Bayesian inference of protein structure from chemical shift data

Harris S, Ramanathan A. Intelligent resolution: Integrating Cryo-EM with AI-driven multi-resolution simulations to observe the severe acute respiratory syndrome coronavirus-2 replication-transcription machinery in action

The severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) replication transcription complex (RTC) is a multi-domain protein responsible for replicating and transcribing the viral mRNA inside a human cell. Attacking RTC function with pharmaceutical compounds is a pathway to treating COVID-19. Conventional tools, e.g., cryo-electron microscopy and all-atom molecular dynamics (AAMD), do not provide sufficiently high resolution or timescale to capture important dynamics of this molecular machine. Consequently, we develop an innovative workflow that bridges the gap between these resolutions, using mesoscale fluctuating finite element analysis (FFEA) continuum simulations and a hierarchy of AI-methods that continually learn and infer features for maintaining consistency between AAMD and FFEA simulations. We leverage a multi-site distributed workflow manager to orchestrate AI, FFEA, and AAMD jobs, providing optimal resource utilization across HPC centers. Our study provides unprecedented access to study the SARS-CoV-2 RTC machinery, while providing general capability for AI-enabled multi-resolution simulations at scale.

Exploring the quality of protein structural models from a Bayesian perspective

We explore how ideas and practices common in Bayesian modeling can be applied to help assess the quality of 3D protein structural models. The basic premise of our approach is that the evaluation of a Bayesian statistical model's fit may reveal aspects of the quality of a structure when the fitted data is related to protein structural properties. Therefore, we fit a Bayesian hierarchical linear regression model to experimental and theoretical ¹³ C^α chemical shifts. Then, we propose two complementary approaches for the evaluation of such fitting: (a) in terms of the expected differences between experimental and posterior predicted values; (b) in terms of the leave-one-out cross-validation point-wise predictive accuracy. Finally, we present visualizations that can help interpret these evaluations. The analyses presented in this article are aimed to aid in detecting problematic residues in protein structures. The code developed for this work is available on: https://github.com/BIOS-IMASL/Hierarchical-Bayes-NMR-Validation.

Informing NMR experiments with molecular dynamics simulations to characterize the dominant activated state of the KcsA ion channel

As the first potassium channel with an x-ray structure determined, and given its homology to eukaryotic channels, the pH-gated prokaryotic channel KcsA has been extensively studied. Nevertheless, questions related, in particular, to the allosteric coupling between its gates remain open. The many currently available x-ray crystallography structures appear to correspond to various stages of activation and inactivation, offering insights into the molecular basis of these mechanisms. Since these studies have required mutations, complexation with antibodies, and substitution of detergents in place of lipids, examining the channel under more native conditions is desirable. Solid-state nuclear magnetic resonance (SSNMR) can be used to study the wild-type protein under activating conditions (low pH), at room temperature, and in bacteriomimetic liposomes. In this work, we sought to structurally assign the activated state present in SSNMR experiments. We used a combination of molecular dynamics (MD) simulations, chemical shift prediction algorithms, and Bayesian inference techniques to determine which of the most plausible x-ray structures resolved to date best represents the activated state captured in SSNMR. We first identified specific nuclei with simulated NMR chemical shifts that differed significantly when comparing partially open vs fully open ensembles from MD simulations. The simulated NMR chemical shifts for those specific nuclei were then compared to experimental ones, revealing that the simulation of the partially open state was in good agreement with the SSNMR data. Nuclei that discriminate effectively between partially and fully open states belong to residues spread over the sequence and provide a molecular level description of the conformational change.

Bayesian-Maximum-Entropy Reweighting of IDP Ensembles Based on NMR Chemical Shifts

Bayesian and Maximum Entropy approaches allow for a statistically sound and systematic fitting of experimental and computational data. Unfortunately, assessing the relative confidence in these two types of data remains difficult as several steps add unknown error. Here we propose the use of a validation-set method to determine the balance, and thus the amount of fitting. We apply the method to synthetic NMR chemical shift data of an intrinsically disordered protein. We show that the method gives consistent results even when other methods to assess the amount of fitting cannot be applied. Finally, we also describe how the errors in the chemical shift predictor can lead to an incorrect fitting and how using secondary chemical shifts could alleviate this problem.

The maximum occupancy condition for the localized property-optimized orbitals

It is shown analytically that the Chemist's Localized Property-optimized Orbitals (CLPOs), which are the localized orbitals obtainable from the results of ab initio calculations by the open-source program JANPA (http://janpa.sourceforge.net/) according to the recently proposed optimal property partitioning condition, form the Lewis structure with nearly maximum possible total electron occupancy. The conditions required for this additional optimality to hold are discussed. In particular, when a single-determinant wavefunction is used to describe the molecular system without a noticeable electron delocalization, CLPOs derived from this wavefunction approximately optimize the same target quantity as the Natural Bond Orbitals (NBOs), establishing in this way the link between the two sets of localized orbitals. The performance of CLPO and NBO methods is compared by using a dataset containing 7101 small molecules, and the relevant methodological features of both methods are discussed.

Unraveling the meaning of chemical shifts in protein NMR

Chemical shifts are among the most informative parameters in protein NMR. They provide wealth of information about protein secondary and tertiary structure, protein flexibility, and protein-ligand binding. In this report, we review the progress in interpreting and utilizing protein chemical shifts that has occurred over the past 25years, with a particular focus on the large body of work arising from our group and other Canadian NMR laboratories. More specifically, this review focuses on describing, assessing, and providing some historical context for various chemical shift-based methods to: (1) determine protein secondary and super-secondary structure; (2) derive protein torsion angles; (3) assess protein flexibility; (4) predict residue accessible surface area; (5) refine 3D protein structures; (6) determine 3D protein structures and (7) characterize intrinsically disordered proteins. This review also briefly covers some of the methods that we previously developed to predict chemical shifts from 3D protein structures and/or protein sequence data. It is hoped that this review will help to increase awareness of the considerable utility of NMR chemical shifts in structural biology and facilitate more widespread adoption of chemical-shift based methods by the NMR spectroscopists, structural biologists, protein biophysicists, and biochemists worldwide. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.

Protein structure refinement using a quantum mechanics-based chemical shielding predictor

We show that a QM-based predictor of a protein backbone and CB chemical shifts is of comparable accuracy to empirical chemical shift predictors after chemical shift-based structural refinement that removes small structural errors (errors in chemical shifts shown in red).

The accurate prediction of protein chemical shifts using a quantum mechanics (QM)-based method has been the subject of intense research for more than 20 years but so far empirical methods for chemical shift prediction have proven more accurate. In this paper we show that a QM-based predictor of a protein backbone and CB chemical shifts (ProCS15, PeerJ, 2016, 3, e1344) is of comparable accuracy to empirical chemical shift predictors after chemical shift-based structural refinement that removes small structural errors. We present a method by which quantum chemistry based predictions of isotropic chemical shielding values (ProCS15) can be used to refine protein structures using Markov Chain Monte Carlo (MCMC) simulations, relating the chemical shielding values to the experimental chemical shifts probabilistically. Two kinds of MCMC structural refinement simulations were performed using force field geometry optimized X-ray structures as starting points: simulated annealing of the starting structure and constant temperature MCMC simulation followed by simulated annealing of a representative ensemble structure. Annealing of the CHARMM structure changes the CA-RMSD by an average of 0.4 Å but lowers the chemical shift RMSD by 1.0 and 0.7 ppm for CA and N. Conformational averaging has a relatively small effect (0.1–0.2 ppm) on the overall agreement with carbon chemical shifts but lowers the error for nitrogen chemical shifts by 0.4 ppm. If an amino acid specific offset is included the ProCS15 predicted chemical shifts have RMSD values relative to experiments that are comparable to popular empirical chemical shift predictors. The annealed representative ensemble structures differ in CA-RMSD relative to the initial structures by an average of 2.0 Å, with >2.0 Å difference for six proteins. In four of the cases, the largest structural differences arise in structurally flexible regions of the protein as determined by NMR, and in the remaining two cases, the large structural change may be due to force field deficiencies. The overall accuracy of the empirical methods are slightly improved by annealing the CHARMM structure with ProCS15, which may suggest that the minor structural changes introduced by ProCS15-based annealing improves the accuracy of the protein structures. Having established that QM-based chemical shift prediction can deliver the same accuracy as empirical shift predictors we hope this can help increase the accuracy of related approaches such as QM/MM or linear scaling approaches or interpreting protein structural dynamics from QM-derived chemical shift.

ProCS15: a DFT-based chemical shift predictor for backbone and Cβ atoms in proteins

We present ProCS15: a program that computes the isotropic chemical shielding values of backbone and Cβ atoms given a protein structure in less than a second. ProCS15 is based on around 2.35 million OPBE/6-31G(d,p)//PM6 calculations on tripeptides and small structural models of hydrogen-bonding. The ProCS15-predicted chemical shielding values are compared to experimentally measured chemical shifts for Ubiquitin and the third IgG-binding domain of Protein G through linear regression and yield RMSD values of up to 2.2, 0.7, and 4.8 ppm for carbon, hydrogen, and nitrogen atoms. These RMSD values are very similar to corresponding RMSD values computed using OPBE/6-31G(d,p) for the entire structure for each proteins. These maximum RMSD values can be reduced by using NMR-derived structural ensembles of Ubiquitin. For example, for the largest ensemble the largest RMSD values are 1.7, 0.5, and 3.5 ppm for carbon, hydrogen, and nitrogen. The corresponding RMSD values predicted by several empirical chemical shift predictors range between 0.7–1.1, 0.2–0.4, and 1.8–2.8 ppm for carbon, hydrogen, and nitrogen atoms, respectively.