Temperature-dependent downhill unfolding of ubiquitin. II. Modeling the free energy surface

To provide evidence for the interpretation of temperature-dependent unfolding kinetics and the downhill unfolding scenario presented in the accompanying experimental article (Part I), the free energy surface of ubiquitin unfolding is calculated using statistical mechanical models of the Muñoz-Eaton (ME) form. The models allow only two states for each amino acid residue, folded or unfolded, and permutations of these states generate an ensemble of microstates. One-dimensional free energy curves are calculated using the number of folded residues as a reaction coordinate. The proposed sequential unfolding of ubiquitin's beta-sheet is tested by mapping the free energy onto two reaction coordinates inspired by the experiment as follows: the number of folded residues in ubiquitin's stable beta-strands I and II and those of the less stable strands III-V. Although the original ME model successfully captures folding features of zipper-like one-dimensional folders, it misses important tertiary interactions between residues that are far from each other in primary sequence. To take tertiary contacts into account, partially folded microstates based on a spherical growth model are included in the calculation and compared with the original model. By calculating the folding probability of each residue for a given point on the free energy surface, the unfolding pathway of ubiquitin is visualized. At low temperature, thermal unfolding occurs along a sequential unfolding pathway as follows: disruption of the beta-strands III-V followed by unfolding of the strands I and II. At high temperature, multiple unfolding routes are formed. The heterogeneity of the transition state explains the global nonexponential unfolding observed in the T-jump experiment at high temperature. The calculation also reports a high stability for the alpha-helix of ubiquitin.