Molecular Dynamics simulations

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Presentation transcript:

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

09-00

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

Molecular Dynamics Simulations 03-34 Interatomic interactions

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|

„Force-Field“ 03-15

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)

BPTI: Molecular Dynamics (300K)

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

Non-bonded interactions Coulomb potential Lennard-Jones potential

Use of constraints to increase 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 03-33

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) 03-47

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

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

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

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