Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Automatic Forward Model Parameterization with Bayesian Inference of Conformational Populations (2405.18532v2)

Published 28 May 2024 in physics.bio-ph, physics.chem-ph, and physics.data-an

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...

Definition Search Book Streamline Icon: https://streamlinehq.com
References (39)
  1. T. Fröhlking, M. Bernetti,  and G. Bussi, “Simultaneous refinement of molecular dynamics ensembles and forward models using experimental data,” The Journal of Chemical Physics 158 (2023).
  2. A. C. Wang and A. Bax, “Determination of the backbone dihedral angles ϕitalic-ϕ\phiitalic_ϕ in human ubiquitin from reparametrized empirical karplus equations,” Journal of the American Chemical Society 118, 2483–2494 (1996).
  3. M. Habeck, W. Rieping,  and M. Nilges, “Bayesian Estimation of Karplus Parameters and Torsion Angles from Three-Bond Scalar Couplings Constants,” Journal of magnetic resonance 177, 160–165 (2005).
  4. J. M. Schmidt, M. Blümel, F. Löhr,  and H. Rüterjans, “Self-consistent 3j coupling analysis for the joint calibration of karplus coefficients and evaluation of torsion angles,” Journal of biomolecular NMR 14, 1–12 (1999).
  5. V. A. Voelz, Y. Ge,  and R. M. Raddi, “Reconciling Simulations and Experiments with BICePs: a Review,” Front. Mol. Biosci. 8, 661520 (2021).
  6. R. M. Raddi, T. Marshall, Y. Ge,  and V. Voelz, “Model selection using replica averaging with bayesian inference of conformational populations,” chemrXiv preprint 10.26434/chemrxiv-2023-396mm  (2023).
  7. V. a. Voelz and G. Zhou, “Bayesian Inference of Conformational State Populations from Computational Models and Sparse Experimental Observables,” J. Comput. Chem. 35, 2215–2224 (2014).
  8. H. Wan, Y. Ge, A. Razavi,  and V. A. Voelz, “Reconciling Simulated Ensembles of Apomyoglobin with Experimental Hydrogen/Deuterium Exchange Data Using Bayesian Inference and Multiensemble Markov State Models.” J. Chem. Theory Comput. 16, 1333–1348 (2020).
  9. M. F. D. Hurley, J. D. Northrup, Y. Ge, C. E. Schafmeister,  and V. A. Voelz, “Metal Cation-Binding Mechanisms of Q-Proline Peptoid Macrocycles in Solution,” J. Chem. Inf. Model. 61, 2818–2828 (2021).
  10. R. M. Raddi, Y. Ge,  and V. A. Voelz, “BICePs V2. 0: Software for Ensemble Reweighting Using Bayesian Inference of Conformational Populations,” Journal of chemical information and modeling 63, 2370–2381 (2023).
  11. Y. Ge and V. A. Voelz, “Model Selection Using BICePs: a Bayesian Approach for Force Field Validation and Parameterization,” J. Phys. Chem. B 122, 5610–5622 (2018).
  12. R. M. Raddi and V. A. Voelz, “Automated optimization of force field parameters against ensemble-averaged measurements with bayesian inference of conformational populations,” arXiv preprint arXiv:2402.11169  (2024).
  13. W. Rieping, M. Habeck,  and M. Nilges, “Inferential Structure Determination,” Science 309, 303–306 (2005).
  14. J. W. Pitera and J. D. Chodera, “On the Use of Experimental Observations to Bias Simulated Ensembles,” Journal of chemical theory and computation 8, 3445–3451 (2012).
  15. A. Cavalli, C. Camilloni,  and M. Vendruscolo, “Molecular Dynamics Simulations with Replica-Averaged Structural Restraints Generate Structural Ensembles According to the Maximum Entropy Principle,” The Journal of chemical physics 138, 03B603 (2013).
  16. A. Cesari, S. Reißer,  and G. Bussi, “Using the Maximum Entropy Principle to Combine Simulations and Solution Experiments,” Computation 6, 15 (2018).
  17. B. Roux and J. Weare, “On the Statistical Equivalence of Restrained-Ensemble Simulations with the Maximum Entropy Method,” The Journal of chemical physics 138, 02B616 (2013).
  18. G. Hummer and J. Köfinger, “Bayesian Ensemble Refinement by Replica Simulations and Reweighting,” The Journal of chemical physics 143, 12B634_1 (2015).
  19. M. Bonomi, C. Camilloni, A. Cavalli,  and M. Vendruscolo, “Metainference: A Bayesian Inference Method for Heterogeneous Systems,” Sci. Adv. 2, e1501177 (2016).
  20. J.-S. Hu and A. Bax, “Determination of ϕitalic-ϕ\phiitalic_ϕ and χ1subscript𝜒1\chi_{1}italic_χ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT angles in proteins from c13superscript𝑐13{}^{13}cstart_FLOATSUPERSCRIPT 13 end_FLOATSUPERSCRIPT italic_c-c13superscript𝑐13{}^{13}cstart_FLOATSUPERSCRIPT 13 end_FLOATSUPERSCRIPT italic_c three-bond j couplings measured by three-dimensional heteronuclear nmr. how planar is the peptide bond?”  (1997).
  21. M. Karplus, “Vicinal proton coupling in nuclear magnetic resonance,” Journal of the American Chemical Society 85, 2870–2871 (1963).
  22. M. R. Shirts and J. D. Chodera, “Statistically Optimal Analysis of Samples from Multiple Equilibrium States,” J. Chem. Phys. 129, 124105–11 (2008).
  23. A. Rizzi, Improving Efficiency and Scalability of Free Energy Calculations through Automatic Protocol Optimization, Ph.D. thesis, Weill Medical College of Cornell University (2020).
  24. D. A. Sivak and G. E. Crooks, “Thermodynamic metrics and optimal paths,” Physical review letters 108, 190602 (2012).
  25. D. K. Shenfeld, H. Xu, M. P. Eastwood, R. O. Dror,  and D. E. Shaw, “Minimizing Thermodynamic Length to Select Intermediate States for Free-Energy Calculations and Replica-Exchange Simulations,” Phys. Rev. E 80, 46705 (2009).
  26. G. Cornilescu, J. L. Marquardt, M. Ottiger,  and A. Bax, “Validation of protein structure from anisotropic carbonyl chemical shifts in a dilute liquid crystalline phase,” Journal of the American Chemical Society 120, 6836–6837 (1998).
  27. B. Richter, J. Gsponer, P. Várnai, X. Salvatella,  and M. Vendruscolo, “The mumo (minimal under-restraining minimal over-restraining) method for the determination of native state ensembles of proteins,” Journal of biomolecular NMR 37, 117–135 (2007).
  28. M. Baek, I. Anishchenko, I. Humphreys, Q. Cong, D. Baker,  and F. DiMaio, “Efficient and accurate prediction of protein structure using rosettafold2,” bioRxiv , 2023–05 (2023).
  29. S. Piana, K. Lindorff-Larsen,  and D. E. Shaw, “Atomic-level description of ubiquitin folding,” Proc. Natl. Acad. Sci. U. S. A. 110, 5915–5920 (2013).
  30. S. Vijay-Kumar, C. E. Bugg,  and W. J. Cook, “Structure of ubiquitin refined at 1.8 åresolution,” Journal of molecular biology 194, 531–544 (1987).
  31. J. Jumper, R. Evans, A. Pritzel, T. Green, M. Figurnov, O. Ronneberger, K. Tunyasuvunakool, R. Bates, A. Žídek, A. Potapenko, et al., “Highly accurate protein structure prediction with alphafold,” Nature 596, 583–589 (2021).
  32. Z. F. Brotzakis, S. Zhang,  and M. Vendruscolo, “Alphafold prediction of structural ensembles of disordered proteins,” bioRxiv , 2023–01 (2023).
  33. G. W. Vuister and A. Bax, “Quantitative j correlation: a new approach for measuring homonuclear three-bond j (hnh. alpha.) coupling constants in 15n-enriched proteins,” Journal of the American Chemical Society 115, 7772–7777 (1993).
  34. M. J. Minch, “Orientational dependence of vicinal proton-proton nmr coupling constants: The karplus relationship,” Concepts in magnetic resonance 6, 41–56 (1994).
  35. M. Mirdita, K. Schütze, Y. Moriwaki, L. Heo, S. Ovchinnikov,  and M. Steinegger, “Colabfold: making protein folding accessible to all,” Nature methods 19, 679–682 (2022).
  36. C. Wehmeyer, M. K. Scherer, T. Hempel, B. E. Husic, S. Olsson,  and F. Noé, “Introduction to markov state modeling with the pyemma software [article v1.0],” Living Journal of Computational Molecular Science 1, 5965 (2019).
  37. H. Wu and F. Noé, “Variational approach for learning markov processes from time series data,” J. Nonlinear Sci. 30, 23–66 (2020).
  38. G. Pérez-Hernández, F. Paul, T. Giorgino, G. De Fabritiis,  and F. Noé, “Identification of slow molecular order parameters for markov model construction,” J. Chem. Phys. 139, 015102 (2013).
  39. M. J, “Some methods for classification and analysis of multivariate observations,” Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics  (1967).

Summary

We haven't generated a summary for this paper yet.