Molecular dynamics simulations of a double unit cell in a protein crystal: volume relaxation at constant pressure and correlation of motions between the two unit cells

gmXtal: Cooking Crystals with GROMACS

Molecular dynamics (MD) simulations are routinely performed of biomolecules in solution, because this is their native environment. However, the structures used in such simulations are often obtained with X-ray crystallography, which provides the atomic coordinates of the biomolecule in a crystal environment. With the advent of free electron lasers and time-resolved techniques, X-ray crystallography can now also access metastable states that are intermediates in a biochemical process. Such experiments provide additional data, which can be used, for example, to optimize MD force fields. Doing so requires that the simulation of the biomolecule is also performed in the crystal environment. However, in contrast to simulations of biomolecules in solution, setting up a crystal is challenging. In particular, because not all solvent molecules are resolved in X-ray crystallography, adding a suitable number of solvent molecules, such that the properties of the crystallographic unit cell are preserved in the simulation, can be difficult and typically is a trial-and-error based procedure requiring manual interventions. Such interventions preclude high throughput applications. To overcome this bottleneck, we introduce gmXtal, a tool for setting up crystal simulations for MD simulations with GROMACS. With the information from the protein data bank (rcsb.org) gmXtal automatically (i) builds the crystallographic unit cell; (ii) sets the protonation of titratable residues; (iii) builds missing residues that were not resolved experimentally; and (iv) adds an appropriate number of solvent molecules to the system. gmXtal is available as a standalone tool https://gitlab.com/pbuslaev/gmxtal .

Two Liberibacter Proteins Combine to Suppress Critical Innate Immune Defenses in Citrus

We adopted a systems-based approach to determine the role of two Candidatus Liberibacter asiaticus (CLas) proteins, LasP ₂₃₅ and Effector 3, in Huanglongbing (HLB) pathogenesis. While a published work suggests the involvement of these CLas proteins HLB pathogenesis, the exact structure-based mechanism of their action has not been elucidated. We conducted the following experiments to determine the structure-based mechanisms of action. First, we immunoprecipitated the interacting citrus protein partners of LasP ₂₃₅ and Effector 3 from the healthy and CLas-infected Hamlin extracts and identified them by Liquid Chromatography with tandem mass spectrometry (LC-MS/MS). Second, we performed a split green fluorescent protein (GFP) assay in tobacco to validate that the interactions observed in vitro are also retained in planta. The notable in planta citrus targets of LasP ₂₃₅ and Effector 3 include citrus innate immune proteins. Third, in vitro and in planta studies were performed to show that LasP ₂₃₅ and Effector 3 interact with and inhibit the functions of multiple citrus proteins belonging to the innate immune pathways. These inhibitory interactions led to a high level of reactive oxygen species, blocking of bactericidal lipid transfer protein (LTP), and induction of premature programed cell death (PCD), all of which are beneficial to CLas lifecycle and HLB pathogenesis. Finally, we performed molecular dynamics simulations to visualize the interactions of LasP ₂₃₅ and Effector 3, respectively, with LTP and Kunitz protease inhibitor. This led to the design of an LTP mimic, which sequestered and blocked LasP ₂₃₅ and rescued the bactericidal activity of LTP thereby proving that LasP ₂₃₅ , indeed, participates in HLB pathogenesis.

Evaluation of SARS-CoV-2 main protease and inhibitor interactions using dihedral angle distributions and radial distribution function

In order to evaluate the interactions between a potential drug candidate like inhibitor N3 and the residues in substrate binding site of SARS-CoV-2 main protease (M pro ), we used molecular docking and dynamics simulations. The structural features describing the degrees of folding states ofM pro formed by beta-barrels and alpha-helices were analyzed by means of root mean square deviation, root mean square fluctuation, radius of gyration, residue velocity, H-bonding, dihedral angle distributions and radial distribution function. All of the residues forming ligand binding domain (LBD) ofM pro lie within the allowed region of the dihedral angle distributions as observed from the equilibrating best pose ofM pro -N3 system. Sharp peaks of radial distribution function (RDF) for H-bonding atom pairs (about 2 Å radial distance apart) describe the strong interactions between inhibitor and SARS-CoV-2M pro . During MD simulations, HSE163 has the lowest residue speed offering a sharp RDF peak whereas GLN192 has the highest residue speed resulting a flat RDF peak for the H-bonding atom pairs ofM pro -N3 system. Along with negative values of coulombic and Lenard-Jones energies, MM/PBSA free energy of binding contributed by the non-covalent interactions betweenM pro and N3 has been obtained to be -19.45 ± 3.6 kcal/mol. These physical parameters demonstrate the binding nature of an inhibitor inM pro -LBD. This study will be helpful in evaluating the drug candidates which are expected to inhibit the SARS-CoV-2 structural proteins.

Toward the correction of effective electrostatic forces in explicit-solvent molecular dynamics simulations: restraints on solvent-generated electrostatic potential and solvent polarization

Despite considerable advances in computing power, atomistic simulations under nonperiodic boundary conditions, with Coulombic electrostatic interactions and in systems large enough to reduce finite-size associated errors in thermodynamic quantities to within the thermal energy, are still not affordable. As a result, periodic boundary conditions, systems of microscopic size and effective electrostatic interaction functions are frequently resorted to. Ensuing artifacts in thermodynamic quantities are nowadays routinely corrected a posteriori, but the underlying configurational sampling still descends from spurious forces. The present study addresses this problem through the introduction of on-the-fly corrections to the physical forces during an atomistic molecular dynamics simulation. Two different approaches are suggested, where the force corrections are derived from special potential energy terms. In the first approach, the solvent-generated electrostatic potential sampled at a given atom site is restrained to a target value involving corrections for electrostatic artifacts. In the second approach, the long-range regime of the solvent polarization around a given atom site is restrained to the Born polarization, i.e., the solvent polarization corresponding to the ideal situation of a macroscopic system under nonperiodic boundary conditions and governed by Coulombic electrostatic interactions. The restraints are applied to the explicit-water simulation of a hydrated sodium ion, and the effect of the restraints on the structural and energetic properties of the solvent is illustrated. Furthermore, by means of the calculation of the charging free energy of a hydrated sodium ion, it is shown how the electrostatic potential restraint translates into the on-the-fly consideration of the corresponding free-energy correction terms. It is discussed how the restraints can be generalized to situations involving several solute particles. Although the present study considers a very simple system only, it is an important step toward the on-the-fly elimination of finite-size and approximate-electrostatic artifacts during atomistic molecular dynamics simulations.

Conformational exchange in a membrane transport protein is altered in protein crystals

Successful macromolecular crystallography requires solution conditions that may alter the conformational sampling of a macromolecule. Here, site-directed spin labeling is used to examine a conformational equilibrium within BtuB, the Escherichia coli outer membrane transporter for vitamin B(12). Electron paramagnetic resonance (EPR) spectra from a spin label placed within the N-terminal energy coupling motif (Ton box) of BtuB indicate that this segment is in equilibrium between folded and unfolded forms. In bilayers, substrate binding shifts this equilibrium toward the unfolded form; however, EPR spectra from this same spin-labeled mutant indicate that this unfolding transition is blocked in protein crystals. Moreover, crystal structures of this spin-labeled mutant are consistent with the EPR result. When the free energy difference between substates is estimated from the EPR spectra, the crystal environment is found to alter this energy by 3 kcal/mol when compared to the bilayer state. Approximately half of this energy change is due to solutes or osmolytes in the crystallization buffer, and the remainder is contributed by the crystal lattice. These data provide a quantitative measure of how a conformational equilibrium in BtuB is modified in the crystal environment, and suggest that more-compact, less-hydrated substates will be favored in protein crystals.

Molecular dynamics simulations of a reversibly folding beta-heptapeptide in methanol: influence of the treatment of long-range electrostatic interactions

Eight 100-ns molecular dynamics simulations of a beta-heptapeptide in methanol at 340 K (within cubic periodic computational boxes of about 6-nm edge) are reported and compared. These simulations were performed with three different charge-state combinations at the peptide termini, one of them with or without a neutralizing chloride counterion, and using either the lattice-sum (LS) or reaction-field (RF) scheme to handle electrostatic interactions. The choice of the electrostatic scheme has essentially no influence on the folding-unfolding equilibrium when the peptide termini are uncharged and only a small influence when the peptide is positively charged at its N-terminus (with or without inclusion of a neutralizing chloride counterion). However, when the peptide is zwitterionic, the LS scheme leads to preferential sampling of the high-dipole folded helical state, whereas the RF scheme leads to preferential sampling of a low-dipole unfolded salt-bridged state. A continuum electrostatics analysis based on the sampled configurations (zwitterionic case) suggests that the LS scheme stabilizes the helical state through artificial periodicity, but that the magnitude of this perturbation is essentially negligible (compared to the thermal energy) for the large box size and relatively polar solvent considered. The results thus provide clear evidence (continuum electrostatics analysis) for the absence of LS artifacts and some indications (still not definitive because of the limited sampling of the folding-unfolding transition) for the presence of RF artifacts in this specific system.

Dynamics of antibody domains studied by solution NMR

Information on local dynamics of antibodies is important to evaluate stability, to rationally design variants, and to clarify conformational disorders at the epitope binding sites. Such information may also be useful for improved understanding of antigen recognition. NMR can be used for characterization of local protein dynamics at the atomic level through relaxation measurements. Due to the complexity of the NMR spectra, an extensive use of this method is limited to small protein molecules, for example, antibody domains and some scFv. Here, we describe a protocol that was used to study the dynamics of an antibody domain in solution using NMR. We describe protein preparation for NMR studies, NMR sample optimization, signal assignments, and dynamics experiments.

Molecular dynamics simulation of the neuroglobin crystal: comparison with the simulation in solution

Neuroglobin (Ngb) is a monomeric protein that, despite the small sequence similarity with other globins, displays the typical globin fold. In the absence of exogenous ligands, the ferric and the ferrous forms of Ngb are both hexacoordinated to the distal and proximal histidines. In the ferrous form, oxygen, nitric oxide or carbon monoxide can displace the distal histidine, yielding a reversible adduct. Crystallographic data show that the binding of an exogenous ligand is associated to structural changes involving heme sliding and a topological reorganization of the internal cavities. Molecular dynamics (MD) simulations in solution show that the heme oscillates between two positions, much as the ones observed in the crystal structure, although the occupancy is different. The simulations also suggest that ligand binding in solution can affect the flexibility and conformation of residues connecting the C and D helices, referred to as the CD corner, which is coupled to the configuration adopted by the distal histidine. In this study, we report the results of 30 ns MD simulations of CO-bound Ngb in the crystal. Our goal was to compare the protein dynamical behavior in the crystal with the results supplied by the previous MD simulation of CO-bound Ngb in solution and the x-ray experimental data. The results show that the different environments (crystal or solution) affect the dynamics of the heme group and of the CD corner.

Molecular dynamics simulations for water and ions in protein crystals

The spatial and temporal properties of water and ions in bionanoporous materials-protein crystals-have been investigated using molecular dynamics simulations. Three protein crystals are considered systematically with different morphologies and chemical topologies: tetragonal lysozyme, orthorhombic lysozyme, and tetragonal thermolysin. It is found that the thermal fluctuations of C(alpha) atoms in the secondary structures of protein molecules are relatively weak due to hydrogen bonding. The solvent-accessible surface area per residue is nearly identical in the three protein crystals; the hydrophobic and hydrophilic residues in each crystal possess approximately the same solvent-accessible surface area. Water distributes heterogeneously and has different local structures within the biological nanopores of the three protein crystals. The mobility of water and ions in the crystals is enhanced as the porosity increases and also by the fluctuations of protein atoms particularly in the two lysozyme crystals. Anisotropic diffusion is found preferentially along the pore axis, as experimentally observed. The anisotropy of the three crystals increases in the order: tetragonal thermolysin < tetragonal lysozyme < orthorhombic lysozyme.

Membrane protein dynamics and detergent interactions within a crystal: a simulation study of OmpA

Molecular dynamics (MD) simulations are used to explore the dynamics of a membrane protein in its crystal environment. A 50-ns-duration simulation (at a temperature of 300 K) is performed for the crystallographic unit cell of the bacterial outer membrane protein OmpA. The unit cell contains four protein molecules, plus detergent molecules and water. An excellent correlation between simulated and experimental values of crystallographic B factors is observed. Effectively, 0.2 micros of protein trajectories are obtained, allowing a critical assessment of simulation quality. Some deficiency in conformational sampling is demonstrated, but averaging over multiple trajectories improves this limitation. The previously undescribed structure and dynamics of detergent molecules in a unit cell are reported here, providing insight into the interactions important in the formation and stabilization of the crystalline environment at room temperature. In particular, we show that at room temperature the detergent molecules form a dynamic, extended micellar structure spreading over adjacent OmpA monomers within the crystal.

Combining the lattice-sum and reaction-field approaches for evaluating long-range electrostatic interactions in molecular simulations

A new scheme, the lattice-sum-emulated reaction-field (LSERF) method, is presented that combines the lattice-sum (LS) and reaction-field (RF) approaches for evaluating electrostatic interactions in molecular simulations. More precisely, the LSERF scheme emulates a RF calculation (based on an atomic cutoff) via the LS machinery. This is achieved by changing the form of the electrostatic interactions in a standard LS calculation (Coulombic) to the form corresponding to RF electrostatics (Coulombic plus quadratic reaction-field correction term, truncated at the cutoff distance). It is shown (both analytically and numerically) that in the limit of infinite reciprocal-space accuracy, (i) the LSERF scheme with a finite reaction-field cutoff and a given reaction-field permittivity is identical to the RF scheme with the same parameters (and an atomic cutoff), and (ii) the LSERF scheme is identical to the LS scheme in the limit of an infinite reaction-field cutoff, irrespective of the reaction-field permittivity. This new scheme offers two key advantages: (i) from a conceptual point of view, it shows that there is a continuity between the RF and LS schemes and unifies them into a common framework; (ii) from a practical point of view, it allows us to perform RF calculations with arbitrarily large reaction-field cutoff distances for the same computational costs as a corresponding LS calculation. The optimal choice for the cutoff will be the one that achieves the best compromise between artifacts arising from the dielectric heterogeneity of the system (short cutoff) and its artificial periodicity (long cutoff). The implementation of the LSERF method is extremely easy, requiring only very limited modifications of any standard LS code. For practical applications to biomolecular systems, the use of the LSERF scheme with large reaction-field cutoff distances is expected to represent a significant improvement over the current RF simulations involving comparatively much shorter cutoffs.

Diffusion of water and sodium counter-ions in nanopores of a β-lactoglobulin crystal: a molecular dynamics study

The dynamics of water and sodium counter-ions (Na(+)) in a C222(1) orthorhombic β-lactoglobulin crystal is investigated by means of 5 ns molecular dynamics simulations. The effect of the fluctuation of the protein atoms on the motion of water and sodium ions is studied by comparing simulations in a rigid and in a flexible lattice. The electrostatic interactions of sodium ions with the positively charged LYS residues inside the crystal channels significantly influence the ionic motion. According to our results, water molecules close to the protein surface undergo an anomalous diffusive motion. On the other hand, the motion of water molecules further away from the protein surface is normal diffusive. Protein fluctuations affect the diffusion constant of water, which increases from 0.646 ± 0.108 to 0.887 ± 0.41 nm(2) ns(-1), when protein fluctuations are taken into account. The pore size (0.63-1.05 nm) and the water diffusivities are in good agreement with previous experimental results. The dynamics of sodium ions is disordered. LYS residues inside the pore are the main obstacles to the motion of sodium ions. However, the simulation time is still too short for providing a precise description of anomalous diffusion of sodium ions. The results are not only of interest for studying ion and water transport through biological nanopores, but may also elucidate water-protein and ion-protein interactions in protein crystals.

Fluctuations and correlations in crystalline protein dynamics: a simulation analysis of staphylococcal nuclease

Understanding collective motions in protein crystals is likely to furnish insight into functional protein dynamics and will improve models for refinement against diffraction data. Here, four 10 ns molecular dynamics simulations of crystalline Staphylococcal nuclease are reported and analyzed in terms of fluctuations and correlations in atomic motion. The simulation-derived fluctuations strongly correlate with, but are slightly higher than, the values derived from the experimental B-factors. Approximately 70% of the atomic fluctuations are due to internal protein motion. For 65% of the protein atoms the internal fluctuations converge on the nanosecond timescale. Convergence is much slower for the elements of the interatomic displacement correlation matrix--of these, >80% converge within 1 ns for interatomic distances less, approximately <6 A, but only 10% for separations approximately =12 A. Those collective motions that converged on the nanosecond timescale involve mostly correlations within the beta-barrel or between alpha-helices of the protein. The R-factor with the experimental x-ray diffuse scattering for the crystal, which is determined by the displacement variance-covariance matrix, decreases to 8% after 10 ns simulation. Both the number of converged correlation matrix elements and the R-factor depend logarithmically on time, consistent with a model in which the number of energy minima sampled depends exponentially on the maximum energy barrier crossed. The logarithmic dependence is also extrapolated to predict a convergence time for the whole variance-covariance matrix of approximately 1 micros.

Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations

Computational studies of proteins based on empirical force fields represent a powerful tool to obtain structure-function relationships at an atomic level, and are central in current efforts to solve the protein folding problem. The results from studies applying these tools are, however, dependent on the quality of the force fields used. In particular, accurate treatment of the peptide backbone is crucial to achieve representative conformational distributions in simulation studies. To improve the treatment of the peptide backbone, quantum mechanical (QM) and molecular mechanical (MM) calculations were undertaken on the alanine, glycine, and proline dipeptides, and the results from these calculations were combined with molecular dynamics (MD) simulations of proteins in crystal and aqueous environments. QM potential energy maps of the alanine and glycine dipeptides at the LMP2/cc-pVxZ//MP2/6-31G* levels, where x = D, T, and Q, were determined, and are compared to available QM studies on these molecules. The LMP2/cc-pVQZ//MP2/6-31G* energy surfaces for all three dipeptides were then used to improve the MM treatment of the dipeptides. These improvements included additional parameter optimization via Monte Carlo simulated annealing and extension of the potential energy function to contain peptide backbone phi, psi dihedral crossterms or a phi, psi grid-based energy correction term. Simultaneously, MD simulations of up to seven proteins in their crystalline environments were used to validate the force field enhancements. Comparison with QM and crystallographic data showed that an additional optimization of the phi, psi dihedral parameters along with the grid-based energy correction were required to yield significant improvements over the CHARMM22 force field. However, systematic deviations in the treatment of phi and psi in the helical and sheet regions were evident. Accordingly, empirical adjustments were made to the grid-based energy correction for alanine and glycine to account for these systematic differences. These adjustments lead to greater deviations from QM data for the two dipeptides but also yielded improved agreement with experimental crystallographic data. These improvements enhance the quality of the CHARMM force field in treating proteins. This extension of the potential energy function is anticipated to facilitate improved treatment of biological macromolecules via MM approaches in general.

Structural features of human initiation factor 4E, studied by X-ray crystal analyses and molecular dynamics simulations

The structural features of human eIF4E were investigated by X-ray crystal analyses of its cap analog (m(7)GTP and m(7)GpppA) complexes and molecular dynamics (MD) simulations of cap-free and cap-bound eIF4Es, as well as the cap-bound Ser209-phosphorylated eIF4E. Crystal structure analyses at 2.0 A resolution revealed that the molecule forms a temple-bell-shaped surface of eight antiparallel beta-structures, three alpha-helices and ten loop structures, where the N-terminal region corresponds to the handle of the bell. This concave backbone provides a scaffold for the mRNA cap-recognition pocket consisting of three receiving parts for the 5'-terminal m(7)G base, the triphosphate, and the second nucleotide. The m(7)G base is sandwiched between the two aromatic side-chains of Trp102 and Trp56. The two (m(7)G)NH-O (Glu103 carboxy group) hydrogen bonds stabilize the stacking interaction. The basic residues of Arg157 and Lys162 and water molecules construct a binding pocket for the triphosphate moiety, where a universal hydrogen-bonding network is formed. The flexible C-terminal loop region unobserved in the m(7)GTP complex was clearly observed in the m(7)GpppA complex, as a result of the fixation of this loop by the interaction with the adenosine moiety, indicating the function of this loop as a receiving pocket for the second nucleotide. On the other hand, MD simulation in an aqueous solution system revealed that the cap-binding pocket, especially its C-terminal loop structure, is flexible in the cap-free eIF4E, and the entrance of the cap-binding pocket becomes narrow, although the depth is relatively unchanged. SDS-PAGE analyses showed that this structural instability is highly related to the fast degradation of cap-free eIF4E, compared with cap-bound or 4E-BP/cap-bound eIF4E, indicating the conferment of structural stability of eIF4E by the binary or ternary complex formation. MD simulation of m(7)GpppA-bound Ser209-phosphorylated eIF4E showed that the size of the cap-binding entrance is dependent on the ionization state in the Ser209 phosphorylation, which is associated with the regulatory function through the switching on/off of eIF4E phosphorylation.