Infer global, predict local: Quantity-relevance trade-off in protein fitness predictions from sequence data

Predicting the effects of mutations on protein function is an important issue in evolutionary biology and biomedical applications. Computational approaches, ranging from graphical models to deep-learning architectures, can capture the statistical properties of sequence data and predict the outcome of high-throughput mutagenesis experiments probing the fitness landscape around some wild-type protein. However, how the complexity of the models and the characteristics of the data combine to determine the predictive performance remains unclear. Here, based on a theoretical analysis of the prediction error, we propose descriptors of the sequence data, characterizing their quantity and relevance relative to the model. Our theoretical framework identifies a trade-off between these two quantities, and determines the optimal subset of data for the prediction task, showing that simple models can outperform complex ones when inferred from adequately-selected sequences. We also show how repeated subsampling of the sequence data is informative about how much epistasis in the fitness landscape is not captured by the computational model. Our approach is illustrated on several protein families, as well as on in silico solvable protein models.Author summary: Is more data always better? Or should one prefer fewer data, but of higher relevance to the task to be performed? Here, we investigate this question in the context of the prediction of fitness effects resulting from mutations to a wild-type protein. We show, based on theory and data analysis, that simple models trained on a small subset of carefully chosen sequence data can perform better than complex ones trained on all available data. Furthermore, we explain how comparing the simple local models obtained with different subsets of training data reveals how much of the epistatic interactions shaping the fitness landscape are left unmodeled.