Functional bottlenecks can emerge from non-epistatic underlying traits

Protein fitness landscapes frequently exhibit epistasis, where the effect of a mutation depends on the genetic context in which it occurs, i.e., the rest of the protein sequence. Epistasis increases landscape complexity, often resulting in multiple fitness peaks. In its simplest form, known as global epistasis, fitness is modeled as a non-linear function of an underlying additive trait. In contrast, more complex epistasis arises from a network of (pairwise or many-body) interactions between residues, which cannot be removed by a single non-linear transformation. Recent studies have explored how global and network epistasis contribute to the emergence of functional bottlenecks - fitness landscape topologies where two broad high-fitness basins, representing distinct phenotypes, are separated by a bottleneck that can only be crossed via one or a few mutational paths. Here, we introduce and analyze a stylized model of global epistasis with an additive underlying trait. We demonstrate that functional bottlenecks arise with high probability if the model is properly calibrated. Furthermore, our results underscore that a proper balance between neutral and non-neutral mutations is needed for the emergence of functional bottlenecks. Author SummaryA central challenge in the study of protein evolution is understanding how interactions between mutations in-fluence evolutionary dynamics. These interactions, collectively known as epistasis, play a key role in shaping protein fitness landscapes, representing maps between amino acid sequences and their functional performance. However, the impact of epistasis on landscape ruggedness and accessibility remains a subject of debate. Recent experiments have revealed the existence of functional bottlenecks: regions of low fitness that restrict evolutionary transitions between proteins with different functionalities. While these bottlenecks represent a significant constraint on evolutionary outcomes and are often attributed to complex networks of interacting mutations, we demonstrate that they can arise in a much simpler setting. Using a stylized model where fitness depends nonlinearly on an underlying additive trait, we show that functional bottlenecks do not require complex network epistasis. Instead, they can emerge from the inherent variability of the mutational effect distribution. Specifically, these bottlenecks arise when the mutational landscape is dominated by small, nearly neutral effects, but remains punctuated by enough strongly non-neutral mutations to create sharp fitness transitions. Our findings offer a new perspective on the constraints shaping protein evolution and highlight the critical role of mutational effect hetero-geneity in determining evolutionary accessibility.