Barrier Crossing by Long Chain Molecules

“A large number of problems in chemical biology involve long chain molecules, climbing over a free energy barrier. In the recent past, very interesting information on such processes have become available, from experiments often done at the single molecule level.   Motivated by these experiments, we have been trying to construct simple models for such processes.  We discuss two such processes.  The first is the process of crossing a barrier in space, which should form a model for translocation of a long chain molecule through a pore.  This is a generalization of the classic Kramers escape problem.  While the Kramers problem is concerned with a single particle climbing over a barrier, our problem involves a chain of large number of particles.  We show that for the simplest model for such a chain (the Rouse model), the problem can be analytically solved.    The second process involves loop formation between the two ends of a semi-flexible polymer.   An outline of our calculations, which lead to a minimum in the loop formation time, considered as function of the chain length will be presented.”