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Abstract Protein sequence evolution in the presence of epistasis makes many previously acceptable amino acid residues at a site unfavorable over time. This phenomenon of entrenchment has also been observed with neutral substitutions using Potts Hamiltonian models. Here, we show that simulations using these models often evolve non-neutral proteins. We introduce a Neutral-with-Epistasis (N×E) model that incorporates purifying selection to conserve fitness, a requirement of neutral evolution. N×E protein evolution revealed a surprising lack of entrenchment, with site-specific amino-acid preferences remaining remarkably conserved, in biologically realistic time frames despite extensive residue coupling. Moreover, we found that the overdispersion of the molecular clock is caused by rate variation across sites introduced by epistasis in individual lineages, rather than by historical contingency. Therefore, substitutional entrenchment and rate contingency may indicate that adaptive and other non-neutral evolutionary processes were at play during protein evolution. 

The voltage dependence of different voltage-gated potassium channels, described by the voltage at which half of the channels are open (V1/2), varies over a range of 80 mV and is influenced by factors such as the number of positive gating charges and the identity of the hydrophobic amino acids in the channel’s voltage sensor (S4). Here we explore by experimental manipulations and molecular dynamics simulation the contributions of two derived features of an electric fish potassium channel (Kv1.7a) that is among the most voltage-sensitive Shaker family potassium channels known. These are a patch of four contiguous negatively charged glutamates in the S3-S4 extracellular loop and a glutamate in the S3b helix. We find that these negative charges affect V1/2 by separate, complementary mechanisms. In the closed state, the S3-S4 linker negative patch reduces the membrane surface charge biasing the channel to enter the open state while, upon opening, the negative amino acid in the S3b helix faces the second (R2) gating charge of the voltage sensor electrostatically biasing the channel to remain in the open state. This work highlights two evolutionary novelties that illustrate the potential influence of negatively charged amino acids in extracellular loops and adjacent helices to voltage dependence. 

Abstract Invariant sites are a common feature of amino acid sequence evolution. The presence of invariant sites is frequently attributed to the need to preserve function through site-specific conservation of amino acid residues. Amino acid substitution models without a provision for invariant sites often fit the data significantly worse than those that allow for an excess of invariant sites beyond those predicted by models that only incorporate rate variation among sites (e.g., a Gamma distribution). An alternative is epistasis between sites to preserve residue interactions that can create invariant sites. Through computer-simulated sequence evolution, we evaluated the relative effects of site-specific preferences and site-site couplings in the generation of invariant sites and the modulation of the rate of molecular evolution. In an analysis of ten major families of protein domains with diverse sequence and functional properties, we find that the negative selection imposed by epistasis creates many more invariant sites than site-specific residue preferences alone. Further, epistasis plays an increasingly larger role in creating invariant sites over longer evolutionary periods. Epistasis also dictates rates of domain evolution over time by exerting significant additional purifying selection to preserve site couplings. These patterns illuminate the mechanistic role of epistasis in the processes underlying observed site invariance and evolutionary rates. 

Transient receptor potential (TRP) proteins are a large family of cation-selective channels, surpassed in variety only by voltage-gated potassium channels. Detailed molecular mechanisms governing how membrane voltage, ligand binding, or temperature can induce conformational changes promoting the open state in TRP channels are still a matter of debate. Aiming to unveil distinctive structural features common to the transmembrane domains within the TRP family, we performed phylogenetic reconstruction, sequence statistics, and structural analysis over a large set of TRP channel genes. Here, we report an exceptionally conserved set of residues. This fingerprint is composed of twelve residues localized at equivalent three-dimensional positions in TRP channels from the different subtypes. Moreover, these amino acids are arranged in three groups, connected by a set of aromatics located at the core of the transmembrane structure. We hypothesize that differences in the connectivity between these different groups of residues harbor the apparent differences in coupling strategies used by TRP subgroups. 

Abstract Potts models and variational autoencoders (VAEs) have recently gained popularity as generative protein sequence models (GPSMs) to explore fitness landscapes and predict mutation effects. Despite encouraging results, current model evaluation metrics leave unclear whether GPSMs faithfully reproduce the complex multi-residue mutational patterns observed in natural sequences due to epistasis. Here, we develop a set of sequence statistics to assess the “generative capacity” of three current GPSMs: the pairwise Potts Hamiltonian, the VAE, and the site-independent model. We show that the Potts model’s generative capacity is largest, as the higher-order mutational statistics generated by the model agree with those observed for natural sequences, while the VAE’s lies between the Potts and site-independent models. Importantly, our work provides a new framework for evaluating and interpreting GPSM accuracy which emphasizes the role of higher-order covariation and epistasis, with broader implications for probabilistic sequence models in general.