Colloquium

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, chemical reactions, or bistable behavior of genetic switc. 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. In this talk, I will present a general theoretical framework termed transition path theory (TPT) for the description of rare reactive events and compare it to other approaches such as the classical transition state theory (TST) and the more recent transition path sampling (TPS). I will also show that TPT can used to design efficient numerical algorithms such as the string method for the identification of the pathway, free energy and rate of the rare events. Both the theory and the numerics will be illustrated via examples.