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

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Presentation transcript:

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

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

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

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

Systems and Questions 1.4698 Å 1.6270Å 117.41º 106.20º hν What are the relaxation dynamics of the photoexcitation of chlorine dioxide?

Systems and Questions Leukocyte Extravasation

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

????????

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

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.

Mathematical Ingredients Velocity Verlet Algorithm

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.

Mathematical Ingredients Langevin (stochastic) Equation Dissipative force Fluctuating force

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)

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.

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

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

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

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

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

Thanks!!! Major Resource: Phillips, et.al. Scalable Molecular Dynamics with NAMD. J Comput Chem. (26) 1781-1802. 2005