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Robustness–epistasis link shapes the fitness landscape of a randomly drifting protein


The distribution of fitness effects of protein mutations is still unknown1,2. Of particular interest is whether accumulating deleterious mutations interact, and how the resulting epistatic effects shape the protein’s fitness landscape. Here we apply a model system in which bacterial fitness correlates with the enzymatic activity of TEM-1 β-lactamase (antibiotic degradation). Subjecting TEM-1 to random mutational drift and purifying selection (to purge deleterious mutations) produced changes in its fitness landscape indicative of negative epistasis; that is, the combined deleterious effects of mutations were, on average, larger than expected from the multiplication of their individual effects. As observed in computational systems3,4,5, negative epistasis was tightly associated with higher tolerance to mutations (robustness). Thus, under a low selection pressure, a large fraction of mutations was initially tolerated (high robustness), but as mutations accumulated, their fitness toll increased, resulting in the observed negative epistasis. These findings, supported by FoldX stability computations of the mutational effects6, prompt a new model in which the mutational robustness (or neutrality) observed in proteins, and other biological systems, is due primarily to a stability margin, or threshold, that buffers the deleterious physico-chemical effects of mutations on fitness. Threshold robustness is inherently epistatic—once the stability threshold is exhausted, the deleterious effects of mutations become fully pronounced, thereby making proteins far less robust than generally assumed.

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We thank F. Kondrashov for insights and inspiration, L. Serrano, U. Alon and G. Schreiber for contributions, and our Department, Institute and the Feinberg Graduate School, for uncompromising support. Author Contributions S.B. designed, performed and analysed the experiments. M.S. and R.B. provided technical assistance. N.T. performed the FoldX computations and helped devise the model. D.S.T. designed and supervised the experiments, and devised the model. S.B. and D.S.T. wrote the manuscript.

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Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests.

Correspondence to Dan S. Tawfik.

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Supplementary Notes

This file contains the Supplementary Methods, Supplementary Figures 1–7 and Supplementary Tables 1–4. (PDF 465 kb)

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Further reading

Figure 1: Negative epistasis underlines the random drift of TEM-1.
Figure 2: The correlation between mutational robustness and negative epistasis.
Figure 3: The physico-chemical and fitness changes accompanying random drifts.


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