A Probabilistic Programming Approach to Protein Structure Superposition

Abstract

Optimal superposition of protein structures is crucial for understanding their structure, function, dynamics and evolution. We investigate the use of probabilistic programming to superimpose protein structures guided by a Bayesian model. Our model THESEUS-PP is based on the THESEUS model, a probabilistic model of protein superposition based on rotation, translation and perturbation of an underlying, latent mean structure. The model was implemented in the deep probabilistic programming language Pyro. Unlike conventional methods that minimize the sum of the squared distances, THESEUS takes into account correlated atom positions and heteroscedasticity (i.e., atom positions can feature different variances). THESEUS performs maximum likelihood estimation using iterative expectationmaximization. In contrast, THESEUS-PP allows automated maximum a-posteriori (MAP) estimation using suitable priors over rotation, translation, variances and latent mean structure. The results indicate that probabilistic programming is a powerful new paradigm for the formulation of Bayesian probabilistic models concerning biomolecular structure. Specifically, we envision the use of the THESEUS-PP model as a suitable error model or likelihood in Bayesian protein structure prediction using deep probabilistic programming.Index Terms-protein superposition, Bayesian modelling, deep probabilistic programming, protein structure prediction .

Plant science in the age of simulation intelligence

“…This allows one to sample vines that grow in a specific shape, such as a letter (Ritchie et al, 2016). PPLs have shown success throughout the biological sciences, for example, in inferring phylogeny (Ronquist et al, 2020), protein structure alignment (Moreta et al, 2019) and inferring signaling pathways (Merrell and Gitter, 2020). There are a plethora of PPLs available, many interfacing with scientifically popular programming languages for sciences, for example, Stan (Stan Development Team, 2023), Pyro (Bingham et al, 2019), or Turing (Holt and Cordy, 1988).…”