1. Molecular Dynamics simulations
Bert de Groot
Max Planck institute for biophysical chemistry
Göttingen, Germany

2. 09-00

3. Molecular Dynamics Simulations
Schrödinger equation
Born-Oppenheimer approximation
Nucleic motion described classically
Empirical force field

4. Molecular Dynamics Simulations
03-34
Interatomic interactions

5. Molecular dynamics-(MD) simulations of Biopolymers
Motions of nuclei are described classically,
Potential function Eel describes the electronic influence on motions of the nuclei and is approximated empirically  „classical MD“:
Covalent bonds
Non-bonded interactions
Eibond
approximated
03-14
exact = R
KBT { 0
|R|

6. „Force-Field“
03-15

7. Molecular Dynamics Simulation
Molecule: (classical) N-particle system
Newtonian equations of motion:
with
Integrate numerically via the „leapfrog“ scheme:
03-08
with
Δt  1fs!
(equivalent to the Verlet algorithm)

8. BPTI: Molecular Dynamics (300K)

9. Solve the Newtonian equations of motion:
Computational task:
Solve the Newtonian equations of motion:
03-15

10. Non-bonded interactions
Coulomb potential
Lennard-Jones potential

11. Use of constraints to increase the integration step
The „SHAKE“ algorithm
Δt = 1fs --> 2 fs

12. Molecular dynamics is very expensive ...
Example: F1-ATPase in water ( atoms), 1 nanosecond:
106 integration steps
8.4 * 1011 flop per step [n(n-1)/2 interactions]
total: * 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 years
+ FAMUSAMM ca years
+ parallel computers ca. 55 days
03-33

13. 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 ( atoms)
only short time spans accessible (ps ... μs)
03-47

14. MD-Experiments with Argon Gas

15. Role of environment - solvent
explicit or
implicit?
box or
droplet?

16. Surface (tension) effects?
periodic boundary conditions
and the minimum image convention

17. „conformational substates“
Proteins jump between many, hierarchically ordered
„conformational substates“
00-09
H. Frauenfelder et al., Science 229 (1985) 337

18. Reversible Folding Dynamics of a β-Peptide
35-bpep_movie.mpg
X. Daura, B. Jaun, D. Seebach, W.F. van Gunsteren, A.E. Mark, J. Mol. Biol. 280 (1998) 925

19. 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
03-47