Statistic Analysis Of Protein Folding Rate Change Upon Point Mutation

Folding of proteins into their characteristic 3D structures is a fundamental aspect of living systems and understanding the folding mechanism is one of the central issues of molecular biophysics. Protein folding mechanisms are probed experimentally using single-point mutant perturbations. The relative effects on the folding(?-values) and unfolding(1- ?) rates are used to infer the detailed structure of the transition-state ensemble(TSE). So far, experimental research has accumulated more than 800 variants folding data from 200 proteins, which provides a foundation for the theory to study problem of protein variant folding rate.The first prediction model which used the quadratic regression models for discriminating the accelerating and decelerating of protein folding rate change upon point mutation was brought by Gromiha’s research group in 2010. During 2012 between 2015, Gromiha and co-workers proposed two quadratic regression or multivariate regression model based on the physicochemical properties of amino acid to predict real value of protein folding rate change upon point mutation. Recently, Mallik and co-workers carried out a relative coevolution order(r CEO) parameters based on residue-level coevolutionary information to predict folding rate change upon point mutation, good results were obtained in this study.Our research is different from Gromiha’s and Mallik’s which aims at the preditiction of a certain variation amount of folding rate,but inspired by paper of Garbuzynskiy and co-workers—“Golden triangle for folding rates of globular proteins”, our study focused on the distributed law of folding rate change upon point mutation. The relative solvent accessibility of the mutated residues can be divided into three types, buried, intermediate and exposed, respectively. After, we statistically analyze the difference between the average value of the absolute increment of the variant folding rate in the three kinds of cases. The results showed that when the mutated residues in the burial location, the absolute increment of variant folding rate is maximum, and the absolute increment of variant folding rate is minimum when the mutated residues in the exposed location. Further, we theoretically put forward a triangle principle of increment of protein variants folding rates depends on the relative solvent accessibility of mutation residues. All of 737 increment of protein variants folding rates measured by experiment fall within this narrow triangle.The triangular rule of increment of protein variants folding rates showed that with the depth of mutated residue burial in the protein increased, the range of increment of protein variants folding rates became expanded. This result indicates that the buried depth of the residue is the main limiting factor for the possible change range of the protein variants folding rate. In addition, we also analyzed the relationship between the mutational point residue contact order and contact number and the increment of protein variants folding rates. The results show that the increment of protein variants folding rates meet rhombus distribution.