Abstract
There are several important questions on the coupling between properties of the protein shape and the rate of protein folding. We have studied a series of structural descriptors intended for describing protein shapes (the radius of gyration, the radius of cross-section, and the coefficient of compactness) and their possible connection with folding behavior, either rates of folding or the emergence of folding intermediates, and compared them with classical descriptors, protein chain length and contact order. It has been found that when a descriptor is normalized to eliminate the influence of the protein size (the radius of gyration normalized to the radius of gyration of a ball of equal volume, the coefficient of compactness defined as the ratio of the accessible surface area of a protein to that of an ideal ball of equal volume, and relative contact order) it completely looses its ability to predict folding rates. On the other hand, when a descriptor correlates well with protein size (the radius of cross-section and absolute contact order in our consideration) then it correlates well with the logarithm of folding rates and separates reasonably well two-state folders from multi-state ones. The critical control for the performance of new descriptors demonstrated that the radius of cross-section has a somewhat higher predictive power (the correlation coefficient is −0.74) than size alone (the correlation coefficient is −0.65). So, we have shown that the numerical descriptors of the overall shape-geometry of protein structures are one of the important determinants of the protein-folding rate and mechanism.
Highlights
There is enormous diversity in the protein folding behavior from small proteins usually folding with simple two-state kinetics to large proteins usually folding with multi-state kinetics
The topology itself cannot explain the differences in the refolding rates for some proteins sharing the same fold (SH3 domains, cold shock proteins, fibronectin domains, proteins of the ferredoxin fold) [8,9,10,11,12]
We have suggested a relationship between the compactness expressed as the number of contacts per residue and folding rates: a-helical proteins have on average the fastest folding kinetics and the smallest number of contacts per residue, whereas a/b proteins have on average the slowest folding kinetics and the largest number of contacts [33]
Summary
There is enormous diversity in the protein folding behavior from small proteins usually folding with simple two-state kinetics to large proteins usually folding with multi-state kinetics. The current statistical analysis of protein folding data shows that all the suggested scalings, from –ln L to –L1/2 and –L2/3 correlate with the observed folding rates nearly : the correlation between folding rates and protein sizes is not large, about 65% [14,15,16,17]. It has been shown, that protein size per se determines folding rates of three-state folding proteins [5]. Protein size, being the major determinant of the type of folding behavior, is not sufficient to determine the folding type of a protein since large proteins do not necessarily exhibit multistate kinetics (for example, large helical protein Variable surface antigen VlsE folds with two-state kinetics [18])
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