Abstract
A now classical argument for the marginal thermodynamic stability of proteins explains the distribution of observed protein stabilities as a consequence of an entropic pull in protein sequence space. In particular, most sequences that are sufficiently stable to fold will have stabilities near the folding threshold. Here, we extend this argument to consider its predictions for epistatic interactions for the effects of mutations on the free energy of folding. Although there is abundant evidence to indicate that the effects of mutations on the free energy of folding are nearly additive and conserved over evolutionary time, we show that these observations are compatible with the hypothesis that a non-additive contribution to the folding free energy is essential for observed proteins to maintain their native structure. In particular, through both simulations and analytical results, we show that even very small departures from additivity are sufficient to drive this effect.
Highlights
The relationship between protein sequence, stability, and function has been a subject of intense investigation for decades
The role of epistasis in long-term protein evolution remains a topic of active debate [1,2,3,4,5]
We have explored a surprising phenomenon where the effects of mutations on the ∆G of folding appear to combine nearly additively, and what little epistasis is present plays a critical role, to the extent that observed sequences would not be able to fold in the absence of these epistatic interactions
Summary
The relationship between protein sequence, stability, and function has been a subject of intense investigation for decades. A nuanced appreciation of the high-dimensional nature of protein sequence space has been essential for resolving questions about protein structure, function, and evolution. With some exceptions [7], this view has been largely replaced with a more parsimonious explanation based on the high dimensionality of sequence space: Marginal stabilities are observed because, far more sequences are marginally stable than maximally stable [8]. The field today has mostly settled on a synthetic understanding of how simple biophysical models of energy and folding, along with the structure of sequence space, conspire to explain the distribution of protein stabilities observed in nature [1,2,3,4,5]
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