Molecular Dynamics simulations

Bert de Groot Max Planck institute for biophysical chemistry Göttingen, Germany

Molecular 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

2 •

Motions of nuclei are described classically,

(



) m a d

2

R

   

E el (

R

1

,...,

R

N ),

  1

,..., dt

•

Potential function E el describes the electronic influence on motions of the nuclei and is approximated empirically



„classical MD“:

N .

E el

 

Bindungen i E i bond

 

Bindungs



E winkel j angle j

 

Dihedral



E k dihe winkel k

 

( E Coul



,



.



E rep .



,

 

E vdW



,



)



..., Covalent bonds Non-bonded interactions E i bond

approximated

K B T

{  0 = = exact

|R|

„Force Field“

Molecular Dynamics Simulation

Molecule: (classical) N-particle system Newtonian equations of motion: with m i d

2 

r i

 

F i ( r ) dt

2 

F i

(

r

)

r



(

 

i V

(

r

)

r

 1

,...,



r N ) Integrate numerically via the „leapfrog“ scheme: with Δt



1fs!

(equivalent to the Verlet algorithm)

BPTI: Molecular Dynamics (300K)

Computational task: Solve the Newtonian equations of motion:

Non-bonded interactions

Lennard-Jones potential Coulomb potential

Use of constraints to increase the integration step

The „SHAKE“ algorithm

Δt = 1fs --> 2 fs

Molecular dynamics is very expensive ...

Example: F 1 -ATPase in water (183 674 atoms), 1 nanosecond: 10 6 integration steps 8.4 * 10 11 flop per step [n(n-1)/2 interactions] total: 8.4 on a 100 Mflop/s workstation: * 10 17 flop ca 250 years ...but performance has been improved by use of: multiple time stepping + structure adapted multipole methods + FAMUSAMM + parallel computers ca. 25 years ca. 6 years ca. 2 years 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 (10 4 ... 10 6 atoms)

•

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

MD-Experiments with Argon Gas

Role of environment - solvent

explicit or implicit?

box or droplet?

Surface (tension) effects?

periodic boundary conditions and the minimum image convention

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