Refinement of NMR structures using implicit solvent and advanced sampling techniques

NMR biomolecular structure calculations exploit simulated annealing methods for conformational sampling and require a relatively high level of redundancy in the experimental restraints to determine quality three-dimensional structures. Recent advances in generalized Born (GB) implicit solvent models should make it possible to combine information from both experimental measurements and accurate empirical force fields to improve the quality of NMR-derived structures. In this paper, we study the influence of implicit solvent on the refinement of protein NMR structures and identify an optimal protocol of utilizing these improved force fields. To do so, we carry out structure refinement experiments for model proteins with published NMR structures using full NMR restraints and subsets of them. We also investigate the application of advanced sampling techniques to NMR structure refinement. Similar to the observations of Xia et al. (J.Biomol. NMR 2002, 22, 317-331), we find that the impact of implicit solvent is rather small when there is a sufficient number of experimental restraints (such as in the final stage of NMR structure determination), whether implicit solvent is used throughout the calculation or only in the final refinement step. The application of advanced sampling techniques also seems to have minimal impact in this case. However, when the experimental data are limited, we demonstrate that refinement with implicit solvent can substantially improve the quality of the structures. In particular, when combined with an advanced sampling technique, the replica exchange (REX) method, near-native structures can be rapidly moved toward the native basin. The REX method provides both enhanced sampling and automatic selection of the most native-like (lowest energy) structures. An optimal protocol based on our studies first generates an ensemble of initial structures that maximally satisfy the available experimental data with conventional NMR software using a simplified force field and then refines these structures with implicit solvent using the REX method. We systematically examine the reliability and efficacy of this protocol using four proteins of various sizes ranging from the 56-residue B1 domain of Streptococcal protein G to the 370-residue Maltose-binding protein. Significant improvement in the structures was observed in all cases when refinement was based on low-redundancy restraint data. The proposed protocol is anticipated to be particularly useful in early stages of NMR structure determination where a reliable estimate of the native fold from limited data can significantly expedite the overall process. This refinement procedure is also expected to be useful when redundant experimental data are not readily available, such as for large multidomain biomolecules and in solid-state NMR structure determination.     

Spectroscopic Properties of Lumiflavin: A Quantum Chemical Study

In this work, the electronic structure and spectroscopic properties of lumiflavin are calculated using various quantum chemical methods. The excitation energies for ten singlet and triplet states as well as the analysis of the electron density difference are assessed using various wave function‐based methods and density functionals. The relative order of singlet and triplet excited states is established on the basis of the coupled cluster method CC2. We find that at least seven singlet excited states are required to assign all peaks in the UV/Vis spectrum. In addition, we have studied the solvatochromic effect on the excitation energies and found differential effects except for the first bright excited state. Vibrational frequencies as well as IR, Raman and resonance Raman intensities are simulated and compared to their experimental counterparts. We have assigned peaks, assessed the effect of anharmonicity, and confirmed the previous assignments in case of the most intense transitions. Finally, we have studied the NMR shieldings and established the effect of the solvent polarity. The present study provides data for lumiflavin in the gas phase and in implicit solvent model that can be used as a reference for the protein‐embedded flavin simulations and assignment of experimental spectra.     

Implicit solvent simulations of DNA and DNA-protein complexes: agreement with explicit solvent vs experiment

Molecular dynamics simulations of biomolecules with implicit solvent reduce the computational cost and complexity of such simulations so that longer time scales and larger system sizes can be reached. While implicit solvent simulations of proteins have become well established, the success of implicit solvent in the simulation of nucleic acids has not been fully established to date. Results obtained in this study demonstrate that stable and efficient simulations of DNA and a protein-DNA complex can be achieved with an implicit solvent model based on continuum dielectric electrostatics. Differences in conformational sampling of DNA with two sets of atomic radii that are used to define the dielectric interface between the solute and the continuum dielectric model of the solvent are investigated. Results suggest that depending on the choice of atomic radii agreement is either closer to experimental data or to explicit solvent simulations. Furthermore, partial conformational transitions toward A-DNA conformations when salt is added within the implicit solvent framework are observed.     

Identifying ligand binding sites and poses using GPU-accelerated Hamiltonian replica exchange molecular dynamics

We present a method to identify small molecule ligand binding sites and poses within a given protein crystal structure using GPU-accelerated Hamiltonian replica exchange molecular dynamics simulations. The Hamiltonians used vary from the physical end state of protein interacting with the ligand to an unphysical end state where the ligand does not interact with the protein. As replicas explore the space of Hamiltonians interpolating between these states, the ligand can rapidly escape local minima and explore potential binding sites. Geometric restraints keep the ligands from leaving the vicinity of the protein and an alchemical pathway designed to increase phase space overlap between intermediates ensures good mixing. Because of the rigorous statistical mechanical nature of the Hamiltonian exchange framework, we can also extract binding free energy estimates for all putative binding sites. We present results of this methodology applied to the T4 lysozyme L99A model system for three known ligands and one non-binder as a control, using an implicit solvent. We find that our methodology identifies known crystallographic binding sites consistently and accurately for the small number of ligands considered here and gives free energies consistent with experiment. We are also able to analyze the contribution of individual binding sites to the overall binding affinity. Our methodology points to near term potential applications in early-stage structure-guided drug discovery.     

Quantum Chemical Microsolvation by Automated Water Placement

We developed a quantitative approach to quantum chemical microsolvation. Key in our methodology is the automatic placement of individual solvent molecules based on the free energy solvation thermodynamics derived from molecular dynamics (MD) simulations and grid inhomogeneous solvation theory (GIST). This protocol enabled us to rigorously define the number, position, and orientation of individual solvent molecules and to determine their interaction with the solute based on physical quantities. The generated solute–solvent clusters served as an input for subsequent quantum chemical investigations. We showcased the applicability, scope, and limitations of this computational approach for a number of small molecules, including urea, 2-aminobenzothiazole, (+)-syn-benzotriborneol, benzoic acid, and helicene. Our results show excellent agreement with the available ab initio molecular dynamics data and experimental results.     

Theoretical study of the effects of solvent environment on photophysical properties and electronic structure of paracyclophane chromophores

We use first-principles quantum-chemical approaches to study absorption and emission properties of recently synthesized distyrylbenzene (DSB) derivative chromophores and their dimers (two DSB molecules linked through a [2.2]paracyclophane moiety). Several solvent models are applied to model experimentally observed shifts and radiative lifetimes in Stokes nonpolar organic solvents (toluene) and water. The molecular environment is simulated using the implicit solvation models, as well as explicit water molecules and counterions. Calculations show that neither implicit nor explicit solvent models are sufficient to reproduce experimental observations. The contact pair between the chromophore and counterion, on the other hand, is able to reproduce the experimental data when a partial screening effect of the solvent is taken into account. Based on our simulations we suggest two mechanisms for the excited-state lifetime increase in aqueous solutions. These findings may have a number of implications for organic light-emitting devices, electronic functionalities of soluble polymers and molecular fluorescent labels, and their possible applications as biosensors and charge/energy conduits in nanoassemblies.     

Conformational heterogeneity observed in simulations of a pyrene-substituted DNA

NMR studies previously carried out for a DNA system with a pyrene-substituted base did not observe NOEs involving the adenine located 5' to the pyrene, and thus the conformation of the adenine was poorly defined in the resulting family of refined structures. However, chemical shift data suggested that an AT base pair may be present. We have carried out fully unrestrained molecular dynamics simulations starting from several members of the family of structures, and these simulations support the existence of an AT base pair for this region. Simulations in both explicit and implicit solvent were carried out, with each converging to either anti or syn conformation for adenine and base pairing in all cases. During these simulations, large and dramatic conformational changes are observed that suggest pathways for complex conformational changes in the highly packed DNA interior. Our analysis reveals little difference in the energies of these syn and anti conformations, in contrast to control calculations carried out for standard DNA (in the absence of a neighboring pyrene). While no interconversion between the conformations was observed in standard simulations, reversible anti/syn exchange was directly simulated using the locally enhanced sampling approach. No exchange was seen in the non-pyrene control sequence. Together, these results suggest that an increased flexibility is introduced as a consequence of the pyrene substitution, offering an explanation that is consistent with the available experimental data. These results increase our optimism that simulations in atomic detail may provide accurate models for experimental observations in complex systems.     

Efficient solvent boundary potential for hybrid potential simulations

A common challenge in computational biophysics is to obtain statistical properties similar to those of an infinite bulk system from simulations of a system of finite size. In this work we describe a computationally efficient algorithm for performing hybrid quantum chemical/molecular mechanical (QC/MM) calculations with a solvent boundary potential. The system is partitioned into a QC region within which catalytic reactions occur, a spherical region with explicit solvent that envelops the quantum region and is treated with a MM model, and the surrounding bulk solvent that is treated implicitly by the boundary potential. The latter is constructed to reproduce the solvation free energy of a finite number of atoms embedded inside a low-dielectric sphere with variable radius, and takes into account electrostatic and van der Waals interactions between the implicit solvent and the QC and MM atoms in the central region. The method was implemented in the simulation program pDynamo and tested by examining elementary steps in the reaction mechanisms of two enzymes, citrate synthase and lactate dehydrogenase. Good agreement is found for the energies and geometries of the species along the reaction profiles calculated with the method and those obtained by previous experimental and computational studies. Directions in which the utility of the method can be further improved are discussed.     

Evaluating force field accuracy with long-time simulations of a β-hairpin tryptophan zipper peptide

We have combined graphics processing unit-accelerated all-atom molecular dynamics with parallel tempering to explore the folding properties of small peptides in implicit solvent on the time scale of microseconds. We applied this methodology to the synthetic β-hairpin, trpzip2, and one of its sequence variants, W2W9. Each simulation consisted of over 8 μs of aggregated virtual time. Several measures of folding behavior showed good convergence, allowing comparison with experimental equilibrium properties. Our simulations suggest that the intramolecular interactions of tryptophan side chains are responsible for much of the stability of the native fold. We conclude that the ff99 force field combined with ff96 φ and ψ dihedral energies and an implicit solvent can reproduce plausible folding behavior in both trpzip2 and W2W9.     

Treating entropy and conformational changes in implicit solvent simulations of small molecules

Implicit solvent models are increasingly popular for estimating aqueous solvation (hydration) free energies in molecular simulations and other applications. In many cases, parameters for these models are derived to reproduce experimental values for small molecule hydration free energies. Often, these hydration free energies are computed for a single solute conformation, neglecting solute conformational changes upon solvation. Here, we incorporate these effects using alchemical free energy methods. We find significant errors when hydration free energies are estimated using only a single solute conformation, even for relatively small, simple, rigid solutes. For example, we find conformational entropy (TDeltaS) changes of up to 2.3 kcal/mol upon hydration. Interestingly, these changes in conformational entropy correlate poorly (R2 = 0.03) with the number of rotatable bonds. The present study illustrates that implicit solvent modeling can be improved by eliminating the approximation that solutes are rigid.     

Electronic structure and conformational analysis of P218: An antimalarial drug candidate

P218 is one of the very important and recent lead compounds for antimalarial research. The 3D structural and electronic details of P218 are not available. In this article, quantum chemical studies to understand the possible 3D structures of P218 are reported and compared with 3D structures from the active site cavities of hDHFR and PfDHFR. The neutral P218, can adopt open chain as well as cyclic arrangements. Under implicit solvent condition a zwitterionic‐cyclic conformer is found to be quite possible. Microsolvation studies using explicit water molecules indicate that one water molecule may bridge the two ends of zwitterionic‐cyclic P218. It was observed that the protonation occurs preferentially at N¹ position of the 2,4‐diaminopyrimidine ring, with a proton affinity of 274.49 kcal/mol (implicit solvent phase) and 236.35 kcal/mol (gas phase). A dimer of P218 may be zwitterionic dimer, the dimer formation can release upto ～28.60 kcal/mol (implicit solvent phase).     

Evaluation of Poisson solvation models using a hybrid explicit/implicit solvent method

Implicit solvent methods have become popular tools in the field of protein dynamics simulations, yet evaluation of their validity has been primarily limited to comparisons with experimental and theoretical data for small molecules. In this paper, we use a recently developed hybrid explicit/implicit solvent methodology to evaluate the accuracy of several Poisson-based implicit solvent models. Specifically, we focus on the calculation of electrostatic solvation free energies of various fixed conformations for two proteins. We show that, among various dielectric boundary definitions, the Lee-Richards molecular surface has the best agreement with hybrid solvent results. Furthermore, certain modifications of the molecular surface Poisson protocol provide varied results. For instance, simple modifications of atomic radii on charged residues generally improve absolute errors but do not significantly reduce relative errors among conformations. On the other hand, using a water-probe radius of 1.0 A, as opposed to the standard value of 1.4 A, to generate the molecular surface, moderately improves both absolute and relative results.     

Tautomeric equilibrium of pyridoxine in water. Thermodynamic characterization by 13C and 15N nuclear magnetic resonance

A remarkable temperature dependence on the 13C NMR and 15N NMR chemical shifts of pyridoxine in water (pH = 7.0) has been observed. C-3, C-6, and N-1 were the most sensitive nuclei to the temperature effect. This dependence has been explained on the basis of an equilibrium shift thermally induced between the neutral and the dipolar form of this molecule. The thermodynamic characterization of tautomeric equilibria that interconvert quickly on the NMR time scale can be carried out from the observed average 13C NMR and 15N NMR chemical shifts at different temperatures (5-90 degrees C). We have developed a new method for the estimation of the thermodynamic parameters of a given equilibrium by fitting the experimental data to a theoretical curve. This new method allows us to improve the fitting results on our previously proposed methodology. We show that there are linear correlations between the average chemical shifts obtained from different nuclei at the same temperature. This indicates that the parameters of the pure forms are related among them. We have carried out a simultaneous multiple function curve fitting of all data obtained from the most sensitive signals together using these linear correlations as restricted conditions in order to diminish the number of independent parameters to fit. To test the new methodology, we have studied the thermodynamics of the tautomeric equilibrium of pyridoxine in water. We have obtained delta H degree values ranging from -23.6 +/- 1.3 to -25.8 +/- 1.7 kJ/mol for this equilibrium depending on the used data set. This kind of methodology has, among others, the following advantages: It allows the use of a great number of experimental points from different signals in the fitting process, it yields very precise and accurate values of the tautomeric process, and it allows the resolution of the problem with only 13C NMR data in some cases saving NMR time.     

Adding explicit solvent molecules to continuum solvent calculations for the calculation of aqueous acid dissociation constants

Aqueous acid dissociation free energies for a diverse set of 57 monoprotic acids have been calculated using a combination of experimental and calculated gas and liquid-phase free energies. For ionic species, aqueous solvation free energies were calculated using the recently developed SM6 continuum solvation model. This model combines a dielectric continuum with atomic surface tensions to account for bulk solvent effects. For some of the acids studied, a combined approach that involves attaching a single explicit water molecule to the conjugate base (anion), and then surrounding the resulting anion-water cluster by a dielectric continuum, significantly improves the agreement between the calculated pK(a) value and experiment. This suggests that for some anions, particularly those concentrating charge on a single exposed heteroatom, augmenting implicit solvent calculations with a single explicit water molecule is required, and adequate, to account for strong short-range hydrogen bonding interactions between the anion and the solvent. We also demonstrate the effect of adding several explicit waters by calculating the pK(a) of bicarbonate (HCO(3)(-)) using as the conjugate base carbonate (CO(3)(2-)) bound by up to three explicit water molecules.     

Root‐mean‐square‐deviation‐based rapid backbone resonance assignments in proteins

We have shown that the methodology based on the estimation of root‐mean‐square deviation (RMSD) between two sets of chemical shifts is very useful to rapidly assign the spectral signatures of ¹H^N, ¹³C^α, ¹³C^β, ¹³C′, ¹H^α and ¹⁵N spins of a given protein in one state from the knowledge of its resonance assignments in a different state, without resorting to routine established procedures (manual and automated). We demonstrate the utility of this methodology to rapidly assign the 3D spectra of a metal‐binding protein in its holo‐state from the knowledge of its assignments in apo‐state, the spectra of a protein in its paramagnetic state from the knowledge of its assignments in diamagnetic state and, finally, the spectra of a mutant protein from the knowledge of the chemical shifts of the corresponding wild‐type protein. The underlying assumption of this methodology is that, it is impossible for any two amino acid residues in a given protein to have all the six chemical shifts degenerate and that the protein under consideration does not undergo large conformational changes in going from one conformational state to another. The methodology has been tested using experimental data on three proteins, M‐crystallin (8.5 kDa, predominantly β‐sheet, for apo‐ to holo‐state), Calbindin (7.5 kDa, predominantly α‐helical, for diamagnetic to paramagnetic state and apo to holo) and EhCaBP1 (14.3 kDa, α‐helical, the wild‐type protein with one of its mutant). In all the cases, the extent of assignment is found to be greater than 85%. Copyright © 2010 John Wiley & Sons, Ltd.     

Stereochemistry of reactions in the 1,2-dimethylsilacyclopentane ring systems. I. Stereospecific transformations

Preparations, separations of geometric isomers, and structural assignments based on nmr and on chemical evidence are described for a number of 1-substituted 1,2-dimethylsilacyclopentanes. A number of stereospecific reactions have been observed, and the stereochemistry is in all cases the same as that observed for acyclic silanes. A discussion of the role of ring strain in determining stereochemical outcome and reaction rates is presented.     

Refractive index of liquid water in different solvent models

We present a combined molecular dynamics/quantum chemical perturbation method for calculating the refractive index of liquid water at different temperatures. We compare results of this method with the refractive index obtained from other solvent models. The best agreement with the experimental refractive index of liquid water and its temperature dependence is obtained using correlated gas-phase polarizabilities in the classical Lorentz-Lorenz expression. Also, the iterative self-consistent reaction field approach in the semicontinuum implementation matches the experimental refractive index reasonably well.     

A novel algorithm for creating coarse-grained, density dependent implicit solvent models

Implicit solvent simulations are those in which solvent molecules are not explicitly simulated, and the solute-solute interaction potential is modified to compensate for the implicit solvent effect. Implicit solvation is well known in Brownian dynamics of dilute solutions but offers promise to speed up many other types of molecular simulations as well, including studies of proteins and colloids where the local density can vary considerably. This work examines implicit solvent potentials within a more general coarse-graining framework. While a pairwise potential between solute sites is relatively simple and ubiquitous, an additional parametrization based on the local solute concentration has the possibility to increase the accuracy of the simulations with only a marginal increase in computational cost. We describe here a method in which the radial distribution function and excess chemical potential of solute insertion for a system of Lennard-Jones particles are first measured in a fully explicit, all-particle simulation, and then reproduced across a range of solute particle densities in an implicit solvent simulation.