Molecular Dynamics simulationsMolecular Dynamics simulations

Bert de Groot

Max Planck institute for biophysical chemistry

Göttingen, Germany

Molecular Dynamics SimulationsMolecular Dynamics Simulations

Schrödinger equation

Born-Oppenheimer approximation

Nucleic motion described classically

Empirical force field

Molecular Dynamics Simulations

Interatomic interactions

Molecular dynamics-(MD) simulations of Biopolymers

• Motions of nuclei are described classically, .N,...,),,...,(Edt

dm)( Nela 112

2

RRR

• Potential function Eel describes the electronic influence on motions of the nuclei and is approximated empirically „classical MD“:

...,)EEE(EEEE vdW,

.rep,

.Coul,

kwinkelDihedral

dihek

iBindungen

jwinkelBindungs

anglej

bondiel

approximated

exact

Eibond

|R|0

KBT {

Covalent bonds Non-bonded interactions

==R

„Force-Field“

Molecular Dynamics Simulation

Molecule: (classical) N-particle system

Newtonian equations of motion: )r(Frdt

dm iii

2

2

)()( rVrF ii

)r,...,r(r N

1with

Integrate numerically via the „leapfrog“ scheme:

(equivalent to the Verlet algorithm)

with

Δt 1fs!

BPTI: Molecular Dynamics (300K)

Computational task:

Solve the Newtonian equations of motion:

Non-bonded interactionsNon-bonded interactions

Lennard-Jones potential Coulomb potential

Use of constraints toUse of constraints toincrease the integration stepincrease the integration step

The „SHAKE“ algorithm

Δt = 1fs --> 2 fs

Molecular dynamics is very expensive ... Example: F1-ATPase in water (183 674 atoms), 1 nanosecond:

106 integration steps

8.4 * 1011 flop per step [n(n-1)/2 interactions]

total: 8.4 * 1017 flop

on a 100 Mflop/s workstation: ca 250 years

...but performance has been improved by use of:

multiple time stepping ca. 25 years

+ structure adapted multipole methods ca. 6 years

+ FAMUSAMM ca. 2 years

+ parallel computers ca. 55 days

Limits of MD-Simulations

• classical description: chemical reactions not described poor description of H-atoms (proton-transfer) poor description of low-T (quantum) effects simplified electrostatic model simplified force field

• only small systems accessible (104 ... 106 atoms)

• only short time spans accessible (ps ... μs)

MD-Experiments with Argon Gas

Role of environment - solventRole of environment - solvent

explicit

or

implicit?

box

or

droplet?

periodic boundary conditions and the minimum image convention

Surface (tension) effects?

Proteins jump between many, hierarchically ordered „conformational substates“

H. Frauenfelder et al., Science 229 (1985) 337

Reversible Folding Dynamics of a β-Peptide

X. Daura, B. Jaun, D. Seebach, W.F. van Gunsteren, A.E. Mark, J. Mol. Biol. 280 (1998) 925

MD Simulations

• external coupling: temperature (potential truncation, integration errors) pressure (density equilibration) system translation/rotation

• analysis

energies (individual terms, pressure, temperature) coordinates (numerical analysis, visual inspection!) mechanisms