Guided by the recent success of empirical model predicting the folding rates of small two-state folding proteins from the relative contact order (CO) of their native structures, by a theoretical model of protein folding that predicts that logarithm of the folding rate decreases with the protein chain length L as L 2/3 , and by the finding that the folding rates of multistate folding proteins strongly correlate with their sizes and have very bad correlation with CO, we reexamined the dependence of folding rate on CO and L in attempt to find a structural parameter that determines folding rates for the totality of proteins. We show that the AbsCO ‫ס‬ CO × L, is able to predict rather accurately folding rates for both two-state and multistate folding proteins, as well as short peptides, and that this AbsCO scales with the protein chain length as L 0.70 ± 0.07 for the totality of studied single-domain proteins and peptides.

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We demonstrate that chain length is the main determinant of the folding rate for proteins with the three-state folding kinetics. The logarithm of their folding rate in water (k(f)) strongly anticorrelates with their chain length L (the correlation coefficient being -0.80). At the same time, the chain length has no correlation with the folding rate for two-state folding proteins (the correlation coefficient is -0.07). Another significant difference of these two groups of proteins is a strong anticorrelation between the folding rate and Baker's "relative contact order" for the two-state folders and the complete absence of such correlation for the three-state folders.

The determination of factors that influence protein conformational changes is very important for the identification of potentially amyloidogenic and disordered regions in polypeptide chains. In our work we introduce a new parameter, mean packing density, to detect both amyloidogenic and disordered regions in a protein sequence. It has been shown that regions with strong expected packing density are responsible for amyloid formation. Our predictions are consistent with known disease-related amyloidogenic regions for eight of 12 amyloid-forming proteins and peptides in which the positions of amyloidogenic regions have been revealed experimentally. Our findings support the concept that the mechanism of amyloid fibril formation is similar for different peptides and proteins. Moreover, we have demonstrated that regions with weak expected packing density are responsible for the appearance of disordered regions. Our method has been tested on datasets of globular proteins and long disordered protein segments, and it shows improved performance over other widely used methods. Thus, we demonstrate that the expected packing density is a useful value with which one can predict both intrinsically disordered and amyloidogenic regions of a protein based on sequence alone. Our results are important for understanding the structural characteristics of protein folding and misfolding.

We have compared structures of 78 proteins determined by both NMR and X-ray methods. It is shown that X-ray and NMR structures of the same protein have more differences than various X-ray structures obtained for the protein, and even more than various NMR structures of the protein. X-ray and NMR structures of 18 of these 78 proteins have obvious large-scale structural differences that seem to reflect a difference of crystal and solution structures. The other 60 pairs of structures have only small-scale differences comparable with differences between various X-ray or various NMR structures of a protein; we have analyzed these structures more attentively. One of the main differences between NMR and X-ray structures concerns the number of contacts per residue: (1) NMR structures presented in PDB have more contacts than X-ray structures at distances below 3.0 A and 4.5-6.5 A, and fewer contacts at distances of 3.0-4.5 A and 6.5-8.0 A; (2) this difference in the number of contacts is greater for internal residues than for external ones, and it is larger for beta-containing proteins than for all-alpha proteins. Another significant difference is that the main-chain hydrogen bonds identified in X-ray and NMR structures often differ. Their correlation is 69% only. However, analogous difference is found for refined and rerefined NMR structures, allowing us to suggest that the observed difference in interresidue contacts of X-ray and NMR structures of the same proteins is due mainly to a difference in mathematical treatment of experimental results.