Molecular Modelling - Lecture 2 Techniques for Conformational Sampling Uses CHARMM force field Written in C++

Molecular Modelling - Lecture 2

Techniques for Conformational Sampling

Uses CHARMM force field

Written in C++

Protein example

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Monte Carlo Simulations

Technique used to perform first computer simulation of a molecular system

“Monte Carlo” = some kind of random sampling

Monte Carlo Methods

Basis of Monte Carlo methods is the use of random selections in calculations that lead to the solution of numerical and physical problems e.g. brownian motion molecular modelling designing nuclear reactors predicting the evolution of stars forecasting the stock market

Each calculation is independent of the others and hence amenable to embarrassingly parallel methods

Monte Carlo Integration : finding value of πMonte Carlo integration

Compute r by generating random points in a square of side 2 and counting how many of them are in the circle with radius 1 (x2+y2<1; π=4*ratio) .

Area= π2

2

Area of square=4


Configurations are generated by making random changes to the positions of the atoms

Importance sampling Samples from 3N dimensional space of positions of

molecules






Z= Configurational integral

Metropolis Monte Carlo

Biases generation of configurations towards those that make the most significant contributions to the integral Low energy states for most thermodynamic

properties Generates states with probability

exp(xand counts them equally (simple Monte Carlo would generate them with equal

probability and then weight them by exp(x



Markov chain of states

Monte Carlo Advantages/DisadvantagesAdvantages:

Does not require a continuous energy function (as in MD)

Number of particles can easily vary (very hard in MD)

Disadvantages Highly correlated motions hard to simulate

Poor sampling of large-scale changes

Molecular Dynamics

Newton’s equations of motions are integrated to propagate the structure through time

€

dx idt

= v i

dv idt

=Fim

Fi =∇ iE

Molecular Dynamics

fast: large systems can be modelledhistory of molecular motion and

interactions conformational distribution for simulation

t

360

0

P

3600

Molecular Dynamics - Integration methodsFinite difference methods

Used to generate molecular dynamics trajectories with continuous potentials

Integration broken into stages separated by time t Total force on each particle at time t is calculated as a

vector sum of all the interactions with other particles From force can determine accelerations

Combined with positions and velocities at time t to calculate positions and velocities at time t + t

Force assumed to be constant during time step

Molecular Dynamics - Integration methodsMany algorithms:

Verlet Leap frog method Predictor-corrector Velocity-Verlet

Molecular Dynamics - Verlet Integration Method



Most widely used method

Timescale Limitations



MD Production Run Protocol



Initial coords obtained from experimental data or theoretical model

Can be done by randomly selecting from a Maxwell-Boltzmann distribution at the temperature of interest







Truncating Long-Range forces and the minimum image conventionNon-bonded interactions most time-

consuming part of a simulation N2

Minimum image convention: Interaction for a molecule i are only counted

between it and it’s closest image

Truncation of potential creates problems with consistent potential and force

Truncating Long-Range forces and the minimum image conventionUse smoothing functions to smoothly

switch off the interaction between a “cut-on” and a “cut-off” distance.

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Simulated Annealing

special case of either MD (`quenched' MD) or MC simulation, in which the temperature is gradually reduced during the simulation.

Often, the system is first heated and then cooled the system is given the opportunity to surmount

energetic barriers in a search for conformations with energies lower than the local-minimum energy found by energy minimization. can lead to more realistic simulations of dynamics at low

temperature more expensive than energy minimization.

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Molecular Modelling - Lecture 2 Techniques for Conformational Sampling Uses CHARMM force field Written in C++