A topological order parameter for describing folding free energy landscapes of proteins.

We studied the refolding free energy landscape of 26 proteins using the Go-like model. The distance between the denaturated state and the transition state, , was calculated using the Bell theory and the nonlinear Dudko-Hummer-Szabo theory, and its relation to the geometrical properties of the native state was considered in detail. We showed that none of the structural parameters, such as the contact order, protein length, and radius of cross section, correlate with for all classes of proteins. To overcome this problem, we have introduced the nematic order parameter , which describes the ordering of the structured elements of the native state. Due to its topologically global nature, is better than other structural parameters in describing the folding free energy landscape. In particular, displays a good correlation with extracted from the nonlinear theory for all three classes of proteins. Therefore, this parameter can be used to predict for any protein, if its native structure is known.