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

Abstract

The distribution of fitness effects of protein mutations is still unknown. 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 beta-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 systems, 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 effects, 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.

Biophysics of protein evolution and evolutionary protein biophysics

“…Experiments showed that many natural globular proteins are robust to mutations [40,53,55,202,360]. The observation that proteins with diverse primary sequences can be grouped into families with very similar structure and function gives further illustration of this robustness [361].…”

“…To implement the mutation, the structure is computationally modified; energy is then recalculated and compared against the pre-mutation wild-type value. DDG prediction is widely used to screen large numbers of mutations, often in combination with laboratory experiments [53][54][55][56][57]. The approach has also served as fitness estimators in simulation studies of protein evolution [58,59].…”

The optimal burst of mutation to create a phenotype

“…A fraction L of all mutations are lethal, and a genome dies if it receives one or more lethal mutations. Thus, (1b) In this manifestation of survival, the surviving fraction of the population is the Poisson fraction that escapes lethal mutations (Shafikhani et al, 1997;Bershtein et al, 2006;Bloom et al, 2007). Log-linear survival across changes in U ̅ requires that L be constant.…”

“…The data on protein survival typically violate strict log-linearity with U ̅ , at least for low mutation rates Bloom et al, 2005Bloom et al, , 2007Bershtein et al, 2006). A further distinction between the survival functions used here and some of those applied to protein survival is that the functions here are based on rates or the average number of mutations per genome/gene.…”

“…This function has also been proposed for exact numbers of mutations (Charlesworth, 1990;Bloom et al, 2007) but used to fit average numbers (Bershtein et al, 2006), as we assume here. The optimum U ̅ L is approximately , thus shifted to less than 1 if the log survival curve drops faster than linear and shifted above 1 if the log survival curve bows upward.…”