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A study on kinetics of protein folding was carried out to understand …

Biology Articles » Biophysics » The Complex Kinetics of Protein Folding in Wide Temperature Ranges » Materials and Methods

In this study, we use the fraction of native conformations as an order parameter to represent the folding progress. The system is assumed to be in quasiequilibrium with respect to , and the states are kinetically locally connected. This is a good approximation when folding has a definite free energy barrier between non-native and native states. It might not be as good for the downhill case, where there is no barrier. The results we obtain in this article, however, seem not to be influenced qualitatively by the kinetic connectivity assumption. It has been shown that in the global kinetic connectivity case, similar kinetic behavior occurs (Saven et al., 1994; J. Wang, W. M. Huang, H. Y. Lu, and E. K. Wang, 2004, unpublished results; Wang et al., 1996). We therefore go ahead with the local kinetic connectivity—the case for diffusion on the underlying folding energy landscape in this article.

In this model there are N residues in a polypeptide chain. For each residue there are + 1 available conformational states, one being the native state. A simplified version of the polypeptide chain energy is expressed as

The kinetic process along the above free-energy landscape is approximated via the use of Metropolis rate dynamics. Using continuous-time random walks, the generalized Fokker-Planck diffusion equation in the Laplace-transformed space can be obtained (Bryngelson and Wolynes, 1989; Lee et al., 2003),

One can rewrite Eq. 3 in its integral-equation representation by integrating it twice over :

In this work we mainly study the behavior of the first passage time (FPT) for the order parameter to reach _{f}. This FPT characterizes the folding time. By taking the derivatives with respect to s in Eq. 5 and taking the limit of s = 0, we can iteratively obtain the moments of the first passage time.

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