Predicted Protein Folding Rates From The View Of Limited Conformational Search Space

Protein folding rate constant is an important kinetic parameter for studying and analyzing the mechanism of protein folding.Increasing the predictability of protein folding rate helps to understand the mechanism of protein folding.Protein chains have the conformation of astronomical numbers,and the natural conformation is only one of them.The Levinthal's paradox states that it is impossible for a protein to obtain its natural conformation using an unbiased random search strategy at the amino acid level.Both in vitro and vivo experiments have shown that the average folding time of single domain globulin was on the order of milliseconds.The contradiction between the huge conformational space of a protein and the fact of rapid folding may be explained follow two ways.On the one hand,proteins use a biased search strategy that is not conducive to wrong conformation to discover the natural conformation?the view of Zwanzig et al.?.On the other hand,proteins may adopt a strategy of limited conformation search space to discover its natural conformation?the views of Finkelstein,Englander,Dill,etc.?.Which strategy the protein folding process follows is still at a controversial stage.Judging from the results of recent theoretical and experimental studies,the second view seems to prevail.If this problem is viewed from the perspective of consequentialism,the hypothesis that can quantitatively explain the folding rate of most proteins should be more reasonable.Based on the idea of limited conformation search space,the conformation search space was reduced from two different approaches,and two models for quantitatively predicting the folding rate of proteins were proposed.Protein folding rates range from 10^-3s^-1 to 10⁶s^-1 across 9 orders of magnitude.Although the folding rates of various proteins vary widely,the folding rates were very insensitive to the structural details of the protein.The distribution of the protein's backbone torsion angles determines its structural framework.Therefore,our group proposed a coarse-grained structure description parameter--cumulative backbone torsion angles?CBTA?between 2015 and 2017.This parameter was a possible representation of the conformational space that the protein folding searches for.And it was not only related to the size of the protein,but also to the structural topology of the protein.Huang,Liang,and Wang applied this parameter to different datasets to test the prediction performances of protein folding rates.The results shown that the parameter's ability to predict the folding rates was efficient and stable.Based on these studies,some ideas were raised.Is there a redundancy in the size of the conformational search space represented by the CBTA?Was it possible to further reduce the conformation space and ensure that the prediction accuracy of the folding rate was not reduced or even improved?Based on this idea,a parameter--effective cumulative backbone torsion angles(CBTA_eff)was defined,which may be a more accurate representation of the conformational search space.CBTA_eff was based on CBTA and only considered the torsional contribution of the optimal amino acid.This parameter ignored the torsional contribution of amino acids,which were not important in folding kinetics and thermodynamics.That is,the conformation search process only spends time on the conformational arrangements of those important amino acids.As expected,the results of CBTA_eff testing on multiple large protein folding rate experimental data sets showed the same prediction accuracy and stability as CBTA.This result indicated that the conformation space to be searched for during protein folding should be only a small part of the entire conformation space,so that it can quickly find the natural state conformation.In addition,if the folding of protein residues and searching with mechanism images only occur at the secondary structure level and the secondary structure is packaged into a tertiary structure through non-local interaction,the cost of conformation search will be greatly reduced,thereby achieving rapid folding.Based on this assumption,Rollins and Dill proposed the“Foldon Funnel Model”with secondary structure as the folding unit in2014.The model successfully estimated the folding rate of 93 proteins across 9 orders of magnitude,and the coefficient of determination between the predicted value and the experimental value was R²=0.63.Finkelstein and Garbuzynskiy successfully explained the Levinthal's paradox based on the assumption that the folding units were secondary structures.Englander et al.used hydrogen exchange?HX?experimental technique to study the folding process of several proteins,and proposed the foldon hypothesis that the protein gradually folded.These theoretical and experimental studies depicted similar folded landscape,which narrows the folded conformation search space to the secondary structures.Following this idea,the secondary structures were taken as folding units.Based on the transition state theory,a prediction model for protein folding rates was constructed,which based on estimating the folding barrier height using the square root of the number of secondary structures,and estimating the folding rate prefactor using the average number of residues involved in long-range interactions in each secondary structure.It achieved the high coefficient of determination R²=0.73 between the predicted values of the folding rates and the observed values over 159 two-state and multi-state folding proteins.If the influence of the optimal amino acid composition was further considered in the folding rate prefactor,the determination coefficient was slightly increased to R²=0.75.The results were better than the existing empirical models and shown that the number of secondary structures and its configurations were the basic elements for control the folding rates.The model supported the folding landscape that implied by the foldon hypothesis proposed by Englander et al.It provided valuable clues for further study of protein folding mechanisms.In summary,the protein folding process only takes place in a limited conformational space,and the secondary structure is a possible search unit for limited conformational space.In addition,the cooperative effect during the formation of secondary structure was not considered in this study,and this kind of cooperative effect may be one of the important factors to further reduce the conformation search time.This is a possible direction that can be considered in future research.