Measuring Selection Across HIV Gag: Combining Physico-Chemistry and Population Genetics

Abstract

We present physico-chemical based model grounded in population genetics. Our model predicts the stationary probability of observing an amino acid residue at a given site. Its predictions are based on the physico-chemical properties of the inferred optimal residue at that site and the sensitivity of the proteins functionality to deviation from the physico-chemical optimum at that site. We contextualize our physico-chemical model by comparing our model fit and parameters it to the more general, but less biologically meaningful entropy based metric: site sensitivity or 1/E. We show mathematically that our physico-chemical model is a more restricted form of the entropy model and how 1/E is proportional to the log-likelihood of a parameter-wise saturated model. Next, we fit both our physico-chemical and entropy models to sequences for subtype Cs Gag poly-protein in the LANL HIV database. Comparing our models site sensitivity parameters G' to 1/E we find they are highly correlated. We also compare the ability of G', 1/E, and other indirect measures of HIV fitness to empirical in vitro and in vivo measures. We find G' does a slightly better job predicting empirical fitness measures of in vivo viral escape time and in vitro spreading rates. While our predictive gain is modest, our model can be modified to test more complex or alternative biological hypotheses. More generally, because of its explicit biological formulation, our model can be easily extended to test for stabilizing vs. diversifying selection. We conjecture that our model could also be extended include epistasis in a more realistic manner than Ising models, while requiring many fewer parameters than Potts models.