Secondary structure, mechanical stability, and location of transition state of proteins

It is well known that the unfolding times of proteins, tau(u), scales with the external mechanical force f as tau(u) = tau(0)(u) exp (-fx(u)/kB(T)),where X-u is the location of the average transition state along the reaction coordinate given by the end-to-end distance. Using the off-lattice Go-like models, we have shown that in terms of X-u, proteins may be divided into two classes. The first class, which includes beta- and beta/alpha-proteins, has X-u approximate to 2-5 angstrom whereas the second class of alpha-proteins has X-u about three times larger than that of the first class, X-u approximate to 7-15 angstrom. These results are in good agreement with the experimental data. The secondary structure is found to play the key role in determining the shape of the free energy landscape. Namely, the distance between the native state and the transition state depends on the helix content linearly. It is shown that X-u has a strong correlation with mechanical stability of proteins. Defining the unfolding force, f(u), from the constant velocity pulling measurements as a measure of the mechanical stability, we predict that x(u) decays with f(u) by a power law, x(u) similar to f(u)(-mu), where the exponent mu approximate to 0.4. We have demonstrated that the unfolding force correlates with the helix content of a protein. The contact order, which is a measure of fraction of local contacts, was found to strongly correlate with the mechanical stability and the distance between the transition state and native state. Our study reveals that x(u) and f(u) might be estimated using either the helicity or the contact order.