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

ji ij

ji

ji ij

ij

ij

ijij

impropersdihedrals

N

n

n

anglesbondsb

Dr

qq

rr

KnK

kbbkV

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612

20

1

20

20

4

cos1

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

l

r

qi qj

Newton’s Law:

Fi=force on ith atommi = mass of ith atomai=acceleration of ith atom

Newton’s Law:Newton’s Law:

i

ii r

VF

iii amF

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