Exploring the large-scale properties of a protein secondary structure genotype-to-phenotype map

We perform a large-scale computational characterization of the map of protein primary to secondary structure using an AVR3a class protein effector domain from the plant pathogen P. palmivora as a case study. We formulate a modified site-scanning approach for exploring the neutral component of secondary structure phenotypes based on predictions from the machine-learning algorithm Porter 5 and apply it to the AVR3a phenotype. We predict a set of sensitive sites within the effector domain that are generally located at or near the boundaries of structured regions, with restrictions on the possible amino acid residues at these sites dictated by the secondary structure type that they participate in within the WT. We characterize a set of mutated phenotypes derived through the exploration of the neutral component of the WT effector domain, selecting them so that they span a range including both very rarely and very commonly seen secondary structures, and that they include both secondary structures nearly identical to the WT and ones far removed from it. We find that all these diverse phenotypes have an estimated robustness of the same order as that of the WT, and that the robustness scales logarithmically phenotype frequency, as seen in other genotype-to-phenotype maps. Furthermore, we observe that the dependence of the estimated phenotype frequency on the Kolmogorov complexity indicates simplicity bias in the protein secondary structure map.