Selection for cooperativity causes epistasis predominately between native contacts and enables epistasis-based structure reconstruction

Abstract

Epistasis and cooperativity of folding both result from networks of energetic interactions in proteins. Epistasis results from energetic interactions among mutants, whereas cooperativity results from energetic interactions during folding that reduce the presence of intermediate states. The two concepts seem intuitively related, but it is unknown how they are related, particularly in terms of selection. To investigate their relationship, we simulated protein evolution under selection for cooperativity and separately under selection for epistasis. Strong selection for cooperativity created strong epistasis between contacts in the native structure but weakened epistasis between nonnative contacts. In contrast, selection for epistasis increased epistasis in both native and nonnative contacts and reduced cooperativity. Because epistasis can be used to predict protein structure only if it preferentially occurs in native contacts, this result indicates that selection for cooperativity may be key for predicting structure using epistasis. To evaluate this inference, we simulated the evolution of guanine nucleotide-binding protein (GB1) with and without cooperativity. With cooperativity, strong epistatic interactions clearly map out the native GB1 structure, while allowing the presence of intermediate states (low cooperativity) obscured the structure. This indicates that using epistasis measurements to reconstruct protein structure may be inappropriate for proteins with stable intermediates.

A computational method for predicting the most likely evolutionary trajectories in the stepwise accumulation of resistance mutations

“…We sought to determine if simulated trajectories using this simple fitness model could capture observed evolutionary trajectories, despite not considering all factors that contribute to DHFR fitness. We simulated the evolutionary trajectories to the quadruple mutants described above for the genes Pf DHFR and Pv DHFR using an evolutionary model, adapted from previous studies ( Eccleston et al, 2021 ; Pollock et al, 2017 ; Pollock et al, 2012 ). In this model, selection acts to reduce the binding affinity between target protein and the antimalarial drug with which the mutations have been associated with resistance.…”

A computational method for predicting the most likely evolutionary trajectories in the step-wise accumulation of resistance mutations

“…Starting from the wild-type protein, with binding free energy Δ G W T and fitness , we extract one sample i from the 250 values of the predicted binding affinity changes for the single mutations to determine the binding free energy after mutation , and calculate the fitness of each single mutant protein . We can calculate the probability the mutation will fix in the population using the Kimura fixation probability for a haploid organism where N e is the effective population size (set to 10 6 as previous models in Eccleston et al (2021 ); Pollock et al (2012 )) and s is the selection coefficient . We also took in to account the mutational bias of Plasmodium falciparum using the nucleotide mutation matrix calculated in Lozovsky et al (2009 ).…”

“…We simulated the evolutionary trajectories to quadruple mutant N51I,C59R,S108N,I164L, using an evolutionary model, adapted from previous studies [42][43][44], in which selection acts to reduce the binding affinity between PfDHFR and pyrimethamine. Briefly, starting from the wild-type protein, we randomly sample a value from the Flex ddG distributions for each of the four single mutations and calculate the fitness of the mutated protein (Eq.…”

“…where Ne is the effective population size (set to 10 as previous models in [43,44]) and s is the selection coefficient 𝑠 = (𝑃 , − 𝑃 )/𝑃 . We also took in to account the mutational bias of Plasmodium falciparum using the nucleotide mutation matrix calculated in [6].…”

“…We simulated the evolutionary trajectories to the quadruple mutants described above for the genes Pf DHFR and PvDHFR using an evolutionary model, adapted from previous studies (Eccleston et al, 2021;Pollock et al, 2012Pollock et al, , 2017. In this model, selection acts to reduce the binding affinity between target protein and the antimalarial drug with which the mutations have been associated with resistance.…”