Life science and nanotechnology software applications L. Litov, P. Petkov, G. Vayssilov

Life science and nanotechnology software applications

L. Litov, P. Petkov, G. Vayssilov University of Sofia

Life science and nanotechnology software applicationsL. Litov Sofia, 10 December 2010

Physics basics Quantum simulations Molecular dynamics Examples – nanotechnology Examples – life science Summary

Outlook


Physics basics


Newton equation

Schrödinger equation

Probability to find the system in (r,t)

)(tx

)()( txdt

dtv )(

2

2

txdx

dmF

),(Ψ),(Ψ=),( * txtxtxP

Physics


Quantum simulations


Quantum simulations

Schrödinger equation

Born- Oppenheimer approximation

Schrödinger equation for electrons

Schrödinger equation fore nuclei

),...,,()...,,(),...,,,...,,( 321321321321 nelNnunN rrrrRRRRrrrrRRRR

),,...,,(),,...,,( 321321 RrrrrERrrrr nelnelel

iI jiiI

I

iiel rijrR

Z

,

2 12/1

)....,,()....,,( 321321 NnutotNnunu RRRRERRRRH

JI IJ

JI

II

Inu R

ZZRE

M ,

2 )(2

1

me≪m

p

)(RE


Quantum simulations

Hartree – Fock approximation - huge computational time Density Functional Theory (DFT) - Hohenberg-Kohn, Kohn- Sham

Ground state properties of many electron system are determined by electron density

Interacting electrons in static external potential non-interacting electrons in effective potential

VASP, CP2K, CPMD, GAMESS, GAUSSIAN, Q-Chem


Molecular Dynamics


Моделиране на взаимодействия на биологични молекули

For particle with mass m in equilibrium and temperature T, the mean value of the

momentum is

Heisenberg uncertainty principle

Follows that the width is

It is possible to omit the quantum effects if the variations x are less than some critical width defining

the accuracy of our calculations..

Critical width

From quantum to classic mechanicsFrom quantum to classic mechanics


Quantum – Classic mechanicsQuantum – Classic mechanics

• Electrons are treated by means of quantum mechanics• Hydrogen and Deuterium atoms at temperature 300 K can not be

considered as a pure classical objects• Heavier atoms can be treated as classical objects (temperatures 300

K). Additional correction are introduced in order to take into account quantum effects.


Solving the equations of motionSolving the equations of motion

Point in the phase space of the system

Hamilton equations

- Liouville operator

In Cartesian coordinates

и Do not commutate

)(2/2 xVmpVKH ii

i where


Time propagator

One step propagator

Applying on

We obtain

Velocity Verlet, Leap Frog algorithms

Solving the equationsSolving the equations


Every atom should be included

-chemical bonds with other atoms

-long distance interactions

Potential – force field

... i

ei

vi

ti

ai

s VVVVVV

Bond strengthSum over all bonds

Bond angleSum over all angles

Torsion

Van der Waals interactions

Coulomb interaction


- Empirical parameters (- Empirical parameters (ppkk))

202

1 θθθ aa kv 202

1 rrkrv bb 0φφcos1φ nkv dd

k

kkN pxVxxxV ;,,, 21


Parameterization of chemical bonds


6

6

12

12

ij

ij

ij

ij

r

C

r

Cijlj rV

ij

ji

r

qqijc rV

0πε4

Parameterization of the other interactionsParameterization of the other interactions

- Empirical parameters (- Empirical parameters (ppkk))

k

kkN pxvxxxV ;,,, 21


AMBER, CHARMM,GROMOS, GROMACS, LAMMPS, NAMD, VMD


New materials - nanothenology


nanothenology

Two examples

Interface between Pt8 cluster and Ce21O42 nanoparticle

Reduction effect - generation of Ce3+ cations

Effect on formation energy of oxygen vacancies

VASP Hydrogen reverse spillover on zeolite-supported clusters

Ab initio MD simulation of Rh4 and Ag4 clusters CP2K

Georgi N. VayssilovGeorgi N. Vayssilov, P. Petkov, H. Aleksandrov (Univ. of Sofia), P. Petkov, H. Aleksandrov (Univ. of Sofia)


Platinum cluster on ceria nanoparticle

Pt/CeO2 - the key component of the automotive catalyst

Model: cluster Pt8 on Ce21O42 nanoparticle

Reduction of one Ce4+ to Ce3+ in the most stable structures

Eads = -5.03 eV

Ns = 4

1 Ce3+

Pt

O2-

Ce4+

Ce3+


Clusters Ce21O42

Plane-wave density-functional calculations

Model clusters Ce21O42

VASP code

PW91 gradient-corrected functional + U = 4 eV

Plane wave basis, cutoff of 415 eV

Spin-polarized calculations (where appropriate)

Unit cells: 202020 Å, allowing ~10 Å vacuum between

neighboring cluster images



Energy for formation of an O vacancy Ef is reduced in the presence of

platinum: ΔEf = 0.44 eV

-1/2 O2

1.23 eV

-1/2 O2

1.67 eV


Ab initio MD simulations of supported clusters

Support - Zeolite MOR - total 295 atoms per unit cell

a = 18.256, b = 20.534, c = 15.084 A

angles = 90.0

Si/Al = 89/7 ≈ 13

Initial M-H distances: ~250, ~275, ~470 … pm

Rh4 Ag4


Ab initio MD simulation of Rh4 and Ag4 clusters

Periodic ab initio MD simulations – CP2K

DFT: PBE; BO MD and optimization

PW basis, 200 eV cutoff for MD and 400 eV for geometry

optimization

NVT ensemble

MD run: time step 1 fs; 1 frame = 10 fs; time ~20 ps

T = 300 K; CSVR thermostat


10ps MD run: Proton transfer to Rh4

Protons to be transferred


10ps MD run: Interaction with OH for Ag4


Life science

Understanding of human interferon-gamma

binding


N-terminusN-terminus

C-terminusC-terminus122-143

Active siteRes 18-26

Active siteRes 18-26

Human Interferon Gamma


Interferon-gamma and its alpha receptor

Residues connected by H-bondsPDB ID: 1fg9


Task To find a possible way to inhibit the gamma-interferon activity

Block the binding sites of the gamma-interferonFind a ligand binding hIFN- and blocking its activity

Block the binding receptors (hIFNR) on the cell surfaceWith mutated hIFN- peptides, lacking biological activityWith some other ligand

Need to understand the mechanism of hIFN- binding to its cell receptors

Gamma interferon binding


High performance computing, large scale simulation anddrug design

hIFNg + hIFNgRa in water 26 ns


D1 domain (125KTGRKRKR132)

D2 domain (137RGRR140)

INF- C-terminus


INF- C-terminus



hINF-hIFNR interaction simulations

GROMACS




PDB ID: 1hpn

Biochem J. 2004 November 15; 384(Pt 1): 93–99. NMR characterization of the interaction between the C-terminal domain of interferon-γ and heparin-derived oligosaccharidesCécile Vanhaverbeke,*1 Jean-Pierre Simorre,* Rabia Sadir,†

Pierre Gans,*2 and Hugues Lortat-Jacob†

Heparin derived oligosaccharide

dp8

dp4

dp2

INF- C-terminus



hIFN-and d8



Ribosome structure model

The goalgoal - construction and verification of a stable full atomistic computer stable full atomistic computer model of the whole ribosomemodel of the whole ribosome, which enables realistic simulations of various biochemical processes in the living cell.

Stable ribosome subunits Construction of the whole ribosome including tRNA, mRNA, and a growing

peptide chain Determination of the structure of the ribosome in water Investigation of the influence of the type of the cations on the stability of the

whole ribosome (role of Na and Mg ions) Non trivial challenging task requiring a Petascale (~3.106 atoms) computing


Ribosome big subunit

CHARMM27 Force Field Explicit solvent MD simulation Crystallographic ions included NAMD 2.6

Time step 2.5 fs NVT

Unstable structure even in about 0.5 ns long MD simulation


Ribosome big subunit with Na+ counter ions

Na+ ions added to crystallographic structure compensating the charge of phosphates

Na+


Trajectories RMSD


COX inhibitors

Investigation of the system – enzyme- inhibitor Cyclooxygenase (COX 1 and COX I2) – responsible for many cell

processes Regulation and production of hormones Regulation of the Ca transfer Thrombosis aggregation Regulation of inflammatory processes ..etc.

COX1 and COX2 bind with arachidonic acid – produces prostaglandines

COX1 and COX2 are targets for all nonsteroidal anti- inflammatory drugs like aspirin, paracetamol etc.



Docking

Docking is based on: Search of the most

suitable ligand orientation with respect to the receptor centre

Define the binding affinity – using different scoring functions

Calculation of the binding energy

DOCK 6.4 Selectivity test 512 ligands There is no binding


Arachidonic acid

Arachidonic acid binding is reproduced correctly (crystallographic structure)

RMSD = 1,820 Å; ECryst

= 55,45 kcal/mol;

ΔE = 4,2 kcal/mol; EDock

= 51,25 kcal/mo


COX1 and COX2 inhibitors

Investigation of inhibitor ligands Crystallographic orientation of

some inhibitors are reproduced well Ibuprofen, Fluribiprofen etc

Binding of specific COX2 inhibitors is under investigationDiclofenak, Celecoxib


Computer simulations: are extremely useful in the design of new materials can play significant role in the understanding of biological processes at atomic

and molecular level significantly reduce time and cost of development of new drugs (in-silco drug

design) Quantum calculations are extremely time consuming – require new algorithms and

more powerful (super)computers. Simulations of large (milions of atoms) systems require supercomputing at

Petascale level Problem with scaling – require new algorithms in order to reduce procesor

communications Reach variety of software is installed on Bulgarian IBM BG/P supercomputer We are welcome to run your jobs at BG supercomputer

Conclusions


Spare slides


Error at every step

Accumulated error

Algorithms for solving the equation of motionAlgorithms for solving the equation of motion


Force field (Gromacs, NAMD) Water model – different for NAMD and GROMACS Box size Periodic boundary conditions Need special investigations

Systematic errors



51

DOS plots of bare CeO2 and Pt8/CeO2:

Pt states appear in the gap between O 2p and Ce 4f “bands”

EFermi

CeO2 - dashed lines

Pt8/CeO2 - solid lines Pt states


Energies for proton transfer to Rh4

H ERS, kJ/mol Rin(M-H), pm

Rh4 1 -272 250

2 -103 275

3 20 475

Energies obtained after optimization of the structures with different number of transferred H

Proton transfer from distant OH group is disfavored

Proton transfer from near OH group to the metal cluster is favored


Systematic errors - models

NAMD GROMACS



Systematic errors – box size


Systematic errors - PBC



Systematic errors - PBC

Life science and nanotechnology software applicationsL. Litov Sofia, 10 December 2010L. Litov


Second workshop IRC-CoSIM,Guletchitsa, 17 October 2009



T = 0 ps

T = 2000 ps

Configuration 1 Configuration 2

INF- C-terminus – dp8 interaction



INF- C-terminus – dp8 interaction

Documents

Life science and nanotechnology software applications L. Litov, P. Petkov, G. Vayssilov