Identifying critical residues in protein folding: Insights from ϕ-value and Pfold analysis

We apply a simulational proxy of the $\varphi$ -value analysis and perform extensive mutagenesis experiments to identify the nucleating residues in the folding “reactions” of two small lattice Gō polymers with different native geometries. Our findings show that for the more complex native fold (i.e., the one that is rich in nonlocal, long-range bonds), mutation of the residues that form the folding nucleus leads to a considerably larger increase in the folding time than the corresponding mutations in the geometry that is predominantly local. These results are compared to data obtained from an accurate analysis based on the reaction coordinate folding probability $P_{\text{fold}}$ and on structural clustering methods. Our study reveals a complex picture of the transition state ensemble. For both protein models, the transition state ensemble is rather heterogeneous and splits up into structurally different populations. For the more complex geometry the identified subpopulations are actually structurally disjoint. For the less complex native geometry we found a broad transition state with microscopic heterogeneity. These findings suggest that the existence of multiple transition state structures may be linked to the geometric complexity of the native fold. For both geometries, the identification of the folding nucleus via the $P_{\text{fold}}$ analysis agrees with the identification of the folding nucleus carried out with the $\varphi$ -value analysis. For the most complex geometry, however, the applied methodologies give more consistent results than for the more local geometry. The study of the transition state structure reveals that the nucleus residues are not necessarily fully native in the transition state. Indeed, it is only for the more complex geometry that two of the five critical residues show a considerably high probability of having all its native bonds formed in the transition state. Therefore, one concludes that, in general, the $\varphi$ -value correlates with the acceleration/deceleration of folding induced by mutation, rather than with the degree of nativeness of the transition state, and that the “traditional” interpretation of $\varphi$ -values may provide a more realistic picture of the structure of the transition state only for more complex native geometries.