Using First Passage Statistics to Extract Environmentally Dependent Amino Acid Correlations

In this work, we study the first passage statistics of amino acid primary sequences, that is the probability of observing an amino acid for the first time at a certain number of residues away from a fixed amino acid. By using this rich mathematical framework, we are able to capture the background distribution for an organism, and infer lengths at which the first passage has a probability that differs from what is expected. While many features of an organism’s genome are due to natural selection, others are related to amino acid chemistry and the environment in which an organism lives, constraining the randomness of genomes upon which selection can further act. We therefore use this approach to infer amino acid correlations, and then study how these correlations vary across a wide range of organisms under a wide range of optimal growth temperatures. We find a nearly universal exponential background distribution, consistent with the idea that most amino acids are globally uncorrelated from other amino acids in genomes. When we are able to extract significant correlations, these correlations are reliably dependent on optimal growth temperature, across phylogenetic boundaries. Some of the correlations we extract, such as the enhanced probability of finding, for the first time, a cysteine three residues away from a cysteine or glutamic acid two residues away from an arginine, likely relate to thermal stability. However, other correlations, likely appearing on alpha helical surfaces, have a less clear physiochemical interpretation and may relate t