May 7: Eric Vanden-Eijnden, CIMS
Modeling rare events in complex systems
Many dynamical processes such as conformation change of macromolecules, chemical reactions in solution, nucleation events during phase transitions etc. involve rare events which pose challenges both for computations and modeling. At the simplest level, these events can be characterized as the hopping over a free energy barrier associated with the motion of the system along some reaction coordinate. Indeed this is the picture underlying classical tools such as transition state theory or Kramers reaction rate theory, and it has been successful to explain rare events in a wide variety of context. However this picture presupposes that we know or can guess beforehand what the reaction coordinate of the event is. In many systems of interest -- protein folding, enzyme kinetics, protein-protein interactions, etc. -- making such educated guesses is hard if not impossible. The question then arises whether we can develop a more general framework to describe rare events, elucidate their pathway and mechanism, and give a precise meaning to a concept such as the reaction coordinate. In this talk I will discuss such a framework and illustrate it using simple example such as the motion of a random walker in a maze or the folding of simplified on-lattice models of proteins.