Automatic Forward Model Parameterization with Bayesian Inference of Conformational Populations

TL;DR

This paper introduces an advanced Bayesian inference framework, BICePs, for refining forward model parameters in structural ensemble predictions, improving agreement with experimental data, and validating force fields using conformational data.

Contribution

It develops two novel methods for optimizing forward model parameters within a Bayesian framework, enhancing force field validation and parameter refinement.

Findings

Refined Karplus relation parameters for J-coupling prediction.

Validated the approach with a toy model and human ubiquitin.

Demonstrated generalization to any differentiable forward model.

Abstract

To quantify how well theoretical predictions of structural ensembles agree with experimental measurements, we depend on the accuracy of forward models. These models are computational frameworks that generate observable quantities from molecular configurations based on empirical relationships linking specific molecular properties to experimental measurements. Bayesian Inference of Conformational Populations (BICePs) is a reweighting algorithm that reconciles simulated ensembles with ensemble-averaged experimental observations, even when such observations are sparse and/or noisy. This is achieved by sampling the posterior distribution of conformational populations under experimental restraints as well as sampling the posterior distribution of uncertainties due to random and systematic error. In this study, we enhance the algorithm for the refinement of empirical forward model (FM) parameters. We introduce and evaluate two novel methods for optimizing FM parameters. The first method treats FM parameters as nuisance parameters, integrating over them in the full posterior distribution. The second method employs variational minimization of a quantity called the BICePs score that reports the free energy of `turning on` the experimental restraints. This technique, coupled with improved likelihood functions for handling experimental outliers, facilitates force field validation and optimization, as illustrated in recent studies (Raddi et al. 2023, 2024). Using this approach, we refine parameters that modulate the Karplus relation, crucial for accurate predictions of J-coupling constants based on dihedral angles between interacting nuclei. We validate this approach first with a toy model system, and then for human ubiquitin, predicting six sets of Karplus parameters. Finally, we demonstrate that our framework naturally generalizes optimization to any differentiable forward model...