Mi3-GPU: MCMC-based inverse Ising inference on GPUs for protein covariation analysis

Abstract

Inverse Ising inference is a method for inferring the coupling parameters of a Potts/Ising model based on observed site-covariation, which has found important applications in protein physics for detecting interactions between residues in protein families. We introduce Mi3-GPU (“mee-three”, for MCMC Inverse Ising Inference) software for solving the inverse Ising problem for protein-sequence datasets with few analytic approximations, by parallel Markov-Chain Monte Carlo sampling on GPUs. We also provide tools for analysis and preparation of protein-family Multiple Sequence Alignments (MSAs) to account for finite-sampling issues, which are a major source of error or bias in inverse Ising inference. Our method is “generative” in the sense that the inferred model can be used to generate synthetic MSAs whose mutational statistics (marginals) can be verified to match the dataset MSA statistics up to the limits imposed by the effects of finite sampling. Our GPU implementation enables the construction of models which reproduce the covariation patterns of the observed MSA with a precision that is not possible with more approximate methods. The main components of our method are a GPU-optimized algorithm to greatly accelerate MCMC sampling, combined with a multi-step Quasi-Newton parameter-update scheme using a “Zwanzig reweighting” technique. We demonstrate the ability of this software to produce generative models on typical protein family datasets for sequence lengths L∼300 with 21 residue types with tens of millions of inferred parameters in short running times. Program summaryProgram Title: Mi3-GPUProgram Files doi:http://dx.doi.org/10.17632/ftbcfy2p35.1Licensing provisions: GPLv3Programming languages: Python3, OpenCL, CNature of problem: Mi3-GPU solves the inverse Ising problem for application in protein covariation analysis. The goal is to infer “coupling” parameters between positions in a Multiple Sequence Alignment of a protein family, with many applications including protein-contact prediction and fitness prediction.Solution method: Mi3-GPU solves the inverse Ising problem with few approximations using Markov-Chain Monte Carlo methods with Quasi-Newton optimization on GPUs. This problem previously has been approached by more approximate methods using analytic approximations including “message Passing”, “Susceptibility Propagation”, “mean-field” methods, pseudolikelihood approximations, and cluster expansion. The software leverages GPU to accelerate MCMC sampling and a histogram reweighting technique to accelerate parameter optimization.