Molecular Dynamics simulations

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Molecular Dynamics simulations
Bert de Groot Max Planck institute for
biophysical chemistry Göttingen, Germany
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Molecular Dynamics Simulations
Schrödinger equation
Born-Oppenheimer approximation
Nucleic motion described classically
Empirical force field
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Molecular Dynamics Simulations
Interatomic interactions
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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
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Force-Field
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Molecular Dynamics Simulation
Molecule (classical) N-particle
system Newtonian equations of motion
with
Integrate numerically via the leapfrog scheme
with ?t ? 1fs!
(equivalent to the Verlet algorithm)
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BPTI Molecular Dynamics (300K)
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Computational task
Solve the Newtonian equations of motion
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Non-bonded interactions
Coulomb potential
Lennard-Jones potential
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Use of constraints toincrease the integration
step
The SHAKE algorithm
?t 1fs --gt 2 fs
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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
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• 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)

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MD-Experiments with Argon Gas
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Role of environment - solvent
explicit or implicit?
box or droplet?
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Surface (tension) effects?
periodic boundary conditions
and the minimum image convention
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Proteins jump between many, hierarchically
ordered conformational substates
H. Frauenfelder et al., Science 229 (1985) 337
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Reversible Folding Dynamics of a ß-Peptide
X. Daura, B. Jaun, D. Seebach, W.F. van
Gunsteren, A.E. Mark, J. Mol. Biol. 280 (1998) 925
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• 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

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