On the role of structural class of a protein with two-state folding kinetics in determining correlations between its size, topology, and folding rate

Abstract

The time it takes for proteins to fold into their native states varies over several orders of magnitude depending on their native-state topology, size, and amino acid composition. In a number of previous studies, it was found that there is strong correlation between logarithmic folding rates and contact order for proteins that fold with two-state kinetics, while such correlation is absent for three-state proteins. Conversely, strong correlations between folding rates and chain length occur within three-state proteins, but not in two-state proteins. Here, we demonstrate that chain lengths and folding rates of two-state proteins are not correlated with each other only when all-alpha, all-beta, and mixed-class proteins are considered together, which is typically the case. However, when considering all-alpha and all-beta two-state proteins separately, there is significant linear correlation between folding rate and size. Moreover, the sets of data points for the all-alpha and all-beta classes define asymptotes of lower and upper limits on folding rates of mixed-class proteins. By analyzing correlation of other topological parameters with folding rates of two-state proteins, we find that only the long-range order exhibits correlation with folding rates that is uniform over all three classes. It is also the only descriptor to provide statistically significant correlations for each of the three structural classes. We give an interpretation of this observation in terms of Makarov and Plaxco's diffusion-based topomer-search model.

Figure 1.

Distribution of α-helical and β-like secondary structure content in two-state proteins included in the data set. All-α proteins are shown by red circles, all-β proteins by green squares, and mixed-class proteins by blue triangles.

Figure 2.

Correlation between natural logarithmic folding rates, ln k_f, and basic structural and topological parameters for proteins belonging to three structural classes. In regression equations, x and y stand for abscissa and ordinate axes quantities; r is the correlation coefficient. (A) ln k_f versus protein chain length, L (the t-test P-values are p _all-α = 5.7 × 10⁻⁴, p _all-β = 6.0 × 10⁻⁵, and p _mixed = 0.71). (B) ln k_f versus relative contact order, RCO (the t-test P-values are p _all-α = 0.43, p _all-β = 0.65, and p _mixed = 0.021). (C) ln k_f versus absolute contact order, ACO (the t-test P-values are p _all-α = 2.3 × 10⁻⁵, p _all-β = 5.5 × 10⁻⁶, and p _mixed = 0.38). (D) ln k_f versus long-range order, LRO (the t-test P-values are p _all-α = 6.4 × 10⁻⁴, p _all-β = 2.6 × 10⁻⁵, and p _mixed = 1.5 × 10⁻³). Structural classes for experimental data and regression lines are defined as in A.

Figure 3.

Correlation of the LRO with total and partial chain lengths. (A) LRO versus the total number of residues (the t-test P-values are p _all-α = 1.3 × 10⁻⁴, p _all-β = 1.3 × 10⁻⁶, and p _mixed = 1.5 × 10⁻²). (B) LRO versus the number of residues in the β-like or coil-like conformations (the t-test P-values are p _all-α = 4.4 × 10⁻⁵, p _all-β = 5.6 × 10⁻⁷, and p _mixed = 1.6 × 10⁻²).