Introduction to Molecular Dynamics Simulation
Protein Folding
Exploring the Folding Landscape
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
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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
2/8MM Energy Function
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Newton’s Law:
Fi=force on ith atommi = mass of ith atomai=acceleration of ith atom
Newton’s Law:Newton’s Law:
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Potential Function Force
Taylor:
Verlet’s Method
Molecular dynamics:Integration timestep - 1 femtosecondSet by fastest varying force.Accessible timescale about 100 nanoseconds.
Bond vibrations - 1 fsCollective vibrations - 1 psConformational transitions - ps or longerEnzyme catalysis - microsecond/millisecondLigand Binding - micro/millisecondProtein Folding - millisecond/second
Timescales.
Ensemble AverageObservable
StatisticalMechanics
1 hr
Ergodic Hypothesis:MD Simulation:
Ensemble Average:
Observable:
Probability density:
StatisticalMechanics
Ergodic Hypothesis:MD Simulation:
e.g.:
Analysis of MD
ConfigurationsAveragesFluctuationsTime Correlations
Analysis of fluctuations
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