Coupling between properties of the protein shape and the rate of protein folding.

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

Structural characteristics of 1399 globular protein domains from classes α/β and α+β.

<p>Structural characteristics of 1399 globular protein domains from classes α/β and α+β.</p

Log-log dependences of accessible surface areas on protein molecular masses for four structural classes of proteins.

<p>Cases (A) and (C) for general dataset of proteins and cases (B) and (D) for re-refined protein structures. In cases (A) and (B), values for all proteins without averaging (the number of points corresponds to the number of proteins in each structural class) were considered. And in cases (C) and (D) these values were averaged in the given region of the protein lengths (six points for each structural class).</p

Structural characteristics of 1155 globular protein domains from classes α and β.

<p>Structural characteristics of 1155 globular protein domains from classes α and β.</p

Dependences of a number of hydrogen bonds on the number of amino acid residues in protein.

<p>Dependences of a number of hydrogen bonds on the number of amino acid residues in protein.</p

Fraction of amino acid residues of each type of secondary structure.

<p>H, helix (α and 3₁₀); E, β structure; C, coil for four structural classes of proteins calculated using the DSSP (A) and YASARA (B) programs.</p

Log-log dependences of accessible surface areas on protein molecular masses for four structural classes of proteins where the number of loop residues per regular secondary structure element varies from 5 to 10.

<p>In case (A), values for all proteins without averaging were considered (the number of points corresponds to the number of proteins in each structural class). And in case (B) these values were averaged in the given region of protein lengths (six points for each structural class).</p

Slopes of straight lines of log-log dependences of accessible surface areas on protein molecular masses for two databases: PDB (2554 proteins) and PDB_REDO (1498 proteins).

<p>Slopes of straight lines of log-log dependences of accessible surface areas on protein molecular masses for two databases: PDB (2554 proteins) and PDB_REDO (1498 proteins).</p

Log-log dependences of accessible surface areas on protein molecular masses for four structural classes of proteins where the fraction of loop residues in the protein structure is as follows: (A, C) 0.4–0.5; (B, D) 0.5–0.6.

<p>In cases (A) and (B), values for all proteins without averaging were considered (the number of points corresponds to the number of proteins in each structural class). And in cases (C) and (D) these values were averaged in the given region of protein lengths (six points for each structural class).</p