Summary

Epistasis, in which protein fitness changes in a non-additive way, is rare in natural evolution and laboratory evolution. Simple statistical models with only additive effects can explain most (80-95%) of changes in activity between variants (12). This has been suggested by multiple studies, which found that the effect of mutations that improve Stability and thermostability was basically entirely additive (see figure below). (56) Park et al. were able to model 92-96% of variance in genome fitness by accounting exclusively for single-point and pairwise interactions plus a sigmoid nonlinearity; e.g., less than <5% of genomes in their test set showed third-order interactions. (7) That said, there are examples where linear models are unable to accurately model fitness ((2,1,8) with Spike protein/ACE2), so the type of statistical model still matters.

Details

Sarkisyan et al. found that some mutations killed fluorescence in some GFP backbones but not others, and that pre-existing evolutionary propensity (e.g., from a PSSM) could not predict this. (9) They conclude that this is the result of destabilization. this made an additive model of fluorescence inappropriate; from that perspective epistasis occurred in 30% of multi-substitution variants. They conclude that this is largely due to threshold robustness, and that these mutations are destabilizing. See Mutation memory half life. Anecdotally (8) came to a similar conclusion.

Beltran et al. measured >500k pathogenic variants in human diseases across 500 domains and found that additive models were sufficient to model almost all fitness changes. (3)

Escobedo et al. found that the effects of substitutions in the hydrophobic core of proteins could be explained by linear models. (6)

Alcantar et al. carried out a “combinatorially complete” analysis of mutations introduced during affinity maturation of de novo designed minibinders and found that the binding improvements were basically entirely additive, which is similar to antibodies (Mutations obtained by antibodies during affinity maturation show epistasis in biophysical properties but not binding). (4)

Figures

Ref (5)

Ref (9)

Figure 2 from (1)

See also

1.
Ding D, Shaw AY, Sinai S, Rollins N, Prywes N, Savage DF, et al. Protein design using structure-based residue preferences. Nature Communications. 2024;15(1). Available from: https://doi.org/10.1038/s41467-024-45621-4
2.
Faure AJ, Martí-Aranda A, Hidalgo-Carcedo C, Beltran A, Schmiedel JM, Lehner B. The genetic architecture of protein stability. Nature. 2024;634(8035):995–1003. Available from: https://doi.org/10.1038/s41586-024-07966-0
3.
Beltran A, Jiang X, Shen Y, Lehner B. Site saturation mutagenesis of 500 human protein domains reveals the contribution of protein destabilization to genetic disease. openRxiv; 2024. Available from: https://doi.org/10.1101/2024.04.26.591310
4.
Alcantar MA, Paulk AM, Moradi S, Bhar D, Keller GLJ, Sanyal T, et al. Mapping the evolution of computationally designed protein binders. openRxiv; 2025. Available from: https://doi.org/10.1101/2025.10.04.680454
5.
Peleg Y, Vincentelli R, Collins BM, Chen K-E, Livingstone EK, Weeratunga S, et al. Community-Wide Experimental Evaluation of the PROSS Stability-Design Method. Journal of Molecular Biology. 2021;433(13):166964. Available from: https://doi.org/10.1016/j.jmb.2021.166964
6.
Escobedo A, Voigt G, Faure AJ, Lehner B. Genetics, energetics and allostery during a billion years of hydrophobic protein core evolution. openRxiv; 2024. Available from: https://doi.org/10.1101/2024.05.11.593672
7.
Park Y, Metzger BPH, Thornton JW. The simplicity of protein sequence-function relationships. Nature Communications. 2024;15(1). Available from: https://doi.org/10.1038/s41467-024-51895-5
8.
Tonner PD, Pressman A, Ross D. Interpretable modeling of genotype–phenotype landscapes with state-of-the-art predictive power. Proceedings of the National Academy of Sciences. 2022;119(26). Available from: https://doi.org/10.1073/pnas.2114021119
9.
Sarkisyan KS, Bolotin DA, Meer MV, Usmanova DR, Mishin AS, Sharonov GV, et al. Local fitness landscape of the green fluorescent protein. Nature. 2016;533(7603):397–401. Available from: https://doi.org/10.1038/nature17995