Abstract

Ron Elber: Long time simulations by milestoning

How long does it take for a protein to fold? How long does it take for a protein to change a conformation from an active to an inactive state? Pretty long time... The fundamental time unit at the molecular scale is a femtosecond (10^(-15) second) while fast folders do so in a millisecond (10^(-3) second), twelve orders of magnitude longer. For comparison, if the fundamental step of an ant is one centimeter in one second, then the analogy to the travel of a protein to the folded conformation is an ant journey of 10 million kilometers (the distance to the moon is roughly 400,000 km). How can we study such processes on the computer using the fundamental step? It takes at least ten milliseconds to compute the molecular forces and move a small protein one (small) step.

I shall describe the method of milestoning developed with Anthony West that provide systematic coarsening in space and time (under some physical assumptions) that extend the time scale of simulations in biophysics (and ant-physics) to the desired level. The coarsening transforms the complex Markovian formulation to a non-Markovian formulation with drastically reduced dimensionality. We solve the reduced model numerically to obtain the long time behavior. Some toy models will be presented, as well as more complex biophysical problems.

Joint work with Anthony West