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Molecular Dynamics simulationsMolecular Dynamics simulations
Bert de Groot
Max Planck institute for biophysical chemistry
Göttingen, Germany
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Molecular Dynamics SimulationsMolecular 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, .N,...,),,...,(Edt
dm)( Nela 112
2
RRR
• Potential function Eel describes the electronic influence on motions of the nuclei and is approximated empirically „classical MD“:
...,)EEE(EEEE vdW,
.rep,
.Coul,
kwinkelDihedral
dihek
iBindungen
jwinkelBindungs
anglej
bondiel
approximated
exact
Eibond
|R|0
KBT {
Covalent bonds Non-bonded interactions
==R
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„Force-Field“
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Molecular Dynamics Simulation
Molecule: (classical) N-particle system
Newtonian equations of motion: )r(Frdt
dm iii
2
2
)()( rVrF ii
)r,...,r(r N
1with
Integrate numerically via the „leapfrog“ scheme:
(equivalent to the Verlet algorithm)
with
Δt 1fs!
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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 interactionsNon-bonded interactions
Lennard-Jones potential Coulomb potential
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Use of constraints toUse of constraints toincrease the integration stepincrease the integration step
The „SHAKE“ algorithm
Δt = 1fs --> 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 - solventRole of environment - solvent
explicit
or
implicit?
box
or
droplet?
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periodic boundary conditions and the minimum image convention
Surface (tension) effects?
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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 β-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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