1. Molecular Dynamics Simulation
Introduction to
Molecular Dynamics Simulation

2. Exploring the
Folding
Landscape
Protein Folding

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

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

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

6. Lysozyme in explicit water

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

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

9. Potential Function  Force
Newton’s Law:

10. Verlet’s Method
Taylor:

11. 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.

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

14. Statistical
Mechanics
Observable:
Ensemble Average:
Probability density:

15. MD Simulation:
Ergodic Hypothesis:
e.g.:

16. Analysis of MD
Configurations
Averages
Fluctuations
Time Correlations

17. Analysis of fluctuations