARMm processes . . . . . . . . . . . . . . . . . . . . . . . 2Commands and command files . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Input and output operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6File formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Converting file formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Command stream control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9CHARMm measurement units . . . . . . . . . . . . . . . . . . . . . . . . . . . 10CHARMm array dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2. Preparing Models for Energy Calculations 13Constructing and using residue topology files . . . . . . . . . . . . . . . 13Using sequence information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Generating and using a principal structure file . . . . . . . . . . . . . . 20

Creating a PSF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Modifying a PSF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Modeling hydrogens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Extended-atom model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24All-hydrogen model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Generating and using coordinates . . . . . . . . . . . . . . . . . . . . . . . . 25CHARMm internal coordinates . . . . . . . . . . . . . . . . . . . . . . 26Building Cartesian coordinates from internal coordinates . . 27Coordinate arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Format of the CHARMm coordinate file . . . . . . . . . . . . . . . 32Constructing hydrogen positions . . . . . . . . . . . . . . . . . . . . . 33

Using parameter files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Ryckaert–Bellemans torsion potential . . . . . . . . . . . . . . . . . 38Example: Parameter file PARM.PRM . . . . . . . . . . . . . . . . . 38

CHARMm Principles / Quanta 4.1 i

Summary examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38Example: Constructing polymer segments joined by

a sulfur bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38Example: Constructing an alpha helix of polyalanine . . . . . .41Example: Generating random conformations of enkephalin .43Example: Constructing an N-methylacetamide dimer . . . . . .46Example: Constructing conformations of cyclohexane . . . . .48

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51

3. Performing Energy and Force Calculations 53Applying the CHARMm energy function . . . . . . . . . . . . . . . . . . .53

Internal energy terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54External energy terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55Other energy terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61Example: Calculating the initial energies of enkephalin . . . .62

Minimizing energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63Minimization methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64Convergence criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66Example: Minimizing enkephalin . . . . . . . . . . . . . . . . . . . . .66Example: Minimizing crambin . . . . . . . . . . . . . . . . . . . . . . . .67

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69

4. Performing Molecular Dynamics 71Understanding molecular dynamics. . . . . . . . . . . . . . . . . . . . . . . .71

Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73Dynamics time step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74Length of trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75

Running dynamic simulation variants . . . . . . . . . . . . . . . . . . . . . .75Langevin dynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75Stochastic boundary molecular dynamics . . . . . . . . . . . . . . .76Constant pressure and temperature dynamics . . . . . . . . . . . .76Quenched molecular dynamics. . . . . . . . . . . . . . . . . . . . . . . .78

Monitoring dynamics simulation output . . . . . . . . . . . . . . . . . . . .79Coordinate trajectory format . . . . . . . . . . . . . . . . . . . . . . . . .79

Using time sets and correlation functions . . . . . . . . . . . . . . . . . . .81Example: Running enkephalin dynamics . . . . . . . . . . . . . . . . . . .82Example: Calculating correlations in enkephalin dynamics . . . . .86References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88

5. Setting Constraints and Periodic Boundaries 89Setting constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .89

Fixed atom restraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90Harmonic atom constraint . . . . . . . . . . . . . . . . . . . . . . . . . . .90Torsion constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91

ii CHARMm Principles / Quanta 4.1

Internal coordinate constraint . . . . . . . . . . . . . . . . . . . . . . . . 91Distance constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91SHAKE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Quartic droplet constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Example: Creating the alanine dipeptide phi/psi map . . . . . 92Example: Using NOE constraints . . . . . . . . . . . . . . . . . . . . . 95

Setting periodic boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Using image options in CHARMm. . . . . . . . . . . . . . . . . . . . 98Using crystal options in CHARMm . . . . . . . . . . . . . . . . . . 101

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

6. Performing Free Energy Simulations 113Understanding the relative free energy Hamiltonian . . . . . . . . . 114Using free energy calculation methods . . . . . . . . . . . . . . . . . . . 116

Perturbation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117Thermodynamic integration method. . . . . . . . . . . . . . . . . . 118Slow-growth method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Running a free energy simulation . . . . . . . . . . . . . . . . . . . . . . . 119Example: Setting up an FES simulation and running

dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Applying scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Post-processing data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Using umbrella sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

7. Setting Stochastic Boundaries 131Basic features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131General procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132Example: Setting up a stochastic boundary . . . . . . . . . . . . . . . . 133

Index 137

CHARMm Principles / Quanta 4.1 iii

iv CHARMm Principles / Quanta 4.1

How to Use This Book

CHARMm Principles describes fundamental operations, concepts, and principles of the CHARMm® program. The book is designed to provide an introduction to the use of CHARMm. Many of the most frequently used applications of CHARMm are covered. The material in this book applies to CHARMm Version 23 and 23.1 used as standalone software or in conjunc-tion with QUANTA®.

The book is divided into the following chapters:

♦ Chapter 1, Introduction to CHARMm — This chapter provides an over-view of CHARMm activities and basic information on operations, including commands and command files, input and output operations, file formats, command stream control, CHARMm measurement units, and CHARMm array dimensions.

♦ Chapter 2, Preparing Models for Energy Calculations — This chapter describes the information that must be available for each molecular model that you want to study with CHARMm and the sources for that information. Information is included on residue topology files, parame-ter files, and generating and using coordinates.

♦ Chapter 3, Performing Energy and Force Calculations — This chapter describes the CHARMm energy function and energy minimization algorithms that can be used to refine structures or locate stationary points for conformational searching for dynamics simulations.

♦ Chapter 4, Performing Molecular Dynamics — This chapter explains how to set up, run, and monitor dynamics simulations. It also describes the use of time sets and correlation functions in dynamics simulations.

♦ Chapter 5, Setting Constraints and Periodic Boundaries— This chapter describes the options for tailoring files and data to focus on the parts of a molecular system in which you are interested. These options include setting constraints on atoms, angles, dihedral angles, and other proper-ties, and introducing periodic boundary conditions in energy calcula-tions.

CHARMm Principles / Quanta 4.1 v


♦ Chapter 6, Performing Free Energy Simulations — This chapter describes three methods available in CHARMm for performing free energy simulations. It includes the calculations that are performed using each method, the process of running a simulation, post-processing of data, applying scaling, and using umbrella sampling.

♦ Chapter 7, Setting Stochastic Boundaries — This chapter describes basic features and the general procedure for setting up stochastic bound-aries.

Each chapter contains scripted examples to highlight functionality. Although the scripts in the book generally match those provided on disk, changes may have been made to the scripts on disk that are not reflected in the book and vice versa. Part of a script may be omitted in the book for the sake of brevity. When this occurs, it is noted within the text of the script.

When you are using this book, also have the CHARMm Dictionary avail-able. Use it to find information on specific commands and keywords used in the example scripts.

Who should use this book

This book is intended as a reference for day-to-day users of CHARMm and QUANTA. It covers both basic and advanced functions and activities, but it is not an exhaustive description of CHARMm or CHARMm functions. For more information about CHARMm, please consult the documentation files that are included online with the software. Be aware that these files are compiled from a variety of sources (many of them non-MSI) and at differ-ent times.

This book is written as though CHARMm is being used as standalone soft-ware. However, the information, is also applicable to users of CHARMm from within QUANTA. All QUANTA users should have a version of CHARMm packaged with the QUANTA software.

Before you begin Before you begin to use CHARMm, you should already be familiar with:

♦ The windowing software on your workstation.

♦ Use of the mouse on the workstation.

♦ Basic UNIX® commands.

vi CHARMm Principles / Quanta 4.1

How to find information

Your workstation should have

♦ An installed, licensed copy of CHARMm.

♦ A home directory in which subdirectories can be created.

How to find information

Using this book with QUANTA books

♦ This book contains information that supplements the QUANTA docu-mentation set. In particular, this book can be used in conjunction with:

♦ CHARMm Dictionary.

♦ QUANTA user’s guides, including:

QUANTA Basic Operations

QUANTA Generating and Displaying Molecules

QUANTA Simulation, Search, and Analysis

If you want to know about… Read…

Basic CHARMm operations Chapter 1, Introduction to CHARMmPreparing models for energy calcula-

tionsChapter 2, Preparing Models for Energy Calculations

Calculating potential energy and molec-ular forces

Chapter 3, Performing Energy and Force Calculations

Performing molecular dynamics simu-lations

Chapter 4, Performing Molecular Dynamics

Setting constraints or using periodic boundaries

Chapter 5, Setting Constraints and Periodic Bound-aries

Performing free energy simulations Chapter 6, Performing Free Energy SimulationsUsing stochastic boundaries Chapter 7, Setting Stochastic Boundaries

CHARMm Principles / Quanta 4.1 vii


Typographical conventions

Unless otherwise noted in the text, CHARMm Principles uses the typo-graphical conventions described below:

♦ Words in italic represent variables. For example:

> runmodeler input_filename

In this example, the name of the input file that you want to use replaces the value input_filename.

♦ Sample syntax and the examples illustrating the contents of files are presented in a fixed-width font. For example, the following illus-trates a line in an input file:

ACAM_HAMMH.CRD

♦ Words you type are presented in bold type. For example:

Enter none if there are no restart minima to add.

viii CHARMm Principles / Quanta 4.1

1 Introduction to CHARMm

CHARMm (Chemistry at HARvard Macromolecular mechanics) is a highly flexible molecular mechanics and dynamics program originally developed in the laboratory of Dr. Martin Karplus at Harvard University. A variety of systems, from isolated small molecules to solvated complexes of large biological macromolecules, can be simulated using CHARMm.

CHARMm uses empirical energy functions to describe the forces on atoms in molecules. These functions, plus the parameters for the functions, con-stitute the CHARMm forcefield. Well validated energy and force calcula-tions form the core of a broad range of calculation and simulation capabilities, including calculation of interaction and conformational ener-gies, local minima, barriers to rotation, time-dependent dynamic behavior, free energy, and vibrational frequencies.

This book describes CHARMm and many of the functions of CHARMm. This first chapter provides an overview of CHARMm activities and basic information on how CHARMm works. It is included, along with Chapters 2 through 5, in the book describing basic CHARMm activities.

This chapter explains ♦ Getting started

♦ Understanding CHARMm processes

♦ Commands and command files

♦ Input and output operations

♦ File formats

♦ Command stream control

♦ CHARMm measurement units

♦ CHARMm array dimensions

CHARMm Principles / Quanta 4.1 1

1. Introduction to CHARMm

Getting started

This section provides information about what you need to do to get started with CHARMm. Most of the book describes CHARMm as standalone, command-driven software. However, the information also applies to CHARMm as it is packaged and used in QUANTA.

Before you begin The software must be ready. That is, you must have properly licensed soft-ware installed and running. If you want to run CHARMm in a standalone mode, you need the CHARMm software. If you want to use CHARMm as part of your QUANTA software, you need the QUANTA software includ-ing CHARMm.

To start CHARMm If you are using CHARMm in a standalone mode, type the following to start the program:

> charmm < input.file > output

If you are using CHARMm from within QUANTA, access it by displaying the CHARMm menu on the QUANTA main menu bar. Many CHARMm commands can be executed using the menu-driven QUANTA interface. Or you can enter commands on the QUANTA command line. For information on using CHARMm in QUANTA, see Chapter 3, Calculating and Minimiz-ing Energy, in QUANTA Generating and Displaying Molecules.

Understanding CHARMm processes

Data within CHARMm are assembled and applied in a specific set of steps. Regardless of the activities and calculations you want to do using CHARMm, the early steps in the process are the same. The following fig-ure summarizes the activity flow to the point of divergence:

2 CHARMm Principles / Quanta 4.1

Understanding CHARMm processes

As illustrated in this figure, the activity flow is:

1. Read model definitions — Information about residues, the basic chem-ical units that compose all models, is stored in residue topology files (RTF). The atoms, atomic properties, bonds, bond angles, torsion angles, improper torsion angles (out-of-plane angles), hydrogen bond donors, acceptors, and antecedents, and nonbond exclusions are all specified on a per-residue basis.

2. Read sequence — Sequence information must be supplied from sequence (.seq) files before a model can be simulated.

3. Read parameters — When a structure has been generated, its energy can be evaluated only if parameters exist for all internal, external, and special energy terms. Parameter files contain parameters that specify force constants, equilibrium geometries, van der Waals radii, and other data needed for calculating energies. The values are derived from exper-imental data and quantum mechanical calculations. Refinement and extension of parameters is a continuing process.

1. Read model definitions from residue topology files (RTFs)

3. Read parameters from parameter files (PARA or PARM)

2. Read sequences from sequence file (.seq)

4. Generate a principal structure file (PSF) containing model information

5. Read or generate Cartesian coordinates for all atoms in the model (COOR)

6. Calculate energy using the PSF, parameter, and coordinate files

7. Perform calculations and simulations including molecular dynamics, free energy perturbation, and imposing periodic boundary conditions and constraints



4. Generate PSF — The principal structure file (PSF) is the concatenation of information in the RTF. It specifies the information for the entire structure. The PSF has a hierarchical organization with atoms collected into groups, groups into residues, and residues into segments that con-stitute the structure. Each atom is uniquely identified within a residue by its IUPAC name, residue identifier, and segment identifier.

5. Read or generate Cartesian coordinates — Cartesian coordinates can be read into the coordinate file or generated from internal coordinates and parameter files. Internal coordinate files contain information about the relative positions of atoms within a structure.

Two sets of Cartesian coordinates are provided. The main set is the default used for all operations involving the positions of atoms. A com-parison or reference set is used for a variety of purposes, such as a ref-erence for rotation or for operations that involve differences between coordinates for a particular molecule. Associated with each coordinate is a general-purpose weighting array.

6. Calculate energy — The main purpose of CHARMm is the evaluation and manipulation of the potential energy of a macromolecular system. Before the energy of a structure can be evaluated and manipulated, the following must be available:

♦ A PSF for the structure generated from the appropriate RTF.

♦ All parameters required by the PSF.

♦ Defined Cartesian coordinates for every atom in the structure.

7. Perform calculations and simulations — This is the point at which the process diverges, depending on the purpose of your study. Using infor-mation in the PSF and parameters files and the energy data you have calculated, you can do any of several things at this point, including molecular dynamics, free energy perturbation, and imposing peri-odic boundaries.

Commands and command files

CHARMm is a command-driven program controlled by entering com-mands either directly and interactively or from a command file. Input command files are constructed using CHARMm commands sequentially to perform a series of operations.


Commands and command files

Many commands are abbreviated in files and scripts. Generally, the first four letters of any command are sufficient to uniquely identify it. Check the CHARMm Dictionary for information if you see commands that are unfa-miliar to you.

In general, ordering of commands is limited only by the data required by the command. For example, energy cannot be calculated unless informa-tion about coordinates, parameters, and so on has already been read into the program

Command file title A command file for CHARMm must begin with a title. This title can describe the overall purpose of the calculation or contain other information to document the run.

A title must also precede all data being entered into CHARMm as part of a command stream or as an external file. A title consists of as many as 32 lines of information. An asterisk (*) must be the first character in each line of the title. Furthermore, a single asterisk must be used to terminate the title. An example of a valid CHARMm title is:

* Example of CHARMm title* Test CHARMm minimization and dynamics run*

Command line Each command line consists of a command and keywords, possibly fol-lowed by other data. The command line is scanned in free-field format.

The command line can be longer than one line. To use more than one line, place a hyphen at the end of the line that is to be continued on the next line.

A comment can be placed on a command line by preceding the comment with an exclamation point (!). Additionally, blank lines are permitted to separate blocks of command lines for increased readability.

As each command is read by CHARMm, it is echoed to the output file. Any output resulting from the execution of a command follows. Some com-mands do not produce any output.

The first word of every command line specifies the command itself. Gen-erally, required keywords of a command must follow in order. Optional keywords can generally be specified in any order. A numeric value is always preceded by a keyword.

Abbreviations are permitted in various contexts. Commands, keywords, and operands can be abbreviated to four characters. However, some key-words used to mark numbers cannot be abbreviated.



Many command options and numerical values are maintained from one invocation of a command to the next. When a value is specified, it is main-tained until it is changed in a subsequent command. For example, if the nonbond cutoff value is specified in an energy command, it is used in a sub-sequent dynamics calculation.

As each command is interpreted by CHARMm, a check is made to see that no extraneous information remains. Extraneous alphanumeric information is usually an indication of a error in entering the command or keywords in the command line.

Input and output operations

CHARMm provides a versatile facility for reading in and writing out data. You can enter data into CHARMm in two ways:

♦ Using a CHARMm command stream file, an input file that you create to direct CHARMm.

A command stream file is a special file consisting entirely of CHARMm commands. When a command stream file is invoked, the file is read and its commands are executed in sequence. Command stream files are con-venient for operations needing several CHARMm commands that are applied repetitively or are used in several contexts.

♦ Using external files.

External files can be manipulated by CHARMm as directed by a com-mand stream file. A variety of commands allow files to be opened and closed and data to be written or read in a number of different formats:

OPEN command — Opens logical units to files specified from the input file rather than from logical name assignments made prior to the run. External files must be opened prior to reading or writing data structures. Implicit file opening is also possible.

READ command — Reads data from external files into data struc-tures in CHARMm. The external files can either be formatted text files or unformatted binary files.

WRITE command — Saves the CHARMm data structures to external files. When you create an external data file using CHARMm, provide a valid title. This title is written at the start of the file and serves to document that file.


File formats

CLOSE command — Closes a previously opened logical unit. This frees the associated file and logical unit so that they can be used for other purposes.

All specification of files is done through FORTRAN unit numbers. Unit numbers 5 and 6 have special significance. All other unit numbers have no pre-defined meaning. Unit 5 is the default input command file interpreted by CHARMm. Unit 6 is the default output file for all printed messages. You can change both the input and output streams by using CHARMm com-mands. As commands are read from input, they are echoed on the output unit.

File formats

CHARMm data structures can be stored in text or an internal binary format. However, there are some restrictions, indicated in the following table:

Data file Text Binary

Residue topology files (RTFs) ✓ ✓

Residue topology files (appended) ✓

Parameter files ✓ ✓

Sequence files ✓

Principal structure files (PSFs) ✓ ✓

Coordinate files ✓ ✓

Dynamics trajectories (coordinate and velocity) a ✓

Constraint (harmonic atom) files ✓ ✓

Crystal image files ✓

Hydrogen bond list files ✓ ✓

Nonbonded list files ✓ ✓

Internal coordinate files ✓ ✓

Image transformation files ✓

Normal mode files (VIBRAN) ✓

aDynamics trajectories can be stored in a machine-independent hexadecimal format.



Converting file formats

The following example contains a script for converting files from ASCII text to binary format, thus creating binary topology and parameter files:

* ...* Copyright (c) 1986, 1987, 1988, 1989, 1990, 1991, 1992* Molecular Simulations Incorporated* Confidential and Proprietary: All Rights Reserved* ...* ...* This input file will create binary data files* ...*upperopen read unit 11 card name masses.rtfread rtf unit 11 cardclose unit 11open read unit 11 card name amino.rtfread rtf unit 11 card appeopen read unit 12 card name parm.prmread para unit 12 cardopen writ unit 12 file name "AMINO.BIN"writ rtf unit 12 file* ... * Topology File for CHARMm Version 22 (Polar Hydrogens Only)* ...* ...* Copyright (c) 1986, 1987, 1988, 1989, 1990, 1991, 1992* Molecular Simulations Incorporated* Confidential and Proprietary: All Rights Reserved* ...* Includes topology definitions for the twenty naturally* occurring* amino acids, some commonly used patches, and water.* Hydrogens are specified for polar atoms (such as N and O).* ... * Latest creation of binary file: $Date: 94/12/27 17:38:27 $* ...*open writ unit 13 file name "PARM.BIN" writ para unit 13 file* ...* Parameter File for CHARMm Version 22* ...* Includes parameters for both polar and all hydrogen topology


Command stream control

*files* ...* Copyright (c) 1986, 1987, 1988, 1989, 1990, 1991, 1992* Molecular Simulations Incorporated* Confidential and Proprietary: All Rights Reserved* ...* Dihedrals are presumed to be automatically generated and * should be totally specified, i.e. amide bonds have 4 dihedral* terms and ethane has 9 dihedral terms. Check the CHARMm PSF* if necessary.* This does not necessarily imply multiple periodicity.* ... * Latest creation of binary file: $Date: 94/12/27 17:38:27 $* ...* stop

Command stream control

To allow maximum control of the command stream, CHARMm provides several commands that can be used to set parameters, check the values of those parameters or energy terms, and move up and down through the com-mand file.

CHARMm parameters The SET command sets up a command line parameter. Command line parameters are substituted into the command line by the command line reader when it encounters the symbol @.

In the current version of CHARMm, a command line parameter token can be a string instead of only a single character (that is, 0–9, a–z, or A–Z). The token is end-delimited by any non-alphanumeric character.

When a token is not found in the parameter table, a check is made to see if the first character of the token is itself a token in the parameter table. If this single-character token is in the table, the corresponding value is substituted. This scheme allows backwards compatibility with the old parameter sub-stitution that allowed parameters to be embedded in strings.

To test if a token is in the parameter table, use @? token. This will substi-tute 1 if a token is in the table and 0 if it is not. This test is useful together with the IF command for setting defaults. Note that @? takes precedence over any of the built-in parameters such as ?ENER. It is parsed first.



For unambiguous token detection, protect your tokens with brackets {}. This also allows you to use non-alphanumerics such as a dash, comma, or underscore character in tokens.

Example: Using a parame-ter token

In this short example, the token is delimited by the period in the filename and the value myjob is substituted in place of @outfile.

SET outfile = myjob OPEN UNIT 1 WRITE CARD NAME @outfile.dat

For more information on parameters, see Using parameter files.

CHARMm variables CHARMm variables can be used in titles or in conjunction with CHARMm parameters. You can query the current value of a number of CHARMm variables by placing a question mark before the variable name. For exam-ple, if you use ?VDW, the current van der Waals energy is reported.

Conditional statements are used to check the values of parameters or vari-ables. Operations such as equal, not equal, and less than are supported. The consequence of using a conditional statement can be to transfer control within the command stream or to perform specific CHARMm commands.

CHARMm measurement units

CHARMm uses a distinct system of units, the AKMA measurement sys-tem. The following table lists the units used in CHARMm in both AKMA and SI units:

Variable AKMA SI

Length 1 Å 1 x 10-10 mEnergy 1 kcal/mol 4186 J/molMass 1 AMU 1.661 x 10-27 kgCharge 1 electron 1.602 x 10-19 CTime 1 time unit 0.04888 x 10-12 secForce 1 kcal/mol-Å 6.95 x 10-1 N


CHARMm array dimensions

Using the AKMA system, the unit of time is 4.888821E-14. Twenty AKMA time units equal 0.978 picoseconds. Although CHARMm com-putes time using AKMA units, output is usually expressed in picoseconds.

Angles are given in degrees for the CHARMm analysis and constraint sec-tions. In parameter files, minimum positions or angles are specified in degrees, but force constants for angles, dihedrals, and dihedral constraints are specified in kcal/mole/radian/radian.

CHARMm array dimensions

The following table lists the dimensions of various CHARMm 23 arrays. These values apply to all versions of CHARMm typically distributed. For Cray supercomputers, both a smaller and a larger configuration are avail-able.

Array definition Dimension

Maximum number of atoms 30,000Maximum number of atoms including image atoms 60,000Maximum number of atom types 500Maximum number of bonds 30,000Maximum number of angles 30,000Maximum number of dihedral angles 60,000Maximum number of improper dihedral angles 9,200Maximum number of groups 12,000Maximum number of residues 14,000Maximum number of segments 1,000Maximum number of hydrogen bonds 8,000Maximum number of hydrogen bond donors or acceptors 8,160Maximum number of image transformations 5,000Maximum number of crystal symmetry operations 192Maximum number of internal coordinate entries 30,000Maximum number of restrained dihedral angles 500Maximum number of NOE restraints 2000Maximum number of SHAKE constraints 10,240



Maximum number of bond parameters 1,500Maximum number of angle parameters 5,500Maximum number of dihedral parameters 700Maximum number of improper dihedral parameters 600Maximum number of hydrogen bond parameters 1,600Maximum number of VDW values 7,000Maximum number of explicit nonbonded exclusions 17,200Maximum number of residues within a topology file 200Maximum number of atoms for all residue definitions 3,000Maximum number of bonds for all residue definitions 3,000Maximum number of internal coordinates for all residue definitions 3,000Maximum number of hydrogen bond acceptors for all residue defini-

tions300

Maximum number of hydrogen bond donors for all residue defini-tions

300

Maximum number of improper dihedral angles for all residue defini-tions

2,000

Maximum number of dihedral angles for all residue definitions 2,000Maximum number of angles for all residue definitions 2,000Maximum number of nonbonded exclusions for all residue defini-

tions2,000

Array definition Dimension


2 Preparing Models for Energy Calculations

A molecular model must be specified before energy calculations can be performed. Model information, ultimately stored in the principal structure file, comes or is generated from a variety of sources, including residue topology and sequence files. Cartesian coordinates must be defined and a set of parameters, including force constants and equilibrium geometries, is also needed. This chapter describes the information that must be available for each molecular model and the sources of that information.

The chapter explains: ♦ Constructing and using residue topology files

♦ Using sequence information

♦ Generating and using a principal structure file

♦ Modeling hydrogens

♦ Generating and using coordinates

♦ Using parameter files

Script examples are included throughout the chapter.

Constructing and using residue topology files

Information about residues, the basic chemical units that compose all mod-els, is stored in residue topology files (RTFs). The atoms, atomic proper-ties, bonds, bond angles, torsion angles, improper torsion angles (out-of-planes), hydrogen bond donors, acceptors, antecedents, and nonbond exclusions are all specified on a per-residue basis.

The purpose of residue topology files is to store the information for gener-ating a representation of a molecule from its sequence. RTFs can be created by editing a file and inserting the appropriate commands and keywords to describe the molecule. Typically, these files are automatically created by


2. Preparing Models for Energy Calculations

QUANTA when you construct or modify a molecule. Libraries of topology files for amino acids, nucleic acids, saccharides, and polymers are also sup-plied with CHARMm.

As with all text files read into CHARMm, the first section of an RTF is a title in the usual format delimited by a line containing only an asterisk in the first column.

The remaining information is read in free-field format as commands to define the RTF. The ordering of the commands is important. For example, atoms of a residue must be defined before the bonds between the atoms can be defined.

File structure If you are constructing an RTF, the recommended structure for the file is as follows:

♦ For each RTF (containing one or more residues):

Title linesVersion numbersMass specification for each atom typeDeclarations of out-of-residue definitionsDefaults for patching on the first and last residuesAutogeneration of angles or dihedrals

♦ For each residue or patch in the RTF:

Name and total charge specificationAtom definitions within the residueGroup definitions of atomsBond specificationsAngle specificationsTorsion angle specificationsImproper torsion angle specificationsDonor specificationsAcceptor specificationsInternal coordinate informationPatching residues to use if defaults are not desired

Example: Creating an RTF containing a water residue

An RTF with one residue for water is written as follows:



* Topology definitions for HOH*18 1MASS 1 H 1.00800MASS 56 OH2 15.99940AUTOGENERATE ANGLES DIHEDRALSRESI WAT 0.00000GROUPATOM OH2 OH2 -0.40000ATOM H1 H 0.20000ATOM H2 H 0.20000BOND OH2 H1BOND OH2 H2DONO H1 OH2 -O -ODONO H2 OH2 -O -OACCE OH2PATCH FIRST NONE LAST NONEEND

This is a simple example. The mass of the atom types is set first. The resi-due name, WAT, is defined and its charge listed.

For the residue to be recognized by CHARMm, the residue name used in the sequence must match that in the RTF. The same definition for WAT might also be used for H2O, HOH, and OH2, residue names commonly used in PDB files for water molecules.

The ATOM keyword matches the atom name to the atom type and defines the partial charge of that atom. The BOND keyword defines the atoms that are bonded. The DONOr and ACCEptor keywords affect the hydrogen-bonding behavior of the molecule.

Example: Creating an RTF containing an alanine residue

An RTF containing a single alanine residue is written as follows:

* Topology definitions for ALA*18 1MASS 1 H 1.00800MASS 2 HA 1.00800MASS 11 C 12.01100MASS 15 CT 12.01100MASS 31 NP 14.00670MASS 51 O 15.99940MASS 56 OH2 15.99940DECL -C



DECL -ODECL +NDECL +HDECL +CADEFA FIRST NTERM LAST CTERMAUTOGENERATE ANGLES DIHEDRALSRESI ALA 0.00000GROUPATOM N NP -0.35ATOM H H 0.25ATOM CA CT 0.00ATOM HA HA 0.10GROUPATOM CB CT -0.30ATOM HB1 HA 0.10ATOM HB2 HA 0.10ATOM HB3 HA 0.10GROUPATOM C C 0.45ATOM O O -0.45BOND N CA N H CA C CA HA CA CB C O C +N CB ND1 CB NB2- CB NB3IMPH N -C CA HIMPH C CA +N ODONO H N -C CAACCE O CIC -C CA *N H 0.0000 0.00 180.00 0.00 0.0000IC -C N CA C 0.0000 0.00 180.00 0.00 0.0000IC N CA C +N 0.0000 0.00 180.00 0.00 0.0000IC +N CA *C O 0.0000 0.00 180.00 0.00 0.0000IC CA C +N +CA 0.0000 0.00 180.00 0.00 0.0000IC N C *CA CB 0.0000 0.00 120.00 0.00 0.0000IC N CA CB HB1 0.0000 0.00 180.00 0.00 0.0000

Two major differences exist between the RTFs for water and for alanine. The first is the statement:

DEFA FIRST NTERM LAST CTERM

This specifies that the first amino acid residue in a sequence will be con-verted to the N-terminus and the last will be converted to the C-terminus automatically with a special patch for the N- and C-termini. For more infor-mation about using patches, see Modifying a PSF.

The second difference is the addition of special atoms in the alanine RFT declared as -C, -O, +N, +H and +CA. These refer to out-of-residue atoms belonging to the preceding (-) and following (+) residue in the sequence. These atoms are then used in the BOND, ANGLE, DIHEDRAL, and



IMPROPER statements. In this case, the angles and dihedral angles are generated automatically. Each statement adds to the list of bonds and angles that are included in an energy calculation.

Example: Creating an RTF definition for glycerol

This CHARMm input file uses RTF definitions to create a model of glyc-erol. This example uses or generates the following files:

♦ Input file: glyc.inp

♦ Created file: GLYCINI.CRD

♦ Other required file: PARM.BIN

*...* Copyright (c) 1994* Molecular Simulations Inc. * All Rights Reserved*! Read the RTF from the CHARMm command fileREAD RTF CARD* RTF FOR GLYCEROL* 20 1! Version numberMASS 1 H 1.00800! Hydrogen bonding hydrogen (neutral group)MASS 3 HA 1.00800! Aliphatic or aromatic hydrogenMASS 10 CT 12.01100! Aliphatic carbon (tetrahedral)MASS 45 OT 15.99940! Hydroxyl oxygen (tetra.)/Ionizable acid - oxygen! Autogenerate all angles in the topology definitionsAUTOGEN ANGLES! During generation, provide no patches on the terminal! residuesDEFAULT FIRST NONE LAST NONE! Topology definition for glycerolRESIDUE GLYC 0.0 GROUP ! H11 O1 -- H1ATOM C1 CT 0.05 ! \ /ATOM H11 HA 0.10 ! C1ATOM H12 HA 0.10 ! / \ATOM O1 OT -0.65 ! H12 \ATOM H1 H 0.40 ! |

GROUP ! |ATOM C2 CT 0.15 ! |ATOM H21 HA 0.10 ! H21 -- C2 -- O2 -- H2ATOM O2 OT -0.65 ! |ATOM H2 H 0.40 ! |

GROUP ! |



ATOM C3 CT 0.05 ! H31 /ATOM H31 HA 0.10 ! \ /ATOM H32 HA 0.10 ! C3ATOM O3 OT -0.65 ! / \ATOM H3 H 0.40 ! H32 O3 -- H3

BOND C1 H11 C1 H12 C1 O1 O1 H1BOND C1 C2BOND C2 H21 C2 O2 O2 H2BOND C2 C3BOND C3 H31 C3 H32 C3 O3 O3 H3DIHE H1 O1 C1 C2DIHE O1 C1 C2 C3DIHE H2 O2 C2 C1DIHE O3 C3 C2 C1DIHE H3 O3 C3 C2! Internal coordinate definitionsIC H1 O1 C1 C2 0.0000 0.00 180.00 0.00 0.0000IC O1 C1 C2 C3 0.0000 0.00 180.00 0.00 0.0000IC H2 O2 C2 C1 0.0000 0.00 180.00 0.00 0.0000IC O3 C3 C2 C1 0.0000 0.00 180.00 0.00 0.0000IC H3 O3 C3 C2 0.0000 0.00 180.00 0.00 0.0000IC O1 C2 *C1 H11 0.0000 0.00 120.00 0.00 0.0000IC O1 C2 *C1 H12 0.0000 0.00 240.00 0.00 0.0000IC C3 C1 *C2 O2 0.0000 0.00 120.00 0.00 0.0000IC C3 C1 *C2 H21 0.0000 0.00 240.00 0.00 0.0000IC O3 C2 *C3 H31 0.0000 0.00 120.00 0.00 0.0000IC O3 C2 *C3 H32 0.0000 0.00 240.00 0.00 0.0000END! Open and read the parameter file (binary)OPEN READ UNIT 11 FILE NAME “$CHM_DATA/PARM.BIN”READ PARAMETERS FILE UNIT 11CLOSE UNIT 11! Read sequence informationREAD SEQUENCE CARDS* Sequence for glycerol*1GLYC! Generate the PSF and set up the internal coordinate tablesGENERATE GLYC SETUP! Generate coordinates from parametersIC PARAMETERSIC SEED 1 O1 1 C1 1 C2IC BUILDPRINT ICPRINT COORDINATES! Write coordinates to disk fileOPEN WRITE UNIT 08 CARD NAME GLYCINI.CRD


Using sequence information

WRITE COORDINATES CARD UNIT 08* Initial coordinates for glycerol generated* from parameter vales*STOP

Using sequence information

After the topology information has been read into CHARMm, you must specify the sequence of residues that will form the molecular model you are building. Sequence information can be included directly in the input file or in a separate sequence file (.seq) that is read into CHARMm. Sequence information can also be read from CRD or PDB files.

Multiple sets of residue sequences can be specified. Each set of residues is included in a segment definition as part of the PSF. Each molecule in CHARMm is composed of one or more segments, with each segment formed from a sequence of residues. A segment can include a single mac-romolecular chain, a collection of water molecules, a prosthetic group, or a collection of small organic molecules. Special commands are available to generate sequences of water molecules in segments that allow you to create bulk solvent without specifying each individual water residue.

For information on the maximum number of residues and segments that CHARMm can handle, see CHARMm array dimensions.

Sequence file format The structure of a sequence file is:

♦ Title line(s)

♦ Number of residues in the sequence, read in free-field format

♦ Residue names, 1 to 20 per line, with as many lines as necessary to spec-ify the number of residues indicated above, read in free-field format

For example, a sequence file to read in the residues for the enkephalin pep-tide would be written as follows:

* Enkephalin sequence*5TYR GLY GLY PHE MET



Generating and using a principal structure file

Before any energy calculations are computed for any structure in CHARMm, a molecular model is specified in a principal structure file (PSF). The PSF is the central molecular model data structure in CHARMm. It is the concatenation of information in an RTF, specifying information for the entire structure.

The PSF maintains every bond, bond angle, torsion angle, and improper torsion angle, as well as information needed to generate the hydrogen bonds and the nonbond list essential for the calculation of the energy of the molecular system. Separate data structures deal with symmetric images of the atoms, parameters, and Cartesian coordinates.

PSFs are created within CHARMm after the sequence information is read and before Cartesian coordinates are generated or read. After a PSF is cre-ated, it can be saved as an external file and used repetitively. A PSF can be created automatically in QUANTA and read as a single file into CHARMm. Generally, it is unnecessary to make manual modifications to a PSF after it is created.

Organization and structure PSFs have a hierarchical organization, with atoms collected into groups, groups into residues, and residues into segments that constitute the struc-ture. Each atom is uniquely identified within a residue by its IUPAC name, residue identifier, and segment identifier.

The structure of a PSF is as follows:

♦ Title line(s)

♦ Number of atoms in each residue for all segments

♦ Atom specification lines that include the following information:

Atom numberSegment nameResidue identifierResidue nameAtom nameAtom typeAtomic chargeAtomic massA flag to indicate whether the atom is constrained

♦ Number of bonds



♦ Bond pairs specified by atom numbers

♦ Number of angles

♦ Angle triplets specified by atom numbers

♦ Number of dihedrals

♦ Dihedral quartets specified by atom numbers

♦ Number of impropers

♦ Improper quartets specified by atom numbers

♦ Number of donors

♦ Donor pairs specified by atom numbers

♦ Number of acceptors

♦ Acceptor pairs specified by atom numbers

Creating a PSF

Two principal methods are available for creating a PSF:

♦ Generating a PSF from a sequence and the residue topology files using the following a set of steps:

a. Read residue topology files (RTFs).

b. Define sequences of segments.

c. Generate segments.

d. Generate a PSF.

e. If necessary, modify the PSF.

♦ Creating a PSF directly from the molecular structure

This method translates an existing model into atomic information (charges and types) and internal coordinates. The information is then grouped and written to an external file. This method is the one used by QUANTA when it transfers molecular models to CHARMm.



Modifying a PSF

After a PSF is created from a sequence of residues, it can be modified by using patch residues. Modifications include the addition of a blocking group to the ends of a polymer, changing a neutral functional group to a charged one, adding disulfide bridges, adding links within a single segment or between segments, deleting atoms, and so on.

The format of a patch residue is similar to that of a standard residue. How-ever, patch residues can also add or delete atoms and energy terms from the PSF and can modify the atom type or charge of a currently defined atom.

Patches differ from residues in another important respect. Because patch residues are applied after a PSF is generated, it is not possible to autogener-ate angle or dihedral energy terms within the patch. Therefore, all patch res-idues that are used after the PSF is generated must contain all necessary angle and dihedral energy terms. The exception is for the patches that are routinely included in the PSF before it is generated. These patches are defined within the RTF as the default first and last patches of a sequence of residues.

Patches can be applied to single or multiple residues within one or more segments. Because unique atom names exist within each residue, no ambi-guity arises in applying patches to a single residue. For example, a patch that protonates an amine group only needs to specify an additional hydro-gen atom and the nitrogen to which it is to be bonded. Even though more than one nitrogen can exist in the residue, each has a unique name.

However, with multiple residues, ambiguity often arises. For example, when a disulfide bridge is formed between two cysteine residues, each sidechain contains the same atom names. To properly place patches between multiple residues, CHARMm allows you to add an index number before an atom name in a patch residue definition to specify the residue that a particular atom is referencing. This index, using numbers one through nine, corresponds to the order in which the residues are given when the patches are applied.

Example: Adding a patch residue to create a sulfur bridge

A patch residue to add a sulfur bridge between two isoprene units is written as follows:



PRES VULC -0.20! Name of the patchATOM S ST -0.12! These atoms are either new (S)ATOM 1C1 CT -0.04! or are modified ATOM 2Cl CT -0.04DELE ATOM 1H2C1! These atoms are deleted fromDELE ATOM 2H2C1! the PSF.BOND S 1C1! New Bonds, angles and BOND S 2C1! dihedrals must be defined.ANGL S 1C1 1C2ANGL S 1C1 1H1C1ANGL S 1C1 1-C4ANGL S 2C1 2C2DIHE 1H1C1 1C1 S 2C1DIHE 1C1 S 2C1 2H1C1IC 1H1C1 1C1 S 2C1 0.00 0.00 180.00 0.00 0.00IC 1C1 S 2C1 2H1C1 0.00 0.00 180.00 0.00 0.00IC 1-C4 1C2 *1C1 S 0.00 0.00 240.00 0.00 0.00IC 2-C4 2C2 *2C1 S 0.00 0.00 240.00 0.00 0.00IC 1H1C1 S *1C1 1C2 0.00 0.00 120.00 0.00 0.00IC 1H1C1 S *1C1 1-C4 0.00 0.00 240.00 0.00 0.00IC 2H1C1 S *2C1 2C2 0.00 0.00 120.00 0.00 0.00IC 2H1C1 S *2C1 S-C4 0.00 0.00 240.00 0.00 0.00

This script includes the following information:

♦ Name of the patch residue and its total charge in the first line

♦ Five lines to define the atoms that will be added, modified, or deleted by this patch:

S is a new atom and will be added.

C1 is a currently existing atom in the isoprene residue. Its charge is to be changed to balance the extra negative charge of the sulfur atom.

Two hydrogens must be deleted so that proper valence is maintained about the C1 atom. All energy terms that include an H2C1 will also be automatically deleted. The 1 and 2 that precede the atom name refer to the first and second residues specified by the PATCH command.

New bonds, angles, and dihedrals that result from the addition of the sulfur atom are defined. Out-of-residue references are indicated by the - or + signs that immediately precede the atom name. New internal coor-dinate table entries are provided. Many of these new entries seem redun-dant, but are needed to construct coordinates of the polymer segment across the bridge given the coordinate on one side.



Modeling hydrogens

CHARMm supports two types of atom models for constructing molecules: the extended-atom model and the all-hydrogen (or all-atom) model.

Extended-atom model

For large molecular systems, you can increase modeling efficiency by com-bining hydrogens with the neighboring heavy atoms to which they are bound. This combined atom is referred to as an extended atom.

For peptide groups and amino acid sidechains, the extended-atom dihedral angle potentials can essentially reproduce those obtained from an all-atom representation The extended-atom representation also has been shown to provide a satisfactory representation of the internal vibrations and bulk properties of small molecules, including simple peptides.

Although large molecular systems are most efficiently modeled in extended-atom mode, keep in mind the advantages and disadvantages of this representation:

Advantages ♦ Significantly reduces the size of most problems. This is especially true for biological or other organic macromolecules, because roughly half the atoms in these molecules are hydrogen. Using extended atoms results in fewer nonbond interactions and internal degrees of freedom that require individual calculation.

♦ Separates motions involving heavy atoms from hydrogen stretching motions. The large gap in the infrared spectra between these two types of motions implies that removing one type should have little effect on the other.

♦ Can use larger dynamics integration step sizes because the small mass of hydrogen atoms requires a smaller time step for accurate integration. Longer dynamics trajectories can be simulated with a larger time step.

♦ No need to build hydrogen coordinates missing from X-ray data.

Disadvantages ♦ Difficult to represent hydrogen bonding accurately because the position of a hydrogen atom has a large effect on the hydrogen bond strength. When only heavy atom positions are included, a crude approximation to the hydrogen bond must be introduced.


Generating and using coordinates

♦ Lose dipole and quadrupole moments. The loss of a dipole in some sit-uations can adversely affect interactions with other nearby groups.

♦ Lose steric effects due to the hydrogens, because an extended atom is always spherical. The steric effect of hydrogens is indirectly simulated by appropriately increasing the van der Waals radius of the extended atom beyond the radius of the heavy atom itself.

♦ Lose hydrogen coordinates that are necessary for some types of analy-sis, including proton and 13C NMR phenomena and neutron diffraction studies.

In a modified form of the extended-atom model called the polar hydrogen model, only aliphatic hydrogens that are not significantly charged and can-not participate in hydrogen bonds are presented as extended atoms. The polar hydrogen model allows hydrogen bonding and dipole–dipole interac-tions to be effectively simulated, eliminating several of the disadvantages of the extended-atom model.

All-hydrogen model

The all-hydrogen (or all-atom) model contains all atoms, including both polar and nonpolar hydrogens. For small molecules, this is the model of choice.


A complete set of Cartesian coordinates must be generated prior to any energy computation. Situations often exist where all coordinates are not available or where some or all of a structure must be modified or built.

CHARMm has general facilities for construction, manipulation, transfor-mation, and interconversion of internal coordinates (ICs) and Cartesian coordinates.

Although crystallographic and simulation results are usually obtained and stored in Cartesian coordinates, it is frequently desirable to transform them either to re-oriented Cartesian frames or to internal coordinates. All the reorientations and transformations can be applied to an easily specified set of atoms. Because a flexible atom-selection facility is provided in



CHARMm, internal coordinates can be specific without regard to the bond-ing between atoms.

CHARMm internal coordinates

Given the positions of any three atoms, the position of a fourth atom can be defined. In CHARMm, this is how internal coordinates are developed. The position of the fourth atom is determined relative to the positions of the three defined atoms using a bond distance, bond angle, and dihedral speci-fication.

In CHARMm, the internal coordinates definition for a chain of atoms takes the form:

IC I J K L Rij �ijk �ijkl �jkl Rkl

The data structure uses five values to define four atoms. In this way, if either end-point is unknown but three atoms are determined, the position of the fourth atom can be found.

The improper type of internal coordinates data structure is used for branch-ing structures. The definition for a branched chain of atoms takes the form:

IC I J *K L Rij �ijk �ijkl �jkl Rkl

The asterisk preceding the Kth atom indicates that this is an improper dihe-dral and K is the central atom.

Because five values exist in the data structure for every atom, the positions are over-specified. When internal coordinates are used to determine atomic

I J K L

I JK

L



positions, CHARMm uses the first acceptable value to build a structure and ignores any redundancies.

The internal coordinates used to build a model can be specified arbitrarily, taken from an existing structure, or chosen from minimum-energy values in parameter tables. For example, specified internal coordinates could be used to construct coordinates for a peptide backbone when only values of the phi and psi dihedral angles are available.

The internal coordinate set can be manipulated so that you can build or modify a coordinate set in terms of bond angles and distances. The ability to take a Cartesian coordinate structure, fill and edit the internal coordinates table to specify modifications in bond distances, angles, or dihedral values, and then construct a new structure is extremely useful. With this feature, entire sections of a molecular model can be moved relative to others in an arbitrary but easily specified manner.

Building Cartesian coordinates from internal coordinates

X-ray crystallography coordinates are sometimes ill-defined or incomplete. In these cases, a method to compute the Cartesian coordinates of any atom in the molecular system is required. Additionally, coordinates need to be easily built for some modeling applications that require modifications to be made in structures.

In CHARMm, internal coordinates of any structure with some known coor-dinate positions can be used to construct Cartesian coordinates for atoms whose positions are unknown. Given the positions of any three atoms, the position of a fourth atom can be defined in relative terms using three values: a distance, an angle, and a torsion specification.

The following commands can be used to generate missing coordinates if the internal coordinates tables were set up during PSF generation:

♦ IC FILL PRESERVE — Fills the internal coordinates table with val-ues of bond lengths, bond angles, and torsions from the known atomic coordinate data. Internal coordinates for atoms that are not placed are zeroed unless the PRESERVE keyword is specified. In this case, the entries are not modified.

♦ IC PARAMETERS — Fills any missing values in the internal coordi-nates table with standard values from the parameter file. For example, all undefined bond lengths (that is, those with a value of 0.0) are replaced with the reference bond length data from the parameter file.



♦ IC BUILD — Computes the Cartesian coordinates for all undetermined atoms from the data in the internal coordinates table. The unknown positions are determined relative to known positions. The IC BUILD command is the logical opposite of the IC FILL command.

♦ IC SEED — Internal coordinates can also be used to construct Carte-sian coordinates in the absence of any 3D data. In this case, the first three atoms are seeded with coordinate positions using this command. The first atom specified is placed at the origin, the second atom along the x axis, and the third atom in the xy plane.

Example: Constructing a model using generated internal coordinates

This example illustrates the standard steps for constructing a model. The first part of the script generates a PSF. An RTF file is read, the sequence of enkephalin is entered, and a segment named ENKP is defined. Generating the segment creates a PSF within CHARMm.

The second part of the script generates a set of Cartesian coordinates for enkephalin using internal coordinates. When three atoms have coordinates, the remaining atoms can be placed by using the relationships defined by the PSF.

This example uses or generates the following files:

♦ Input file: enkp.inp

♦ Generated file: ENKPINI.CRD

♦ Other required files:

AMINO.RTFPARM.PRM

*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved* ! Open and read an all hydrogen amino acid topology fileOPEN READ UNIT 11 FILE NAME “$CHM_DATA/AMINOH.BIN”READ RTF UNIT 11 FILECLOSE UNIT 11! Read the sequence for met-enkephalin. Following the! title, the number of residues in the sequence is ! specified. The next line(s) contain the residue! sequence.



READ SEQUENCE CARD* Pentapeptide sequence for met-enkephalin* 5TYR GLY GLY PHE MET! Open and read the parameter fileOPEN READ UNIT 12 FILE NAME “$CHM_DATA/PARM.BIN”READ PARAMETERS UNIT 12 FILECLOSE UNIT 12! Generate the PSF with a segment identifier of ENKP.! Set up the internal coordinate tables.GENERATE ENKP SETUP! Construct initial Cartesian coordinates from the! parameter values. Initially place (seed) the first! three atoms of the peptide sequence.IC PARAMETERSIC SEED 1 N 1 CA 1 CIC BUILD! Print the coordinates in the output file.PRINT COORDINATES! Use the WRITE command to output coordinates to an external ! file. All WRITE commands must be preceded with an OPEN ! command.OPEN WRITE UNIT 08 CARD NAME ENKPINI.CRDWRITE COORDINATES UNIT 08 CARD* Initial coordinates for met-enkephalin created by* using parameter data and the internal coordinate* tables.*! Exit CHARMmSTOP

This example only saves the coordinates, but it can be modified to also save the PSF by adding the following lines to the script before exiting CHARMm:

WRITE PSF CARD NAME ENKP.PSF*PSF for enkephalin*

The saved PSF can be used in other CHARMm scripts.

Example: Converting a PDB file to a PSF

This example presents a situation encountered frequently by CHARMm users. A set of coordinates is available for a structure from the Brookhaven



Protein Data Base (PDB). The data must be converted and additional data generated before any CHARMm calculations can be performed.

A PDB file contains sequence information, atom names, and Cartesian coordinates for a molecule. Although proper PDB files contain connect records that describe the connectivity, CHARMm does not use these. An RTF for amino acids must be supplied by CHARMm. The connectivity, atom types, and charges are defined by the RTF.

PDB files do not contain hydrogens. Hydrogens are created in CHARMm and stored in the PSF. Generally, CHARMm uses polar hydrogens defined in the RTF file for this task. Cartesian coordinates for these atoms are also generated by CHARMm.

In the following script, the RTF and parameters are first read into CHARMm. A PDB file is opened and the sequence is read directly from the file. This provides sufficient information to generate the PSF. CHARMm then returns to the beginning of the PDB file (REWIND) and reads the Car-tesian coordinates from it.


♦ Input file: gluc.inp

♦ Created file: GLUCINI.CRD


AMINO.BINPARM.BIN1gcn.pdb

*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved*! Open and read polar hydrogen amino acid topology file(binary)OPEN READ UNIT 11 FILE NAME “$CHM_DATA/AMINO.BIN”READ RTF UNIT 11 FILECLOSE UNIT 11! Open and read parameter file (binary)OPEN READ UNIT 12 FILE NAME “$CHM_DATA/PARM.BIN”READ PARAMETERS UNIT 12 FILECLOSE UNIT 12! Read the sequence from the protein data bank fileOPEN READ UNIT 13 CARD NAME 1GCN.PDBREAD SEQUENCE PDB UNIT 13



! Generate segment 1GCN and set up internal coordinate tableGENERATE 1GCN SETUP! Rewind the protein data bank file for reading of coordinates REWIND UNIT 13! Read glucagon PDB coordinatesREAD COORDINATES PDB UNIT 13CLOSE UNIT 13! Print coordinates to output file. Missing coordinates! (hydrogens) are assigned values of 9999.0PRINT COORDINATES ! Construct hydrogen positionsHBUILD! Print coordinates to output file. All hydrogen! positions constructedPRINT COORDINATES! If necessary, any additional missing coordinates! can be placed using the following commandsIC FILL PRESERVEIC PARAMETERSIC BUILD! Write the coordinates to a disk fileOPEN WRITE UNIT 14 CARD NAME GLUCINI.CRDWRITE COORDINATES CARD UNIT 14* Glucagon coordinates* Heavy atom positions taken from PDB file* Hydrogen positions generated*STOP

Coordinate arrays

CHARMm maintains two parallel internal arrays for coordinates: the main coordinate array and the comparison coordinate array.

In the name of the second array, the word comparison is historical. This array was used almost exclusively for comparison purposes in early ver-sions of CHARMm. CHARMm now utilizes this array for a variety of functions related to coordinate operations. For example, atomic forces (direction and magnitude) can be stored in the comparison coordinate array. Examples in this book use the comparison coordinate array for temporary storage or for analysis of coordinates.

Most CHARMm commands operating on the main coordinate array can also operate on the comparison coordinate array by simply adding the key-word COMP to the command line. This allows great flexibility in studying multiple conformations of structures or in comparing structures at different



points of a trajectory. Most often, coordinates are copied to the comparison array with the line:

COOR COPY COMP

Format of the CHARMm coordinate file

CHARMm coordinate files contain information about the location of each atom in Cartesian (3D) space. The format of the ASCII (CARD) CHARMm coordinate files is:

♦ Title line(s)

♦ Number of atoms in file

♦ Coordinate line (one for each atom in the file)

The coordinate lines contain specific information about each atom in the model and consist of the following fields:

♦ Atom number (sequential)

♦ Residue number (specified relative to first residue in the PSF)

♦ Residue name

♦ Atom type

♦ X coordinate

♦ Y coordinate

♦ Z coordinate

♦ Segment identifier

♦ Residue identifier

♦ Weighting array value

The FORTRAN FORMAT statement for the coordinate lines is:I5, I5, 1X, A4, 1X, A4, 3(F10.5), 1X, A4, 1X, A4, F10.5

Example: Coordinate file for a two-segment model

The following example illustrates a coordinate file for a multi-segment model with two segments (SEG1 and PEP2):



* Two dipeptides, each in a separate segment*36 1 1 ALA N 0.00000 0.00000 0.00000 SEG1 1 0.00000 2 1 ALA HT1 -0.34665 -0.98053 0.00000 SEG1 1 0.00000 3 1 ALA HT2 -0.34665 0.49026 0.84916 SEG1 1 0.00000 4 1 ALA HT3 -0.34665 0.49026 -0.84916 SEG1 1 0.00000 5 1 ALA CA 1.47000 0.00000 0.00000 SEG1 1 0.00000 6 1 ALA CB 1.95113 -0.74250 -1.24824 SEG1 1 0.00000 7 1 ALA C 2.02771 1.40861 0.00000 SEG1 1 0.00000 8 1 ALA O 1.31114 2.40216 0.00000 SEG1 1 0.00000 9 2 ALA N 3.37163 1.46259 0.00000 SEG1 2 0.0000010 2 ALA H 3.92937 0.63258 0.00000 SEG1 2 0.0000011 2 ALA CB 3.51425 3.52492 1.24824 SEG1 2 0.0000012 2 ALA C 5.50913 2.71647 0.00000 SEG1 2 0.0000013 2 ALA OCT1 6.04832 1.61095 0.00000 SEG1 2 0.0000014 2 ALA OCT2 6.14262 3.77078 0.00000 SEG1 2 0.0000015 2 ALA CA 3.99557 2.78255 0.00000 SEG1 2 0.0000016 3 THR N 0.00000 0.00000 0.00000 PEP2 1 0.0000017 3 THR HT1 -0.34665 -0.98053 0.00000 PEP2 1 0.0000018 3 THR HT2 -0.34665 0.49026 0.84916 PEP2 1 0.0000019 3 THR HT3 -0.34665 0.49026 -0.84916 PEP2 1 0.0000020 3 THR CA 1.47000 0.00000 0.00000 PEP2 1 0.0000021 3 THR CB 1.95287 -0.73967 -1.24925 PEP2 1 0.0000022 3 THR OG1 3.38262 -0.75331 -1.27229 PEP2 1 0.0000023 3 THR HG1 3.63799 -1.21844 -2.05787 PEP2 1 0.0000024 3 THR CG2 1.43958 -0.04232 -2.51065 PEP2 1 0.0000025 3 THR C 2.02771 1.40861 0.00000 PEP2 1 0.0000026 3 THR O 1.31114 2.40216 0.00000 PEP2 1 0.0000027 4 THR N 3.37163 1.46259 0.00000 PEP2 2 0.0000028 4 THR H 3.92937 0.63258 0.00000 PEP2 2 0.0000029 4 THR CB 3.51754 3.52536 1.24925 PEP2 2 0.0000030 4 THR OG1 4.10882 4.82690 1.28535 PEP2 2 0.0000031 4 THR HG1 3.78782 5.25025 2.07049 PEP2 2 0.0000032 4 THR CG2 3.92118 2.75819 2.50997 PEP2 2 0.0000033 4 THR C 5.50913 2.71647 0.00000 PEP2 2 0.0000034 4 THR OCT1 6.04832 1.61095 0.00000 PEP2 2 0.0000035 4 THR OCT2 6.14262 3.77078 0.00000 PEP2 2 0.00000 36 4 THR CA 3.99557 2.78255 0.00000 PEP2 2 0.00000

Constructing hydrogen positions

Coordinates that are provided from experimental data normally give posi-tions only for heavy, non-hydrogen atoms. However, CHARMm requires the coordinates for all atoms given in the topological definitions of the indi-vidual residues in order to compute the empirical energy functions.



If necessary, CHARMm builds and optimizes all undefined hydrogen coor-dinates for the molecule as well as for the surrounding water. In the first part of hydrogen building, all proton positions of the molecule are con-structed. The protons are initially classified according to their respective environments. These classifications are defined below. The donor atom is the heavy atom to which the proton is connected.

Class 1

A proton bound to a donor with at least two heavy atom donor antecedents

Class 2

A proton bound to a donor with one heavy atom donor antecedent and no other proton

Class 3

A proton bound to a donor with one heavy atom antecedent and one other proton

Class 4

A proton bound to a donor with one heavy atom antecedent and two other protons

Proton positions are generated using the following steps:

1. All protons of Class 1 are placed using reference bond lengths, angles, and torsions. These protons are over-determined if there is more than one heavy atom donor antecedent. In these cases, all possible ways to place the proton are averaged to give one position.

2. Protons of all other classes (2–4) are constructed. For these classes, there is an additional degree of freedom for placing the protons. To find an optimum position, the torsion angle with the symmetry axis anteced-ent-donor is modified in small steps (using the keyword PHIStp) over a certain range determined by the symmetry of the donor group:

a. For each dihedral angle, the protons of the donor are placed accord-ing to their reference geometry.

b. Relative energy of the corresponding configuration is evaluated. The energy is determined by using the hydrogen bond potential, the van der Waals term, the electrostatic term, and the torsion term derived from the full energy expression of CHARMm.


Using parameter files

c. The torsion angle that yields the lowest energy is chosen, and the protons of the donor group are placed using this optimum torsion angle.

In this step, this procedure is performed in the order given by the residue sequence of the molecule. Protons that have not yet been constructed have no influence on the current energy evaluations.

3. After construction of all explicit protons, water protons are constructed:

a. A sequence of water molecules is determined independent of any other sequence.

b. Waters are ordered with respect to the minimum distance of the water oxygen to any atoms in the molecule.

c. Protons of waters near the molecule are constructed first. Three classes of water molecules are handled by this method:

Water able to form two different hydrogen bonds to an acceptor atom — Protons are placed by performing a rotation of the water molecule in the plane defined by the two best hydrogen bonds, taking the min-imum energy configuration.

Water able to form only one hydrogen bond to acceptor atoms — One proton is placed on the (linear) hydrogen bond and the other proton is placed using the reference geometry. The minimum energy configuration is taken. The evaluated relative energy is the sum of the van der Waals, electrostatic, and hydrogen-bonding terms.

Water forming no hydrogen bonds — Protons are placed in a stan-dard manner (that is, H1 on the x axis, and H2 in the xy plane) after all other protons have been placed.


Parameter files contain values for force constants, reference geometries, van der Waals radii, stretching constants, and other constants necessary to calculate the energy of a molecule. The parameter files allow CHARMm to impart constraints upon any structure.

File structure A parameter file must start with a valid CHARMm title. The remaining information is read in free-field format as commands to read in parameter



data. Each section of parameters is initiated by a single CHARMm param-eter keyword. The structure of a parameter file is:

♦ Title

♦ BOND

♦ Atom-type atom-type force-constant distance

♦ ANGLE (or THETA)

♦ Atom-type atom-type atom-type force-constant angle

♦ DIHEDRAL (or PHI)

♦ Atom-type atom-type atom-type atom-type force-constant periodicity phase

♦ IMPROPER (or IMPHI)

♦ Atom-type atom-type atom-type atom-type force-constant periodicity phase

♦ NBOND (or NONBONDED)

♦ Atom-type polarizability energy VDW-radius [1-4 polarizability energy VDW-radius]

♦ NBFIX

♦ Atom-type atom-type energy distance [1-4 energy 1-4 distance]

♦ HBOND

♦ Donor-atom-type acceptor-atom-type energy distance

No wildcard usage is allowed for bonds or angles.

For dihedrals, two parameter specifications can be used:

♦ A-B-C-D (All four atom types specified, double parameters can be pro-vided and used as long as two sets of dihedrals are included in the topol-ogy file)

Or

♦ X-A-B-X (Only the two middle atoms of the dihedral specified, using an X to indicate any atom type)

For impropers, five different parameter specifications can be used:

♦ A-B-C-D (All four atom types specified)



♦ A-X-X-B (The out-of-plane deformation atom types being specified only for this and following specifications)

♦ X-A-B-C

♦ X-A-B-X

♦ X-X-A-B

When an improper dihedral (out-of-plane) is classified, the first acceptable match (from the above order) is chosen. The match can be made in either direction.

Wildcard atom types can be used in specifying NBOND, NBFIX, or HBOND interaction parameters.

The periodicity value for torsions and out-of-plane terms must be an inte-ger. If it is positive, then a cosine functional form is used. Only positive val-ues 1, 2, 3, 4, 5, and 6 are allowed. Phase is either 0.0 or 180.0 for dihedrals with the minimum-energy configuration staggered or eclipsed, respec-tively.

When periodicity is given as 0.0, a harmonic restoring potential phi-phi_min is used. The phase value gives phi_min for this option. This functional form can be used for either torsions or out-of-planes. For torsions, the selection is usually based on the middle two atoms. For out-of-planes, the selection is usually based on the outer two atoms. When periodicity is given as 0.0 for other than the first torsion in a multiple torsion set, amplitude is a constant added to the energy. This is needed for the Ryckaert–Bellemans potential of hydrocarbons.

Nonbond parameters are determined based on how values are listed:

♦ If the second number is negative, it is used as Emin with Eminij = sqrt (Emin(i)*Emin(j)).

♦ If the second number is positive, it is used as the number of effective electrons, and the Slater–Kirkwood formula is used to compute Eminij.

Nonbond parameters for 1–4 interactions can be specified by placing the extra set of parameters after the first. By default, the same parameters are used for 1–4 interactions as for all other interactions.

The NBFIX set of parameters allows individual atom type van der Waals pair interactions to be specified. These parameters are processed in order. In case of duplicate specifications, the last specification is used.



Ryckaert–Bellemans torsion potential

To calculate the Ryckaert–Bellemans torsion potential for butane and other extended-atom hydrocarbons, the following terms should be included in the parameter file:

PHICH3E CH2E CH2E CH3E 0.470467 5 0.0CH3E CH2E CH2E CH3E 0.783947 4 0.0CH3E CH2E CH2E CH3E 2.53516 3 0.0CH3E CH2E CH2E CH3E 1.56789 2 0.0CH3E CH2E CH2E CH3E 2.34787 1 0.0CH3E CH2E CH2E CH3E -4.70368 0 0.0

This potential should be used with SHAKE (described in Setting Con-straints and Periodic Boundaries). A zero periodicity term should not be the first in the set, or the term is assumed to relate to an out-of-plane torsion.

Example: Parameter file PARM.PRM

For an example of a parameter file, see the file $CHM DATA/ PARM.PRM in your CHARMm software.

Summary examples

The following scripts contain typical examples of model preparation. These examples cover generation and use of residue topology files, PSFs, internal and Cartesian coordinates, parameter files, and other information that can be used for preparing models for energy calculations and analysis.

Example: Constructing polymer segments joined by a sulfur bridge

This script illustrates how to use a patch residue to modify a PSF. Two poly-mer segments are created using the ISOP residue, then a sulfur bridge is created to connect them. The sulfur bridge uses the patch residue VULC.



Summary examples

♦ Input file: rubber.inp

♦ Created file: RUBBER.CRD

♦ Other required file: PARM.BIN*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved* ...* This CHARMm command file builds two short polymer segments* of natural rubber and joins them with a sulfur bridge.* ...* READ RTF CARD

* Topology file containing the isoprene residue, terminal * patches, and the sulfur bridge patch* 22 2 ! CHARMm Version #! MASS statements deleted for brevity! Out of residue declarationsDECL -C4DECL +C1DECL +C2! Autogenerate all angles during generation of the PSF AUTOGENERATE ANGLES DIHEDRALS! Apply terminal patches TER1 and TER2 by default during! generation of the PSFDEFA FIRS TER1 LAST TER2! The isoprene residueRESI ISOP 0.00ATOM C1 CT -0.20ATOM H1C1 HA 0.10ATOM H2C1 HA 0.10ATOM C2 CUA1 0.00ATOM C3 CUA1 -0.10ATOM H1C3 HA 0.10ATOM C4 CT -0.20ATOM H1C4 HA 0.10ATOM H2C4 HA 0.10ATOM C5 CT -0.30ATOM H1C5 HA 0.10ATOM H2C5 HA 0.10ATOM H3C5 HA 0.10BOND C1 C2 C2 C3 C3 C4 C2 C5 C4 +C1BOND C1 H1C1 C1 H2C1BOND C3 H1C3BOND C4 H1C4 C4 H2C4BOND C5 H1C5 C5 H2C5 C5 H3C5IC -C4 C1 C2 C3 0.00 0.00 180.00 0.00 0.00IC C1 C2 C3 C4 0.00 0.00 0.00 0.00 0.00IC C2 C3 C4 +C1 0.00 0.00 180.00 0.00 0.00IC C3 C4 +C1 +C2 0.00 0.00 180.00 0.00 0.00IC -C4 C2 *C1 H1C1 0.00 0.00 120.00 0.00 0.00IC -C4 C2 *C1 H2C1 0.00 0.00 240.00 0.00 0.00IC C1 C3 *C2 C5 0.00 0.00 180.00 0.00 0.00IC C2 C4 *C3 H1C3 0.00 0.00 180.00 0.00 0.00IC C3 +C1 *C4 H1C4 0.00 0.00 120.00 0.00 0.00IC C3 +C1 *C4 H2C4 0.00 0.00 240.00 0.00 0.00IC C1 C2 C5 H1C5 0.00 0.00 180.00 0.00 0.00IC C2 H1C5 *C5 H2C5 0.00 0.00 120.00 0.00 0.00



IC C2 H1C5 *C5 H3C5 0.00 0.00 240.00 0.00 0.00! The terminal patchesPRES TER1 -0.20ATOM H3C1 HA 0.10ATOM C1 CT -0.30BOND H3C1 C1DIHE H3C1 C1 C2 C3IC H3C1 C1 C2 C3 0.00 0.00 180.00 0.00 0.00IC H3C1 C2 *C1 H1C1 0.00 0.00 120.00 0.00 0.00IC H3C1 C2 *C1 H2C1 0.00 0.00 240.00 0.00 0.00PRES TER2 -0.20ATOM H3C4 HA 0.10ATOM C4 CT -0.30BOND H3C4 C4DIHE H3C4 C4 C3 C2IC H3C4 C4 C3 C2 0.00 0.00 180.00 0.00 0.00IC H3C4 C3 *C4 H1C4 0.00 0.00 120.00 0.00 0.00IC H3C4 C3 *C4 H2C4 0.00 0.00 240.00 0.00 0.00! The sulfur bridge patchPRES VULC -0.20ATOM S ST -0.12ATOM 1C1 CT -0.04ATOM 2C1 CT -0.04DELE ATOM 1H2C1DELE ATOM 2H2C1BOND S 1C1 S 2C1ANGL S 1C1 1C2 S 1C1 1H1C1 S 1C1 1-C4 S 2C1 2C2ANGL S 2C1 2H1C1 S 2C1 2-C4DIHE 1H1C1 1C1 S 2C1 1C1 S 2C1 2H1C1IC 1H1C1 1C1 S 2C1 0.00 0.00 180.00 0.00 0.00IC 1C1 S 2C1 2H1C1 0.00 0.00 180.00 0.00 0.00IC 1-C4 1C2 *1C1 S 0.00 0.00 240.00 0.00 0.00IC 2-C4 2C2 *2C1 S 0.00 0.00 240.00 0.00 0.00IC 1H1C1 S *1C1 1C2 0.00 0.00 120.00 0.00 0.00IC 1H1C1 S *1C1 1-C4 0.00 0.00 240.00 0.00 0.00IC 2H1C1 S *2C1 2C2 0.00 0.00 120.00 0.00 0.00IC 2H1C1 S *2C1 2-C4 0.00 0.00 240.00 0.00 0.00END! Read in the parameter fileOPEN READ UNIT 12 FILE NAME “$CHM_DATA/PARM.BIN”READ PARA UNIT 12 FILECLOSE UNIT 12! Generate the first segment (3 isoprene residues)READ SEQU CARD* TEST*3ISOP ISOP ISOPGENE RBR1 SETUP! Generate the second segment (3 isoprene residues)READ SEQUENCE CARD* TEST*3ISOP ISOP ISOPGENERATE RBR2 SETUP! Apply the patch to bridge the two segments with a sulfur ! atomPATCH VULC RBR1 2 RBR2 2 SETUP! Initialize the internal coordinate arrays and build! the coordinatesIC PURGEIC PARAMETERS


Summary examples

IC SEED 1 C1 1 C2 1 C3IC BUILDIC PRINT! Merge the segments into one segmentJOIN RBR1 RBR2 RENU! Rename the segment newly merged segment RBBRRENAME SEGI RBBR SELE SEGI RBR1 END! Write the initial coordinates to diskOPEN WRITE UNIT 11 CARD NAME RUBBER.CRDWRITE COORDINATES UNIT 11 CARD* TEST*! The following commands are not referenced in this! exampleUPDATE INBFRQ -1 IHBFRQ 0 RDIEMINI ABNR NSTEP 1000 NPRINT 50 TOLENR 0.000001 TOLGRD 0.000001STOP

Example: Constructing an alpha helix of polyalanine

This script builds an alpha helix of polyalanine. The script is simple, creat-ing a polyalanine sequence and PSF, then building coordinates. The key lines in this script are in the four lines:

SET 1 1SET 2 11OPEN READ UNIT 18 CARD NAME HELIX.STRSTREAM UNIT 18

The first two lines of this group assign values to the variables 1 and 2. Vari-able 1 is set to 1 and variable 2 is set to 11. The variables can be used as counters for loops in scripts, and they can also be substituted as values using the @ sign. So the command:

SET 3 @1

sets the variable 3 to the value of variable 1.

The next line opens an external file. The STREAM command instructs CHARMm to read every line in the file as a CHARMm command.

The second part of this example is the file HELIX.STR. This file shows some of the flow control elements that can be used in a CHARMm script including labels, if statements, and goto statements. In this script, the dihe-dral angles of each successive residue are set to an alpha-helical conforma-tion.


♦ Input file: helix.inp



♦ Created file: ALPHAHLX.CRD


AMINO.BINPARM.BINHELIX.STR

Script part 1

*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved! Open and read the topology and parameter files (binary)OPEN READ UNIT 11 FILE NAME “$CHM_DATA/AMINO.BIN”READ RTF UNIT 11CLOSE UNIT 11OPEN READ UNIT 11 FILE NAME “$CHM_DATA/PARM.BIN”READ PARA UNIT 11 FILECLOSE UNIT 11! Read the sequence for polyalanineREAD SEQU ALA 11* Polyalanine (11 residues)*GENERATE HELX SETUP! Generate coordinates from parameter data; first fill the! internal coordinateIC PARAMETERS! Define the range of residues to be defined as an alpha! helix; set CHARMm parameter 1 to be the first residue and! CHARMm parameter 2 to be the last residueSET 1 1SET 2 11OPEN READ UNIT 18 CARD NAME HELIX.STRSTREAM UNIT 18! Initially place three coordinates, and build the restIC SEED 1 N 1 CA 1 CIC BUILD! Write coordinates to disk fileOPEN WRITE UNIT 04 CARD NAME ALPHAHLX.CRDWRITE COORDINATES CARDS UNIT 04* Initial helix coordinates constructed using IC EDIT* and IC BUILD*STOP


Summary examples

Script part 2

*...* Copyright (c) 1994 * Molecular Simulations Inc.* All Rights Reserved*...* HELIX.STR*...* This stream file edits the internal coordinate table* by defining the phi and psi angles to be an alpha helix* for a range of residues (CHARMm parameters 1 and 2)*! Define variables for residues i+1 and i+2SET 3 @1SET 4 @1INCR 3 BY 1INCR 4 BY 2LABEL START! Invoke IC EDIT mode, and define phi and psi! dihedral angles for an alpha helixIC EDITDIHE @1 C @3 N @3 CA @3 C -57.0DIHE @3 N @3 CA @3 C @4 N -47.0END! Increment counters and check for last specified residueINCR 1 BY 1INCR 3 BY 1INCR 4 BY 1IF 4 GT @2 GOTO STOPGOTO STARTLABEL STOPRETURN

Example: Generating random conformations of enkephalin

Another example of how to use stream files is provided below. Here, 100 random conformations are generated and their energies computed. The main script is used to set up the PSF while the generation of the conforma-tions and energies is performed in the stream file. This generic stream file could easily be inserted into other input files or customized for other pur-poses.


♦ Input file: enkpconf.inp



♦ Generated files:

ENKP.ICR — Internal coordinates tableENKPCONF000.CRD through ENKPCONFxxx.CRD — Conformer Cartesian coordinate filesENKPCONFENG.LST


AMINO.BINPARM.BINRANDCONF.STR

Script part 1

*...* Copyright (c) 1994 * Molecular Simulations Inc.* All Rights Reserved! Open and read the topology and parameter filesOPEN READ UNIT 11 FILE NAME “$CHM_DATA/AMINOH.BIN”READ RTF UNIT 11CLOSE UNIT 11OPEN READ UNIT 12 FILE NAME “$CHM_DATA/PARM.BIN”READ PARA UNIT 12CLOSE UNIT 12! Generate the PSF and initial coordinatesREAD SEQU CARD* Enkephalin*5TYR GLY GLY PHE METGENE MAIN SETUIC PARAIC SEED 1 N 1 CA 1 CIC BUIL! Write internal coordinate table to external fileOPEN WRIT UNIT 15 CARD NAME ENKP.ICRIC WRIT UNIT 15 CARD* Enkephalin initial internal coordinate table*! Compute an initial energy; write out initial! coordinates and open a log file for conformation! energiesUPDATEGETEOPEN WRIT UNIT 24 CARD NAME ENKPCONF000.CRDWRIT COOR UNIT 24 CARD


Summary examples

* Enkephalin initial conformation with energy?ener*OPEN WRIT UNIT 25 CARD NAME ENKPCONFENG.LSTWRIT TITL UNIT 25* Enkephalin initial conformation energy = ?ener*! Stream random conformation generation fileOPEN READ UNIT 28 CARD NAME RANDCONF.STRSTREAM UNIT 28CLOSE UNIT 24CLOSE UNIT 28STOP

Script part 2

* ...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved* ...* This stream file randomly generates values for the* dihedral * angles phi and psi in all residues of a protein* ...*! Set counter to 0SET 1 0! Main loop: increment and check counter against the maximum! number of conformations desiredLABEL STARTINCR 1 BY 1IF 1 GT 100 GOTO STOP! Temporarily save internal coordinate table; keep only those! dihedrals that correspond to phi and psi and assign random! values to these internal coordinates; print results to! output fileIC SAVEIC KEEP FIRST SELE ATOM * * N .OR. ATOM * * CA ENDIC KEEP SECO SELE ATOM * * CA .OR. ATOM * * C ENDIC KEEP THIRD SELE ATOM * * C .OR. ATOM * * N ENDIC KEEP FOURTH SELE ATOM * * N .OR. ATOM * * CA ENDIC RAND IC PRIN! Restore full internal coordinate table preserving randomly! assigned values of phi and psi; initialize and rebuild all! Cartesian coordinatesIC REST PRESCOOR INIT



IC SEED 1 N 1 CA 1 CIC BUIL! Compute an energy and write to log fileGETEWRITE TITLE UNIT 25* Enkephalin conformation @1 energy = ?ener*! Check value of energy; if less than 0.0, write! coordinates to unique file; if not, generate another! conformationSET 2 ?ENERIF 2 GT 0.0 GOTO STARTSET 3 ENKPCONFIF 1 LT 100 SET 3 ENKPCONF0IF 1 LT 10 SET 3 ENKPCONF00OPEN WRITE UNIT 44 CARD NAME @[email protected] COOR UNIT 44 CARD* Enkephalin conformation @1 with energy ?ener*GOTO STARTLABEL STOPRETURN

Example: Constructing an N-methylacetamide dimer

The following input file uses many of the coordinate manipulation com-mands to generate a copy of the N-methylacetamide molecule and position it so that the energetics of the dimer can be studied.


♦ Input file: nma.inp

♦ Generated files: NMAINI.CRD

♦ Other required files: PARM.BIN

*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved* ...* This CHARMm command file uses the coordinate manipulation* tools of CHARMm to generate and model the N-methylacetamide* dimer* ...*


Summary examples

READ RTF CARDS* RTF for N-methyl acetamide* 22 2MASS 1 H 1.00800 ! Hydrogen bonding hydrogen (neutral group)MASS 13 CH3E 15.03500 ! Extended atom C with three hydrogensMASS 14 C 12.01100 ! Carbonyl or Guanidinium carbonMASS 32 NP 14.00670 ! Peptide/amide nitrogenMASS 40 O 15.99940 ! Carbonyl oxygen for acids/amidesAUTOGENERATE ANGLES DIHEDRALSRESI NMA 0.00GROU ATOM CL CH3E 0.00GROU ATOM C C 0.55 ATOM O O -0.55GROU ATOM N NP -0.35 ATOM H H 0.25 ATOM CA CH3E 0.10BOND N CA N HBOND CL C C N C OIMPH C CL N OIMPH N C CA HIC N CL *C O 0.0000 0.00 180.00 0.00 0.0000IC CL C N CA 0.0000 0.00 180.00 0.00 0.0000IC C CA *N H 0.0000 0.00 180.00 0.00 0.0000PATCH FIRST NONE LAST NONEEND! Open and read the parameter file (binary)OPEN READ UNIT 11 FILE NAME “$CHM_DATA/PARM.BIN”READ PARA UNIT 11 FILECLOSE UNIT 11! Read the sequence informationREAD SEQUENCE CARDS* SEQUENCE FOR N-METHYL ACETAMIDE*1NMA! Generate the first segment (A); generate the second! segment (B) by duplicating the firstGENERATE A SETUPGENERATE B SETUP DUPLICATE A! Construct coordinates for the first segmentIC PARAMETERSIC SEED 1 C 1 N 1 CAIC BUILDPRINT COORDINATES



! Orient the amide nitrogen and hydrogen of segment a! along the x-axisCOOR ORIE SELE ATOM A 1 N .OR. ATOM A 1 H END! Duplicate the coordinates of segment A to segment BCOOR DUPLICATE SELE ATOM A * * END SELE ATOM B * * END! Temporarily save the coordinates in the comparison setCOOR COPY COMP! Orient the coordinates such that the carbonyl oxygen! and carbon of segment B is aligned with the x-axis;! this will also reorient the coordinates of segment ACOOR ORIE SELE ATOM B 1 C .OR. ATOM B 1 O END! Retrieve coordinates of segment A from the comparison setCOOR COPY SELE SEGI A END! Define a vector between the amide hydrogen of! segment A and the carbonyl oxygen of segment B;! this command also determines the distance between! these atomsCOOR AXIS SELE ATOM A 1 H END SELE ATOM B 1 O END! Translate the coordinates of segment B along the x-axis! by the distance determined from the COOR AXIS command;! this will place the hydrogen of segment A and the oxygen! of segment B in the same placeCOOR TRANS SELE SEGI B END AXIS FACT -1.0! Translate the coordinates of segment B another 1.8 A,! the optimum hydrogen bond distanceCOOR TRANS SELE SEGI B END XDIR 1.8! Write the initial coordinates to diskOPEN WRITE CARD UNIT 12 NAME NMAINI.CRDWRITE COORDINATES CARD UNIT 12* NMA INITIAL COORDINATES*STOP

Example: Constructing conformations of cyclohexane

This example uses the CHARMm internal coordinates commands to con-struct the chair and boat conformations of cyclohexane. Cartesian coordi-nates are generated directly from idealized torsion angles.

The following files are used or generated in this script:

♦ Input file: cyclo.inp



Summary examples

CHAIR.CRDCYCLO.TXTBOAT.CRD

♦ Other required files: PARM.BIN

*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved* ...* This CHARMm command file uses the internal coordinate (IC) * commands of CHARMm to generate the chair and boat * conformers of cyclohexane* ...*! Read the RTF topology file for cyclohexaneREAD RTF CARDS* RTF for cyclohexane* 22 2 ! Version number! MASS Statements removed for brevityAUTOGENERATE ANGLES DIHEDRALSRESIDUE CYCL 0.00000GROUP ATOM C1 CH2E 0.00 ATOM C2 CH2E 0.00 ATOM C3 CH2E 0.00 ATOM C4 CH2E 0.00 ATOM C5 CH2E 0.00 ATOM C6 CH2E 0.00BOND C1 C2 C2 C3 C3 C4 C4 C5 C5 C6 C6 C1IC C1 C2 C3 C4 0.0000 0.00 +60.0 0.00 0.0000IC C2 C3 C4 C5 0.0000 0.00 -60.0 0.00 0.0000IC C3 C4 C5 C6 0.0000 0.00 +60.0 0.00 0.0000IC C4 C5 C6 C1 0.0000 0.00 -60.0 0.00 0.0000IC C5 C6 C1 C2 0.0000 0.00 +60.0 0.00 0.0000IC C6 C1 C2 C3 0.0000 0.00 -60.0 0.00 0.0000PATC FIRST NONE LAST NONEEND! Open and read the parameter file (binary)OPEN READ UNIT 11 FILE NAME “$CHM_DATA/PARM.BIN”READ PARAMETERS UNIT 11 FILECLOSE UNIT 11! Read the sequence information and generate the PSFREAD SEQUENCE CARDS* SEQUENCE FOR CYCLOHEXANE*



1CYCLGENERATE A SETUP! Generate coordinates for the chair conformer! (defined by the IC commands in the RTF)IC PARAMETERSPRINT ICIC SEED 1 C1 1 C2 1 C3IC BUILDOPEN WRITE CARD NAME CHAIR.CRD UNIT 13WRITE COORDINATES CARD UNIT 13* Chair conformation coordinates for cyclohexane*! Compute the static energyNBONDS CUTNB 99.0 CDIE VSWITCH SWITCHENERGY! Use the ?ener variable to output text to a fileOPEN WRITE UNIT 33 CARD NAME CYCLO.TXTWRITE TITLE UNIT 33* Energy for chair cyclohexane is ?ener kcal*! Close contact searchesCOOR DIST ENERGY CLOSE 14EXCLUSIONS NONBONDS! Generate the boat conformer by editing the internal! coordinate tablesIC EDITDIHEDRAL 1 C1 1 C2 1 C3 1 C4 0.0DIHEDRAL 1 C2 1 C3 1 C4 1 C5 -60.0DIHEDRAL 1 C3 1 C4 1 C5 1 C6 +60.0DIHEDRAL 1 C4 1 C5 1 C6 1 C1 0.0DIHEDRAL 1 C5 1 C6 1 C1 1 C2 -60.0DIHEDRAL 1 C6 1 C1 1 C2 1 C3 +60.0END! Initialize the coordinate values and build new! coordinatesCOOR INITIC SEED 1 C1 1 C2 1 C3IC BUILDWRITE COORDINATES CARD UNIT 45* Boat conformation coordinates for cyclohexane*NBONDS CUTNB 99.0 CDIE VSWITCH SWITCHENERGYCOOR DIST ENERGY CLOSE 14EXCLUSIONS NONBONDSSTOP


References

References

Slater, J. C; Kirkwood, J. G., Phys. Rev., 37 682 (1931).

Ryckaert, J. P; Bellemans, A., Chem. Phys. Lett., 30 123 (1975).

Ryckaert, J. P.; Bellemans, A., Disc. Farad. Soc., 66 95 (1978).




3 Performing Energy and Force Calculations

The potential energy for any molecular structure can be computed in CHARMm given a PSF, a full parameter set with appropriate force con-stants and reference geometries, and Cartesian coordinates. In addition to the energy, forces on each of the atoms in the molecular system can also be computed. Force calculations are particularly important during molecular dynamics simulations.

This chapter describes the CHARMm energy function and energy minimi-zation algorithms that can be used to refine structures or locate stationary points for conformational searching for dynamics simulations.

This chapter explains ♦ Applying the CHARMm energy function

♦ Minimizing energy


Applying the CHARMm energy function

CHARMm uses a flexible and comprehensive empirical energy function that is a summation of many individual energy terms. The energy function is based on separable internal coordinate terms and pairwise nonbond inter-action terms (Brooks et al. 1983). The total energy is expressed by the fol-lowing equation:

Potential Energy =Ebond + Etheta + Ephi + Eimpr +(internal) Eelec + Evdw +(external)Econs + Euser + Eother(special)

Evaluation of the energy of a molecular system is used as a step in minimi-zation or dynamics. Additionally, the computed energy can be used for con-formation comparisons, computing thermodynamic properties, calculating interaction energies and forces, projecting forces onto internal coordinates,


3. Performing Energy and Force Calculations

evaluating structures during conformational searching, and computing sub-limation energies.

To perform all of these functions, you are given a great deal of flexibility in using the empirical energy function. Almost everything can be customized, from parameters and the specification of individual energy terms to user-supplied energy routines.

Internal energy terms

Internal energy terms are listed as specified in residue topology files and include:

♦ Ebond — Bond potential:

Eq. 1

♦ Etheta — Bond angle potential:

Eq. 2

♦ Ephi — Dihedral angle (torsion) potential:

Eq. 3

Where n = 1, 2, 3, 4, 6

♦ Eimpr — Improper (out-of-plane) torsions:

Eq. 4

The first two terms account for bond length and bond angle deformations. The harmonic approximations used for the bond stretching and angle bend-ing terms are valid at ordinary temperatures and in the absence of chemical reaction.

The dihedral angle (torsion) energy term is a four-atom potential based on the dihedral angle about an axis defined by the middle pair of atoms.

Ebond kb r r0–� �2�=

E� k� � �0–� �2�=

E� k� k� n�� cos–�=

E� k� � �0–� �2

�=



The improper torsion (outd-of-plane) potential is designed to maintain chirality about a tetrahedral extended heavy atom, such as an amino acid alpha carbon without an explicit hydrogen, and to maintain planarity about sp2 hybridized atoms, such as carbonyl carbons with a quadratic distortion potential. Without such a term, out-of-plane potentials tend to be quartic. Additionally, this term provides a better forcefield near the minimum-energy geometry, a consideration that is important for dynamics calcula-tions and vibrational analysis.

External energy terms

External energy terms include:

♦ Eelec — Electrostatic. The constant dielectric equation is:

Eq. 5

For distance-dependent, shifted groups and extended modifications of this equation, see Brooks et al. (1983).

♦ Evdw — van der Waals:

Eq. 6

For a detailed explanation of this equation, see Brooks et al. (1983).

Nonbond energy terms

Electrostatic and van der Waals interactions together are called nonbond interactions.

Computing electrostatic potential

Electrostatic potential is computed using the partial atomic charges pro-vided in the RTF. Several different approaches are included in CHARMm for treating the electrostatic interactions:

♦ Option one — Applies regular Coulombic electrostatic interaction terms.

Eelecqiqj

4��0rij------------------

excl i j�� 1=�=

EvdWAij

rij12

-------Bij

rij6

------– � � �

sw rij2 ron

2 roff2

� ��

excl i j�� 1=�=



♦ Option two — Introduces an approximate solvent screening term in the dielectric constant by setting the dielectric constant proportional to r, that is,

resulting in the electrostatic interaction of the form

.

This option is intended as an approximate way to deal with solvent effects without explicitly including solvent.

♦ Option three (extended electrostatics) — Uses a multipole approxima-tion to permit efficient (that is, time-saving) evaluation of all the elec-trostatic interactions in the system. The approach treats short-range interactions in the usual way, but expresses long-range, group–group interactions in terms of multipoles. Multipole expansion is truncated after quadrupole moments. A constant dielectric is used.

This approach is designed particularly for simulations where solvent is being included explicitly and the details of solvation and solvent polar-ization are of interest.

Computing van der Waals energy

The van der Waals energy is approximated in the CHARMm empirical energy function by the Lennard–Jones potential energy function. This func-tion is often referred to as a 6–12 potential because the attractive force is proportional to R-6, while the repulsive force is modeled by R-12.

Nonbond list External terms are defined by nonbond and hydrogen-bond lists specified by the user. Nonbond interactions refer to van der Waals terms and electro-static interactions between atom pairs.

To maximize the efficiency of the nonbond calculations, a list is created that contains all pair interactions to be considered. Atom pairs are not included in the list if they are too far apart (beyond the long-range cutoffs) or if they are directly connected (through a bond or a bond angle). In the latter case, the atoms are in the excluded list.

The list generation approach was chosen over other alternatives (such as a pairwise search) for two reasons:

♦ During minimization or dynamics, the relative positions between atoms do not change radically between one step and the next. Also, a pairwise

� r� � �0 r�=

q1q2 �0� r2



search through the list of atoms is relatively costly in computational terms.

The list of atoms is updated periodically during minimization or dynam-ics to account for changes in atomic positions. If electrostatic groups are used, the list is stored in terms of group pairs. This leads to improved efficiency and a smaller list, as well as the ability to handle long-range group interactions.

♦ Nonbond terms are defined on atom pairs and, for a first approximation, would require N2 calculations if N is the total number of atoms. To avoid this computational burden, various truncation and approximation schemes can be employed in constructing the nonbond lists.

The nonbond calculation encompasses two steps: list generation and energy computation. The same nonbond specification should be used for all energy calculations within a given project. Should it be necessary to use different nonbond specifications, the implications of these changes must be carefully evaluated.

The nonbond list is primarily generated with the UPDATE command, although it can be generated or modified by providing nonbond-list speci-fications with other commands, including:

♦ NBONDS

♦ ENERGY

♦ MINIMIZE

♦ DYNAMICS

Updating nonbond lists During an energy minimization or molecular dynamics simulation, the non-bond list can be updated according to a frequency that you set. The INB-FRQ keyword is used to indicate the frequency for updating the nonbond list. Three choices are available:

♦ =0 — The nonbond list is not updated at all during minimization or dynamics

♦ =n — The nonbond list is updated every n steps of minimization or dynamics

♦ =-1 — A heuristic test is performed at each step of minimization or dynamics, and an update is performed if necessary

The heuristic test for determining whether the nonbond list needs updating follows this procedure:



♦ Every time energy is called, displacement is computed for each atom since the list update.

♦ If any atom has moved by more than (CUTNB – CTOFNB)/2.0, it is possible that some atom pairs in which the two atoms are now separated by less than CTOFNB are not in the atom pairs list. Therefore, a list update is done.

♦ If all atoms have moved by less than (CUTNB - CTOFNB)/2.0, then all atom pairs within the CTOFNB distance are already accounted for in the nonbond list and no update is necessary.

Nonbond cutoffs For a typical macromolecule, nonbond interactions account for most of the energy evaluation time. The efficiency of the nonbond calculation is increased by including in a nonbond list only atom pairs that are closer than a cutoff distance. The cutoff distance criterion, while computationally effi-cient, has some disadvantages. The possibility always exists that the overall nonbond interactions at long range are not negligible because such interac-tions are very numerous. However, the slope of the van der Waals and elec-trostatic potentials in this region is very small. Because the nonbond interaction vanishes at a greater rate than the total energy, the cutoff makes very little difference for most calculations.

A more significant disadvantage is that a discontinuity in the energy func-tion results at the cutoff distance. For energy minimization of molecular dynamics calculations, this discontinuity can significantly distort computa-tional results. For example, the total energy of the molecular system may not be conserved under such circumstances.

To resolve these difficulties, both the van der Waals and electrostatic energy terms can be modified by techniques that smooth the function around the cutoff distance:

♦ Switching function — The size of the nonbond lists can be made smaller by indicating a distance to be applied to a switching function beyond which no interaction is computed.

Two variables corresponding to the start and finish of the switching regions (ron and roff, respectively) are required to define the switching function. Depending on the value of rij, the following values are used to multiply individual electrostatic or van der Waals energy terms:

♦ If rij < ron, then use 1.0

♦ If ron < rij < roff, then use:



♦ If rij > roff, then use 0.0

However, energy can still be significant at the cutoff distance, which can result in artificially large forces at long range. This is especially true for relatively short (that is, less than 12 Å) cutoff distances and small buffer regions (that is, when roff – ron < 3 Å).

♦ Shifted potential — The shifted potential modifies the radial function so that energy and forces go to zero at some cutoff distance. Eq. 7 defines the functional form of the shifted potential. This term is simply multiplied with the individual electrostatic or van der Waals terms in the empirical energy function:

Eq. 7

One disadvantage to this function is that it has a discontinuity in the sec-ond derivatives at the cutoff distance.

♦ Groups — Another choice is to compute the potential energy based on groups rather than individual atoms. If two groups are neutral with non-zero dipoles, their long range interaction is proportional to 1/R3, which decays faster than the individual atom interactions 1/R.

All these options are available as part of the empirical energy function in CHARMm.

Dielectric constant The dielectric constant is an experimentally derived property of the bulk solvent that reflects the polarizability of the solvent molecules. A polariz-able solvent such as water has a greater dielectric constant than less polar liquids. Electrostatic interactions in such high dielectric polarizable sol-vents are greatly attenuated.

A dielectric constant of 1.0 is sufficient for solvated simulations that include an atomic polarizability term. Because most calculations do not include these factors, a number of models have been used to simulate the dielectric behavior for such systems.

roff rij–� �2 roff 2rij 3ron–+� �

roff ron–� �3--------------------------------------------------------------------------� ��

1rij

rcutoff---------------� �� 2

–� �� 2



The EPS keyword is used to specify an explicit value for the dielectric con-stant. A relatively large dielectric constant can be used for simulating the aqueous environment of small systems. However, most calculations on molecular systems use a smaller dielectric constant. For example, a dielec-tric constant between 2.0 and 10.0 has been employed for simulations in the interior of a protein.

For electrostatic interactions in closely packed molecules, the number of solvent molecules between two interacting charges is usually less than what would be experienced in the bulk solvent. Thus, the dielectric constant for the solvent microenvironment is often not as great as for the bulk solvent. To simulate this effect, a distance-dependent dielectric “constant” can be used. This constant also acts as an approximate solvent screening term, causing the electrostatic interaction to be attenuated as the two charges are separated. The RDIE keyword is used to specify the use of this distance-dependent dielectric constant in energy calculations.

Hydrogen bonds

The generation of hydrogen bonds is one of the major steps in evaluating the energy of a system. The process of hydrogen bond generation involves looking at all possible pairs of hydrogen bond donors and acceptors and selecting those that are good. The meaning of “good” is determined by the parameters described below. The generation routine is also responsible for constructing positions for all uncoordinated hydrogens and adding them to the coordinate list.

The selection of hydrogen bonds involves three checks:

♦ Any good hydrogen bond has a length less than a defined cutoff.

♦ Angle linearity between the donor and acceptor has a value less than a defined cutoff. Typically, the best hydrogen bond has an angle D–H–A of 180°.

♦ If a hydrogen donor has more than one acceptor that satisfies the above constraints, the routine selects the acceptor with the lowest energy.

Because cutoffs are involved with the selection of hydrogen bonds and because the hydrogen bond list must be updated during dynamics and energy must be conserved, switching functions are needed to smooth the transition over a cutoff. The specification of hydrogen bond generation also allows specification of switching function parameters.



However, certain choices for the hydrogen bond selection process never conserve energy in a dynamics run. This is true, for example, if you use the extended-atom representation for your calculations.

The function used in CHARMm to calculate the hydrogen bond energy is:

Hydrogen bond energy is not included as a default energy term. The current CHARMm parameter set has been derived in such a way that hydrogen bond effects are adequately described by the combination of electrostatic and van der Waals forces.

Other energy terms

Other (special) energy terms include:

♦ Econs — For some purposes, it is useful to restrict the changes that occur in a structure. For this reason, CHARMm provides the option of including different types of constraints on the energy when manipulat-ing the structure through minimization or dynamics. An energy con-straint term can be included when the following constraints are applied:

Atom constraint — Used to rigidly maintain the position of certain atoms and delete the energy terms involving only these atoms. This can serve as an effective way of simulating a small part of a very large sys-tem with relative ease and increased computational efficiency.

Atom harmonic constraint — Used primarily to avoid large displace-ments of atoms when minimizing, often when bad contacts are present, while still allowing the structure to relax.

Dihedral constraint — Used to maintain certain local conformations or to examine a series of different conformations when making potential energy maps.

E A

rAD6

--------- � � � B

rA4

----- � � �

– � � �

�A H– D–� �cosm �AA A– H–� �cosn=

xswitch rAD2 ron

2 roff2

� �( )

xswitch �AHD� �cos2 �on� �cos2 �off� �cos2� �( )



NOE constraint — Used to incorporate nuclear Overhauser effect con-straints (representing experimentally derived inter-proton distances) in the energy function.

Euser — CHARMm also allows the addition of a user-supplied routine to the energy function that calculates an arbitrary energy term.

Example: Calculating the initial energies of enkephalin

This example uses the same model, enkephalin, as does Example: Con-structing a model using generated internal coordinates. In fact, if you cre-ated and saved a PSF, this script could be modified to use the same PSF.

This script begins by generating a PSF and coordinates for enkephalin. The coordinates are copied to the COMP array. The energy of the system is then calculated in several different ways:

♦ ENERGY — Calculates the energy of the system.

♦ ENERGY COMP — Calculates the energy using the coordinates in the COMP array. This uses the same PSF. Only the Cartesian coordinates are changed. This can be very useful. For example, after copying the coordinates to the COMP array, you can request an energy minimiza-tion. You can then compare the starting energy ENERGY COMP (the COMP array contains the starting coordinates) with the final ENERGY and make a decision based on the energy difference.

♦ SKIPE — Skips certain energy terms and examines individual energy terms (for example, only the van der Waals component).

The following files are used in this example:

♦ Input file: energy.inp


AMINO.BINPARM.BIN

*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved*! Open and read an all hydrogen amino acid topology fileOPEN READ UNIT 11 FILE NAME “$CHM_DATA/AMINOH.BIN”READ RTF UNIT 11 FILE


Minimizing energy

CLOSE UNIT 11! Open and read the parameter fileOPEN READ UNIT 12 FILE NAME “$CHM_DATA/PARM.BIN”READ PARA UNIT 12 FILE! Read the enkephalin sequenceREAD SEQUENCE CARD* Pentapeptide sequence for met-enkephalin*TYR GLY GLY PHE MET ! Generate the PSF with a segment identifier of ENKP.GENERATE ENKP SETUP! Construct initial Cartesian coordinatesIC PARAMETERSIC SEED 1 N 1 CA 1 C! Copy coordinates to comparison setCOOR COPY COMP! Update nonbond listsUPDATE RDIE SHIFT VSHIFT! Get energy using standard routinesFAST 0ENERGYENERGY COMPGETE PRINTFAST 1! Get energy using optimized routinesENERGY! Get nonbond energy onlySKIPE ALL EXCL VDW ELECENERGY! Restore default energy termsSKIPE EXCL ALLENERGYSTOP

Minimizing energy

The goal of energy minimization is to find a set of coordinates representing a molecular conformation such that the potential energy of the system is at a minimum. Because even the simplest of macromolecules has many degrees of freedom, this task can be computationally quite difficult.

CHARMm has five different minimization methods, all working in Carte-sian space, that provide a flexible array of iterative methods to facilitate energy minimization. Although the resulting conformation may represent



only a local minimum, even macromolecules can be energy minimized effi-ciently using several of these techniques.

All the minimization methods take a molecular structure to a local mini-mum in the potential energy surface. There is no guarantee that this is a glo-bal minimum. Small-molecular systems can be minimized to a global minimum, but multiple runs from different starting points should be done to confirm that a global minimum has indeed been found.

With macromolecules, a very low probability exists that a local minimum is the global minimum. In fact, a global minimum may never be found because of the complexity of the potential energy surface.

Using minimization Minimization used as part of a programmed conformational search can yield many minima that can be useful in understanding large parts of the molecule’s conformational space.

For example, minimization is an important tool in analyzing proteins gen-erated through site-directed mutagenesis. After substituting, inserting, or deleting residues in a sequence, minimization, along with sidechain confor-mation scanning, can be used to determine whether the resulting mutuant structure is very much perturbed with respect to the wild type. If the pertur-bation is minimal, it is possible to model the structure of the mutant protein without resorting to X-ray diffraction.

Minimization methods

Each of the minimization methods available in CHARMm, together with implementation considerations, is listed below:

♦ Steepest descents (SD) — A simple first-derivative method. Uses only first-derivative information and saves only the current location of the coordinates from iteration to iteration. In general, the steepest descents method converges very slowly to a local minimum in a complex poten-tial energy surface. This method is very useful for small changes, such as the removal of unfavorable steric contacts.

♦ Conjugate gradient (CONJ) — Exhibits better convergence than the steepest descents method. The method is iterative and makes use of the previous history of minimization steps and the current gradient to deter-mine the next step.


Minimizing energy

♦ Powell (POWE) — A variation of the conjugate-gradient method with improved efficiency. Use whenever the ABNR method (described below) is not possible.

♦ Newton-Raphson (NRAP) — Implementation in CHARMm involves diagonalization of the second-derivative matrix, then finding the opti-mum step size along each eigenvector.

When one or more negative eigenvalues exist, blind application of the equations will find a saddle point in the potential. To overcome this problem, a single additional energy and gradient determination is per-formed along the eigenvector displacement for each small or negative eigenvalue. From this additional data, the energy function is approxi-mated by a cubic potential and the step size that minimizes this function is adopted.

The advantages of this algorithm are that it avoids saddle points in the potential energy surface and converges rapidly when the potential is nearly quadratic.

The major disadvantage is that this technique is time consuming and memory demanding for large molecules. Additionally, it is currently not possible to use SHAKE (described in Setting Constraints and Periodic Boundaries) or images with this method.

♦ Adopted basis-set Newton-Raphson (ABNR) — Similar to conjugate gradients, but fewer energy evaluations are usually necessary, because the linear interpolation phase of conjugate gradients is avoided.

This method performs energy minimization using a Newton–Raphson algorithm applied to a subspace of the coordinate vector spanned by the displacement coordinates of the last positions. The second-derivative matrix is constructed numerically from the change in the gradient vec-tors and is inverted by an eigenvector analysis that allows the routine to recognize and avoid saddle points in the energy surface. At each step, the residual gradient vector is calculated and used to add a steepest-descents step, incorporating the new direction into the basis set.

This is the method of choice for most applications. Because it avoids the large storage requirements of the full NRAP second-derivative method, larger systems can be minimized more efficiently.

For a general discussion of minimization methods, see Fletcher (1969) and Press et al. (1987). For specific discussion of the conjugate gradient method, see Fletcher and Reeves (1964). For specific discussion of the Powell method, see Powell (1977) and Gunsteren and Karplus (1980).



Convergence criteria

As minimization is proceeding, CHARMm computes the values of several terms that can be monitored for energy convergence. These are:

♦ Rms gradient

♦ Step size

♦ Energy change

If any of these terms is smaller than the default or the user-defined toler-ance, minimization stops.

Although a zero rms gradient is a necessary condition for a minimum, it is not a satisfying condition (that is, saddle points on the potential energy sur-face have zero gradient but are not minima).

Minimization requirements Because all energy minimizations involve calculating the potential energy of the system, you must have a PSF, coordinates, and a parameter file avail-able. Hydrogen-bond and nonbond lists must also be created prior to any energy evaluation and subsequent minimization.

Example: Minimizing enkephalin

Energy minimization is used in this example to relax the initial Cartesian coordinates of a pentapeptide generated from idealized internal coordi-nates.

The following files are used or generated in this example:

♦ Input file: enkpmin.inp


AMINO.BINPARM.BINENKPINI.CRD

♦ Created file: ENKPMIN.CRD

*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved*! Open and read the topology and parameter files (binary)


Minimizing energy

OPEN READ UNIT 11 FILE NAME “$CHM_DATA/AMINOH.BIN”READ RTF UNIT 11 FILECLOSE UNIT 11OPEN READ UNIT 12 FILE NAME “$CHM_DATA/PARM.BIN”READ PARAMETERS UNIT 12 FILECLOSE UNIT 12! Read the sequence information and generate the PSFREAD SEQUENCE CARDS* Enkephalin sequence*5TYR GLY GLY PHE METGENERATE ENKP SETUPOPEN READ UNIT 08 CARD NAME ENKPINI.CRDREAD COOR CARD UNIT 08CLOSE UNIT 08FAST 1UPDATE RDIE SHIFT VSHIFT CUTNB 16.0 INBFRQ 10 IHBFRQ 0! First set of minimizationMINIMIZE CONJ NSTEP 100 NPRINT 10! Second set of minimizationMINIMIZE ABNR NSTEP 200 NPRINT 10! Write out the minimize coordinatesOPEN WRITE UNIT 04 CARD NAME ENKPMIN.CRDWRITE COORDINATES CARD UNIT 04* Minimized enkephalin coordinates*STOP

Example: Minimizing crambin

This example illustrates how CHARMm can be used to take an initial crys-tal structure for a protein and compute the rms differences of internal coor-dinates before and after energy minimization.


♦ Input file: crnmin.inp


AMINO.BINPARM.BIN

♦ Created files:



CRNINI.CRDCRNMIN.CRD

*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved*...* This CHARMm command file generates a PSF for crambin* and performs several minimizations on the structure* and computes the changes relative to the starting * coordinates.*...*! Open and read an all hydrogen amino acid topology file (binary)! and parameter fileOPEN READ UNIT 11 FILE NAME “$CHM_DATA/AMINOH.BIN”READ RTF UNIT 11 FILECLOSE UNIT 11! Open and read the parameter file (binary)OPEN READ UNIT 12 FILE NAME “$CHM_DATA/PARM.BIN”READ PARA UNIT 12 FILECLOSE UNIT 12! Read the sequence information and generate the PSFREAD SEQUENCE CARDS* Sequence for crambin as taken from PDB file*46THR THR CYS CYS PRO SER ILE VAL ALA ARG SER ASN PHEASN VAL CYS ARG LEU PRO GLY THR PRO GLU ALA ILE CYSALA THR TYR THR GLY CYS ILE ILE ILE PRO GLY ALA THRCYS PRO GLY ASP TYR ALA ASN

! Generate the PSF with a segment identifier of 1CRN.! and set up the internal coordinate tables.GENERATE 1CRN SETUP! Patch disulfide bonds in to the PSFPATCH DISU 1CRN 3 1CRN 40 SETUPPATCH DISU 1CRN 4 1CRN 32 SETUPPATCH DISU 1CRN 16 1CRN 26 SETUP! Read the PDB coordinatesOPEN READ UNIT 13 CARD NAME 1CRN.PDBREAD COORDINATES PDB UNIT 13CLOSE UNIT 13! Build and optimize all hydrogen positionsHBUILD! Build any remaining coordinatesIC FILL PRESERVE


References

IC PARAMETERSIC BUILD! Setting up comparison coordinate set for future analysisCOOR COPY COMP! Write the coordinates to diskOPEN WRITE UNIT 13 CARD NAME CRNINI.CRDWRITE COORDINATES CARD UNIT 13* Crambin initial coordinates *UPDATE RDIE SHIFT VSHIFT! First set of minimizationMINIMIZE SD NSTEP 100 INBFRQ -1 CUTNB 30 STEP 0.010 NPRINT 10! Comparisons based on RMSCOOR RMS MASS! Second set of minimizationMINIMIZE SD NSTEP 150 INBFRQ -1 CUTNB 30 STEP 0.0050 NPRINT 10! Comparisons based on RMSCOOR RMS MASS! Internal coordinate comparisons; select and print! only the phi/psi internal coordinatesIC FILLIC DIFFIC KEEP SECO SELE ATOM * * N .OR. ATOM * * CA ENDIC KEEP THIR SELE ATOM * * CA .OR. ATOM * * C ENDIC DELE FOUR SELE ATOM * * O ENDIC PURGIC PRIN! Write out crambin minimized coordinatesOPEN WRITE UNIT 04 CARD NAME CRNMIN.CRDWRITE COORDINATES CARD UNIT 04

* Crambin coordinates after 250 steps of SD minimization*STOP

References

Brooks, B. R.; Bruccoleri, R. E.; Olason, B. D.; States, D. J.; Swaminathan, S.; Karplus, M., J Comp. Chem. 4 187 (1983).

Fletcher, R. (ed.) Optimization, Academic Press, New York, 1969.

Flectcher, R.; Reeves, C. M., The Computer Journal 7 149 (1964).



Powell, M. J. D. “Restart procedure for the conjugate gradient method,” Mathematical Programming 12 241 (1977).

Press, W. H.; Flannery, B. P.; Teukolshy, S. A.; Vetrrling, W. T. Numerical Recipes: The Art of Scientific Computing, University Press, Cam-bridge, 1987.

Gunsteren, W. F.; Karplus, M., J. Comp. Chem. 1 266 (1980).


4 Performing Molecular Dynamics

One of the most important computational techniques in CHARMm is molecular dynamics simulations. In CHARMm, molecular dynamics sim-ulations are performed using a classical mechanics approach, in which Newton’s equations of motion are integrated for all atoms in the system. As with energy evaluations, a defined PSF, a set of coordinates, and a set of parameters are required to initiate a molecular dynamics run.

Molecular dynamics can be used to generate a realistic picture of a struc-ture’s motions, perform conformational searching, do a time series analysis of structural and energetic properties, explore energy decay, and analyze solvent effects. In addition to exploring more global aspects of macromo-lecular structure than can be accomplished with minimization techniques, molecular dynamics can help with understanding critical aspects of protein function that involve both small-scale and large-scale atomic movements.

This chapter explains ♦ Understanding molecular dynamics

♦ Running dynamic simulation variants

♦ Monitoring dynamics simulation output

♦ Using time sets and correlation functions


Understanding molecular dynamics

The essence of the molecular dynamics technique is in the numerical inte-gration of Newton’s second law, relating the mass and acceleration of an atom in the system to the gradient of the potential energy field. Given accel-eration, an approximate velocity for the atom can be computed for a given period of time, and changes in atomic coordinates can be determined.

Several methods are available for numerical integration. In CHARMm, the Verlet method is implemented. Leapfrog and velocity Verlet variants are


4. Performing Molecular Dynamics

also available. For detailed discussion of these methods and other numeri-cal methods for integrating differential equations, see Haile (1992) or Allen and Tildesley (1987).

Basic steps A typical molecular dynamics run involves the following basic steps:

1. Preliminary preparation — A molecular structure with all Cartesian coordinates defined is required for a dynamics simulation. After deter-mining the internal coordinate values of the molecule, total energy as a function of the Cartesian coordinates is computed by evaluating the individual terms of the energy equation.

2. Minimization — All dynamics simulations begin with an initial struc-ture that may be derived from experimental data. Energy minimization is performed on structures prior to dynamics to relax the conformation and remove steric overlaps that produce bad contacts. In the absence of an experimental structure, a minimized geometry can be used as a start-ing point.

3. Heating — A minimized structure represents the molecule at a temper-ature close to absolute zero. Heating is accomplished by initially assign-ing random velocities according to a gaussian distribution appropriate for that low temperature and then running dynamics. The temperature is gradually increased by assigning greater random velocities to each atom at predetermined time intervals.

4. Equilibration — Equilibration is achieved by allowing the system to evolve spontaneously for a period of time and integrating the equations of motion until the average temperature and structure remain stable. This is facilitated by periodically reassigning velocities appropriate to the desired temperature. Generally, the procedure is continued until var-ious statistical properties of the system become independent of time.

5. Production — In the final molecular dynamics simulation, CHARMm takes the equilibrated structure as its starting point. In a typical simula-tion, the trajectory traces the motions of the molecule through a period of at least 10 ps (picoseconds). Just as with energy minimization, provi-sion is made to update the nonbond and hydrogen-bond lists periodi-cally. Additional options are available, making the dynamics facility quite flexible.

6. Quenching — The logical opposite of heating, this optional step takes the molecule from the equilibrated temperature to zero. Quenching is a form of minimization, utilizing molecular dynamics to slowly remove all kinetic energy from the system.


Understanding molecular dynamics

Strictly speaking, minimization and heating are not necessary, provided the equilibration process is long enough. However, these steps can serve as a means to arrive at an equilibrated structure in an effective way.

A molecular dynamics run generates a dynamics trajectory consisting of a set of frames of coordinates and velocities that represent the trajectory of the atoms over time. Using trajectory data, you can compute the average structure and analyze fluctuations of geometric parameters, thermodynam-ics properties, and time-dependent processes of the molecule.

Preliminary analysis is possible using commands provided in the coordi-nate manipulation facility. Gross changes, as well as more detailed pertur-bations, can be monitored using correlation functions.

Because molecular dynamics runs often require considerable amounts of computer time, a restart facility is available that allows you to suspend and resume the calculation.

Temperature

The instantaneous kinetic temperature (T) at which each dynamics step is defined is directly proportional to the kinetic energy of the molecular sys-tem of N atoms and given by the equation:

Eq. 8

Where:

mi and vi are the mass and velocity of the ith atom

kb is the Boltzmann constant

Average kinetic energy is proportional to the kinetic temperature:

Where:

12--- mivi

2

� � � � 3

2---NkbTinst=

Ek� � limt �� 1

t--- Ek PN

� �dt

t0

t0 t+� �

�32---NkBT= =



Dynamics time step

Because the potential energy field changes as a molecular structure is adjusted, accelerations must also change. Consequently, the time step in molecular dynamics must be very small. The smaller the time step, the bet-ter the approximation.

The choice of the integration time step is very important. The time step should be at least an order of magnitude smaller than the time correspond-ing to the fastest motion in a molecule. Typically, this is the vibration of a bond containing a hydrogen (with a period less than 0.001 ps), which requires a time step of 0.0005 ps.

Another factor to be considered is the simulation time necessary, which can range from ten to hundreds of picoseconds or even nanoseconds. The char-acteristic times for common molecular events are:

To allow larger time steps and shorter real-time dynamics simulations, the energy and force of certain high-frequency motions such as bond stretching may be removed by constraining them to their initial or equilibrium values. This is a reasonable approximation, because it is assumed that the harmonic stretching of bonds is restricted by a very large force constant and, particu-

Ek PN� �

12--- mivi

2

i 1=

N

�pi

2

2mi---------

i 1=

N

�= =

Event Time

Bond stretching ~1 to 20 fsElastic domain modes 100 fs to several psWater reorientation 4 psInter-domain bending 10 ps to 100 nsGlobular protein tumbling 1 to 10 nsAromatic ring flipping 100 �s to several secAllosteric shifts 2 �s to several secLocal denaturation 1 ms to several sec


Running dynamic simulation variants

larly for bonds containing hydrogens, is not significantly coupled to other motions of the system.

The method used in CHARMm to constrain these motions is the SHAKE algorithm. SHAKE may be applied to all bonds or only to bonds containing hydrogens and to all angles or only angles containing hydrogens. To main-tain a high degree of accuracy during the dynamics simulation, as well as to provide a larger integration time step, apply SHAKE only to bonds con-taining hydrogens. A two-fold increase in the time step (to 0.001 ps) is then allowed.

Length of trajectory

The length of a trajectory needed to calculate a property depends on the time variation of the property under consideration. If the property is a slowly varying function, the dynamics integration should be extended to cover several periods.

If a property varies randomly about a mean value with a decay time of t, and the simulation is run for time T, the variance in the estimate is propor-tional to the square root of t/T. When multiple independent samples are present (for example, each water molecule in a solvent simulation), the samples can be averaged to improve sampling.


Several variants of the standard molecular dynamics simulations are avail-able in CHARMm and are described briefly in the following sections.

Langevin dynamics

The Langevin dynamics method (McCammon et al. 1976; Levy et al. 1979) approximates a full molecular dynamics simulation of a system by elimi-nating unimportant or uninteresting degrees of freedom. The effects of the eliminated degrees of freedom are simulated by mean and stochastic forces. For example, instead of simulating hundreds of solvent molecules sur-rounding the solute molecules, the solvent can be ideally represented by a viscous fluid described in terms of dissipative and fluctuative equations.



Stochastic boundary molecular dynamics

The stochastic boundary molecular dynamics method uses a combination of both Langevin and Newtonian dynamics. With this method, the molecu-lar system is partitioned into a reaction region where Newtonian dynamics simulation is run, a buffer region where Langevin dynamics is run, and a reservoir region.

In this way, atoms far from the interesting sites in a large macromolecular system can be eliminated from detailed analysis. This allows detailed stud-ies of localized portions of interacting molecular systems, for example, enzyme–substrate active site interactions.

Constant pressure and temperature dynamics

CHARMm supports the use of constant-pressure and constant-temperature algorithms in molecular dynamics simulations. Only a few added specifi-cations are needed in the standard CHARMm dynamics input file to run a constant-pressure/constant-temperature simulation: the isothermal com-pressibility (for solvated systems, a value of 0.0000463 atm-1 is suggested), temperature and pressure coupling constants (5.0 ps for each), and a refer-ence temperature and pressure (298.0 K and 1.0 atm, respectively).

For constant-pressure dynamics, you must use the CHARMm crystal facil-ity. Constant-pressure scaling only works with cubic, orthorhombic, and triclinic unit cells. Shape matrix propagation and coordinates scaling for triclinic unit cells are done according to Brown and Clark (1991).

Pressure and pressure statistics can be evaluated for static coordinate frames. The external isotropic pressure and tensor are calculated if a vol-ume is present and a temperature is given. Average pressure and fluctua-tions are also computed.

Example: Molecular dynamics using the Berendsen CPT algorithm

This example sets up a crystal of the alanine tetrapeptide and performs a constant-temperature and -pressure dynamics simulation.



* Molecular dynamics using the Berendsen CPT algorithm.*stream datadir.defRead rtf card...<read topology file>...Read sequence card<Read sequence>...Generate ALA4 setup<read coordinates>...Read coor card* OPTIMISED COORDINATES FOR THE FULL UNIT CELL OF CRYSTALLINE* ALANINE (4 MOLECULES). THE LATTICE IS OPTIMISED WITH-* A = 5.59967,* B = 12.19617 AND C = 5.40430 ANGSTROMS.<Read coordinates>...! Save the coordinates.Coor copy comp! Define the crystal.Crystal Define orthorhombic 5.59967 12.19617 5.40430 90.0 -90.0 90.0! Read in an existing transformation file.Crystal Read card<read crystal file>...! Calculate an energy with an update.Energy imgfrq 10 inbfrq 10 ihbfrq 0 cutim 999.0! Do 100 steps of constant temperature dynamics.Dynamics CPT TConstant TCouple 0.4 TReference 300.0 - strt nstep 100 timestep 0.001 - iprfrq 100 ihtfrq 0 ieqfrq 0 ntrfrq 0 - nprint 1 nsavc 0 nsavv 0 - firstt 300.0 finalt 300.0! Do a further 100 steps of constant pressure and temperature! dynamics and test restartopen write card unit 1 name @9xtlala3.rst



Dynamics CPT TConstant TCouple 0.4 TReference 300.0 - PConstant Compressibility 0.00005 PCouple 0.1 - PReference 1.0 - strt nstep 50 timestep 0.001 - iprfrq 100 ihtfrq 0 ieqfrq 0 ntrfrq 0 - nprint 1 nsavc 0 nsavv 0 iunwri 1 - firstt 300.0 finalt 300.0! now test restart; dynamics should use crystal data from the ! restart file!open read card unit 1 name @9xtlala3.rstCrystal Define orthorhombic 6. 12. 5. 90.0 90.0 90.0Dynamics rest CPT TConstant TCouple 0.4 TReference 300.0 - PConstant Compressibility 0.00005 PCouple 0.1 - PReference 1.0 - strt nstep 50 timestep 0.001 - iprfrq 100 ihtfrq 0 ieqfrq 0 ntrfrq 0 - nprint 1 nsavc 0 nsavv 0 iunrea 1 - firstt 300.0 finalt 300.0! Compare the coordinates.Coordinates RMS MassPrint CoordinatesStop

Quenched molecular dynamics

Quenched molecular dynamics can be run in at least two different ways, as illustrated in the following short examples.

Using Langevin dynamics The following CHARMm script fragment can be used for quenched Lan-gevin dynamics:

dyna langevin nstep 1000 TBATH 1000. npri 100 dyna langevin nstep 1000 TBATH 500. npri 100 dyna langevin nstep 1000 TBATH 500. npri 100dyna langevin nstep 1000 TBATH 250. npri 100dyna langevin nstep 1000 TBATH 125. npri 100dyna langevin nstep 1000 TBATH 0. npri 100

Using Newtonian dynam-ics

The following CHARMm script fragment can be used for quenched New-tonian dynamics with velocity scaling:

dyna nstep 5000 FIRStt 1000. FINAlt 0. TEMInc -20. IHTFrq 100 -npri 100


Monitoring dynamics simulation output

Monitoring dynamics simulation output

Dynamics simulations output a large amount of data:

♦ After the dynamics command has been read, information about every keyword, whether specified or not, is listed.

♦ If a restart file is read, data from the previous run are also given.

♦ During heating and equilibration, information about the assignment or scaling of velocities is printed at their respective frequency updates.

♦ Periodically, a summary of the energy terms is printed. Additionally, at the end of each printing, frequency, update, averages, and rms fluctua-tions for the previous dynamics history are written. Following this are statistics providing details about the short- and long-range drift in the energy.

Certain terms and values written to the output file should be monitored closely. After the molecular system has been equilibrated, a short trajectory of free dynamics should be run to determine the stability of the energy and the temperature.

Because the system has no external forces, conservation of energy must be maintained. Check this by comparing the starting total energy term to the last total energy term. A ratio of the rms fluctuation of the total energy to the rms fluctuation of the kinetic energy for the free dynamics trajectory is an excellent measure of the accuracy of the run. A value of 0.001 or less is expected.

The average temperature and its fluctuation, printed at the end of the trajec-tory output, should also be noted. A temperature near the one specified by FINALT with a relatively small fluctuation is required. If constant temper-ature cannot be maintained, the system may have heated too rapidly or may not have completely equilibrated.

Coordinate trajectory format

The coordinate trajectories produced by CHARMm are in binary format. The principal reason for this is that binary files require much less disk space than their text file counterparts. Also, reading binary data is much faster than reading text data. Because trajectories are used extensively during analysis, the speed with which they may be read is important.



Binary formats, however, are machine dependent and cannot be easily moved from one machine to another. To overcome this limitation, CHARMm provides a way to format dynamics trajectories in a machine-independent manner. The resulting coordinate trajectory files can be easily copied from one machine to another. CHARMm is then used to return the files to the standard binary version to be used for analysis or graphic dis-play. For this procedure to work properly, you must have CHARMm installed on both machines.

The format of the binary trajectory (DCD) file is illustrated in the following example:

♦ For the first coordinate set:

HDR,ICNTRL ! character*4 HDR, integer ICNTRL(20)NTITL,(TITLE(J),J=1,NTITL) ! integer NTITL, CHARACTER*80 TITLE(*)NATOM ! integer NATOM

♦ If fixed atoms exist (for example, NFREAT.NE.NATOM), an extra record exists with the list of free (movable) atoms:

FREEAT(I),I=1,NFREAT) ! INTEGER FREEAT(*)

♦ If this is crystal-type calculation (for example, a constant-pressure job), an extra record exists with unit cell parameters in lower-triangle form:

XTLABC ! REAL*8 XTLABC(6)(X(I),I=1,NATOM) ! real X(NATOM)(Y(I),I=1,NATOM) ! real Y(NATOM)(Z(I),I=1,NATOM) ! real Z(NATOM)

For all subsequent coordinate sets, only movable atoms are written.

♦ If this is a crystal-type calculation (such as a constant-pressure job), an extra record exists with unit cell parameters in lower-triangle form:

XTLABC(X(FREEAT(I)),I=1,NFREAT)(Y(FREEAT(I)),I=1,NFREAT)(Z(FREEAT(I)),I=1,NFREAT)

Where HDR = ‘CORD’ or ‘VELD’ for coordinates and velocities, respectively:


Using time sets and correlation functions

ICNTRL(1)=NFILE ! number of frames in trajectory fileICNTRL(2)=NPRIV ! number of steps in previous runICNTRL(3)=NSAVC ! frequency of savingICNTRL(4)=NSTEP ! total number of steps NFILE=NSTEP/NSAVCICNTRL(8)=NDEGF ! number of degrees of freedomICNTRL(9)=NATOM-NFREAT ! number of fixed atomsICNTRL(10)=DELTA4 ! coded time stepICNTRL(11)=stoi(XTLTYP,ALPHABET) ! coded crystallographic ! group (or zero)ICNTRL(20)=VERNUM ! version number

All other entries (12–19) are zero.

Using time sets and correlation functions

After running a dynamics simulation on a molecule, you may want to extract data on the extent and nature of the changes that occurred in the sys-tem. CHARMm can calculate a time series for an extensive set of properties of the total system trajectory or for some of its components.

The properties for which a time series can be calculated are averages over a set of individual properties of the molecule. Some of the individual prop-erties encompass calculations on the position of an atom, the energy or geometry of internal coordinates, the vector joining two atoms, the scalar product of two such vectors, the scalar product of the position vectors of two atoms, fluctuations in the positions of two atoms, the scalar product of the functions of two atoms, or the velocity/kinetic energy of an atom.

The time series can also be evaluated for certain global properties such as the radius of gyration and the number density of the molecule. The ability to average vectors or internal coordinates over a set of atoms is helpful in defining and studying the behavior of local regions. If the requested corre-lation is a cross-correlation between two different sets, then both sets are evaluated simultaneously and stored.

A time series can be manipulated, saved, plotted, or used to generate corre-lation functions. Examples of experimental quantities that can be calculated using correlation functions are frictional coefficients, IR line widths, fluo-rescence depolarization rates, spectral densities (the Fourier transform of the correlation function), and NMR relaxation times.



Alternatively, a covariance matrix can be computed for a collection of time series. This option computes a full matrix to use in entropy calculations or in other applications. For this option, only one TRAJectory command is allowed.

A typical protocol for using time series and correlation functions in CHARMm takes the following basic form:

1. Read coordinate or velocity sets of a dynamics trajectory. Evaluate the specified property for each set, then store the data.

2. Manipulate the time series (Qt) to evaluate certain functions of the time series.

3. Integrate the resultant time series (Ft) subset to obtain correlation func-tions.

4. Manipulate the correlation function (Ct) to determine some function of the correlation function (Gt).

5. Analyze and plot either the time series (Ft) or the correlation functions (Ct) during any of these processes.

When the correlation function is calculated, several operations can be per-formed on it. The integral, the integral of the square, and the logarithm of the correlation function can be evaluated, and the Fourier transform of the correlation function can be taken to obtain the spectral density.

Example: Running enkephalin dynamics

A simple molecular dynamics simulation is performed in this example. Fol-lowing the simulation, some of the CHARMm dynamic analysis com-mands are used to compute average atomic positions and fluctuations.


♦ Input files: enkpdyn.inp


ENKPA(BC).RSTENKPA(BC).DCDENKPA(BC).DVLENKPA(BC).ENEENKPH.CRD



ENKPE.CRDENKPD.CRDENKPAVG.CRDENKPDIF.CRD


AMINO.BINPARM.BINENKPMIN.CRD

*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved*...*...* This CHARMm command file generates a dynamics trajectory* for met-enkephalin, from which the average structure and* fluctuations are computed.*...*!! Open and read an all hydrogen amino acid topology file! and parameter fileOPEN READ UNIT 02 FILE NAME “$CHM_DATA/AMINOH.BIN”READ RTF UNIT 02 FILECLOSE UNIT 01OPEN READ UNIT 02 FILE NAME “$CHM_DATA/PARM.BIN”READ PARA UNIT 02 FILECLOSE UNIT 02! Read the sequence for met-enkephalinREAD SEQUENCE CARD* Pentapeptide sequence for met-enkephalin* 5TYR GLY GLY PHE MET! Generate the PSF with a segment identifier of ENKP.! Set up the internal coordinate tables.GENERATE ENKP SETUP! Read in minimized coordinates OPEN READ UNIT 04 CARD NAME “ENKMIN.CRD”READ COOR UNIT 04 CARDCLOSE UNIT 04! Shake all bonds with hydrogensSHAKE BONH! Open the files necessary for the dynamics trajectory:! A restart file



! A coordinates file (the coordinate trajectory)! A velocities file (the velocity trajectory)! An energy file!OPEN WRITE UNIT 31 CARD NAME ENKPA.RSTOPEN WRITE UNIT 32 FILE NAME ENKPA.DCDOPEN WRITE UNIT 33 FILE NAME ENKPA.DVLOPEN WRITE UNIT 34 CARD NAME ENKPA.ENEDYNA STRT VERLET NSTEP 3000 TIME 0.001 RDIE - VSWITCH SWITCH - IPRFRQ 100 IHTFRQ 50 IEQFRQ 0 INBFRQ -1 IHBFRQ 0 - IUNREA -1 IUNWRI 31 IUNCRD 32 IUNVEL 33 KUNIT 34 - NPRINT 50 NSAVC 50 NSAVV 50 - FIRSTT 0.0 FINALT 300.0 TEMINC 5 - TWINDH 10.0 TWINDL -10.0 - IASORS 1 IASVEL 1 ICHECW 0OPEN WRITE UNIT 41 CARD NAME ENKPH.CRDWRITE COOROORDINATES UNIT 41 CARD* COORDINATES AFTER HEATING*CLOSE UNIT 31CLOSE UNIT 32CLOSE UNIT 33CLOSE UNIT 34CLOSE UNIT 41OPEN READ UNIT 30 CARD NAME ENKPA.RSTOPEN WRITE UNIT 31 CARD NAME ENKPB.RSTOPEN WRITE UNIT 32 FILE NAME ENKPB.DCDOPEN WRITE UNIT 33 FILE NAME ENKPB.DVLOPEN WRITE UNIT 34 CARD NAME ENKPB.ENEDYNA RESTART VERLET NSTEP 2000 TIME 0.001 RDIE - VSWITHC SWITCH - IPRFRQ 100 IHTFRQ 0 IEQFRQ 200 INBFRQ -1 IHBFRQ 0 - IUNREA 30 IUNWRI 31 IUNCRD 32 IUNVEL 33 KUNIT 34 - NPRINT 50 NSAVC 50 NSAVV 50 - FIRSTT 300.0 FINALT 300.0 - TWINDH 10.0 TWINDL -10.0 - IASORS 0 ISCVEL 0 ICHECW 1OPEN WRITE UNIT 41 CARD NAME ENKPE.CRDWRITE COOR UNIT 41 CARD* COORDINATES AFTER EQUILIBRATION*CLOSE UNIT 30CLOSE UNIT 31CLOSE UNIT 32CLOSE UNIT 33CLOSE UNIT 34CLOSE UNIT 41OPEN READ UNIT 30 CARD NAME ENKPB.RST



OPEN WRIT UNIT 31 CARD NAME ENKPC.RSTOPEN WRIT UNIT 32 FILE NAME ENKPC.DCDOPEN WRIT UNIT 33 FILE NAME ENKPC.DVLOPEN WRIT UNIT 34 CARD NAME ENKPC.ENEDYNA RESTART VERLET NSTEP 5000 TIME 0.001 RDIE - VSWITCH SWITCH - IPRFRQ 100 IHTFRQ 0 IEQFRQ 0 INBFRQ -1 IHBFRQ 0 - IUNREA 30 IUNWRI 31 IUNCRD 32 IUNVEL 33 KUNIT 34 - NPRINT 50 NSAVC 50 NSAVV 50 - FIRSTT 300.0 FINALT 300.0 - TWINDH 10.0 TWINDL -10.0 - ICHECW 0OPEN WRITE UNIT 41 CARD NAME ENKPD.CRDWRITE COOR UNIT 41 CARD* COORDINATES AFTER DYNAMICS*CLOSE UNIT 30CLOSE UNIT 31CLOSE UNIT 32CLOSE UNIT 33CLOSE UNIT 34CLOSE UNIT 41COOR INIT! Calculate the average structure and isotropic! fluctuations from the free dynamics trajectoryOPEN READ UNIT 51 FILE NAME ENKPC.DCDCOOR DYNAMIC FIRSTU 51CLOSE UNIT 51OPEN WRITE UNIT 17 CARD NAME ENKPAVG.CRDWRITE COORDINATES CARD UNIT 17* Average structure and isotropic fluctuations*CLOSE UNIT 17! Print out the average positions and fluctuations! of the backbone atomsPRINT COORDINATES SELE ATOM * * N .OR. ATOM * * CA .OR. - ATOM * * C END! Compare the minimized coordinates with the! average coordinates; store the average! coordinates in the comparison setCOOR COPY COMPCOOR INITOPEN READ UNIT 21 CARD NAME enkmin.crdREAD COOR UNIT 21 CARDCLOSE UNIT 21COOR DIFFOPEN WRITE UNIT 22 CARD NAME ENKPDIF.CRDWRITE COOR UNIT 22 CARD



* Difference in atomic positions between dynamics* average coordinates and minimized coordinates*CLOSE UNIT 22PRINT COORDINATES SELE ATOM * * N .OR. ATOM * * CA .OR. - ATOM * * C END! Restore the average coordinates to the main setCOOR INITCOOR COPY! Fill the internal coordinate arrays with the average! ic values from the free dynamics trajectoryIC FILLOPEN READ UNIT 51 FILE NAME ENKPC.DCDIC DYNA AVERAGE FIRSTU 51CLOSE UNIT 51PRINT IC! Fill the internal coordinate arrays with the! fluctuations to the ic averages from the free! dynamics trajectoryOPEN READ UNIT 51 FILE NAME ENKPC.DCDIC DYNA FLUCTUATIONS FIRSTU 51CLOSE UNIT 51PRINT ICSTOP

Example: Calculating correlations in enkephalin dynamics

The trajectory from the enkephalin dynamics simulation of the previous example is used here to compute internal correlated motion of enkephalin.

The following files are used in this example:

♦ Input file: enkpcorr.inp


AMINOH.BINPARM.BINENKPC.DCD


Example: Calculating correlations in enkephalin dynamics

*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved*! Open and read an all hydrogen amino acid topology file! and parameter fileOPEN READ UNIT 02 FILE NAME “$CHM_DATA/AMINOH.BIN”READ RTF UNIT 02 FILECLOSE UNIT 02OPEN READ UNIT 02 FILE NAME “$CHM_DATA/PARM.BIN”READ PARA UNIT 02 FILECLOSE UNIT 02! Read the sequence for met-enkephalinREAD SEQUENCE CARD* Pentapeptide sequence for met-enkephalin* 5TYR GLY GLY PHE MET! Generate the PSF with a segment identifier of ENKP.! Set up the internal coordinate tables.GENERATE ENKP SETUP! Open the enkephalin dynamics fileOPEN READ UNIT 51 FILE NAME “$GUIDE0601/ENKPC.DCD”! Enter the correlation facility; specify a maximum of! 500 dynamics coordinate files and a maximum of 4! time series (1 each for the dihedrals). The maximum! number of atoms required is 20 (4 for each of the four! dihedral time series atoms plus 1 for the codes value).CORREL MAXTIM 500 MAXSERIES 10 MAXATOMS 20! Time series for correlation of the phi and psi! dihedrals of the second and third residuesENTER PHI2 DIHE ENKP 1 C ENKP 2 N ENKP 2 CA ENKP 2 C GEOMETRYENTER PSI2 DIHE ENKP 2 N ENKP 2 CA ENKP 2 C ENKP 3 N GEOMETRYENTER PHI3 DIHE ENKP 2 C ENKP 3 N ENKP 3 CA ENKP 3 C GEOMETRYENTER PSI3 DIHE ENKP 3 N ENKP 3 CA ENKP 3 C ENKP 4 N GEOMETRY! trajectoryTRAJECTORY FIRSTU 51 NUNIT 1 BEGIN 5050 STOP 10000 SKIP 50! Report on statisticsSHOW ALL! Apply correlation functions. First, use both the FFT! and DIRECT methods to compute the correlation between



! phi and psi for the second residue (to check for! accuracy). Then, apply the correlation function to! all other combinations of phi and psi.CORFUN PHI2 PSI2 FFTCORFUN PHI2 PSI2 DIRECT! Autocorrelation of the dihedralsCORFUN PHI2 PHI2CORFUN PSI2 PSI2CORFUN PHI3 PHI3CORFUN PSI3 PSI3! Cross-correlation of the dihedralsCORFUN PHI2 PSI3CORFUN PSI2 PHI3CORFUN PHI2 PHI3CORFUN PSI2 PSI3CORFUN PHI2 PSI2CORFUN PHI3 PSI3! Exit correlation facilityENDSTOP

References

Allen, M. P.; Tildesley, D. J. Computer Simulations of Liquids, Oxford Uni-versity Press, Oxford, 1987.

Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, A.; DiNola, W. F.; Haak, J. R. J. Chem. Phys. 81 3684 (1984).

Brooks III, C. L.; Brunger, A. T.; Karplus, M. Biopolymers 24 843 (1985).

Brown, D.; Clark, J. H. R. Comp. Phys. Comm. 62 360 (1991).

Haile, J. M. Molecular Dynamic Simulations: Elementary Methods, John Wiley & Sons, New York, 1992.

Levy, R. M.; McCammon, J. A.; Karplus, M. Chem. Phys. Lett. 64 4 (1979).

McCammon, J. A.; Gelin, B. R.; Karplus, M.; Wolynes, P. G. Nature 262 325-326 (1976).


5 Setting Constraints and Periodic Boundaries

In CHARMm, a variety of options can help you tailor your files and data to focus on the parts of a system in which you are interested. These include setting constraints on atoms, angles, torsion angles, and other properties and introducing periodic boundary conditions in energy calculations.

This chapter explains ♦ Setting constraints

♦ Setting periodic boundaries

Example scripts are found throughout the chapter.

Setting constraints

Constraints can be used during minimization or dynamics, as well as during normal mode calculations, to fix or restrict the motion of specific atoms. Restricting atom movement can:

♦ Improve exploration of some portion of the potential energy surface

♦ Impose boundary forces to prevent solvent molecules from escaping

♦ Remove high-frequency vibrations during dynamics

♦ Generate additional experimental data by including NOE constraints during molecular dynamics simulations

CHARMm provides seven basic types of constraints:

♦ Fixed atom constraint

♦ Harmonic atom constraint

♦ Torsion constraint

♦ Internal coordinate constraint


5. Setting Constraints and Periodic Boundaries

♦ Distance constraint

♦ SHAKE

♦ Quartic droplet potential

Fixed atom restraint

The simplest type of constraint is to fix atoms to fixed points in space so that they do not move during a minimization or dynamics simulation. You can then save computation time by calculating only those energy terms that involve at least one atom that is free to move. Energy terms between fixed atoms remain the same between energy evaluation steps. CHARMm auto-matically omits from the nonbond and hydrogen-bond lists any interactions that include only fixed atoms.

Harmonic atom constraint

For some applications, it is not desirable to fix atoms, but preferable to allow them some freedom while constraining them to be near a particular position in space. CHARMm achieves this by calculating an additional energy term for all atoms that are to be constrained. This term has the form:

Where:

Econs Constraint energy

ki Force constant

mi Mass of atom i (if mass weighing is used) or 1

ri Position of the atom

r0i Reference position about which the atom is to be centered

exp Exponent

Econs kimassi ri r0 i–� �exp

i� � ��

=


Setting constraints

Torsion constraint

Constraining a torsion angle near a selected value is essential for some studies. CHARMm uses a harmonic potential to restrict the motion of a tor-sion angle, usually to a value close to a reference position. For example, if you are investigating the adiabatic energy barrier to rotation about a bond, you must fix the value of that particular torsion and minimize the rest of the structure. When the procedure is repeated for a set of values of the angle in the range 0° to 360°, a complete energy profile for rotation about the bond emerges. A similar process is used to generate phi/psi maps and other multi-dimensional energy surfaces for the study of molecular conforma-tions.

Internal coordinate constraint

In addition to specifying torsion angle constraints, you can apply more gen-eral internal coordinate constraints by applying constraints to the bonds, angles, or torsion angles that have entries in the internal coordinates table. This facility is global in nature and is not applicable to specific internal coordinates.

Distance constraint

A distance constraint in CHARMm places a potential between two or more atoms, to constrain the distance between these atoms to a certain value. The constraining potential used in CHARMm is:

For r < rmin:

Eq. 9

For rmin < r < rmax:

Eq. 10

For rmax < r < rlim:

Eq. 11

For rlim < r:

E r� �12---kmin r rmin–� �2=

E r� � 0.0=

E r� �12---kmin r rmax–� �2=



Eq. 12

Where rlim is the value of r where the force equals fmax.

This constraint is primarily used for the incorporation of NOE inter-proton distance information into a molecular dynamics simulation.

SHAKE

SHAKE uses an algorithm that restores specified internal coordinates to their reference values after a minimization or dynamics step. Use of the SHAKE algorithm during dynamics can effectively allow for a larger time step during simulation.

Quartic droplet constraint

The quartic droplet constraint term is designed to put the entire molecule in a cage by constructing a constraining sphere around it. The potential is scaled so that atom positions furthest from the center of the sphere have the greatest restraining force applied.

The quartic droplet constraint term is based on the center of mass or the center of geometry. No net force or torque is introduced by the center of mass term. The potential function is:

Eq. 13

Example: Creating the alanine dipeptide phi/psi map

This example shows how constraints can be used to explore the conforma-tion space and energetics of a molecule. The core of the example is con-tained in PHIPSI.STR, where the phi/psi angles of a dipeptide are constrained to specific torsion angles and the molecule’s energy is com-puted to create a potential energy map.

In PHIPSI.STR, two variables are used to hold the phi and psi angles. These variables are then used in two constraints commands:

E r� � fmax rrlim rmax+

2---------------------------–

�=

Edroplet k mi ri rcom–� �exp

i� � ��

=


Setting constraints

! Constrain the phi and psi dihedral angles at the current! values of phi and psi (parameters 1 and 2)CONS DIHE MAIN 1 CNT MAIN 1 N MAIN 1 CA MAIN 1 C FORC 1000.0 -MIN @1CONS DIHE MAIN 1 N MAIN 1 CA MAIN 1 C MAIN 1 NCT FORC 1000.0 -MIN @2

The first command sets a torsional constraint on four atoms:

(MAIN 1 CNT) - (MAIN 1 N) - (MAIN 1 CA) - (MAIN 1 C)

with a force of 1000 kcal mol-1 and a minimum at @1. This means that the value stored in variable 1 is substituted in this position. The second con-straint sets the constraint on the psi torsion angle defined by the atoms N-CA-C-NCT.

The structure is then minimized. This is critical, because setting the con-straint does not actually change the torsion angle in the structure; it simply moves the minimum of the energy function. Minimization allows the mol-ecule to move to the new low-energy conformation. The dihedral con-straints are then removed (CONS CLDH), and the energy of the structure without the constraints is measured. The script then loops and decrements the appropriate values until the entire grid is scanned.

This example uses or creates the following files:

♦ Input file: phipsi.inp

♦ Created file: PHIPSI.MAP


AMINO.BINPATCHAH.RTFPARM.BINPHIPSI.STR

*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved*! Open and read the amino acid topology file, the patch! topology file, and the parameter fileOPEN READ UNIT 11 FILE NAME “$CHM_DATA/AMINOH.BIN”READ RTF UNIT 11 FILEOPEN READ UNIT 12 CARD NAME “$CHM_DATA/PATCHAH.RTF”READ RTF UNIT 12 CARD APPEOPEN READ UNIT 13 FILE NAME “$CHM_DATA/PARM.BIN”READ PARA UNIT 13 FILE



! Read in the sequence, a single alanine residue to! which a N-acetamide and a C-methylamine patch will! be applied to simulate an alanine dipeptideREAD SEQU CARD* Alanine residue for phi/psi map*1ALA! Generate the segment and apply the patchesGENE MAIN SETUP! Patch the N & C terminiPATC NACT MAIN 1 SETUP WARNPATC CMAM MAIN 1 SETUP WARN! Construct initial coordinatesIC PARAIC SEED 1 N 1 CA 1 CIC BUILD! Fill the nonbond list with all possible pairs of atoms! (CUTNB=999Å). Then set the update frequency to 0 because no! updates are necessary - all nonbond interactions are ! included.UPDAT INBFRQ 1000 IHBFRQ 0 CUTNB 999.0 CTONNB 997.0 CTOFNB 998.0 RDIEUPDAT INBFRQ 0! Set parameter 0 to 20, the unit to which the energies! will be writtenSET 0 20! Open a file to store the energiesOPEN WRIT UNIT @0 CARD NAME PHIPSI.MAP! Stream the looping procedure to create the mapOPEN READ UNIT 30 CARD NAME PHIPSI.STRSTREAM UNIT 30STOP

Reference stream file

*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved*...* PHIPSI.STR*...* This stream file will loop through all combinations of phi * and psi at 30 degree increments. The CHARMm parameter 0 is * required as the output unit for the energies*...*! Set phi and psi to 180


Setting constraints

SET 1 180.0LABEL RESET2SET 2 180.0LABEL CONTINUE! Constrain the phi and psi dihedral angles at the current! values of phi and psi (parameters 1 and 2)CONS DIHE MAIN 1 CNT MAIN 1 N MAIN 1 CA MAIN 1 C FORC 1000.0 -MIN @1CONS DIHE MAIN 1 N MAIN 1 CA MAIN 1 C MAIN 1 NCT FORC 1000.0- MIN @2! Minimize the structureMINI POWE NSTEP 2000 TOLGRD 0.001 NPRINT 200MINI ABNR NSTEP 100 NPRINT 20! Clear the constraints, and compute the energyCONS CLDHENER! Write the energy to the unit specified by parameter 0WRITE TITLE UNIT @0* fOR PHI = @1, PSI = @2, THE POTENTIAL ENERGY =?ENER*! Check values of phi and psi, and continue if necessaryDECR 2 BY 20.0IF 2 LT -180.0 GOTO RESET1GOTO CONTINUELABEL RESET1DECR 1 BY 20.0IF 1 LT -180.0 GOTO MAPDONEGOTO RESET2LABEL MAPDONERETURN

Example: Using NOE constraints

NOE (or distance) constraints are used in this example to force an extended conformation into a helical conformation. Following a final minimization, the structure is examined to measure the deviations from an idealized geometry.


♦ Input file: glucnoe.inp

♦ Created file: GLUCNOE.CRD


AMINO.BINPARM.BIN1gcn.pdb



*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved*! Open and read the amino acid topology file and parameter fileOPEN READ UNIT 11 FILE NAME “$CHM_DATA/AMINO.BIN”READ RTF UNIT 11 FILECLOSE UNIT 11READ PARAMETERS UNIT 12 FILECLOSE UNIT 12! Open and read the glucagon sequence from the Protein Data! Bank file; generate the peptide segmentOPEN READ UNIT 13 CARD NAME “1gcn.pdb”READ SEQUENCE PDB UNIT 13GENERATE 1GCN SETUP! Generate initial coordinates for the extended conformationIC PARAMETERSIC SEED 1 N 1 CA 1 CIC BUILD! Reset the NOE facilityNOERESETEND! Since looping is not supported in the NOE facility, set ! CHARMm parameters and loop labels before starting ! assignments of NOE constraintsSET 1 1SET 2 4LABEL STARTNOE! Assign two constraints between the oxygen of residue i and! the nitrogens of residues i+3 and i+4; scale all constraints! by 5.0. As the calculation proceeds, the assigned constraints! will be added to any already present.ASSIGN SELE ATOM 1GCN @1 O END SELE ATOM 1GCN @2 N END 3.20 0.10 0.20ASSIGN SELE ATOM 1GCN @1 O END SELE ATOM 1GCN @3 N END 3.10 0.10 0.20SCALE 5.0END! Fix in place all residues except those for which NOE ! constraints have been assignedCONS FIX SELE.NOT. RESI 1: @3 END! Minimize all free atoms in the structure (i.e. those atoms in! residues for which NOE constraints have been assigned)FAST 1UPDA INBFRQ 50 IHBFRQ 0 RDIE SHIFT VSHIFTMINI CONJ NSTEP 100 NPRINT 50! Update CHARMm parameters; check whether the last residue has


Setting periodic boundaries

! been processedINCR 1 BY 1INCR 2 BY 1INCR 3 BY 1IF 3 GT 29 GOTO STOPGOTO STARTLABEL STOP! Analyze NOE constraints after initial minimizationNOEANALYZEEND! Confirm that no atoms are currently fixed in placeCONS FIX SELE NONE END! Final minimization of peptide subject only to NOE constraintsMINI CONJ NSTEP 1000 NPRINT 50! Write coordinates to diskOPEN WRIT UNIT 16 CARD NAME GLUCNOE.CRDWRIT COOR UNIT 16 CARD* Glucagon (alpha helix defined by NOE constraints)*! Final analysis of NOE constraintsNOEANALYZEENDSTOP


CHARMm has general and flexible implementations for introducing peri-odic boundary conditions in energy calculations. Two such methods are available:

♦ Images — CHARMm has a general image support system that allows simulation of almost any crystal and finite pointgroup. This facility uses symmetry operations to reduce the size of the problem. Symmetry can be finite, as with symmetric dimers such as those found in hemoglobin, or infinite, as for crystal simulations or other systems with periodic boundary conditions. Because possible translation and rotation matrices can be arbitrarily chosen, any crystal can be simulated.

A facility is also available to introduce bond linkages (with additional energy terms including angles, torsions, and out-of-planes) between the primary atoms and the image atoms. This allows polymers such as DNA or protein alpha helices to be studied. For infinite systems, an asymmet-



ric unit can be studied, because rotations and reflections are allowed transformations.

♦ Crystals — An extension to the image facility is provided by the crystal options. With these options, lattice parameters and symmetry operations are used in conjunction with coordinates and images to optimize both the primary structure and the crystal environment.

Using image options in CHARMm

An image object is an identical copy of the initially defined atoms (the pri-mary structure) that has been transformed in some way. Many advantages result from using images:

♦ Boundary effects are minimized.

♦ Images allow larger systems to be modeled, because only the coordi-nates of the primary structure are stored internally.

♦ Images are kept as transformation matrices. The primary structure and its images are treated as a single molecular system.

Implementation of image options in CHARMm is general, flexible, and efficient, but some restrictions exist:

♦ No treatment is available for the second derivatives of the energy for image atoms. Thus, Newton–Raphson minimization and vibrational analysis cannot be used when you use the image facility.

♦ Perfect symmetry is maintained between the primary structure and all its image objects. For many applications, this condition is satisfactory. However, it is not possible to study, for example, cooperative changes between image objects due to artificial symmetry restrictions.

Image centering An important aspect of the image facility is image centering. When image centering is used, molecules that migrate out of the primary structure into one of its image objects reappear in the primary structure from its inverse image object. A constant number of atoms is maintained in the PSF and no molecules are lost, no matter how far they may diffuse during a calculation.

For example, a cube of water as the primary structure is set up with image objects in the positive and negative x direction (named XIMG and AIMG, respectively). During a dynamics calculation, one water molecule diffuses along the x axis in the positive direction to the edge and is now closer to molecules in XIMG than to the primary structure. The water molecule con-



r

ox

tinues to move into the image XIMG. To compensate, the corresponding water from AIMG can now enter the primary image along the x axis from the negative direction. However, if this water diffuses along the x axis to XIMG, no corresponding water exists in AIMG to compensate for its loss. Therefore, the minimum-image convention (or image centering) is invoked, whereby waters that diffuse in the positive x direction reappear in the negative x direction.

General procedure The general procedure for using images in CHARMm follows these steps:

1. Construct the PSF for the primary structure.

2. Provide the Cartesian coordinates for all atoms in the PSF.

3. Read the image transformation file. The commands in this file place each defined image object around the primary structure.

4. If appropriate, specify image centering.

5. If necessary, process image patching.

6. Update the image lists.

7. Update the nonbond and hydrogen-bond lists that include both primary and image atoms.

8. Evaluate the energy of the molecular system. Steps 6 and 7 are implicit in this step.

9. Minimize or integrate equations of motion for a dynamics trajectory.

10.Repeat Steps 8 and 9 as necessary, updating the image, nonbond, and hydrogen-bond lists only at specified intervals.

Note

Image transformation file

Because no coordinates are stored for image objects, an image transforma-tion file is required for all operations in CHARMm that use the image facil-ity. This file contains commands to define an image object and place it relative to the primary structure.

When you use periodic boundary conditions for non-crystal simulations (foexample, solute in a cubic water box), you must use the minimum-image convention. Therefore, use cutoffs that are smaller than L/2 where L is the bdimension. For more information, see Allen and Tildesley (1987).



All defined image objects must have an inverse. An image object and its inverse are always the same distance from the atoms in the primary struc-ture.

Image transformations consist of a rotation, a translation, an inversion, or a mix of any of the three. A convenient scaling operation is also provided. When image atoms are required in an energy calculation, the appropriate transformation matrices are applied to the primary structure coordinates.

The format of the image transformation file is:

* Valid CHARMm title*IMAGE transformation subcommandsEND

For example, if the primary object is a box of water with 12 Å dimensions, and you want to create images in both the positive and negative x direc-tions, this image transformation file is used:

* Sample Image Transformation File*! Scale all transformations by 12.0 in each direction;! this is the size of the box of waterSCALE 12.0 12.0 12.0! Define an image object named XIMAGE X! Translate this image object in the x-direction; it is! automatically scaled by the factor define in the SCALE ! subcommand.TRANSLATE 1.0 0.0 0.0! Define an object named A and translate this in the! -x- direction.IMAGE ATRANSLATE -1.0 0.0 0.0! Terminate the image transformation fileEND

Remember that all defined objects must have an inverse. If the inverse is assumed to be present, then the time taken to evaluate the primary image energies and forces can be greatly reduced.

Images output

When image lists are updated, information about image centering can be provided if it is requested. The atoms, segments, or residues that are oper-ated upon are listed with the transformation that performed the operation.



After image lists are updated, the numbers of atoms, groups, and residues in each image object as a result of a particular transformation are listed. Only the transformations that are used in the calculation are listed. Their inverses are assumed. Finally, the minimum distance between any atom in the image object and the primary structure is listed.

Because these lists depend on the results of the image list update, the non-bond and hydrogen-bond lists are regenerated only after the image lists are updated.

If images are used during any energy calculation, energy values for terms corresponding to the images (such as van der Waals and electrostatic inter-action between the primary and image objects) are printed, in addition to the values for the normal energy terms.

Using crystal options in CHARMm

A crystal of any desired symmetry can be constructed by repeatedly apply-ing a small number of transformations to an asymmetric collection of atoms (the primary structure). The transformations include the primitive lattice translations common to all crystals and a set of additional transformations that determine the spacegroup symmetry. Crystal options generate a data structure of all transformations that produce images lying within a specified cutoff distance of the primary atoms. The data structure can then be used to represent the complete crystal of the system in subsequent calculations.

The CHARMm image facility enables energies of crystals to be calculated, but the input required to use the facility is often difficult and cumbersome to set up. It is much simpler to introduce an extra data structure that defines the crystal in terms of a set of symmetry operations and lattice translations. This additional data structure can also provide for the optimization of the lattice parameters a, b, c,��, �, and �.

Although the crystal data structure and the values of the lattice parameters define the crystal, individual transformations have to be worked out, explicitly to calculate energies, harmonic frequencies, and other data. The CHARMm image facility is used for this purpose. Restrictions imposed by the use of images, such as the requirement that each image have an inverse, are also present for crystals.

Because crystal patching is not available, bonds between images are not permitted. Similarly, hydrogen bond interactions described by an explicit



hydrogen bond function are forbidden. The only forces that can be calcu-lated between primary and image atoms are nonbond forces.

General procedure The general procedure for defining and using crystals in CHARMm is:

1. Construct the PSF for the primary structure.

2. Provide the Cartesian coordinates for all atoms in the PSF.

3. Define the crystal lattice type.

4. Specify symmetry operations (transformations).

5. Update image lists.

6. Update the nonbond list that includes both primary and image atoms.

7. Evaluate the energy of the molecular system.

8. Minimize the structure and, optionally, lattice parameters.

Crystal data file

The crystal data file is divided into three parts:

♦ Title lines

♦ A symmetry declaration section including the identity transformation that must be explicitly listed

♦ An image section where images are defined in terms of symmetry trans-formations and lattice translations

Crystal file example An example of a crystal file for a P212121 crystal is given below. Only the three image transformations defining asymmetric units within the unit cell and inverses are listed:



* Crystal file for a P212121 crystal*SYMMETRY(X,Y,Z)(X+1/2,-Y+1/2,-Z)(-X,Y+1/2,-Z+1/2)(-X+1/2,-Y,Z+1/2)ENDIMAGES2 0 0 03 0 0 04 0 0 02 -1 0 03 0 -1 04 0 0 -1END

Crystal files of this type are automatically produced by CHARMm when the WRITE CRYSTAL command is used after building the crystal. How-ever, it may sometimes be necessary for you to construct a unique crystal file using the format described above and then read the data using the READ CRYSTAL command.

Minimizing crystals

The minimization of crystal lattice parameters (either alone or together with the full structure) is supported by all algorithms except steepest descents.

Crystal output

The CRYSTAL BUILD command reads the number of symmetry opera-tions specified, then computes and prints each transformation. The maxi-mum number of transformations allowed by the image facility is 100.

Periodically during minimization, current lattice parameters (and their nor-malized gradients) are printed, together with the standard values for each energy term. The values for lattice parameters, though stored internally, cannot be written to an external file. You must ensure that the proper values are used when you start a crystal energy calculation.



Example: Creating a water box

This script creates a water box with 64 molecules and runs dynamics to equilibrate the structure. The script can be easily customized to create larger boxes or to replace water molecules with another solvent.

* BOX.INP *bomlev 5OPEN READ UNIT 1 CARD NAME "$CHM_DATA/MASSES.RTF"read rtf CARD unit 1OPEN READ UNIT 1 CARD NAME "$CHM_DATA/TIP3.RTF"read rtf CARD unit 1 appendOPEN READ UNIT 12 CARD NAME "$CHM_DATA/PARM.PRM"read parameter card unit 12set g setup warn - ! CUSTOMIZE: GENERATE command optionsfirst none last none noan nodiset m tip3 ! CUSTOMIZE: the name of the molecule from RTFread sequence @m 1generate solv @gread coor card unit 5 ! CUSTOMIZE: coordinates*...*31 1 TIP3 OH2 .00000 .06577 .00000 SOLV 1 .000002 1 TIP3 H1 .75902 -.52198 .00000 SOLV 1 .000003 1 TIP3 H2 -.75907 -.52195 .00000 SOLV 1 .00000coor orie massset s x ! generate copies along x axisset d 3.10432 ! <- CUSTOMIZE displacementset n 4 ! <- CUSTOMIZE number of copiesstream "box.STR"set s y ! generate copies along y axisset d 3.10432 ! <- CUSTOMIZE displacementset n 4 ! <- CUSTOMIZE number of copiesstream "box.STR"set s z ! generate copies along z axisset d 3.10432 ! <- CUSTOMIZE displacementset n 4 ! <- CUSTOMIZE number of copiesstream "box.STR"! each solvent molecule is rotated randomly! around its center of massRANDOM UNIFORM SCALE 360. OFFSET -180.set r ?nresset i 0label randomizeincr i by 1COOR STATistics MASS SELE resid @i END



COOR ROTAte xdir ?RAND ydir ?RAND zdir ?RAND PHI ?RAND -XCEN ?XAVE YCEN ?YAVE ZCEN ?ZAVE sele resid @i end

if i lt @r goto randomize! CUSTOMIZE: box dimensions for desired density! for 64 molecules of water volume should be 1914.608 A^3! to get 1 Atm pressure at 300K.set a 12.4173set b 12.4173set c 12.4173shake bond ! use shake for tip3 water <- CUSTOMIZEcrystal define orthorhombic @a @b @c 90. 90. 90. Crystal Build cutoff 7.0 noperations 0update inbfrq -1 ihbfrq 0 imgfrq 10 -CUTNB 9. CTOFNB 7. CTONNB 5. CUTIM 9.! update inbfrq -1 ihbfrq 0 imgfrq 20 CUTIM 9.image byres xcen 0. ycen 0. zcen 0.! mini sd nstep 100 npri 20 tolg 0.9 ixtfrq 0! run constant volume Langevine dynamics! to thermalize molecules in the box! CUSTOMIZE: dynamics parameters!open write card unit 32 name box.rst!open write file unit 31 name box.dcdscalar fbeta set 10.0 sele all enddyna lang leap strt nstep 100 timestep 0.002 - tbath 300. rbuf 0. iunrea -30 - iprfrq 1000 ihtfrq 0 ieqfrq 0 ntrfrq 0 - nprint 100 nsavc 0 iuncrd -31 nsavv 0 iunwri -32 - firstt 300.0 finalt 300.0coor statwrite coor card name "$SCRATCH/box.out"* thermalized ?nres @m box: a=@a; b=@b; c=@c*stopinclude box.STR

Example: Solvating glycerol in a box of water

This input file combines many of the concepts discussed thus far. A small molecule is solvated in a box of water. Using periodic boundary conditions, an infinite molecular system is generated. The system is minimized and then a molecular dynamics simulation is run. Various analyses are per-formed on the resulting trajectory.


♦ Input file: glycimp.inp

♦ Created files:



GLCSOLINI.CRDGLCSOLMIN.CRDGLCSOLA(B).RSTGLCSOLA(B).DCDGLCSOLA(B).DVLGLCSOLA(B).ENEGLCSOLH.CRDGLCSOLAVG.CRDGLCSOLDIF.CRD


GLYC.RTFPARM.BINGLYCINI.CRDWATER1000.CRDWATER.IMG

*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved*! Open and read the glycerol topology file; included in this! RTF is the topology definition for TIP3. Read in the! standard parameter file.OPEN READ UNIT 11 CARD NAME GLYC.RTFREAD RTF UNIT 11 CARDOPEN READ UNIT 12 FILE NAME “$CHM_DATA/PARM.BIN”READ PARA UNIT 12 FILE! Generate the solute (one glycerol molecule); read in! the initial coordinates created in Example 2.4.READ SEQU CARD* Glycerol*1GLYCGENE SOLU SETUOPEN READ UNIT 13 CARD NAME GLYCINI.CRDREAD COOR UNIT 13 CARD! Center the solute about the origin.COOR ORIE! Read in 125 TIP3 solvent molecules and their! equilibrated coordinates.READ SEQU TIP3 125GENE SOLV SETU NOANGLEOPEN READ UNIT 14 CARD NAME WATER1000.CRD



READ COOR UNIT 14 CARD APPE! Delete any waters which overlap the solute.DELE ATOM SELE ( .BYRES. ( SEGID SOLV .AND. TYPE OH2 .AND. - ( ( .NOT. SEGID SOLV .AND. .NOT. HYDROGEN ) - .AROUND. 2.60 ) ) ) END! Write out the initial coordinates of solvated! glycerolOPEN WRIT UNIT 08 CARD NAME GLCSOLINI.CRDWRIT COOR UNIT 08 CARD* Solvated glycerol: initial coordinates*! Set parameter 9 to 15.5516 A, the length of one side! of the box of water. This value will be used as a scale! factor for all image transformations.SET 9 15.5516! Open and read the image transformation file for creating! 26 image objects around the primary structureOPEN READ UNIT 15 CARD NAME WATER.IMGREAD IMAG UNIT 15 CARD! Apply image centering to all water moleculesIMAGE BYRES XCEN 0.0 YCEN 0.0 ZCEN 0.0 SELE SEGI SOLV END! Update the nonbond and image lists; it is not necessary! to update the hydrogen bond lists as hydrogen bonding! interactions are accounted for in the force field by! nonbond terms. Compute the energy of the system.UPDA INBFRQ 1 IHBFRQ 0 IMGFRQ 1 CUTNB 30.0 CUTIMG 30.0 - CDIE VSHI SHIFENER! Print image forces in addition to the image PSF.PRIN IMAGE FORCES PSF! Constrain the glycerol molecule to allow for the solvent! to minimize with respect to the solute.CONS FIX SELE SEGI SOLU ENDUPDA INBFRQ 5 IHBFRQ 0 IMGFRQ 5MINI ABNR NSTEP 100 TOLGRD 0.0001 NPRINT 25 VSHI SHIF CDIE! Release constraints and minimize entire structureCONS FIX SELE NONE ENDUPDA INBFRQ 25 IHBFRQ 0 IMGFRQ 25 VSHI SHIF CDIEMINI ABNR NSTEP 50 TOLGRD 0.0001 NPRINT 5! Write the minimized coordinates to diskOPEN WRIT UNIT 08 CARD NAME GLCSOLMIN.CRDWRIT COOR UNIT 08 CARD* Solvated glycerol: minimized water*! Print the forces of the image object on the primary ! structure.PRIN IMAG FORCE! Shake all bonds with hydrogens



SHAKE BONH! Open the files necessary for the dynamics trajectory:! A restart file! A coordinates file (the coordinate trajectory)! A velocities file (the velocity trajectory)! An energy fileOPEN WRIT UNIT 31 CARD NAME GLCSOLA.RSTOPEN WRIT UNIT 32 FILE NAME GLCSOLA.DCDOPEN WRIT UNIT 33 FILE NAME GLCSOLA.DVLOPEN WRIT UNIT 34 CARD NAME GLCSOLA.ENEDYNA STRT VERL NSTE 300 TIME 0.001 CDIE IMGFRQ 50 - IPRFRQ 100 IHTFRQ 50 IEQFRQ 0 INBFRQ 50 IHBFRQ 0 - IUNREA -1 IUNWRI 31 IUNCRD 32 IUNVEL 33 KUNIT 34 - NPRINT 50 NSAVC 50 NSAVV 50 - FIRSTT 0.0 FINALT 300.0 TEMINC 5 - TWINDH 10.0 TWINDL -10.0 - IASORS 1 IASVEL 1 ICHECW 0 VSHI SHIFOPEN WRIT UNIT 41 CARD NAME GLCSOLH.CRDWRIT COOR UNIT 41 CARD* COORDINATES AFTER HEATING*CLOS UNIT 31CLOS UNIT 34OPEN READ UNIT 30 CARD NAME GLCSOLA.RSTOPEN WRIT UNIT 31 CARD NAME GLCSOLB.RSTOPEN WRIT UNIT 32 FILE NAME GLCSOLB.DCDOPEN WRIT UNIT 33 FILE NAME GLCSOLB.DVLOPEN WRIT UNIT 34 CARD NAME GLCSOLB.ENE! Only two picoseconds of equilibration are specified! here. This is certainly too short a period for! adequate equilibration of such a large molecular! system and is included here for illustration! purposes only.DYNA REST VERL NSTE 200 TIME 0.001 CDIE IMGFRQ 50 - IPRFRQ 100 IHTFRQ 0 IEQFRQ 50 INBFRQ 50 IHBFRQ 0 - IUNREA 30 IUNWRI 31 IUNCRD 32 IUNVEL 33 KUNIT 34 - NPRINT 50 NSAVC 50 NSAVV 50 - FIRSTT 0.0 FINALT 300.0 - TWINDH 10.0 TWINDL -10.0 - IASORS 0 ISCVEL 0 ICHECW 1 VSHI SHIFOPEN WRIT UNIT 41 CARD NAME GLCSOLE.CRDWRIT COOR UNIT 41 CARD* COORDINATES AFTER EQUILIBRATION*CLOS UNIT 30CLOS UNIT 34COOR INIT! Calculate the average structure and isotropic



! fluctuations from the equilibrated dynamics trajectoryOPEN READ UNIT 51 FILE NAME GLCSOLB.DCDCOOR DYNAMIC FIRSTU 51OPEN WRITE UNIT 16 CARD NAME GLCSOLAVG.CRDWRITE COOR CARD UNIT 16* Average structure and isotropic fluctuations*! Print the average position and fluctuation for the! solute and any solvent within 4.0 A of the solutePRIN COOR SELE .BYRES. ( SEGI SOLU .AROUND. 4.0 ) END! Compare the minimized coordinates with the! average coordinates; store the average! coordinates in the comparison setCOOR COPY COMPCOOR INITOPEN READ UNIT 21 CARD NAME GLCSOLMIN.CRDREAD COOR UNIT 21 CARDCLOSE UNIT 21COOR DIFFOPEN WRIT UNIT 22 CARD NAME GLCSOLDIF.CRDWRIT COOR UNIT 22 CARD* Difference in atomic positions between dynamics* average coordinates and minimized coordinates*! Print out the difference in position for the! solute between the minimized and dynamic averaged! coordinatesPRIN COOR SELE SEGI SOLU END! Restore the average coordinates to the main setCOOR INITCOOR COPY! Fill the internal coordinate arrays with the average! ic values from the equilibrated dynamics trajectoryIC FILLOPEN READ UNIT 51 FILE NAME GLCSOLB.DCDIC DYNA AVERAGE FIRSTU 51PRINT IC! Fill the internal coordinate arrays with the! fluctuations to the ic averages from the free! dynamics trajectoryOPEN READ UNIT 51 FILE NAME GLCSOLB.DCDIC DYNA FLUCTUATIONS FIRSTU 51PRINT ICSTOP



Example: Optimizing an alanine crystal

This example creates an alanine crystal and performs crystal minimization in which both the molecular structure and the lattice parameters are opti-mized.


♦ Input file: alaxtl.inp

♦ Created files:

ALAINI.CRDALA.XTLALAXTL.CRD


AMINOH.BINPARM.BIN

*...* Copyright (c) 1994* Molecular Simulations Inc.* All Rights Reserved*! Open and read the amino acid and parameter data filesOPEN READ UNIT 11 FILE NAME “$CHM_DATA/AMINOH.BIN”READ RTF UNIT 11 FILEOPEN READ UNIT 12 FILE NAME “$CHM_DATA/PARM.BIN”READ PARA UNIT 12 FILECLOS UNIT 11CLOS UNIT 12! Read in an alanine residue and construct the PSF; define! initial coordinatesREAD SEQU ALA 1 ! AlanineGENE MAIN SETUIC PARAIC SEED 1 N 1 CA 1 CIC BUILD! Minimize the initial structureUPDATE RDIE SHIFT VSHIFTMINI ABNR NSTEP 500 NPRINT 10 TOLGRD 0.00001 TOLENR 0.00001OPEN WRIT UNIT 14 CARD NAME ALAINI.CRDWRIT COOR UNIT 14 CARD* Initial coordinates for single alanine*! Build alanine crystal using P212121 space groupCRYSTAL DEFINE ORTHORHOMBIC 6.0 12.0 6.0 90.0 90.0 90.0


References

CRYSTAL BUILD NOPER 3 CUTOFF 10.0(X+1/2,-Y+1/2,-Z)(-X,Y+1/2,-Z+1/2)(-X+1/2,-Y,Z+1/2)OPEN WRIT UNIT 12 CARD NAME ALA.XTLWRIT CRYS UNIT 12 CARD* Alanine crystal file*! Update the nonbond and image lists; minimize the! structure and optimize the lattice parametersUPDATE IMGFRQ 50 CUTIM 99.0 MINI ABNR NSTEP 500 NPRINT 10 LATTICE - TOLENR 0.00001 TOLGRD 0.00001OPEN WRIT UNIT 14 CARD NAME ALAXTL.CRDWRIT COOR UNIT 14 CARD IMAGE* Alanine crystal structure* STOP

References

Allen, M. P.; Tildesley, D. J. “Periodic Boundary conditions” and “Poten-tial truncation.” In: Computer Simulations of Liquids, Oxford Univer-sity Press, Oxford, 1987.




6 Performing Free Energy Simulations

CHARMm supports several methods of performing free energy simula-tions and includes several implementations of these methods. This chapter describes the methods that are available, the calculations performed for each method, and the implementation of each method.

This chapter explains ♦ Understanding the relative free energy Hamiltonian

♦ Using free energy calculation methods

♦ Running a free energy simulation

♦ Applying scaling

♦ Post-processing data

♦ Using umbrella sampling

Use of the term free energy simulations is a misnomer for two reasons:

♦ Temperature derivative thermodynamic properties (�E and �S) are also calculated.

♦ It is not possible to calculate absolute free energies. In fact, generally you are limited to calculating relative changes in free energies (that is, ��A’s).

For example, calculation of free energies of solvation or drug–enzyme binding is computationally very difficult. If you are satisfied with relative changes in free energies, it is more tractable to transmutate various parts of a system in a way that is usually physically unreasonable, but computation-ally feasible. The result is one in which relative changes in free energies (��A) are calculated in a simulation that is thermodynamically equivalent to the physical process. The relationships used for computing the relative free energy differences are all exact in the statistical mechanical sense.

For an overview of free energy simulation methods, consult Mezei and Beveridge (1986), Straatsma (1987), or Fleischman and Brooks (1987).


6. Performing Free Energy Simulations

Understanding the relative free energy Hamiltonian

In all the methods for calculating relative free energy in CHARMm, a hybrid Hamiltonian is used:

Eq. 14

Where:

HE Environment part of the Hamiltonian

HR Reactant part of the Hamiltonian

HP Product part of the Hamiltonian

� Coupling parameter (extent of transformation)

N Integer exponent

The molecular system is divided into four sets of atoms:

♦ Reactant atoms — Atoms that are actually being changed.

♦ Product atoms — Atoms that are actually being changed.

♦ Co-located charge atoms — Atoms in which only charge changes in going from reactant to product.

♦ Environment atoms — All other atoms (that is, solvent atoms and parts of the molecule common to both reactant and product).

Reactant and product designations are arbitrary and are used as a conven-tion to denote the direction in which the molecular system is being trans-formed. The process starts with reactant and ends with product.

For example, examine the calculation of the relative change in the solvation free energies of methanol and ethane. This example is taken from Fleis-chman and Brooks (1987).

The system is represented by water molecules (usually a box of 125 or more, using periodic boundary conditions) and the hybrid methanol/ethane system.

Figure 1 illustrates the transformation of methanol to ethane:

Using the above depiction, the reactant atoms are the hybrids O1 and H1. The product atom is the hybrid C1 methyl group (not shown). The C2

H �� HE 1 �–� �NHR �

NHP+ +=


Understanding the relative free energy Hamiltonian

hybrid molecule’s methyl group changes charge as the transformation goes from reactant to product. The co-located charge atom starts with the meth-anol methyl group charge and ends up (at � = 1.0) with the ethyl-methyl group charge. C2 is also considered an environment atom. The atoms of the water molecules constitute the actual environment atoms in this system. If the hybrid molecule were larger, it could contain additional environment atoms.

All potential energy terms involving reactant atoms, as well as electrostatic interactions involving co-located charge atoms with their reactant charges, go into HR. Kinetic energies of the reactant atoms are also included in this term.

Similarly, potential energy terms involving product atoms and co-located product charge electrostatic interactions, along with kinetic energies of the product atoms, go into HP. The rest of the energy terms are incorporated into HE.

For a potential energy term to be included in HR, only one atom in the given interaction has to be a reactant atom. The same is true for product terms.

Electrostatic terms involving co-located charge atoms are calculated twice: once with the reactant charges and again with the product charges. Terms

Figure 1. Transformation of methanol to ethane

C1C2

O1

H1



between co-located reactant or product charges and reactant or product atoms are omitted.

CHARMm assumes that, when the hybrid molecule is constructed in the residue topology file, no internal coordinate energy terms exist involving reactant and product atoms. Similarly, CHARMm assumes that nonbond exclusions have been specified between reactant and product atoms. No checking is done in the program.

In CHARMm, the Hamiltonian is constructed exactly as specified in Eq. 14. In other implementations, the � dependence of the Hamiltonian is more complex. Complexity is higher in those implementations where force constants and other parameters in the energy terms are factored by � rather than by calculating various energy terms and factoring those terms.

In a statistical mechanical sense, no particular reason exists to factor the Hamiltonian one way or another. The thermodynamic interactions hold regardless of path. The equipartition theorem for obtaining kinetic energy works just as well although, in some implementations, factoring of kinetic energy sometimes appears to be ignored.

Certain advantages result from constructing the Hamiltonian as is done in CHARMm:

♦ A certain conceptual simplicity exists in factoring the Hamiltonian con-sistently for all reactant and product terms.

♦ Obtaining the derivatives of the Hamiltonian with respect to � and �E(�)/�� is made programmatically simple. These derivatives are needed in the thermodynamic integration and the related slow-growth methods for free energy simulation.

♦ Factoring energy terms rather than functional parameters permits a more modular design and makes incorporating changes to energy terms easier.

Using free energy calculation methods

Three basic methods are available for calculating relative changes in free energy and temperature derivative properties:

♦ Perturbation method

♦ Thermodynamic integration method


Using free energy calculation methods

♦ Slow-growth method (a modification of the thermodynamic integration method)

Perturbation method

The method that is used most frequently is the thermodynamic perturbation method. For this, the free energy change is:

Eq. 15

All the averages are at �.

To get the total �A:

Eq. 16

You must assure that the whole � range is covered. For example, in a meth-anol-to-ethane calculation, three � values could be used: � = 0.125, 0.500, and 0.875. To cover the range completely, you must perform six simula-tions:

� to �': 0.125 to 0.000 and 0.125 to 0.250;

� to �': 0.500 to 0.250 and 0.500 to 0.750;

� to �': 0.875 to 0.750 and 0.875 to 1.000.

Double-wide sampling Dynamics calculations are run and two �A’s are calculated: one lower and one higher than the corresponding �. This is termed double-wide sampling. The simulations are joined at common �s.

Windowing The technique for running these simulations is called windowing. With windowing, simulations are run at a discrete number of � points. If very few points are used, long simulations are required to smoothly join the results from the trajectories. If many points are used (tens to hundreds), shorter simulations are required.

For thermodynamic perturbation, the total free energy change is pieced together from perturbations done in each window.

�A� �

��

kBTln exp�V� ��

kBT-----------------–

��

–=

�A �A �i ��i–� �

i�=



Thermodynamic integration method

The thermodynamic integration method uses this expression:

Eq. 17

Integration is done by a quadrature method. In this implementation, the ensemble average is fitted as a function of � to a cubic spline polynomial and the polynomial is integrated analytically. No extrapolation to endpoints is done.

Expressions for energy and entropy changes can be derived for this equa-tion and are incorporated into CHARMm. The expressions suffer from very high uncertainties due to the presence of ensemble averages over the total energy that are multiplied by ensemble averages over �H/��. You will probably get better results by averaging energies at the endpoints and sub-tracting.

Slow-growth method

Slow growth is an approximation of the thermodynamic integration method. In this method, instead of � being constant for a given trajectory, the parameter varies monotonically with each time step, as indicated in Eq. 18:

Eq. 18

Where:

��i��i - �i

H Hamiltonian

��= 0

�n= 1

�A A� 1= A� 0=– �H ��

----------------� ��

d�

0

1

�= =

�A H �i ��i+� � H �i� �–

i 0=

n 1–

�=


Running a free energy simulation

Advantages Some advantages are associated with this method:

♦ The actual input and management of the problem is generally easier than with the window method, in that the free energy is determined in one trajectory. However, because you generally run transformation in both directions, the simplification is not that great.

♦ The steady continuous change in � may be a more stable way to achieve the transformation than the discrete jumps of the window method.

♦ The nonlinear scaling window technique is problematical for the ther-modynamic perturbation method.

♦ It is not clear that you can get viable results with a few � points and numerical quadrature in the thermodynamic integration window method.

Disadvantages Some disadvantages are also associated with this method:

♦ Error analysis is not easy to do.

♦ Because � is changed with every step, no method is available to tack on additional trajectories.

♦ Paths are not reversible. The usual (but not totally satisfactory) proce-dure is to average the two directions.

♦ Free energy change is calculated during the dynamics run, so a temper-ature must be assumed.

♦ The only property calculated is the free energy change.

♦ The derivative �H/�� is determined by finite difference H(�') – H(�) (that is, a perturbation to �' at each step).


CHARMm includes three implementations of the free energy simulation (FES) calculations:

♦ PERT— The perturb implementation allows scaling of energy between PSFs to use in energy analysis, comparisons, slow-growth free energy simulations, windowing free energy simulation, and slow-growth homology modeling.



This flexible implementation allows connectivity to change. Also, the energy restrain terms harmonic, dihedral, and NOE are subject to change, allowing a flexible way to compute free energy differences between conformations. The implementation works with all minimizers and integrators.

♦ BLOCK — This implementation partitions the molecular system into blocks and uses coefficients to scale the interaction energies between blocks. Specific commands have been implemented to carry out free energy simulations with this component analysis scheme.

♦ TSM — For thermodynamics perturbation calculations, energy values are factored by � and never by the energy functions themselves. Stan-dard energy routines are unchanged, but can be modified without requiring changes to the perturbation routines as long as the calling sequence remains the same.

Potential energy terms are written to output during a trajectory and, for the window method, trajectories can be combined. Any ��to�� can be calculated following analysis, and additional points can be added as appropriate.

This implementation is described in more detail in the rest of this sec-tion.

FES calculation The calculation is done in three steps:

1. Setting up a simulation

2. Running dynamics

3. Post-processing data

The first two steps occur in the same input file. The last step is generally done with a separate input file, because the output of several trajectories is usually used.

Setting up a simulation To set up the free energy simulation input file, gather or generate the usual files for a dynamics simulation, including a PSF, coordinates, parameters, and image or stochastic boundary condition input.

The exact syntax of the free energy commands depends on the method you choose for the calculation. For example, the TSM commands define reac-tant, product, and co-located charge lists and the procedure for simulation (slow growth or window). Both thermodynamic simulation and thermody-namic integration can be done with the window procedure.



Most minimization routines work using the hybrid V(�) potential. To remove bad contacts, minimization is generally done prior to dynamics, with the hybrid molecule unperturbed.

Running dynamics After the free energy simulation has been set up, dynamics can be run with no changes in the commands. Normally, you run some thermalization runs with data being discarded. For a thermalization run, the SAVE command in the free energy simulation command sequence is generally not used. For production runs using thermodynamic integration or thermodynamic sim-ulation, the SAVE option must be issued in the free energy simulation input. This results in the output of V� and V�� in a formatted file.

Example: Setting up an FES simulation and running dynamics

Below is a fragment of the input file for setting up the thermalization of an ethanol-to-propane hybrid. Windowing is used during the simulation.

♦ Reactant atoms — O1 and H1.

♦ Product atom — C3.

♦ Co-located charge atom — C2.

♦ Environment atom — C1 methyl group present in both reactant and product and, in this model, its charge does not change in going from reactant to product.

The system represented in the figure below is partitioned as follows:

For this example, the extended-atom model is used, with aliphatic hydro-gens considered part of the carbon to which they are attached. The example also provides for linear scaling of �, although nonlinear � scaling can be specified.

C3

C2 H1O1C1



*Ethanol -> Propane*! Read topology fileREAD RTF CARD* TOPOLOGY FILE ethanol -> propane* 20 1! Version numberMASS 1 H 1.00800! hydrogen which can h-bond to neutral atomMASS 13 CH2E 14.02700! - “ - twoMASS 14 CH3E 15.03500 ! - " - threeMASS 53 OH1 15.99940 ! hydroxy oxygen! This is put in to force the necessity of using a GENERATE! Noangles in the input file. The standard topology files use!this statement.AUTOGENERATE ANGLEsRESI ETP 0.000GROUC1 CH3E 0. ! environment atomC2 CH2E 0.265 ! co-located charge atomO1 OH1 -0.7 ! reactant atomH1 H 0.435 C3 ! reactant atom note the non-bonded exclusion! with GROUC3 CH3E 0. ! product atomBOND C1 C2 !environment termBOND C2 O1 O1 H1 !reactant termsBOND C2 C3 !product term! the angles MUST be specified. Note the absence of O1 C2 C3! between reactant and product atomsANGLe C1 C2 C3 !product termANGLe C1 C2 O1 C2 O1 H1 !reactant terms! this will be a V(R) term.DIHED C1 C2 O1 H1! don't really need it but what the heck.DONO H1 O1ACCE O1IC C1 C2 O1 H1 1.54 111. 180. 109.5 0.96IC C2 O1 H1 BLNK 0. 0. 0. 0. 0.IC C3 C2 C1 BLNK 0. 0. 0. 0. 0.PATCH FIRST NONE LAST NONEEND! Read parameter fileREAD PARAM CARD* parameter file for ETP hybrid.BONDCH2E CH3E 225.0 1.54CH2E OH1 400.0 1.42OH1 H 450.0 0.96THETA



CH3E CH2E CH3E 45.0 112.5CH3E CH2E OH1 45.0 111.0CH2E OH1 H 35.0 109.5PHICH3E CH2E OH1 H 0.5 3 0.0NONBONDED NBXMOD 5 ATOM CDIEL SHIFT VATOM VDISTANCE VSWIT -CUTNB 8.0 CTOFNB 7.5 CTONNB 6.5 EPS 1.0 E14FAC 0.4 WMIN 1.5! Emin Rmin! (kcal/mol) (A)H 0.0440 -0.0498 0.8000CH2E 1.77 -0.1142 2.235 1.77 -0.1 1.9CH3E 2.17 -0.1811 2.165 1.77 -0.1 1.9OH1 0.8400 -0.1591 1.6000HBOND AEXP 4 REXP 6 HAEX 0 AAEX 0 NOACCEPTORS - HBNOEXCLUSIONS ALL - CUTHB 0.5 CTOFHB 5.0 CTONHB 4.0 CUTHA 90.0 CTOFHA 90.0 CTONHA 90.0H* N% -0.00 2.0 ! WER potential adjustmentH* O* -0.00 2.0END! read the sequence of one residue, read sequence card* ETP*1ETP! Generate the hybrid molecule. Note that we use the NOANGLE ! command because of the AUTOGENERATE ANGLES command in the RTF ! file.GENERATE ETP SETUP NOANGLE! determine the geometry and coordinatesIC SEED 1 C1 1 C2 1 O1IC PARAMIC PURGEIC BUILD! The Hybrid molecule is built. Now set up the FES stuff.TSM! Assign reactant list:REAC sele etp 1 O1 .or. etp 1 H1 end! Assign product list:PROD sele etp 1 C2 end! Set lambda - we will use TI or TP.! The lambda dependence of the Hamiltonian will be linear.! This is the default and the POWEr 1 command is actually ! unnecessary.LAMBda .125 POWEr 1! The common methyl group is a co-located chargeatom. Since ! the charge in the rtf was for the reactant the RCHArge ! command is actually unnecessary.co-located chargeETM 1 C2 PCHArge 0. RCHArge 0.265! This is a thermalization run - so no save statement.! Just terminate the FES setup with an END statement.



END! Set up dynamics.! Since we are interested in the thermodynamic properties and ! not the dynamics, we can use Langevin heat bath dynamics to ! maintain title* etp: Ethanol To Propane*! a simple expedientshake bond angle! Set-up Langevin dynamics for temperature controlscalar fbeta set 50.0 sele .not. hydrogen end! open restart file for outputopen unit 3 write form name etp0.resdynamics langevin timestep 0.001 nstep 10 nprint 2 iprfrq 2 - firstt 298.0 finalt 298.0 twindl -5.0 twindh 5.0 - ichecw 1 teminc 60 ihtfrq 20 ieqfrq 200 - iasors 0 iasvel 1 iscvel 0 - iunwri 3 nsavc 0 nsavv 0 iunvel 0 - iunread -1- !{* Nonbond options *} inbfrq 10 imgfrq 10 ilbfrq 0 tbath 300.0 rbuffer 0.0 - eps 1.0 cutnb 8.0 cutim 8.0 ctofnb 7.75stop

Detailed descriptions of the commands provided in this example can be found in the CHARMm Dictionary.

Setup for slow-growth method

If both reactants and products exist, set up a slow-growth thermalization with the LAMBDA command (not the SLOW command), and use a � value a little away from 0 (for the 0 to 1 transformation) or 1 (for the 1 to 0 transformation). Run slow-growth production dynamics.

You can switch direction in one of two ways. The easiest way is to issue the SLOW command, as follows:

SLOW LFROM 1. LTO 0. TEMP 298.

The calculation is transforming from the product to the reactant.

The more difficult alternative is to switch the reactant and product designa-tions. If you do this, remember to switch the PCHARGE and RCHARGE values for the co-located charge atoms. Use of the RCHARGE parameter is mandatory, because the default is to assume that the charge in the RTF (or set by a SCALAR command) is the REACTANT charge.


Applying scaling

Applying scaling

Because approximations to ensemble averages are obtained from finite-length trajectories, determining values of these quantities becomes compu-tationally intractable. In both the thermodynamic integration and thermo-dynamic perturbation methods, calculating the dynamics trajectory is generally problematical, with large movements of the atoms resulting in bad van der Waals contacts and fraying of bonds with � approaching zero or one.

Another way of viewing the situation is that at � = 0 or 1, the product or reactant atoms, respectively, do not yet exist. Doing a simulation to �' or viewing the derivative �H/�� as a simulation to � + �� requires having coordinates of atoms that do not exist either yet or any longer.

Thermodynamic integra-tion method

The thermodynamic integration integral over �� tends to diverge when lin-ear scaling is used. This is the result of the fact that, as � approaches zero or one, the affected atoms (mostly product or reactant atoms and sometimes the environment atoms bonded to them) feel forces that approach zero and thus can have positions anywhere in phase space.

Nonlinear scaling for the thermodynamic integration method can be used to avoid this difficulty. This scaling method has one major advantage. At � = 0, the components of the derivatives �H(�)/�� due to the product part of the Hamiltonian are identically zero. Similarly, at � = 1, the components due to the reactant part of the Hamiltonian are zero. This solves the �-goes-to-zero problem.

Another way to avoid the problem is to scale the thermodynamic integra-tion method integral by a function that reduces the weight of the integrand as � approaches 0 or 1.

If the thermodynamic integration method with nonlinear � scaling is used, a command should be issued to delete the product atoms from the hybrid molecule RTF prior to the free energy simulation commands at � = 0. For example:

DELEte ATOMs SELEct etp 1 C2 END

This is a standard CHARMm PSF modification command and is issued after segment generation.

Furthermore, the free energy simulations command sequence changes slightly from the ethane-to-propane example, as follows:



TSMREAC sele etp 1 O1.or. etp 1 H1 end! no product atom at lambda = 0PROD NONE! nonlinear lambda scalingLAMBda .125 POWEr 2END

Because no product atoms exist at � = 0, the PROD NONE command is issued. Also, there is no need for the COLO command. For � = 1, an equiv-alent procedure is used.

Thermodynamic perturba-tion method

To get around the same problem when you use the thermodynamic pertur-bation method with linear scaling, do not run dynamics at � = 0 or 1. Instead, run dynamics at values of � a small distance away from 0 or 1 and extrapolate to the endpoints.

One problem can occur with this procedure. For transformation of hydro-phobic solute in aqueous solution, where water structure rearrangements around the solute are the major contributing factor to the free energy change, not sampling at � = 0 or 1 can mean that the significant part of phase space for the rearrangement is not adequately sampled. If, in going from reactant to product (or vice versa), a significant volume becomes newly accessible to the solvent, the presence of the r-12 repulsive forces from the almost (but not completely) disappeared atoms can conceivably prevent the necessary configurations of the water molecules from appear-ing in the finite-length trajectory. This problem has not been fully investi-gated.

Other considerations Nonlinear scaling may be preferred for sampling efficiency. However, problems can result because the monotonicity of the integrand in the ther-modynamic integration method integral is no longer assured. In this method, nonlinear scaling forces result in very small perturbations from�� to �', and the nonlinear exponent makes �V(� to �') very large. For exam-ple, if the exponent is 6,�� is 0.5 and �' is 0.25 (a reasonable window), the potential energy term for the product is multiplied by 0.56 (giving 0.16 for �) and by 0.256 (giving 0.00024 for �'). You end up with the term exp(-�(0.16V�� - 0.00024V��) in the ensemble average, causing extremely slow convergence.

For the temperature derivative related properties, you also run into prob-lems with floating-point overflows.

To deal with these difficulties, add a SAVE statement to the free energy simulation commands before the END statement in production runs.


Post-processing data

Repeat the procedure for more�� points. Then, do a thermalization run at each value of��, followed again by production runs.

The advantage of this implementation is that you can always run additional trajectories at any given value of � and add the output to previous runs. You can also insert trajectories at other values of � and recalculate thermody-namic properties.

Post-processing data

You must post-process output files so that you can compute free energy changes. For purposes of this discussion, assume you are working with three free energy simulation output files: etp1.prt, etp2.prt, and etp3.prt for � = 0.125, 0.500, and 0.875, respectively. For comparison purposes, assume there are three additional files named etp4.prt, etp5.prt, and etp6.prt for � = 0.125, 0.500, and 0.875, respectively.

The following input file processes output files:



* Post-processing Example ETP: ethanol -> propane vacuum.* TP method linear lambda scaling.*! open FES data files for input.open unit 10 form read etp1.prtopen unit 11 form read etp2.prtopen unit 12 form read etp3.prtopen unit 13 form read etp4.prtopen unit 14 form read etp5.prtopen unit 15 form read etp6.prt!! now the post-processing input!TSM POST PSTAck 6 PLOT! lambda = .125 -> lambda' = 0.PROC FIRST 10 NUNIT 2 LAMB 0.0 TEMP 298.0 DELT 10. BINS 100 CTEM! lambda = .125 -> lambda' = 0.25PROC FIRST 10 NUNIT 2 LAMB 0.25 TEMP 298.0 DELT 10. BINS 100 CTEM! lambda = .5 -> lambda' = 0.25PROC FIRST 12 NUNIT 2 LAMB 0.0 TEMP 298.0 DELT 10. BINS 100 CTEM! lambda = .5 -> lambda' = 0.75PROC FIRST 12 NUNIT 2 LAMB 0.0 TEMP 298.0 DELT 10. BINS 100 CTEM! lambda = .875 -> lambda' = 0.75PROC FIRST 14 NUNIT 2 LAMB 0.0 TEMP 298.0 DELT 10. BINS 100 CTEM! lambda = .875 -> lambda' = 1.0PROC FIRST 14 NUNIT 2 LAMB 0.0 TEMP 298.0 DELT 10. BINS 100 CTEM!! the END command tells the post-processor to tally everything ! up.ENDSTOP

An explanation of the commands in this script can be found in the CHARMm Dictionary.

Removing correlation dependence

A major problem with free energy simulations is that the data are very highly correlated. To get around this, the data are divided into bins, and deviations of the bin averages from the total trajectory average are calcu-lated to get a variance. Using bin averages removes the correlated depen-dence of the variance.

In the preceding example, a bin size of 100 is used. The estimated error depends on the choice of bin size. You hope to get convergence as a func-tion of bin size. If you don’t, trajectory lengths are probably not long enough.

Property variance A method for determining the variance of a property that uses correlation functions has been developed (Straatsma et al. 1986). This method looks


Using umbrella sampling

promising as long as you visually monitor the correlation function behavior and extrapolate at the longer lag times. However, an error in the approxi-mation of the correlation function is introduced. The developers of this method use an exponential extrapolation to overcome this error.

When the variance of the ensemble averages is calculated, the uncertainty in thermodynamic properties is determined by propagation of errors. For thermodynamic integration, necessary derivatives are determined by numerical differentiation. Total uncertainties are determined by summing the variances for each window.

Using umbrella sampling

When you want to sample torsional minima separated by barriers that make transitions infrequent (> 1 kT), you can use umbrella or importance sam-pling. Use a modified potential with lower barriers, then correct the approx-imation to the ensemble average with the actual potential energy at the end:

Eq. 19

Where:

w exp(-�(Vactual - Vsurrogate))

<A> The corrected ensemble average of property A

The ensemble averages on the right side of the equation are those that result from having the surrogate potential energy term in the Hamilto-nian.

In the current implementation, an umbrella correction is available for the ensemble averages used to calculate �A, �E, and �S in the free energy sim-ulations. It is presently limited to modifying the three-fold torsion term.

CHARMm assumes that the surrogate potential is the one in the parameter file. If torsion angles of the same type as the one that is to be subjected to umbrella sampling exist and you do not want to treat the angles the same way, you must give different type names to the atoms and modify the parameter file.

A� �

Aw----� �

w1w----� �

w

-------------=



Using the umbrella com-mand

Assume your study is the transformation of n-butane into propane in aque-ous solution or vacuum, and the hybrid molecule has a segment name of btp. The umbrella command looks like this:

UMBR btp 1 C1 btp 1 C2 btp 1 C3 btp 1 C4 VACT 1.6

The four atoms of the butane torsion are specified and the 3-fold term for the actual potential is given. The surrogate term is present in the parameter file. If the molecule had more than one torsion angle around the same cen-tral axis, all would be specified in separate umbrella commands.

Invoking the umbrella command causes the free energy simulation output to have an additional field (that is, the W term in Eq. 19). The header line after the title in the datafile has a field that indicates that this additional field is present.

For post-processing, you must add the flag parameter UMBR to each pro-cess command to indicate that the umbrella correction is to be applied.

References

Fleischman, S. H.; Brooks III, C. L. “Thermodynamics of aqueous solva-tion: Solution properties of alcohols and alkanes” J. Chem. Phys. 87 3029 (1987).

Mezei, M.; Beveridge, D. L.;“Free energy simulations,” Ann. New York Acad. Sci. 482 1 (1986).

Straatsma, T. P. Free Energy Evaluation by Molecular Dynamics Simula-tions, Ph.D. dissertation, University of Groningen, Netherlands, (1987).

Straatsma, T. P.; Berendsen, H. J. C.; Stam, A. J. Molecular Physics 57 89 (1986).


7 Setting Stochastic Boundaries

Stochastic boundaries allow you to simulate infinite systems by using stan-dard molecular dynamics techniques for a local region of the molecule while other parts of the structure are treated stochastically. For example, in studying the solvated active site of a protein, you can use molecular dynam-ics to study the active site and simulate solvent molecules by setting a sto-chastic boundary.

This chapter explains This chapter explains the basic features of stochastic boundary molecular dynamics and the general procedure for running a calculation. A scripted example of how to set up a stochastic boundary is included.

Basic features

Stochastic boundary molecular dynamics uses elements of both Langevin dynamics and Newtonian dynamics. The goal of the method is to eliminate atoms distant from, for example, an active site, allowing detailed studies of a spatially localized portion of the reacting molecular system.

The basic features of the model are similar to Langevin dynamics. Lan-gevin dynamics represents an approximation method for eliminating unim-portant or uninteresting degrees of freedom from dynamics simulation. The effects of eliminated degrees of freedom on the system are simulated by boundary (mean) and stochastic forces. To use this model, you apply boundary forces and stochastic forces. The kinetic bath effects (dissipation and fluctuation) balance each other to maintain thermal equilibrium.

A solvent boundary force is computed from the analytic deformable bound-ary model. Structure boundary forces are derived from atomic mean-square displacements. In addition to these mean forces, stochastic forces exist that are analogous to those from Langevin dynamics.

This stochastic boundary method also requires you to partition the structure around a localized region. This is to formally isolate the region in which


7. Setting Stochastic Boundaries

you are interested. This partitioning is schematically illustrated in the fol-lowing figure:

Newtonian dynamics is applied in the reaction region and Langevin dynamics in the buffer region.

General procedure

The steps for running a stochastic boundary molecular dynamics calcula-tion are:

1. Compute the required mean forces for input into the reduced particle equations of motion.

2. Set up and partition the full system into a reaction region, a buffer region, and a reservoir region.

3. Generate a stochastic boundary potential and read it into CHARMm.

4. Set up the mapping CHARMm uses to connect the table entries with the boundary constrained atoms.

5. Thermalize and equilibrate the reduced particle system.

6. Carry out production dynamics simulation and analyze the trajectories for desired properties.

Reservoir region

Buffer region (Langevin dynamics)

Stochastic bound-ary

Reaction region (Newtonian dynamics)

Reservoir region


Example: Setting up a stochastic boundary


This script is an example of how to set up a stochastic boundary. Because the script is too long to include in its entirety, critical fragments are pre-sented and discussed. For clarity, these script fragments differ somewhat from those in actual scripts.

This example uses the following files:

♦ Input file: sbmd.inp


SBMD1.STRSBMD2.STRSBMD3.STRSBMD4.STRSBMD5.STRSBMD6.STRSBMD7.STRSBMD8.STRSBMD9.STR

SBMD1.STR reads the initial coordinates and sets up the PSF. For conve-nience, the region of interest is translated to (0,0,0). A 15-Å sphere of water centered at (0,0,0) is appended and waters that overlap the protein are removed. The fragment of the script that codes these activities is:

open unit 1 form read name “$CHM_DATA/SPHERE15.CRD”read sequ coor resi unit 1rewind unit 1generate SOLV nodiread coor card append unit 1close unit 1! delete waters which overlap proteindele atom sele .byres. (segid SOLV .and. type OH2 .and. - ((.not. segid SOLV .and. .not. (hydrogen .or. lone)) - .around. 2.8 )) end! delete all solvent atoms more than 12A from the center! of the reaction zonedele atom sele .byres. (.not. (point 0.0 0.0 0.0 cut 12) - .and. (segid SOLV .and. type OH2)) end

SBMD2.STR performs a brief minimization to remove any bad contacts.



SBMD3.STR performs the following tasks:

♦ Sets up solvent boundary potential (for solvent only!) and solvent fric-tion (FBETA)

♦ Fixes all protein atoms and waters in the reservoir region

♦ Performs an initial dynamics run to shake up the initial water structure (protein atoms are kept fixed)

The dynamics statements include the keywords LANGEVIN and RBUF, which are required for this process:

***** SBMD3.STR* (A) set-up stochastic boundary for bulk water* (B) begin thermalization of the solvent within the reaction ! zone*! (A) set up solvent boundary - for bulk waters and crystal! waters only within the 11 A reaction zone.! The boundary potential file wat11.pot was generated! using supplementary software (see sbmd.doc for more! details).open unit 1 form read name WAT11.POTsbound read unit 1close unit 1sbound set xref 0. yref 0. zref 0. - assign 1 sele (( .byres. (point 0.0 0.0 0.0 cut 11)) - .and. resn TIP3 .and. type O*) end! set up solvent frictionscalar FBETA set 62.0 sele resn TIP3 .and. type OH2 end! fix all protein atoms and all crystal waters outside! the reaction zonecons fix sele segid LYSZ .or.(.byres. (segid SOLV .and. resn ! TIP3 .and. .not. (point 0.0 0.0 0.0 cut @2))) end! shake bonds to hydrogens. TIP3 bonds are automatically! shakenshake bonh tolerance 1.0e-06 param! AT LAST! Run dynamics on the reaction zone waters.! First without temperature scaling to get a higher ! temperature.open unit 3 form write name “LYSO_3A.RST”dynamics langevin nstep 100 timest 0.001 - ilbfrq 1 iseed 685963 iasvel 1 firstt 300 - tbath 300 rbuf 9.0 nprint 10 iprfrq 100 - ieqfrq 0 twindh 10.0 twindl -10.0 - iunwrite 3 nsavc 100 nsavv 0open unit 3 form read name “LYSO_3A.RST”open unit 4 form write name “LYSO_3B.RST”



open unit 1 unform write name “LYSO_3.DCD”! bring waters to final temperature, 300Kdynamics langevin restart nstep 100 timest 0.001 - ilbfrq 10 iseed 364569 iasvel 1 firstt 300 - tbath 300 rbuf 9 nprint 100 iprfrq 100 - ieqfrq 0 twindh 10.0 twindl -10.0 - isvfrq 100 iunwrite 4 iunread 3 nsavc 100 nsavv 0 iuncrd 1return

SBMD4.STR does another overlay of waters onto the system to fill any holes that might have occurred as the first waters settle into the protein sur-face.

SBMD5.STR performs additional equilibration dynamics on the water, still keeping the protein fixed.

SBMD6.STR defines the reaction and reservoir zones of the system.

! define reaction regionscalar xcomp set 1.0 - sele (.byres. (point 0.0 0.0 0.0 cut 9)) - .and. .not. ((type N .or. type CA .or. type C .or. type O) - .and. .not. point 0.0 0.0 0.0 cut 10) end! save reaction region flags in storage array 1scalar xcomp store 1 ! This stores the selection in array “1”.! define initial buffer region! RECALL 1 refers to the reaction region stored in array “1”.scalar ycomp set 1.0 - sele (.byres. (point 0.0 0.0 0.0 cut 11)) - .and. .not. recall 1 end! save buffer region flags in storage array 2scalar ycomp store 2! define Langevin atoms! RECALL 2 in the selection selects the buffer region! stored in storage array “2”.scalar zcomp set 1.0 - sele recall 2 .and. .not. (hydrogen .or. lone .or. resn TIP3) end! save Langevin region flags in storage array 3scalar zcomp store 3! define reservoir region atoms if anyscalar wcomp set 1.0 - sele .not. (recall 1 .or. recall 2) end! write boundary flags, file flags.proopen unit 1 form write name "FLAGS.PRO"write coor card comp unit 1* HEW - TRP 62 SBMD* Reduced region partitioning for 11A region about Trp 62.* Column 1: Reaction region atoms, 9A .byres. partitioning



* Column 2: Buffer region atoms, .byres. within 11A but not * in 9A plus all mainchain atoms within 10A* Column 3: Protein Langevin atoms* Column 4: Reservoir region atoms*close unit 1

A large part of this script involves partitioning the system into different parts and applying constraints. The remainder (not included here) involves setting up various constraints on the reaction and buffer regions.


Index

AACCEPTOR keyword, B-15AKMA measurement system, B-10ATOM keyword, B-15

BBOND keyword, B-15

CCHARMm

array dimensions, B-11data structures, B-7force field, B-1QUANTA mode, B-2stand-alone mode, B-2starting, B-2

CHARMm processescalculating energy, B-4generating a PSF, B-4generating Cartesian coordinates, B-4performing calculations and simulations, B-4reading model definitions, B-3reading parameters, B-3reading sequences, B-3

Chemistry at Harvard Macromolecular Mechanics, see CHARMm

CLOSE command, B-7command files

format, B-5title, B-5

command line, B-5command stream

controlling, B-9command stream file, see command filescommands, B-5

CLOSE, B-7HBOND, B-37IC BUILD, B-28IC FILL, B-27

IC PARAMETERS, B-27IC SEED, B-28NBFIX, B-37NBOND, B-37numeric values, B-6OPEN, B-6options, B-6PATCH, B-23READ, B-6REWIND, B-30STREAM, B-41WRITE, B-6

COMP keyword, B-31conditional statements, B-10conformations

generating, B-43, B-48coordinate arrays

comparison, B-31main, B-31

coordinatesbuilding Cartesian, B-27file format, B-32generating, B-25internal, B-26using, B-25–B-35

Ddiamers

constructing, B-46DONOR keyword, B-15

Eexternal files, B-6

Hharmonic restoring potential, B-37HBOND command, B-37hydrogen


Index

all-hydrogen model, B-25constructing positions, B-33extended atom model, B-24modeling, B-24

IIC BUILD command, B-28IC FILL command, B-27IC PARAMETERS command, B-27IC SEED command, B-28index number, B-22input files, see command filesinternal coordinates, B-26ISOP residue, B-38IUPAC name, B-20

Kkeywords, B-5

ACCEPTOR, B-15ATOM, B-15BOND, B-15COMP, B-31DONOR, B-15PRESERVE, B-27

NNBFIX command, B-37NBOND command, B-37

OOPEN command, B-6output file, B-5

Pparameter files

structure, B-35using, B-35–B-38

parametersnonbonded, B-37specifying dihedrals, B-36specifying impropers, B-36


wildcard atom-types, B-37PATCH command, B-23patch residue, B-22

applying, B-22definition, B-22

periodicity value, B-37polyalanine helix

constructing, B-41polymer segments

joining, B-38PRESERVE keyword, B-27principal structure file, see PSFPSF

creating, B-21modifying, B-22structure, B-20using, B-20–B-23

RREAD command, B-6residue identifier, B-20residue topology files, see RTFREWIND command, B-30RTF, B-3

constructing and using, B-13–B-19file structure, B-14

Ryckaert-Bellemans torsional potential, B-38

Sscripts

flow control, B-41goto statements, B-41if statements, B-41labels, B-41

segment identifier, B-20.seq, B-19sequence

file format, B-19using information, B-19

STREAM command, B-41

Vvariables, B-10VULC patch residue, B-38

Index

WWRITE command, B-6


Index


Documents

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