Overcoming extrapolation challenges of deep learning by incorporating physics in protein sequence-function modeling

Understanding protein sequence-to-function relationship is crucial to assist studies of genetic diseases, protein evolution, and protein engineering. The sequence-to-function relationship of proteins is inherently complex due to multi-site high-dimensional correlation and structural dynamics. Deep learning algorithms such as (graph) convolutional neural networks and recently transformers have become very popular for learning the protein sequence-to-function mapping from deep mutational scanning data and available structures. However, it remains very challenging for these models to achieve accurate extrapolation when predicting functional effect of variants with positions or mutation types not seen in the training data. We propose that incorporating the physics of protein interactions and dynamics can be an effective approach to overcome the extrapolation limitations. Specifically, we demonstrate that biophysics-based modeling can be used to quantify the energetic effects of mutations and that incorporating these physical energetics directly within the convolution and graph convolution neural networks can significantly improve the performance of positional and mutational extrapolation compared to models without biophysics-inspired features. Our results support the effectiveness of leveraging physical knowledge in overcoming the limitation of data scarcity.