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