Molecular dynamics–quantum mechanical/molecular mechanical simulation of amide I infrared spectra to identify protein conformational ensembles: a case study of chignolin

As quantum chemistry plays a more and more central role in many complicated chemical problems, it has become necessary to obtain accurate results for large molecular systems. Conventional quantum chemistry methods are either too expensive to apply to large systems or too approximate for the results to be reliable, and they fail to satisfy this requirement. A variety of different approaches is being developed with the aim of achieving this goal: local correlation methods; divide-and-conquer methods; linear-scaling density functional methods based on the fast multipole and other approximations; effective potential methods; and hybrid methods. ONIOM (our N-layered integrated molecular orbital plus molecular mechanics method), developed by the authors, is a hybrid method in which a large molecular system is divided into onion-skin-like layers, and different quantum chemistry/molecular mechanics methods are used for different parts of the system; the results are combined to extrapolatively estimate the results of high-level calculation for the real system. Several applications of ONIOM will be discussed.

Molecular Mechanism of SSR128129E, an Extracellularly Acting, Small-Molecule, Allosteric Inhibitor of FGF Receptor Signaling

NMR (nuclear magnetic resonance) spectroscopy allows for important atomistic insights into the structure and dynamics of biological macromolecules; however, reliable assignments of experimental spectra are often difficult. Herein, quantum mechanical/molecular mechanical (QM/MM) calculations can provide crucial support. A major problem for the simulations is that experimental NMR signals are time-averaged over much longer time scales, and since computed chemical shifts are highly sensitive to local changes in the electronic and structural environment, sufficiently large averages over representative structural ensembles are essential. This entails high computational demands for reliable simulations. For NMR measurements in biological systems, a nucleus of major interest is 31P since it is both highly present (e.g., in nucleic acids) and easily observable. The focus of our present study is to develop a robust and computationally cost-efficient framework for simulating 31P NMR chemical shifts of nucleotides. We apply this scheme to study the different stages of the ATP hydrolysis reaction catalyzed by p97. Our methodology is based on MM molecular dynamics (MM-MD) sampling, followed by QM/MM structure optimizations and NMR calculations. Overall, our study is one of the most comprehensive QM-based 31P studies in a protein environment and the first to provide computed NMR chemical shifts for multiple nucleotide states in a protein environment. This study sheds light on a process that is challenging to probe experimentally and aims to bridge the gap between measured and calculated NMR spectroscopic properties.

Correctly calculating the structure of metal coordination sites in a protein during the process of nuclear magnetic resonance (NMR) structure determination and refinement continues to be a challenging task. In this study, we present an accurate and convenient means by which to include metal ions in the NMR structure determination process using molecular dynamics (MD) simulations constrained by NMR-derived data to obtain a realistic and physically viable description of the metal binding site(s). This method provides the framework to accurately portray the metal ions and its binding residues in a pseudo-bond or dummy-cation like approach, and is validated by quantum mechanical/molecular mechanical (QM/MM) MD calculations constrained by NMR-derived data. To illustrate this approach, we refine the zinc coordination complex structure of the zinc sensing transcriptional repressor protein Staphylococcus aureus CzrA, generating over 130 ns of MD and QM/MM MD NMR-data compliant sampling. In addition to refining the first coordination shell structure of the Zn(II) ion, this protocol benefits from being performed in a periodically replicated solvation environment including long-range electrostatics. We determine that unrestrained (not based on NMR data) MD simulations correlated to the NMR data in a time-averaged ensemble. The accurate solution structure ensemble of the metal-bound protein accurately describes the role of conformational sampling in allosteric regulation of DNA binding by zinc and serves to validate our previous unrestrained MD simulations of CzrA. This methodology has potentially broad applicability in the structure determination of metal ion bound proteins, protein folding and metal template protein-design studies.

Structure and dynamics are both critical to RNA’s vital functions in biology. Numerous techniques can elucidate the structural dynamics of RNA, but computational approaches based on experimental data arguably hold the promise of providing the most detail. In this Account, we highlight areas wherein molecular dynamics (MD) and quantum mechanical (QM) techniques are applied to RNA, particularly in relation to complementary experimental studies.We have expanded on atomic-resolution crystal structures of RNAs in functionally relevant states by applying explicit solvent MD simulations to explore their dynamics and conformational changes on the submicrosecond time scale. MD relies on simplified atomistic, pairwise additive interaction potentials (force fields). Because of limited sampling, due to the finite accessible simulation time scale and the approximated force field, high-quality starting structures are required.Despite their imperfection, we find that currently available force fields empower MD to provide meaningful and predictive information on RNA dynamics around a crystallographically defined energy minimum. The performance of force fields can be estimated by precise QM calculations on small model systems. Such calculations agree reasonably well with the Cornell et al. AMBER force field, particularly for stacking and hydrogen-bonding interactions. A final verification of any force field is accomplished by simulations of complex nucleic acid structures.The performance of the Cornell et al. AMBER force field generally corresponds well with and augments experimental data, but one notable exception could be the capping loops of double-helical stems. In addition, the performance of pairwise additive force fields is obviously unsatisfactory for inclusion of divalent cations, because their interactions lead to major polarization and charge-transfer effects neglected by the force field. Neglect of polarization also limits, albeit to a lesser extent, the description accuracy of other contributions, such as interactions with monovalent ions, conformational flexibility of the anionic sugar−phosphate backbone, hydrogen bonding, and solute polarization by solvent. Still, despite limitations, MD simulations are a valid tool for analyzing the structural dynamics of existing experimental structures. Careful analysis of MD simulations can identify problematic aspects of an experimental RNA structure, unveil structural characteristics masked by experimental constraints, reveal functionally significant stochastic fluctuations, evaluate the structural role of base ionization, and predict structurally and potentially functionally important details of the solvent behavior, including the presence of tightly bound water molecules. Moreover, combining classical MD simulations with QM calculations in hybrid QM/MM approaches helps in the assessment of the plausibility of chemical mechanisms of catalytic RNAs (ribozymes).In contrast, the reliable prediction of structure from sequence information is beyond the applicability of MD tools. The ultimate utility of computational studies in understanding RNA function thus requires that the results are neither blindly accepted nor flatly rejected, but rather considered in the context of all available experimental data, with great care given to assessing limitations through the available starting structures, force field approximations, and sampling limitations. The examples given in this Account showcase how the judicious use of basic MD simulations has already served as a powerful tool to help evaluate the role of structural dynamics in biological function of RNA.

Stromal interaction molecule 1 (STIM1) has recently been identified as a key player in store-operated Ca2+ entry. Endoplasmic reticulum (ER) luminal Ca2+ depletion results in STIM1 redistribution from ER membrane homogeneity to distinctly localized aggregates near the plasma membrane; these changes precede and are linked to cytoplasmic Ca2+ influx via Ca2+ release-activated channels (CRACs). The molecular mechanisms initiating ER STIM1 redistribution and plasma membrane CRAC activity are not well understood. We recombinantly expressed the Ca2+-sensing region of STIM1 consisting of the EF-hand together with the sterile alpha-motif (SAM) domain (EF-SAM) to investigate its Ca2+-related conformational and biochemical features. We demonstrate that Ca2+-loaded EF-SAM (holo) contains high alpha-helicity, whereas EF-SAM in the absence of Ca2+ (apo) is much less compact. Accordingly, the melting temperature (Tm) of the holoform is approximately 25 degrees C higher than apoform; heat and urea-derived thermodynamic parameters indicate a Ca2+-induced stabilization of 3.2 kcal mol(-1). We show that holoEF-SAM exists as a monomer, whereas apoEF-SAM readily forms a dimer and/or oligomer, and that oligomer to monomer transitions and vice versa are at least in part mediated by changes in surface hydrophobicity. Additionally, we find that the Ca2+ binding affinity of EF-SAM is relatively low with an apparent dissociation constant (Kd) of approximately 0.2-0.6 mM and a binding stoichiometry of 1. Our results suggest that EF-SAM actively participates in and is the likely the molecular trigger initiating STIM1 punctae formation via large conformational changes. The low Ca2+ affinity of EF-SAM is reconciled with the confirmed role of STIM1 as an ER Ca2+ sensor.

We use the PBE0/6-31G* density functional method to perform ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations under periodic boundary conditions with rigorous electrostatics using the ambient potential composite Ewald method in order to test the convergence of MM → QM/MM free energy corrections for the prediction of 17 small-molecule solvation free energies and eight ligand binding free energies to T4 lysozyme. The "indirect" thermodynamic cycle for calculating free energies is used to explore whether a series of reference potentials improve the statistical quality of the predictions. Specifically, we construct a series of reference potentials that optimize a molecular mechanical (MM) force field's parameters to reproduce the ab initio QM/MM forces from a QM/MM simulation. The optimizations form a systematic progression of successively expanded parameters that include bond, angle, dihedral, and charge parameters. For each reference potential, we calculate benchmark quality reference values for the MM → QM/MM correction by performing the mixed MM and QM/MM Hamiltonians at 11 intermediate states, each for 200 ps. We then compare forward and reverse application of Zwanzig's relation, thermodynamic integration (TI), and Bennett's acceptance ratio (BAR) methods as a function of reference potential, simulation time, and the number of simulated intermediate states. We find that Zwanzig's equation is inadequate unless a large number of intermediate states are explicitly simulated. The TI and BAR mean signed errors are very small even when only the end-state simulations are considered, and the standard deviations of the TI and BAR errors are decreased by choosing a reference potential that optimizes the bond and angle parameters. We find a robust approach for the data sets of fairly rigid molecules considered here is to use bond + angle reference potential together with the end-state-only BAR analysis. This requires QM/MM simulations to be performed in order to generate reference data to parametrize the bond + angle reference potential, and then this same simulation serves a dual purpose as the full QM/MM end state. The convergence of the results with respect to time suggests that computational resources may be used more efficiently by running multiple simulations for no more than 50 ps, rather than running one long simulation.

Multidimensional infrared (IR) spectroscopy has emerged as a viable tool to study molecular structure and dynamics in condensed phases, and the third-order vibrational response function is the central quantity underlying various nonlinear IR spectroscopic techniques, such as pump–probe, photon echo and two-dimensional (2D) IR spectroscopy. In this paper, a new computational method is presented that calculates this nonlinear response function in the classical limit from a series of classical molecular dynamics (MD) simulations, employing a quantum mechanical/molecular mechanical (QM/MM) force field. The method relies on the stability matrix formalism where the dipole–dipole quantum mechanical commutators appearing in the exact quantum response function are replaced by the corresponding Poisson brackets. We present the formulation and computational algorithm of the method for both the classical and the QM/MM force fields and apply it to the 2D IR spectroscopy of carbon monoxide (CO) and N-methylacetamide (NMA), each solvated in a water cluster. The conventional classical force field with harmonic bond potentials is shown to be incapable of producing a reliable 2D IR signal because intramolecular vibrational anharmonicity, essential to the production of the nonlinear signal, is absent in such a model. The QM/MM force field, on the other hand, produces distinct 2D spectra for the NMA and CO systems with clear vertical splitting and cross peaks, reflecting the vibrational anharmonicities and the vibrational couplings between the underlying vibrational modes, respectively. In the NMA spectrum, the coupling between the amide I and II modes is also well reproduced. While attaining the converged spectrum is found to be challenging with this method, with an adequate amount of computing it can be straightforwardly applied to new systems containing multiple chromophores with little modeling effort, and therefore it would be useful in understanding the multimode 2D IR spectrum of complex molecular systems.

Summary Although chemically close to DNA, RNA can adopt a wide range of structures from regular helices to complex globular conformations, showing a complexity similar to that of proteins. The determination of the structure of RNA molecules, crucial for functional understanding, is severely handicapped by their size and flexibility, which makes the systematic use of experimental approaches difficult. Simulation techniques are also suffering from very severe problems related to the accuracy of the methods and their ability to sample a large and complex conformational landscape. Here, we systematically review recent approaches created to reduce the shortcoming of the current generation of simulation methods—from highly accurate models able to deal with small systems to coarse-grained approaches that are less accurate but applicable to dealing with large models.

We compare the conformational distributions of Ace-Ala-Nme and Ace-Gly-Nme sampled in long simulations with several molecular mechanics (MM) force fields and with a fast combined quantum mechanics/molecular mechanics (QM/MM) force field, in which the solute's intramolecular energy and forces are calculated with the self-consistent charge density functional tight binding method (SCCDFTB), and the solvent is represented by either one of the well-known SPC and TIP3P models. All MM force fields give two main states for Ace-Ala-Nme, beta and alpha separated by free energy barriers, but the ratio in which these are sampled varies by a factor of 30, from a high in favor of beta of 6 to a low of 1/5. The frequency of transitions between states is particularly low with the amber and charmm force fields, for which the distributions are noticeably narrower, and the energy barriers between states higher. The lower of the two barriers lies between alpha and beta at values of psi near 0 for all MM simulations except for charmm22. The results of the QM/MM simulations vary less with the choice of MM force field; the ratio beta/alpha varies between 1.5 and 2.2, the easy pass lies at psi near 0, and transitions between states are more frequent than for amber and charmm, but less frequent than for cedar. For Ace-Gly-Nme, all force fields locate a diffuse stable region around phi = pi and psi = pi, whereas the amber force field gives two additional densely sampled states near phi = +/-100 degrees and psi = 0, which are also found with the QM/MM force field. For both solutes, the distribution from the QM/MM simulation shows greater similarity with the distribution in high-resolution protein structures than is the case for any of the MM simulations.

The term “lethal synthesis” was coined for enzymatic formation of fluorocitrate, but this classic problem of enzyme stereoselectivity remains poorly understood. Here, we show that high-level ab initio quantum mechanics/ molecular mechanics (QM/MM) modeling can accurately capture this enzymatic enantioselectivity and the results provide detailed insight into its origin. Citrate synthase (CS) performs the first reaction in the citric acid cycle: the formation of citrate from oxaloacetate and acetate in the form of acetyl-CoA. When fluoroacetyl-CoA (from fluoroacetate) is used as a substrate instead of acetyl-CoA, 2fluorocitrate is formed, which inhibits aconitase, the next enzyme in the citric acid cycle. This process is responsible for the lethal toxicity of fluoroacetate to humans and other mammals. The fluorocitrate enantiomer that is predominantly formed by CS, (2R,3R)-fluorocitrate (Figure 1), is the same enantiomer that specifically inhibits aconitase. The only (semi-)quantitative experimental study published to date indicates that the minor product of the enzymatic formation of fluorocitrate, (2S,3R)-fluorocitrate, amounts to 2–3% of the major product. Using transition-state theory, this translates to a difference in activation free energy (DDG ) of 2.06– 2.30 kcalmol . The causes of this selectivity remain uncertain. We have previously modeled the two initial reaction steps for the natural substrates, proton abstraction from acetylCoA and condensation with oxaloacetate (OAA), in CS with high-level QM/MM methods. For the reaction with fluoroacetyl-CoA (FaCoA), the distinction between enantiomers is made in the proton-abstraction step, where either an Eor a Z-enolate is formed. Here, we show that 1) the calculated relative energy of the enolates accurately predicts the experimentally observed enantiospecificity and 2) the enantiospecificity is mostly due to the inherent energy difference of the reacting species. A model of the enzyme with OAA and FaCoA bound was built for QM/MM simulation, with the Asp375 side chain from Cb, the methylthioester part of FaCoA, and OAA in the QM region. QM/MM molecular dynamics indicated that preE and pre-Z conformations in the CS active site can be sampled in the same trajectory. Five different approximate transition-state conformations for both E-enolate and Zenolate formation were generated by QM/MM umbrella sampling molecular dynamics (see the Supporting Information). These conformations were used to perform high-level QM/MM modeling of proton abstraction, using the established reaction coordinate r= d(OAsp375H) d(CFaCoAH). Geometries were optimized at the B3LYP/6-31+G(d)//MM level and energies calculated at the SCS-MP2/aug-cc-pVDZ// MM level. This describes the reaction of CS with acetyl-CoA accurately, in agreement with local coupled-cluster QM/MM results. The QM/MM energy profiles for enolate formation show correctly that formation of the E-enolate is preferred (Figure 2). Boltzmann-weighted energy differences between the E and Z profiles are 1.80 and 2.05 kcalmol 1 for the activation energy and reaction energy in this step, respectively. Entropy contributions for Eand Z-enolate formation are expected to be (nearly) identical (supported by AM1/MM free energy profiles, see the Supporting Information). The Figure 1. Conversion of fluoracetyl-CoA to fluorocitrate by CS.

Light‐responsive proteins are widely employed in bioimaging, for example, fluorescent proteins (FPs), which are comprised of a chromophore centered within a barrel‐shaped protein. FPs exhibit remarkable one‐ and multi‐photon absorption (1PA and MPA, respectively) in addition to their emissive properties. Over the last two decades, many types of quantum mechanical, molecular dynamics, and combined quantum mechanical/molecular‐mechanical (QM/MM) approaches have been employed in the study of the photophysics of FPs. Among the latter, QM/MM approaches have proven to be capable of capturing the strong correlation between FPs' light‐responsive properties and their chromophore–environment interactions. In particular, polarizable embedding QM/MM methods are gaining attention by reason of their outstanding performance in the computation of MPA in FPs. Herein, we discuss the outcomes of some of the investigations performed on the 1PA, MPA, and emissive features of FPs using QM/MM approaches. In addition, critical aspects of the use of QM/MM approaches to study FPs' 1PA and MPA features are described. To those researchers interested in starting to perform MPA computations for FPs using QM/MM methods, this review aims to be a compass to navigate among the relevant available literature.This article is categorized under: Electronic Structure Theory > Combined QM/MM Methods Structure and Mechanism > Computational Biochemistry and Biophysics

A new formalism for quantum mechanical / molecular mechanical (QM/MM) dynamics of chemical species in solution has been developed, which does not require the construction of any other potential functions except those for solvent–solvent interactions, maintains all the advantages of large simulation boxes and ensures the accuracy of ab initio quantum mechanics for all forces acting in the chemically most relevant region. Interactions between solute and more distant solvent molecules are incorporated by a dynamically adjusted force field corresponding to the actual molecular configuration of the simulated system and charges derived from the electron distribution in the solvate. The new formalism has been tested with some examples of hydrated ions, for which accurate conventional ab initio QM/MM simulations have been previously performed, and the comparison shows equivalence and in some aspects superiority of the new method. As this simulation procedure does not require any tedious construction of two-and three-body interaction potentials inherent to conventional QM/MM approaches, it opens the straightforward access to ab initio molecular dynamics simulations of any kind of solutes, such as metal complexes and other composite species in solution.

RNAPack: An Integrated NMR Approach to RNA Structure Determination

We developed a quantum mechanical/molecular mechanical (QM/MM) free energy geometry optimization method by which the geometry of a quantum chemically treated (QM) molecule is optimized on a free energy surface defined with thermal distribution of the surrounding molecular environment obtained by molecular dynamics simulation with a molecular mechanics (MM) force field. The method called QM/MM reweighting free energy self-consistent field combines a mean field theory of QM/MM free energy geometry optimization developed by Yamamoto (Yamamoto, T. J. Chem. Phys.2008, 129, 244104) with a reweighting scheme for updating the MM distribution introduced by Hu et al. (Hu, H., et al. J. Chem. Phys.2008, 128, 034105) and features high computational efficiency suitable for exploring the reaction free energy surface of extensive protein conformational space. The computational efficiency with improved treatment of a long-range electrostatic (ES) interaction using the Ewald summation technique permits one to take into account global conformational relaxation of an entire protein of an enzyme in the free energy geometry optimization of its reaction center. We applied the method to an enzymatic reaction of a substrate complex of psychrophilic α-amylase from Antarctic bacterium Pseudoalteromonas haloplanktis and succeeded in geometry optimizations of the reactant and the product of the catalytic reaction that involve large conformational changes of protein loops adjacent to the reaction center on time scales reaching sub-microseconds. We found that the adjacent loops in the reactant and the product form in different conformations and produce catalytic ES potentials on the reaction center.