Abstract
An optimization model is introduced in which proteins try to evade high energy regions of the folding landscape, and prefer low entropy loss routes during folding. We make use of the framework of optimal control whose convenient solution provides practical and useful insight into the sequence of events during folding. We assume that the native state is available. As the protein folds, it makes different set of contacts at different folding steps. The dynamic contact map is constructed from these contacts. The topology of the dynamic contact map changes during the course of folding and this information is utilized in the dynamic optimization model. The solution is obtained using the optimal control theory. We show that the optimal solution can be cast into the form of a Gaussian Network that governs the optimal folding dynamics. Simulation results on three examples (CI2, Sso7d and Villin) show that folding starts by the formation of local clusters. Non-local clusters generally require the formation of several local clusters. Non-local clusters form cooperatively and not sequentially. We also observe that the optimal controller prefers “zipping” or small loop closure steps during folding. The folding routes predicted by the proposed method bear strong resemblance to the results in the literature.
Highlights
Recent studies on protein folding lead to the suggestion that folding rates of two-state proteins are largely determined by a topological property of its three dimensional native structure [1], namely the contact order, CO, defined as the number of primary sequence bonds between contacting residues in space
Formation of the G helix is initiated early but its complete formation (f = 1) takes about the same time as b3{b4. Once these local clusters form, ECO decreases and formation of the non-local clusters is facilitated. This confirms the observation made by [5] in that non-local clusters generally require the formation of several local clusters. b2{b3 contacts are initiated after the two turns sufficiently form as concluded in [5] as well
The contact map information of the native state, we formulated the prediction of folding trajectories as a dynamic optimization problem that has a thermodynamic basis
Summary
Recent studies on protein folding lead to the suggestion that folding rates of two-state proteins are largely determined by a topological property of its three dimensional native structure [1], namely the contact order, CO, defined as the number of primary sequence bonds between contacting residues in space. Unlike CO, ECO is sensitive to the order in which contacts are formed, and an indicator of folding mechanisms or folding routes. According to the ZA hypothesis, the protein avoids searching the whole conformational space and essentially picks the low entropy loss routes (or low ECO routes) on a folding landscape [5]. The knowledge of the contact map of the native state and the adoption of low entropy loss routes during folding are the two essential ingredients for understanding the sequence of events during the folding of a protein
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