Molecular Dynamics Simulation

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Presentation transcript:

Molecular Dynamics Simulation Introduction to Molecular Dynamics Simulation

Exploring the Folding Landscape Protein Folding

Uses of Molecular Dynamics Simulation: structure flexibility solvent effects chemical reactions ion channels thermodynamics (free energy changes, binding) spectroscopy NMR/crystallography

Atomic-Detail Computer Simulation Model System Molecular Mechanics Potential Energy Surface  Exploration by Simulation..

Model System set of atoms explicit/implicit solvent periodic boundary conditions Potential Function empirical chemically intuitive quick to calculate Tradeoff: simplicity (timescale) versus accuracy

Lysozyme in explicit water

MM Energy Function 2/8 l q f r q i j

Newton’s Law: Fi=force on ith atom mi = mass of ith atom ai=acceleration of ith atom

Potential Function  Force Newton’s Law:

Verlet’s Method Taylor:

Timescales. Bond vibrations - 1 fs Collective vibrations - 1 ps Conformational transitions - ps or longer Enzyme catalysis - microsecond/millisecond Ligand Binding - micro/millisecond Protein Folding - millisecond/second Molecular dynamics: Integration timestep - 1 femtosecond Set by fastest varying force. Accessible timescale about 100 nanoseconds.

Statistical Mechanics Observable Ensemble Average Ergodic Hypothesis: MD Simulation: 1 hr

Statistical Mechanics Observable: Ensemble Average: Probability density:

MD Simulation: Ergodic Hypothesis: e.g.:

Analysis of MD Configurations Averages Fluctuations Time Correlations

Analysis of fluctuations