Role of Long-Range Contacts and Structural Classification in Understanding the Free Energy of Unfolding of Two-State Proteins

Free energy of unfolding (ΔGu) is the difference between the free energy values of the folded and unfolded structures of a protein. A successful model describing both folding/unfolding rates of proteins should be able to provide considerable insight on free energy of unfolding. In our earlier works, we have shown that Long-range Order (LRO) correlates well with both folding/unfolding rates of two-state proteins. In the present work, we examine the extent to which LRO can be used to predict the free energy of unfolding. For a standard data set of 29 two-state proteins, no significant correlation was observed between ΔGu and LRO. However after grouping the proteins according to their structural class, all-alpha and all-beta proteins showed a better correlation of r = 0.77 and r = 0.89, whereas mixed-class proteins still showed a poor correlation. We have also analyzed the relationship between various other structure derived topological parameters with ΔGu values and the results observed showed that all these parameters also gave a poor correlation with ΔGu values when structural classification was not taken into account. Similar to LRO, after structural classification better improvement in correlation was observed for all-alpha and all-beta proteins and not a single topological parameter showed reasonable correlation with ΔGu values of mixed-class proteins and suggested that understanding ΔGu values of mixed-class proteins remains complicated. Our present work implies that theoretical models to understand stability of proteins can be developed based on their 3-D structures and further experimental/theoretical studies will shed light on these predictions.