Topological determinants of protein folding

Abstract

The folding of many small proteins is kinetically a two-state process that represents overcoming the major free-energy barrier. A kinetic characteristic of a conformation, its probability to descend to the native state domain in the amount of time that represents a small fraction of total folding time, has been introduced to determine to which side of the free-energy barrier a conformation belongs. However, which features make a protein conformation on the folding pathway become committed to rapidly descending to the native state has been a mystery. Using two small, well characterized proteins, CI2 and C-Src SH3, we show how topological properties of protein conformations determine their kinetic ability to fold. We use a macroscopic measure of the protein contact network topology, the average graph connectivity, by constructing graphs that are based on the geometry of protein conformations. We find that the average connectivity is higher for conformations with a high folding probability than for those with a high probability to unfold. Other macroscopic measures of protein structural and energetic properties such as radius of gyration, rms distance, solvent-accessible surface area, contact order, and potential energy fail to serve as predictors of the probability of a given conformation to fold.

Figure 1

The three-dimensional structure of the CI2 protein in post- (a) and pretransition (b) states. The protein graphs are constructed based on the structure of post- (c) and pretransition (d) states. Each node of protein graphs corresponds to an amino acid, whereas each edge between a pair of nodes corresponds to that pair of amino acids that are geometrically in contact with each other. For both CI2 and C-Src SH3 domain proteins' graph constructions, the contact between two amino acids is considered to be present if the distance between corresponding C_α atoms is less than 8.5 Å. In a and b, residues A16, L49, and I57 belonging to the specific nucleus of CI2 (8) are denoted by red spheres. A16, L49, and I57 form a triad of contacts in posttransition conformations (a), whereas such contacts are missing in the pretransition conformations. In both pre- and posttransition states the number of edges (contacts) are approximately the same.

Figure 2

The dependence of the average minimal distance L(k) between a node k and the rest of the nodes on CI2 (a) and C-Src SH3 domain (b) proteins' graphs for post- (●) and pretransition (■) states. The error bars represent the standard deviation from the average values of L(k) over all post- and pretransition states. In a, by the open circles (○) we denote amino acids M40 and E41 that do not affect the protein three-dimensional structure after cleavage of the 40–41 bond (19), and by the open boxes (□) we denote the folding nucleus of CI2 (8), A16, L49, and I57.

Figure 3

Plot of the degrees of each node versus the residue number for post- (thick solid line) and pretransition (thick broken line) states for CI2. The thin line represents the difference in node degrees between pre- and posttransition states.