Searching for a mechanistic description of pairwise epistasis in protein systems
Jonathan E. Barnes1,3*, Craig R. Miller2,3, F. Marty Ytreberg1,3,4
1 Department of Physics, University of Idaho, Moscow, ID, United States of America, 2 Department of Biological Sciences, University of Idaho, Moscow, ID, United States of America 3 Institute for Modeling Collaboration and Innovation, University of Idaho, Moscow, ID, United States of America, 4 Institute for Bioinformatics and Evolutionary Studies, University of Idaho, Moscow, ID, United States of America *jonathan@barnes.science
Acknowledgements
The research was supported by the Center for Modeling Complex Interactions sponsored by the National Institute of General Medical Sciences (https://www.nigms.nih.gov) under award number P20 GM104420 and the National Science Foundation (https://www.nsf.gov) EPSCoR Track-II under award number OIA1736253. Computer resources were provided in part by the Institute for Bioinformatics and Evolutionary Studies Computational Resources Core sponsored by the National Institutes of Health (NIH P30 GM103324). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Abstract
When two or more amino acid mutations occur in protein systems, they can interact in a non-additive fashion termed epistasis. One way to quantify epistasis between mutation pairs in protein systems is by using free energy differences: ϵ = 𝚫𝚫G1,2 - (𝚫𝚫G1 + 𝚫𝚫G2) where 𝚫𝚫G refers to the change in the Gibbs free energy, subscripts 1 and 2 refer to single mutations in arbitrary order and 1,2 refers to the double mutant. In this study, we explore possible biophysical mechanisms that drive pairwise epistasis in both protein-protein binding affinity and protein folding stability. Using the largest available datasets containing experimental protein structures and free energy data, we derived statistical models for both binding and folding epistasis (ϵ) with similar explanatory power (R2) of 0.299 and 0.258, respectively. These models contain terms and interactions that are consistent with intuition. For example, increasing the Cartesian separation between mutation sites leads to a decrease in observed epistasis for both folding and binding. Our results provide insight into factors that contribute to pairwise epistasis in protein systems and their importance in explaining epistasis. However, the low explanatory power indicates that more study is needed to fully understand this phenomenon.
Keywords: epistasis, binding affinity, folding stability, non-additivity, statistical modeling