[Protein structure prediction from analogy. I. New database of spatially similar and dissimilar structures of protein domains for testing and optimization of prediction methods].

The paper describes creation and analysis of a database 3Dfold_test. This database consists of a large set of pairs of spatially-similar structures of protein domains and of an accompanying, much larger control set of "decoys", i.e., spatially-dissimilar protein structures, having approximately the same size and compactness as each member of a pair of spatially-similar proteins. The database 3Dfold_test can be found at the site http://phys.protres.ru/resources/prediction analogy/3Dfold/.

[The relationship between protein accessible surface area and number of native contacts in its structure].

The degree of folding for a protein is usually characterized by either solvent-accessible surface area or by number of formed native contacts. It is clearly that these two values must be coupled with each other, since the decrease in solvent-accessible surface area must be accompanied with the corresponding increase in the number of native contacts. In this study we show that this relationship does exist and is excellent (correlation coefficient is higher than 99%), which can be used for accurate and fast estimate of accessible surface area by means of number of native contacts. Among commonly used methods for native contacts calculation thebest correlation is observed for atom-atom scheme, if hydrogen atoms are taken into account and cutoff value for the distance between atoms' centers is 8 angstroms. The latter means that for hiding protein interior from water two layers of surface atoms are necessary.

Theoretical study of a landscape of protein folding-unfolding pathways. Folding rates at midtransition.

This paper presents a new method for calculating the folding-unfolding rates of globular proteins. The method is based on solution of kinetic equations for a network of folding-unfolding pathways of the proteins. The rates are calculated in the point of thermodynamic equilibrium between the native and completely unfolded states. The method has been applied to all the proteins listed by Jackson [Jackson, S. E. (1998) Folding Des. 3, R81-R91] and some peptides. Although the studied protein chains differ by more than 1 order of magnitude in size and exhibit two- as well as three-state kinetics in water, and their folding rates cover more than 11 orders of magnitude, the theoretical estimates are reasonable close to the experimentally measured folding rates in midtransition (the correlation coefficient being as high as 0.78). This means that the presented theory (having no adjustable parameters at all) is consistent with the experimental observations.

[Kinetics of folding nuclei formation in proteins]. / Nukleatsiia i skorost' svorachivaniia v belkakh.

When a protein folds or unfolds, it passes through many half-folded microstates. Only a few of them can accumulate and be seen experimentally, and this happens only when the folding (or unfolding) occurs far from the point of thermodynamic equilibrium between the native and denatured states. The universal features of folding, though, are observed in the vicinity of the equilibrium point. Here the "two-state" transition proceeds without any accumulation of metastable intermediates, and only the transition state ("folding nucleus") is outlined by its key influence on the folding/unfolding kinetics. This review covers recent experimental and theoretical studies of folding nuclei.

Folding nuclei in proteins.

When a protein folds or unfolds, it passes through many half-folded microstates. Only a few of them can accumulate and be seen experimentally, and this happens only when the folding (or unfolding) occurs far from the point of thermodynamic equilibrium between the native and denatured states. The universal features of folding, though, are observed just close to the equilibrium point. Here the 'two-state' transition proceeds without any accumulation of metastable intermediates, and only the transition state ('folding nucleus') is outlined by its key influence on the folding-unfolding kinetics. Our aim is to review recent experimental and theoretical studies of the folding nuclei.

Folding nuclei in 3D protein structures.

This paper presents and analyzes the results of several new approaches to the problem of finding the folding nucleus in a given 3D protein structure. Firstly, we show that the participation of residues in the hydrophobic core and the secondary structure of native protein has a rather modest correlation with the experimentally found phi values characterizing the participation of residues in the folding nuclei. Then we tried to find the nuclei as the free energy saddle points on the network of the folding/unfolding pathways using the branch-and-bound technique and dynamic programming. We also attempted to estimate the phi values from solving of kinetic equations for the network of protein folding/unfolding pathways. These approaches give a better correlation with experiment, and the estimated folding time is consistent with the experimentally observed rapid folding of small proteins.