Global epistasis from a physical learning perspective

Epistasis in proteins refers to the phenomenon where mutations at different amino acid sites interact in a non-additive way to affect protein function. There is now considerable evidence that most epistatic interactions are the result of a nonlinear mapping from an underlying additive trait; this concept is called global epistasis. We study epistasis from a physical learning perspective. We use physical networks that can adapt to perform diverse functions [1,2], such as protein allostery, and apply mutations to its edges. In particular, we examine electrical networks composed of nodes connected by conductive edges with discrete conductance values, mimicking the variety of amino acids in proteins. The network learns by adjusting its edge conductances to minimize a cost function, which penalizes deviations from a target response while satisfying Kirchhoff’s law. This results in a dual optimization process, where conductances are adjusted to lower the cost function, and node voltages minimize power dissipation.

From the cost Hessian, we identify key edges where conductance changes impact the cost function most [1,2]. Then, by applying random mutations we probe the resulting changes in the cost function, drawing parallels with genotype-phenotype maps. Applying current tools to detect global epistasis in real proteins [3,4], we further investigate how interactions between edges affect the network’s overall response. A comparison of the cost Hessian with the global epistasis analysis reveals a strong agreement in the identification of the key edges, providing new insights into the mechanisms that drive global epistasis.

[1] M. Stern, A.J. Liu, V. Balasubramanian, The Physical Effects of Learning, Phys. Rev. E 109, 024311 (2024).

[2] M. Stern, M. Guzman, F. Martins, A.J. Liu, V. Balasubramanian, Physical Networks Become What They Learn, arXiv:2406.09689.

[3] J. Otwinowski, D.M. McCandlish, J.B. Plotkin, Inferring the Shape of Global Epistasis, Proc. Natl. Acad. Sci. USA 115, E7550 (2018).

[4] A. Tareen et al. MAVE-NN: Learning Genotype-phenotype Maps from Multiplex Assays of Variant Effect, Genome Biol. 23, 98 (2022).