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A Pinch of Verlet-Velocity Algorithm, A Dash of Langevin Dynamics:

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

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A Pinch of Verlet-Velocity Algorithm, A Dash of Langevin Dynamics:

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  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 • 1985-1994:Laboratory Chemist • 1994-2002: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. 08/05/03 Austral Winter 11/04/03 Austral Spring Systems and Questions Chlorofluorocarbon’s (CFC’s) Role in Ozone Depletion

  6. hν 1.6270Å 1.4698 Å 106.20º 117.41º Systems and Questions 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. Mathematical Ingredients Classical Equations of Motion: Newton leads the way

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

  12. Velocity Verlet Algorithm Mathematical Ingredients

  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 Fluctuating force Dissipative 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. SMD atom DUMMY ATOM ν Spring with Constant k Mathematical Ingredients Steered Molecular Dynamics There are two methods for adding an additional force to the system 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) 1781-1802. 2005

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