Numerical Simulation of Folding and Unfolding of Proteins

The thesis examines in detail the folding and unfolding processes of a number of proteins including hbSBD, DDLNF4, single and multi Ubiquitin. Using simplified coarse-grained off-lattice Go model and CD experiments we have shown the two-state behavior of hbSBD protein. It was shown that refolding pathways of single Ubiquitin depend on what end is anchored to the surface. Namely, the fixation of the N-terminal changes refolding pathways but anchoring the C-terminal leaves them unchanged. Interestingly, the end fixation has no effect on multi-domain Ubiquitin. Using the Go modeling and all-atom models with explicit water, we have studied the mechanical unfolding mechanism of DDFLN4 in detail. We predict that, contrary to the AFM experiments, an additional unfolding peak would occur at the end-to-end $\Delta R \approx 1.5 $nm in the force-extension curve. Our study reveals the important role of non-native interactions which are responsible for a peak located at $\Delta R \approx 22 $nm. This peak can not be encountered by the Go models in which the non-native interactions are neglected. Our finding may stimulate further experimental and theoretical studies on this protein. The cooperativity of denaturation transition was investigated using lattice and off-latice models. Our studies reveal that the sharpness of the transition enhances as the number of amino acids grows. The corresponding scaling behavior is governed by an universal critical exponent. A new force replica exchange (RE) method was developed for efficient configuration sampling of biomolecules pulled by an external mechanical force. Contrary to the standard temperature RE, the exchange is carried out between different forces (replicas). Our method was successfully applied to study thermodynamics of a three-domain Ubiquitin