1. A Pinch of Verlet-Velocity Algorithm, A Dash of Langevin Dynamics:
A Recipe for Classical Molecular Dynamics
Kim Gunnerson
Undergraduate Mathematics Seminar
Wed Oct. 25, 2006

2. Today’s Outline
Who am I and How did I get here?
Systems and Questions
Examples of Mathematics Used
Summary

3. Who am I? How did I get here?
1987-BS Chemistry from PLU
:Laboratory Chemist
:HS Chemistry and MS science teacher including stint as science department chair
2002-today:Physical Chemistry grad student and GK-12 Project Manager

4. Systems and Questions Chlorine dioxide relaxation*
P-selectin/PSGL-1 conformation*
Carbon nanotubes
Crystal kinetics
*Dissertation subject

5. Chlorofluorocarbon’s (CFC’s) Role in Ozone Depletion
Systems and Questions
Chlorofluorocarbon’s (CFC’s) Role in Ozone Depletion
08/05/03
Austral Winter
11/04/03
Austral Spring

6. Systems and Questions Å
1.6270Å
117.41º
106.20º hν
What are the relaxation dynamics of the photoexcitation of chlorine dioxide?

7. Systems and Questions
Leukocyte Extravasation

8. Systems and Questions
Are there conformational changes in the protein and/or ligand in response to an external force?

9. ????????

10. Classical Equations of Motion:
Mathematical Ingredients
Classical Equations of Motion:
Newton leads the way

11. Mathematical Ingredients
Potential:
Intermolecular
Intramolecular
Lennard-Jones 6-12 Potential
Electrostatic Interaction
Force Fields: Contain values determined via a combination of empirical techniques and quantum mechanical calculations.

12. Mathematical Ingredients
Velocity Verlet Algorithm

13. Mathematical Ingredients
Problem: Need to represent the correct ensemble distribution for the specified temperature and pressure.
Solution: Slightly modify the Newtonian equations in order to take into account the temperature (and pressure) dependency of the molecular system.

14. Mathematical Ingredients
Langevin (stochastic) Equation
Dissipative force
Fluctuating force

15. Mathematical Ingredients
Now the integration of position and velocity changes as well…Brünger-Brooks-Karplus (BBK) method
Potential force
Dissipative term
Fluctuating term
Note: This will reduce to the Verlet algorithm as γ→0 (limit of Newtonian dynamics)

16. Mathematical Ingredients
One final ingredient for the bio-chemical system, the hemodynamic force experienced by the leukocyte is modeled by adding an additional force…this method is called steered molecular dynamics.

17. Mathematical Ingredients
Steered Molecular Dynamics
There are two methods for adding an additional force to the system ν
DUMMY ATOM
SMD atom
Spring with
Constant k
Constant velocity: OR
SMD atom F
Constant Force

18. Summary
Computational chemistry relies heavily on algorithms to do simulation of molecular systems.
Velocity Verlet Algorithm
Langevin Dynamics
BBK Method

19. Summary
Processor speed is a limiting factor for size of system and time-scale of simulation.
Faster processor speeds
Parallel Computing
High speed cluster

20. Summary
Optimization of algorithms is a possible solution to the limits of computer technology
Future Dream: Quantum Computers

21. Summary
Classical Molecular Dynamics is a powerful tool used by computational chemists to study molecular systems.

22. Thanks!!!
Major Resource: Phillips, et.al. Scalable Molecular Dynamics with NAMD. J Comput Chem. (26)