Molecular Dynamics simulations

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

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

4. Molecular Dynamics Simulations Interatomic interactions

5. = = R 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 exact KBT { 0 |R|

6. „Force-Field“

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

8. BPTI: Molecular Dynamics (300K)

9. Computational task: Solve the Newtonian equations of motion:

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

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

12. 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

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 (104 ... 106 atoms) • only short time spans accessible (ps ... μs)

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. Proteins jump between many, hierarchically ordered „conformational substates“ H. Frauenfelder et al., Science229 (1985) 337

18. 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

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