Fragment libraries are often used in protein structure prediction, simulation and design as a means to significantly reduce the vast conformational search space. Current state-of-the-art methods for fragment library generation do not properly account for aleatory and epistemic uncertainty, respectively due to the dynamic nature of proteins and experimental errors in protein structures. Additionally, they typically rely on information that is not generally or readily available, such as homologous sequences, related protein structures and other complementary information. To address these issues, we developed BIFROST, a novel take on the fragment library problem based on a Deep Markov Model architecture combined with directional statistics for angular degrees of freedom, implemented in the deep probabilistic programming language Pyro. BIFROST is a probabilistic, generative model of the protein backbone dihedral angles conditioned solely on the amino acid sequence. BIFROST generates fragment libraries with a quality on par with current state-of-the-art methods at a fraction of the run-time, while requiring considerably less information and allowing efficient evaluation of probabilities.

Optimally superimposing protein structures is essential to study their structure, function, dynamics and evolution. We present THESEUS NUTS (No U-Turn Sampler), a Bayesian version of the THESEUS model [1] -[3] which relies on maximum likelihood estimation. The probabilistic model interprets each protein as a rotated and translated noisy observation of a latent mean structure. Unlike conventional methods [4], THESEUS takes into account the differences in correlations between the atoms in the structure. This paper extends the previous THESEUS MAP (Maximum A Posteriori) model, [5] to full Bayesian inference by making use of the iterative NUTS [6], a Hamiltonian Monte Carlo method. The model delivers consistent results and is computationally efficient thanks to its implementation in the probabilistic programming language NumpPyro [7], [8] which in turn relies upon JAX [9], a system for high-performance machine learning.

Optimal superposition of protein structures or other biological molecules is crucial for understanding their structure, function, dynamics and evolution. Here, 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 probabilistic programming language Pyro. Unlike conventional methods that minimize the sum of the squared distances, THESEUS takes into account correlated atom positions and heteroscedasticity (ie. atom positions can feature different variances). THESEUS performs maximum likelihood estimation using iterative expectation-maximization. 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.