Modeling Macromolecular Motions by X-Ray-Scattering-Constrained Molecular Dynamics

Abstract

A fundamental problem for structural biology in combining solution x-ray scattering data with atomic resolution structures determined by crystallography is to find effective ways to model motions accessible to molecules outside the crystal environment. Motions can be derived when multiple conformations are experimentally observed or can be inferred through computational methods such as normal modes, molecular dynamics, and Monte Carlo-based techniques. Small-angle x-ray scattering (SAXS) is a complete, resolution-limited structural measurement of the solution state for macromolecules. Because of this, it is an ideal constraint for performing accurate MD simulations that involve functional movements. Herein we discuss a new article on the interpretation of solution x-ray scattering by explicit-solvent molecular dynamics. This article is not another fitting algorithm for SAXS data; it is, instead, an exciting method for learning much more about a structure and its functional movements using molecular dynamics, which is constrained by the SAXS data. Seeing how something moves can often explain how a process works. Consider the sailing stones of Death Valley National Park in California. These stones reside in an inhospitable, large dry lakebed known as Racetrack Playa. Long, straight tracks (10–100 m) trail behind these heavy stones and in many cases, these tracks run parallel to others, suggesting a concerted, deliberate motion from a set of inanimate objects (Fig. 1). This sailing-stone mystery persisted for nearly 100 years, until Norris et al. (1Norris R.D. Norris J.M. Jackson B. et al.Sliding rocks on Racetrack Playa, Death Valley National Park: first observation of rocks in motion.PLoS ONE. 2014; 9: e105948Crossref PubMed Scopus (17) Google Scholar) used GPS tracking and photography to capture these stones in motion. In this issue of the Biophysical Journal, Chen and Hub (2Chen P.-c. Hub J.S. Interpretation of solution x-ray scattering by explicit-solvent molecular dynamics.Biophys. J. 2015; 108: 2573-2584Abstract Full Text Full Text PDF PubMed Scopus (75) Google Scholar) report an advancement in modeling protein motions in the solution state by incorporating small-angle x-ray scattering (SAXS) information during molecular dynamics simulations. As SAXS data provide unbiased macromolecular structural characterizations in solution (3Rambo R.P. Tainer J.A. Accurate assessment of mass, models and resolution by small-angle scattering.Nature. 2013; 496: 477-481Crossref PubMed Scopus (536) Google Scholar), the coupling of SAXS to molecular dynamics (MD) simulations reveals macromolecular structures in motion under biologically relevant solution conditions. In structural biology, we are often trying to understand how a process works through the lens of solid-state techniques, such as cryo-electron microscopy (cryo-EM) and macromolecular x-ray crystallography (MX). Our structural instincts, developed from the >100,000 structures deposited in the Protein Data Bank (PDB; http://www.rcsb.org/pdb/home/home.do) consisting of ∼1200 unique structural classifications of protein folds, allows us to make reliable assertions, such as that active site residues will be spatially close and that complexes form through the stabilization of complementary binding surfaces and charges. Furthermore, bioinformatic tools that map sequence conservation onto a structure may suggest additional features of unknown function. Unfortunately, structural biology has neither the requisite atomistic GPS tracking tools nor the macromolecular video camera for recording structures in the solution state, so learning how an enzyme works can be a long, challenging task. In the case of T7 RNA polymerase (Fig. 1 B), understanding how the enzyme works required crystal structures of the enzyme at various stages along its catalytic cycle (4Steitz T.A. The structural basis of the transition from initiation to elongation phases of transcription, as well as translocation and strand separation, by T7 RNA polymerase.Curr. Opin. Struct. Biol. 2004; 14: 4-9Crossref PubMed Scopus (51) Google Scholar). Amazingly, the transition of the enzyme from the initiation state to the elongation state occurs through a complete refolding of the N-terminal domain. In the absence of the elongation state and starting with only the complex in the initiation state, an entirely explicit MD simulation would likely fail at demonstrating the transition of the complex to the elongation state. Although additional objective, quantitative experimental measures of flexibility and disorder in solution are limited, SAXS provides, via application of the Porod-Debye law, a critical technology to assess macromolecular flexibility versus switching between discrete states as well as shape and assembly (5Rambo R.P. Tainer J.A. Characterizing flexible and intrinsically unstructured biological macromolecules by SAS using the Porod-Debye law.Biopolymers. 2011; 95: 559-571Crossref PubMed Scopus (371) Google Scholar). MD simulations, however, can validate solution ensembles defined by wide-angle and small-angle x-ray scattering data (SWAXS) (6Chen P.-c. Hub J.S. Validating solution ensembles from molecular dynamics simulation by wide-angle x-ray scattering data.Biophys. J. 2014; 107: 435-447Abstract Full Text Full Text PDF PubMed Scopus (90) Google Scholar). Indeed, SAXS can provide comprehensive, quantitative, and objective (superposition-independent) perspectives on solution state conformations (7Hura G.L. Budworth H. Tainer J.A. et al.Comprehensive macromolecular conformations mapped by quantitative SAXS analyses.Nat. Methods. 2013; 10: 453-454Crossref PubMed Scopus (97) Google Scholar). Yet, exploratory MD simulations tend to sample local perturbations of a structure, where transitions to experimentally observed states require the observed state to be a constraint during the simulation. Thus, it is not surprising that MD is not routinely used for discovering accessible states of a biological particle when only a single state of the structure is known a priori. MD has been shown to be a reliable tool in structure determination and refinement. Here, electron density maps, NMR constraints, and knowledge-based libraries augment the limitations of the MD force fields by providing powerful empirical-based constraints to steer the simulation toward a valid structural state (8Gabel F. Simon B. Sattler M. A target function for quaternary structural refinement from small angle scattering and NMR orientational restraints.Eur. Biophys. J. 2006; 35: 313-327Crossref PubMed Scopus (26) Google Scholar, 9Boldon L. Laliberte F. Liu L. Review of the fundamental theories behind small angle x-ray scattering, molecular dynamics simulations, and relevant integrated application.Nano. Rev. 2015; 6: 25661Crossref PubMed Google Scholar, 10Grishaev A. Wu J. Bax A. et al.Refinement of multidomain protein structures by combination of solution small-angle x-ray scattering and NMR data.J. Am. Chem. Soc. 2005; 127: 16621-16628Crossref PubMed Scopus (192) Google Scholar, 11Rambo R.P. Tainer J.A. Super-resolution in solution x-ray scattering and its applications to structural systems biology.Annu. Rev. Biophys. 2013; 42: 415-441Crossref PubMed Scopus (159) Google Scholar). Pioneering work showed that improvements in the tertiary and quaternary structures of large multidomain proteins can be achieved by integrating SAXS information into NMR-based MD refinement (8Gabel F. Simon B. Sattler M. A target function for quaternary structural refinement from small angle scattering and NMR orientational restraints.Eur. Biophys. J. 2006; 35: 313-327Crossref PubMed Scopus (26) Google Scholar). Importantly, the integration is through a SAXS-based gradient function, which helps steer the refinement (7Hura G.L. Budworth H. Tainer J.A. et al.Comprehensive macromolecular conformations mapped by quantitative SAXS analyses.Nat. Methods. 2013; 10: 453-454Crossref PubMed Scopus (97) Google Scholar, 8Gabel F. Simon B. Sattler M. A target function for quaternary structural refinement from small angle scattering and NMR orientational restraints.Eur. Biophys. J. 2006; 35: 313-327Crossref PubMed Scopus (26) Google Scholar, 9Boldon L. Laliberte F. Liu L. Review of the fundamental theories behind small angle x-ray scattering, molecular dynamics simulations, and relevant integrated application.Nano. Rev. 2015; 6: 25661Crossref PubMed Google Scholar, 10Grishaev A. Wu J. Bax A. et al.Refinement of multidomain protein structures by combination of solution small-angle x-ray scattering and NMR data.J. Am. Chem. Soc. 2005; 127: 16621-16628Crossref PubMed Scopus (192) Google Scholar, 11Rambo R.P. Tainer J.A. Super-resolution in solution x-ray scattering and its applications to structural systems biology.Annu. Rev. Biophys. 2013; 42: 415-441Crossref PubMed Scopus (159) Google Scholar, 12Gorba C. Tama F. Normal mode flexible fitting of high-resolution structures of biological molecules toward SAXS data.Bioinform. Biol. Insights. 2010; 4: 43-54PubMed Google Scholar). However, although a structure is refined or determined by these methods, a mystery persists as to how a particular protein may function in the solution state. Yet, SAXS of biological particles in solution provides a complete structural description of the thermodynamic state (3Rambo R.P. Tainer J.A. Accurate assessment of mass, models and resolution by small-angle scattering.Nature. 2013; 496: 477-481Crossref PubMed Scopus (536) Google Scholar, 11Rambo R.P. Tainer J.A. Super-resolution in solution x-ray scattering and its applications to structural systems biology.Annu. Rev. Biophys. 2013; 42: 415-441Crossref PubMed Scopus (159) Google Scholar). A single SAXS measurement is typically made from 1000s of billions of molecules at a minimum exposure of 100 ms. Every available microstate at a given temperature is sampled and observed. Notwithstanding particle concentration and background matching, the SAXS observation will be a resolution-limited, structural description of the thermodynamic state. This structural description is illustrated by the Fourier transformation of the SAXS data to real-space giving the pair-distance, P(r), distribution function (Fig. 1, C and D). The P(r) distribution is the set of all electron-electron pair distances within the scattering particle and defines the distance bounds of the thermodynamic state. Because of this, we have proposed that SAXS is an ideal constraint for MD simulations (11Rambo R.P. Tainer J.A. Super-resolution in solution x-ray scattering and its applications to structural systems biology.Annu. Rev. Biophys. 2013; 42: 415-441Crossref PubMed Scopus (159) Google Scholar). The ability to use SAXS as a constraint requires a formalism that 1) is accurate in terms of its ability to calculate a SAXS profile from an atomistic model and 2) enables a gradient function (derivative with respect to the atomic coordinates) to describe the discrepancy between the atomic model and SAXS data. The gradient function is essential as it can be incorporated into the force calculations during the MD simulation (11Rambo R.P. Tainer J.A. Super-resolution in solution x-ray scattering and its applications to structural systems biology.Annu. Rev. Biophys. 2013; 42: 415-441Crossref PubMed Scopus (159) Google Scholar). Reported by Chen and Hub (2Chen P.-c. Hub J.S. Interpretation of solution x-ray scattering by explicit-solvent molecular dynamics.Biophys. J. 2015; 108: 2573-2584Abstract Full Text Full Text PDF PubMed Scopus (75) Google Scholar) is an exciting combination of SWAXS and MD. Here, a SWAXS-based potential is derived from an explicit description of the SWAXS experiment. Notably SWAXS is a difference measurement where the signal is derived from the difference in intensities between the SWAXS of the buffer (background) and sample. In this regard, Chen and Hub develop a method that simulates both the background and sample during the MD simulation. This provides a more accurate description of the SWAXS signal and includes an explicit hydration of the particle. Using three different biological particles where each particle has a previously determined open or closed state, Chen and Hub showed that in the absence of SAXS data, and starting with either of the two states, the simulation fails to transition to the opposing state in the presence or absence of ligand. This suggests that the MD simulation resides in a local energy well and cannot predict the other biologically relevant state. When empirical data of the opposite state are introduced through the SAXS potential, the simulation transitions quickly to the appropriate state. This has two profoundly important implications: First, the ability of the SWAXS data to drive the MD simulation into biological relevant states means SAXS can determine structures that may not be amendable to crystallography or cryo-EM. Second, the implementation of a SAXS potential explicitly validates the MD simulation as it bounds the biological particle to the confines of the resolution-limited P(r) distribution. Interestingly, in the analysis of CRM1 protein, Chen and Hub showed that dependencies on the choice of force field (CHARMM22 versus AMBER99sb) could be effectively removed with a SAXS potential, thereby minimizing simulation artifacts. Macromolecular x-ray crystallography and cryo-EM provide exquisite details of a macromolecular structure at the atomic level whereas SAXS provides a coarse, structural snapshot of the thermodynamic solution state (9Boldon L. Laliberte F. Liu L. Review of the fundamental theories behind small angle x-ray scattering, molecular dynamics simulations, and relevant integrated application.Nano. Rev. 2015; 6: 25661Crossref PubMed Google Scholar, 11Rambo R.P. Tainer J.A. Super-resolution in solution x-ray scattering and its applications to structural systems biology.Annu. Rev. Biophys. 2013; 42: 415-441Crossref PubMed Scopus (159) Google Scholar). The structural thermodynamic information lends itself to defining a very natural relationship between SAXS and MD. The SAXS information acts as a global constraint for the simulation whereas the MD algorithm extends the interpretation of the SAXS experiment to the residue level. Gaining functional insights on atomic structure motions can be a difficult task, particularly when only one structure is available. Now with high-throughput SAXS techniques that screen and structure most solution, ligand, and partner conditions (13Hura G.L. Menon A.L. Tainer J.A. et al.Robust, high-throughput solution structural analyses by small angle x-ray scattering (SAXS).Nat. Methods. 2009; 6: 606-612Crossref PubMed Scopus (505) Google Scholar), accessible structural states could be comprehensively identified and used in SAXS-driven MD simulations. Going forward, SAXS and MD simulations, starting from high-resolution structures, will allow us to discover how the domains of the particle move in response to solution conditions and seeing how a protein moves will undoubtedly prove to be rich in inspiring researcher hypotheses. Interpretation of Solution X-Ray Scattering by Explicit-Solvent Molecular DynamicsChen et al.Biophysical JournalMay 19, 2015In BriefSmall- and wide-angle x-ray scattering (SWAXS) and molecular dynamics (MD) simulations are complementary approaches that probe conformational transitions of biomolecules in solution, even in a time-resolved manner. However, the structural interpretation of the scattering signals is challenging, while MD simulations frequently suffer from incomplete sampling or from a force-field bias. To combine the advantages of both techniques, we present a method that incorporates solution scattering data as a differentiable energetic restraint into explicit-solvent MD simulations, termed SWAXS-driven MD, with the aim to direct the simulation into conformations satisfying the experimental data. Full-Text PDF Open Archive