Colin LaMont

Michael N. Pun, Andrew Ivanov, Quinn Bellamy et al.

Proteins play a central role in biology from immune recognition to brain activity. While major advances in machine learning have improved our ability to predict protein structure from sequence, determining protein function from structure remains a major challenge. Here, we introduce Holographic Convolutional Neural Network (H-CNN) for proteins, which is a physically motivated machine learning approach to model amino acid preferences in protein structures. H-CNN reflects physical interactions in a protein structure and recapitulates the functional information stored in evolutionary data. H-CNN accurately predicts the impact of mutations on protein function, including stability and binding of protein complexes. Our interpretable computational model for protein structure-function maps could guide design of novel proteins with desired function.

Jakub Otwinowski, Colin LaMont

Evolutionary algorithms, inspired by natural evolution, aim to optimize difficult objective functions without computing derivatives. Here we detail the relationship between population genetics and evolutionary optimization and formulate a new evolutionary algorithm. Optimization of a continuous objective function is analogous to searching for high fitness phenotypes on a fitness landscape. We summarize how natural selection moves a population along the non-euclidean gradient that is induced by the population on the fitness landscape (the natural gradient). Under normal approximations common in quantitative genetics, we show how selection is related to Newton's method in optimization. We find that intermediate selection is most informative of the fitness landscape. We describe the generation of new phenotypes and introduce an operator that recombines the whole population to generate variants that preserve normal statistics. Finally, we introduce a proof-of-principle algorithm that combines natural selection, our recombination operator, and an adaptive method to increase selection. Our algorithm is similar to covariance matrix adaptation and natural evolutionary strategies in optimization, and has similar performance. The algorithm is extremely simple in implementation with no matrix inversion or factorization, does not require storing a covariance matrix, and may form the basis of more general model-based optimization algorithms with natural gradient updates.