  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.
