Dynamics of folding and unfolding transition in a globular protein studied by time correlation functions from computer simulation

Randomness of the process of protein folding

How specific or definite are pathways of folding and unfolding in globular proteins? In order to study this question, computer simulation of the folding-unfolding transition was carried out in a two-dimensional lattice model of proteins in which it is assumed that strongly specific intramolecular interactions contribute to the stability of the native conformation. This specificity of the interactions should tend to make the pathways of folding and unfolding more definite than reality. Yet, the analysis of the record of simulation indicated the process of transition to be stochastic rather than definite. This poses a fundamental problem of how to describe the pathways of folding and unfolding transition. It is argued that the description should consist of (i) a definition of intermediate states in terms of characteristic conformational features and (ii) stochastic rules of transitions between these intermediate states. The simplest would be the case in which the transitions occur as a markoffian process.

Markoffian description of the process of protein folding

A long record of computer simulation of folding-unfolding transition in a two-dimensional lattice model of protein as monitored by one conformational order parameter was studied to see if it could be approximated by a markoffian process. For this purpose the normalized time correlation functions of the order parameter were calculated (i) directly from the record of simulation and (ii) by assuming the markoffian behavior of the record. Both of them can be well approximated by a sum of two simple exponential terms. The relaxation time of the slow relaxing term, which corresponds to the overall folding-unfolding transition, becomes very short when the markoffian assumption is made. From this observation we conclude that intermediate states defined by one more-or-less arbitrarily chosen conformational parameter are, in general, collections of very heterogeneous conformations and therefore transitions between them cannot be markoffian. This indicates the importance of multi-parameter observation of dynamic process of folding. Characteristic features of the method of trapping disulfide intermediates are discussed.