Mathematics in Science and Society
Eric Vanden-Eijnden
Courant Institute
Modeling and simulation of reactive events
The dynamics of biomolecular systems is typically characterized by a wide range of time scales, complicating their study via computer simulations. Of particular difficulty are situations which involve rare reactive events such as conformation changes of macromolecules, nucleation events during first-order phase transitions, or chemical reactions. The occurrence of these rare events is related to the presence of dynamical bottlenecks of energetic and/or entropic origin which effectively partition the configuration space of the system into metastable basins. The system spends most of its time fluctuating within these long-lived metastable states and only rarely makes transitions between them. The rare events then determine the long-time evolution of the system which is often of most interest to us but is typically beyond the reach of brute-force simulations. In this talk, I will discuss basic statistical mechanics questions related to the description of rare reactive events, explain why such a statistical description is not only useful but also necessary, and present numerical methods that permit us to identify the pathway, free energy and rate of these events.