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Boltzmann machines (BM) are widely used as generative models. For example, pairwise Potts models (PM), which are instances of the BM class, provide accurate statistical models of families of evolutionarily related protein sequences. Their parameters are the local fields, which describe site-specific patterns of amino-acid conservation, and the two-site couplings, which mirror the coevolution between pairs of sites. This coevolution reflects structural and functional constraints acting on protein sequences during evolution. The most conservative choice to describe the coevolution signal is to include all possible two-site couplings into the PM. This choice, typical of what is known as Direct Coupling Analysis, has been successful for predicting residue contacts in the three-dimensional structure, mutational effects, and in generating new functional sequences. However, the resulting PM suffers from important over-fitting effects: many couplings are small, noisy and hardly interpretable; the PM is close to a critical point, meaning that it is highly sensitive to small parameter perturbations. In this work, we introduce a general parameter-reduction procedure for BMs, via a controlled iterative decimation of the less statistically significant couplings, identified by an information-based criterion that selects either weak or statistically unsupported couplings. For several protein families, our procedure allows one to remove more than $90%$ of the PM couplings, while preserving the predictive and generative properties of the original dense PM, and the resulting model is far away from criticality, hence more robust to noise.
Proteins are essential components of living systems, capable of performing a huge variety of tasks at the molecular level, such as recognition, signalling, copy, transport, ... The protein sequences realizing a given function may largely vary across
Background: Typically, proteins perform key biological functions by interacting with each other. As a consequence, predicting which protein pairs interact is a fundamental problem. Experimental methods are slow, expensive, and may be error prone. Man
Determining which proteins interact together is crucial to a systems-level understanding of the cell. Recently, algorithms based on Direct Coupling Analysis (DCA) pairwise maximum-entropy models have allowed to identify interaction partners among par
Significant progress in computer hardware and software have enabled molecular dynamics (MD) simulations to model complex biological phenomena such as protein folding. However, enabling MD simulations to access biologically relevant timescales (e.g.,
Generative modeling for protein engineering is key to solving fundamental problems in synthetic biology, medicine, and material science. We pose protein engineering as an unsupervised sequence generation problem in order to leverage the exponentially