A simple formalism on dynamics of proteins on potential energy landscapes.

We present a simple formalism for the dynamics of proteins on a potential energy landscape, using connectedness of configurational domains as an order parameter. This formalism clearly shows that the energy bias required to form a unit correct contact toward the native configuration of a two-state folder, to overcome Levinthal's paradox, is E(bias) congruent with RT ln 2. This result agrees well with earlier studies and indicates that the bias is mainly due to hydrophobic interaction. Further investigations have shown that the landscape funnel could be experimentally mapped onto a two-dimensional space formed by denaturant concentration and the connectedness of configurational domains. The theoretical value of the depth-of-folding funnel in terms of denaturant concentration has been calculated for a model protein (P450cam), which agrees well with the experimental value. Using our model, it is also possible to explain the turnover nature of heat-capacity change upon unfolding of proteins and the existence of enthalpy and entropy convergence temperatures during unfolding without any strict assumptions as proposed in earlier studies.