Forecasting protein evolution by combining birth-death population models with structurally constrained substitution models

In recent years, evolutionary predictions in population genetics and ecology have increased probably motivated by the improvements in the accuracy of models of evolution. In this regard, we present a forecasting protein evolution method based on evolutionary constraints on the protein folding stability to consider adaptation promoted by selection at the molecular level. In contrast to the unrealistic assumption made in traditional population genetics methods where molecular evolution is simulated separately from the evolutionary history, the present method combines a substitution model of protein evolution and a birth-death population genetics process to simultaneously model forward-in-time protein evolution. For every protein variant, we apply a fitness function that considers the folding stability of the variant to determine its forward-in-time birth-death evolutionary trajectories and, evolve the variant upon them under a structurally constrained substitution model of protein evolution. We implemented the method into a freely available computer framework. Next, we evaluated the accuracy of the predictions with several monitored viral proteins of general interest. In general, the method showed acceptable errors in predicting the folding stability of the forecasted protein variants while, as expected, the errors increased for the prediction of the specific protein sequences. We conclude that forecasting protein evolution can be feasible but further work is required to improve the accuracy of models of evolution, and we provide fundaments for successive approaches for forecasting evolution.