BICePs v2.0: Software for Ensemble Reweighting Using Bayesian Inference of Conformational Populations.

Bayesian Inference of Conformational Populations (BICePs) version 2.0 (v2.0) is a free, open-source Python package that reweights theoretical predictions of conformational state populations using sparse and/or noisy experimental measurements. In this article, we describe the implementation and usage of the latest version of BICePs (v2.0), a powerful, user-friendly and extensible package which makes several improvements upon the previous version. The algorithm now supports many experimental NMR observables (NOE distances, chemical shifts, J-coupling constants, and hydrogen-deuterium exchange protection factors), and enables convenient data preparation and processing. BICePs v2.0 can perform automatic analysis of the sampled posterior, including visualization, and evaluation of statistical significance and sampling convergence. We provide specific coding examples for these topics, and present a detailed example illustrating how to use BICePs v2.0 to reweight a theoretical ensemble using experimental measurements.

Expanded ensemble predictions of absolute binding free energies in the SAMPL9 host-guest challenge.

As part of the SAMPL9 community-wide blind host-guest challenge, we implemented an expanded ensemble workflow to predict absolute binding free energies for 13 small molecules against pillar[6]arene. Notable features of our protocol include consideration of a variety of protonation and enantiomeric states for both host and guests, optimization of alchemical intermediates, and analysis of free energy estimates and their uncertainty using large numbers of simulation replicates performed using distributed computing. Our predictions of absolute binding free energies resulted in a mean absolute error of 2.29 kcal mol-1 and an R2 of 0.54. Overall, results show that expanded ensemble calculations using all-atom molecular dynamics simulations are a valuable and efficient computational tool in predicting absolute binding free energies.

Stacking Gaussian processes to improve [Formula: see text] predictions in the SAMPL7 challenge.

Accurate predictions of acid dissociation constants are essential to rational molecular design in the pharmaceutical industry and elsewhere. There has been much interest in developing new machine learning methods that can produce fast and accurate pKa predictions for arbitrary species, as well as estimates of prediction uncertainty. Previously, as part of the SAMPL6 community-wide blind challenge, Bannan et al. approached the problem of predicting [Formula: see text]s by using a Gaussian process regression to predict microscopic [Formula: see text]s, from which macroscopic [Formula: see text] values can be analytically computed (Bannan et al. in J Comput-Aided Mol Des 32:1165-1177). While this method can make reasonably quick and accurate predictions using a small training set, accuracy was limited by the lack of a sufficiently broad range of chemical space in the training set (e.g., the inclusion of polyprotic acids). Here, to address this issue, we construct a deep Gaussian Process (GP) model that can include more features without invoking the curse of dimensionality. We trained both a standard GP and a deep GP model using a database of approximately 3500 small molecules curated from public sources, filtered by similarity to targets. We tested the model on both the SAMPL6 and more recent SAMPL7 challenge, which introduced a similar lack of ionizable sites and/or environments found between the test set and the previous training set. The results show that while the deep GP model made only minor improvements over the standard GP model for SAMPL6 predictions, it made significant improvements over the standard GP model in SAMPL7 macroscopic predictions, achieving a MAE of 1.5 [Formula: see text].

Automatic Forward Model Parameterization with Bayesian Inference of Conformational Populations.

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 ( ϕ ) between interacting nuclei. We validate this approach first with a toy model system, and then for human ubiquitin, predicting six sets of Karplus parameters for J H N H α 3 , J H α C ' 3 , J H N C ß 3 , J H N C ' 3 , J C ' C ß 3 , J C ' C ' 3 . This approach, which does not rely on any predetermined parameterization, enhances predictive accuracy and can be used for many applications.

Markov State Model of Solvent Features Reveals Water Dynamics in Protein-Peptide Binding.

In this work, we investigate the role of solvent in the binding reaction of the p53 transactivation domain (TAD) peptide to its receptor MDM2. Previously, our group generated 831 µs of explicit-solvent aggregate molecular simulation trajectory data for the MDM2-p53 peptide binding reaction using large-scale distributed computing and subsequently built a Markov State Model (MSM) of the binding reaction (Zhou et al. 2017). Here, we perform a tICA analysis and construct an MSM with similar hyperparameters while using only solvent-based structural features. We find a remarkably similar landscape but accelerated implied timescales for the slowest motions. The solvent shells contributing most to the first tICA eigenvector are those centered on Lys24 and Thr18 of the p53 TAD peptide in the range of 3-6 Å. Important solvent shells were visualized to reveal solvation and desolvation transitions along the peptide-protein binding trajectories. Our results provide a solvent-centric view of the hydrophobic effect in action for a realistic peptide-protein binding scenario.

Reconciling Simulations and Experiments With BICePs: A Review.

Bayesian Inference of Conformational Populations (BICePs) is an algorithm developed to reconcile simulated ensembles with sparse experimental measurements. The Bayesian framework of BICePs enables population reweighting as a post-simulation processing step, with several advantages over existing methods, including the proper use of reference potentials, and the estimation of a Bayes factor-like quantity called the BICePs score for model selection. Here, we summarize the theory underlying this method in context with related algorithms, review the history of BICePs applications to date, and discuss current shortcomings along with future plans for improvement.