Chemical relaxation of co-operative conformational transitions of linear biopolymers

Abstract

The kinetics and chemical relaxation of co-operative conformational changes of linear (bio)polymers (e.g. helix-coil transitions of polypeptides) are discussed on the basis of the linear ISING model. Chemical relaxation is in general shown to be described by 4 N−5 relaxation times if the polymer chain consists of N elementary reaction sites. It is pointed out that nevertheless substantial simplifications of the theory can be achieved in many special cases of practical interest. Sufficiently short chains exhibit first-order kinetics resulting in a single relaxation time whereas for certain medium chain lengths zero-order kinetics plays a principal role in the relaxation process. For the particularly interesting case of very long chains a set of four relaxation equations is derived. The corresponding relaxation times are calculated assuming strong co-operativity and slow nucleation rates. However, it is almost exclusively the largest one of these relaxation times which actually controls the conformational change as turns out by means of a new approach to compute amplitude factors.