Molecular dynamics simulations of the d(CCAACGTTGG)(2) decamer: influence of the crystal environment

Molecular dynamics (MD) simulations of the DNA duplex d(CCAACGTTGG)(2) were used to study the relationship between DNA sequence and structure. Two crystal simulations were carried out; one consisted of one unit cell containing two duplexes, and the other of two unit cells containing four duplexes. Two solution simulations were also carried out, one starting from canonical B-DNA and the other starting from the crystal structure. For many helicoidal parameters, the results from the crystal and solution simulations were essentially identical. However, for other parameters, in particular, alpha, gamma, delta, (epsilon - zeta), phase, and helical twist, differences between crystal and solution simulations were apparent. Notably, during crystal simulations, values of helical twist remained comparable to those in the crystal structure, to include the sequence-dependent differences among base steps, in which values ranged from 20 degrees to 50 degrees per base step. However, in the solution simulations, not only did the average values of helical twist decrease to approximately 30 degrees per base step, but every base step was approximately 30 degrees, suggesting that the sequence-dependent information may be lost. This study reveals that MD simulations of the crystal environment complement solution simulations in validating the applicability of MD to the analysis of DNA structure.     

Reproducible polypeptide folding and structure prediction using molecular dynamics simulations

The folding of a polypeptide from an extended state to a well-defined conformation is studied using microsecond classical molecular dynamics (MD) simulations and replica exchange molecular dynamics (REMD) simulations in explicit solvent and in vacuo. It is shown that the solvated peptide folds many times in the REMD simulations but only a few times in the conventional simulations. From the folding events in the classical simulations we estimate an approximate folding time of 1-2 micros. The REMD simulations allow enough sampling to deduce a detailed Gibbs free energy landscape in three dimensions. The global minimum of the energy landscape corresponds to the native state of the peptide as determined previously by nuclear magnetic resonance (NMR) experiments. Starting from an extended state it takes about 50 ns before the native structure appears in the REMD simulations, about an order of magnitude faster than conventional MD. The calculated melting curve is in good qualitative agreement with experiment. In vacuo, the peptide collapses rapidly to a conformation that is substantially different from the native state in solvent.     

Long time dynamics of Met-enkephalin: comparison of explicit and implicit solvent models

Met-enkephalin is one of the smallest opiate peptides. Yet, its dynamical structure and receptor docking mechanism are still not well understood. The conformational dynamics of this neuron peptide in liquid water are studied here by using all-atom molecular dynamics (MD) and implicit water Langevin dynamics (LD) simulations with AMBER potential functions and the three-site transferable intermolecular potential (TIP3P) model for water. To achieve the same simulation length in physical time, the full MD simulations require 200 times as much CPU time as the implicit water LD simulations. The solvent hydrophobicity and dielectric behavior are treated in the implicit solvent LD simulations by using a macroscopic solvation potential, a single dielectric constant, and atomic friction coefficients computed using the accessible surface area method with the TIP3P model water viscosity as determined here from MD simulations for pure TIP3P water. Both the local and the global dynamics obtained from the implicit solvent LD simulations agree very well with those from the explicit solvent MD simulations. The simulations provide insights into the conformational restrictions that are associated with the bioactivity of the opiate peptide dermorphin for the delta-receptor.     

Experimental verification of lipid bilayer structure through multi-scale modeling

Great progress has been made in applying coarse-grain molecular dynamics (CGMD) simulations to the investigation of membrane biophysics. In order to validate the accuracy of CGMD simulations of membranes, atomistic scale detail is necessary for direct comparison to structural experiments. Here, we present our strategy for verifying CGMD lipid bilayer simulations. Through reverse coarse graining and subsequent calculation of the bilayer electron density profile, we are able to compare the simulations to our experimental low angle X-ray scattering (LAXS) data. In order to determine the best match to the experimental data, atomistic simulations are run at a range of areas (in the NP_NAT ensemble), starting from distinct configurations extracted from the CGMD simulation (run in the NPT ensemble). We demonstrate the effectiveness of this procedure with two small, single-component bilayers, and suggest that the greater utility of our algorithm will be for CGMD simulations of more complex structures.     

Exploring the energy landscape of protein folding using replica-exchange and conventional molecular dynamics simulations

Two independent replica-exchange molecular dynamics (REMD) simulations with an explicit water model were performed of the Trp-cage mini-protein. In the first REMD simulation, the replicas started from the native conformation, while in the second they started from a nonnative conformation. Initially, the first simulation yielded results qualitatively similar to those of two previously published REMD simulations: the protein appeared to be over-stabilized, with the predicted melting temperature 50-150K higher than the experimental value of 315K. However, as the first REMD simulation progressed, the protein unfolded at all temperatures. In our second REMD simulation, which starts from a nonnative conformation, there was no evidence of significant folding. Transitions from the unfolded to the folded state did not occur on the timescale of these simulations, despite the expected improvement in sampling of REMD over conventional molecular dynamics (MD) simulations. The combined 1.42 micros of simulation time was insufficient for REMD simulations with different starting structures to converge. Conventional MD simulations at a range of temperatures were also performed. In contrast to REMD, the conventional MD simulations provide an estimate of Tm in good agreement with experiment. Furthermore, the conventional MD is a fraction of the cost of REMD and continuous, realistic pathways of the unfolding process at atomic resolution are obtained.     

Molecular dynamics simulations of concentrated aqueous electrolyte solutions

Transport properties of concentrated electrolytes have been analysed using classical molecular dynamics simulations with the algorithms and parameters typical of simulations describing complex electrokinetic phenomena. The electrical conductivity and transport numbers of electrolytes containing monovalent (KCl), divalent (MgCl₂), a mixture of both (KCl+MgCl₂) and trivalent (LaCl₃) cations have been obtained from simulations of the electrolytes in electric fields of different magnitude. The results obtained for different simulation parameters have been discussed and compared with experimental measurements of our own and from the literature. The electroosmotic flow of water molecules induced by the ionic current in different cases has been calculated and interpreted with the help of the hydration properties extracted from the simulations.     

A multiscale coarse-grained model of the SARS-CoV-2 virion

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the causative agent of the COVID-19 pandemic. Computer simulations of complete viral particles can provide theoretical insights into large-scale viral processes including assembly, budding, egress, entry, and fusion. Detailed atomistic simulations are constrained to shorter timescales and require billion-atom simulations for these processes. Here, we report the current status and ongoing development of a largely “bottom-up” coarse-grained (CG) model of the SARS-CoV-2 virion. Data from a combination of cryo-electron microscopy (cryo-EM), x-ray crystallography, and computational predictions were used to build molecular models of structural SARS-CoV-2 proteins, which were then assembled into a complete virion model. We describe how CG molecular interactions can be derived from all-atom simulations, how viral behavior difficult to capture in atomistic simulations can be incorporated into the CG models, and how the CG models can be iteratively improved as new data become publicly available. Our initial CG model and the detailed methods presented are intended to serve as a resource for researchers working on COVID-19 who are interested in performing multiscale simulations of the SARS-CoV-2 virion.     

Conformational transitions of flanking purines in HIV-1 RNA dimerization initiation site kissing complexes studied by CHARMM explicit solvent molecular dynamics

Dimerization of HIV-1 genomic RNA is initiated by kissing loop interactions at the Dimerization Initiation Site (DIS). Dynamics of purines that flank the 5' ends of the loop-loop helix in HIV-1 DIS kissing complex were explored using explicit solvent molecular dynamics (MD) simulations with the CHARMM force field. Multiple MD simulations (200 ns in total) of X-ray structures for HIV-1 DIS Subtypes A, B, and F revealed conformational variability of flanking purines. In particular, the flanking purines, which in the starting X-ray structures are bulged-out and stack in pairs, formed a consecutive stack of four bulged-out adenines at the beginning of several simulations. This conformation is seen in the crystal structure of DIS Subtype F with no interference from crystal packing, and was frequently reported in our preceding MD studies performed with the AMBER force field. However, as CHARMM simulations progressed, the four continuously stacked adenines showed conformational transitions from the bulged-out into the bulged-in geometries. Although such an arrangement has not been seen in any X-ray structure, it has been suggested by a recent NMR investigation. In CHARMM simulations, in the longer time scale, the flanking purines display the tendency to move to bulged-in conformations. This is in contrast with the AMBER simulations, which indicate a modest prevalence for bulged-out flanking base positions in line with the X-ray data. The simulations also suggest that the intermolecular stacking between purines from the opposite hairpins can additionally stabilize the kissing complex.     

Simulating force-induced conformational transitions in polysaccharides with the SMD replica exchange method

Conventional steered molecular dynamics (SMD) simulations do not readily reproduce equilibrium conditions of atomic force microscopy (AFM) stretch and release measurements of polysaccharides undergoing force-induced conformational transitions because of the gap between the timescales of computer simulations ( approximately 1 mus) and AFM measurements ( approximately 1 s). To circumvent this limitation, we propose using the replica exchange method (REM) to enhance sampling during SMD simulations. By applying REM SMD to a small polysaccharide system and comparing the results with those from AFM stretching experiments, we demonstrate that REM SMD reproduces the experimental results not only qualitatively but quantitatively, approaching near equilibrium conditions of AFM measurements. As tested in this work, hysteresis and computational time of REM SMD simulations of short polysaccharide chains are significantly reduced as compared to regular SMD simulations, making REM SMD an attractive tool for studying forced-induced conformational transitions of small biopolymer systems.     

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

Eight molecular dynamics simulations of a double crystal unit cell of ubiquitin were performed to investigate the effects of simulating at constant pressure and of simulating two unit cells compared to a single unit cell. To examine the influence of different simulation conditions, the constant-pressure and constant-volume simulations were each performed with and without counterions and using two different treatments of the long-range electrostatic interactions (lattice-sum and reaction-field methods). The constant-pressure simulations were analyzed in terms of unit cell deformation and accompanying protein deformations. Energetic and structural properties of the proteins in the simulations of the double unit cell were compared to the results of previously reported one-unit-cell simulations. Correlation between the two unit cells was also investigated based on relative translational and rotational movements of the proteins and on dipole fluctuations. The box in the constant-pressure simulations is found to deform slowly to reach convergence only after 5-10 ns. This deformation does not result from a distortion in the structure of the proteins but rather from changes in protein packing within the unit cell. The results of the double-unit-cell simulations are closely similar to the results of the single-unit-cell simulations, and little motional correlation is found between the two unit cells.     

Molecular‐Dynamics Simulation of Dioxygen Egress from 12/15‐Lipoxygenase?Arachidonic Acid Complex

Extensive random‐acceleration molecular‐dynamics (RAMD) simulations of the egress of dioxygen (O₂) from a model of rabbit 12/15‐lipoxygenase? arachidonic acid complex disclosed several exit portals in addition to those previously described from implicit ligand sampling calculations and limited MD simulations.     

Construction of a risk model through the fusion of experimental data and finite element modeling: Application to car crash-induced TBI

This article introduces a new approach for the construction of a risk model for the prediction of Traumatic Brain Injury (TBI) as a result of a car crash. The probability of TBI is assessed through the fusion of an experiment-based logistic regression risk model and a finite element (FE) simulation-based risk model. The proposed approach uses a multilevel framework which includes FE simulations of vehicle crashes with dummy and FE simulations of the human brain. The loading conditions derived from the crash simulations are transferred to the brain model thus allowing the calculation of injury metrics such as the Cumulative Strain Damage Measure (CSDM). The framework is used to propagate uncertainties and obtain probabilities of TBI based on the CSDM injury metric. The risk model from FE simulations is constructed from a support vector machine classifier, adaptive sampling, and Monte-Carlo simulations. An approach to compute the total probability of TBI, which combines the FE-based risk assessment as well as the risk prediction from the experiment-based logistic regression model is proposed. In contrast to previous published work, the proposed methodology includes the uncertainty of explicit parameters such as impact conditions (e.g., velocity, impact angle), and material properties of the brain model. This risk model can provide, for instance, the probability of TBI for a given assumed crash impact velocity.     

A test of improved force field parameters for urea: molecular-dynamics simulations of urea crystals

Molecular-dynamics (MD) simulations of urea crystals of different shapes (cubic, rectangular prismatic, and sheet) have been performed using our previously published force field for urea. This force field has been validated by calculating values for the cohesive energy, sublimation temperature, and melting point from the MD data. The cohesive energies computed from simulations of cubic and rectangular prismatic urea crystals in vacuo at 300 K agreed very well with the experimental sublimation enthalpies reported at 298 K. We also found very good agreement between the melting points as observed experimentally and from simulations. Annealing the crystals just below the melting point leads to reconstruction to form crystal faces that are consistent with experimental observations. The simulations reveal a melting mechanism that involves surface (corner/edge) melting well below the melting point, and rotational disordering of the urea molecules in the corner/edge regions of the crystal, which then facilitates the translational motion of these molecules.     

Heat capacities of supercritical fluids via Grand Canonical ensemble simulations

In this work, suitable mathematical relationships to compute isobaric heat capacities from molecular simulations in the Grand Canonical (GC) ensemble are derived and tested via Monte Carlo methods. Using atomistic classical force fields, the residual isobaric heat capacities of pure carbon dioxide (CO₂) and pure methanol (MeOH) were obtained at supercritical conditions (with critical properties estimated from a finite-size scaling analysis). The total isobaric heat capacity was determined by combining the residual isobaric heat capacity obtained from molecular simulations with the ideal gas contributions obtained from experimental correlations. Isobaric heat capacities generated from both GC and Isothermal–Isobaric ensemble simulations were compared to predictions from accurate equations of state (EOS)s for CO₂ and MeOH at corresponding reduced temperatures and pressures. Isobaric heat capacities calculated from both ensembles were in good agreement with those obtained from the Span and Wagner EOS for CO₂ and the IUPAC EOS for MeOH. For comparable computation times, simulations run in the GC ensemble generate results with significantly lower statistical uncertainty than those run in the Isothermal–Isobaric ensemble.     

Refinement of protein structure homology models via long, all-atom molecular dynamics simulations

Accurate computational prediction of protein structure represents a longstanding challenge in molecular biology and structure-based drug design. Although homology modeling techniques are widely used to produce low-resolution models, refining these models to high resolution has proven difficult. With long enough simulations and sufficiently accurate force fields, molecular dynamics (MD) simulations should in principle allow such refinement, but efforts to refine homology models using MD have for the most part yielded disappointing results. It has thus far been unclear whether MD-based refinement is limited primarily by accessible simulation timescales, force field accuracy, or both. Here, we examine MD as a technique for homology model refinement using all-atom simulations, each at least 100 μs long-more than 100 times longer than previous refinement simulations-and a physics-based force field that was recently shown to successfully fold a structurally diverse set of fast-folding proteins. In MD simulations of 24 proteins chosen from the refinement category of recent Critical Assessment of Structure Prediction (CASP) experiments, we find that in most cases, simulations initiated from homology models drift away from the native structure. Comparison with simulations initiated from the native structure suggests that force field accuracy is the primary factor limiting MD-based refinement. This problem can be mitigated to some extent by restricting sampling to the neighborhood of the initial model, leading to structural improvement that, while limited, is roughly comparable to the leading alternative methods.     

Simplified boundary conditions alter cortical-trabecular load sharing at the distal radius; A multiscale finite element analysis

High-resolution peripheral quantitative computed tomography (HR-pQCT) derived micro-finite element (FE) modeling is used to evaluate mechanical behavior at the distal radius microstructure. However, these analyses typically simulate non-physiologic simplified platen-compression boundary conditions on a small section of the distal radius. Cortical and trabecular regions contribute uniquely to distal radius mechanical behavior, and various factors affect these regions distinctly. Generalized strength predictions from standardized platen-compression analyses may not adequately capture region specific responses in bone. Our goal was to compare load sharing within the cortical-trabecular compartments between the standardized platen-compression BC simulations, and physiologic BC simulations using a validated multiscale approach. Clinical- and high-resolution images were acquired from nine cadaveric forearm specimens using an HR-pQCT scanner. Multiscale FE models simulating physiologic BCs, and micro-FE only models simulating platen-compression BCs were created for each specimen. Cortical and trabecular loads (N) along the length of the distal radius micro-FE section were compared between BCs using correlations. Principal strain distributions were also compared quantitatively. Cortical and trabecular loads from the platen-compression BC simulations were strongly correlated to the physiologic BC simulations. However, a 30% difference in cortical loads distally, and a 53% difference in trabecular loads proximally was observed under platen BC simulations. Also, distribution of principal strains was clearly different. Our data indicated that platen-compression BC simulations alter cortical-trabecular load sharing. Therefore, results from these analyses should be interpreted in the appropriate mechanical context for clinical evaluations of normal and pathologic mechanical behavior at the distal radius.     

Conformational Dynamics of a Ligand-Free Adenylate Kinase

Adenylate kinase (AdK) is a phosphoryl-transfer enzyme with important physiological functions. Based on a ligand-free open structure and a ligand-bound closed structure solved by crystallography, here we use molecular dynamics simulations to examine the stability and dynamics of AdK conformations in the absence of ligands. We first perform multiple simulations starting from the open or the closed structure, and observe their free evolutions during a simulation time of 100 or 200 nanoseconds. In all seven simulations starting from the open structure, AdK remained stable near the initial conformation. The eight simulations initiated from the closed structure, in contrast, exhibited large variation in the subsequent evolutions, with most (seven) undergoing large-scale spontaneous conformational changes and approaching or reaching the open state. To characterize the thermodynamics of the transition, we propose and apply a new sampling method that employs a series of restrained simulations to calculate a one-dimensional free energy along a curved pathway in the high-dimensional conformational space. Our calculated free energy profile features a single minimum at the open conformation, and indicates that the closed state, with a high (∼13 kcal/mol) free energy, is not metastable, consistent with the observed behaviors of the unrestrained simulations. Collectively, our simulations suggest that it is energetically unfavorable for the ligand-free AdK to access the closed conformation, and imply that ligand binding may precede the closure of the enzyme.     

Dimerization of the p53 oligomerization domain: identification of a folding nucleus by molecular dynamics simulations

Dimerization of the p53 oligomerization domain involves coupled folding and binding of monomers. To examine the dimerization, we have performed molecular dynamics (MD) simulations of dimer folding from the rate-limiting transition state ensemble (TSE). Among 799 putative transition state structures that were selected from a large ensemble of high-temperature unfolding trajectories, 129 were identified as members of the TSE via calculation of a 50% transmission coefficient from at least 20 room-temperature simulations. This study is the first to examine the refolding of a protein dimer using MD simulations in explicit water, revealing a folding nucleus for dimerization. Our atomistic simulations are consistent with experiment and offer insight that was previously unobtainable.     

Modeling and simulations of a bacterial outer membrane protein: OprF from Pseudomonas aeruginosa

OprF is a major outer membrane protein from Pseudomonas aeruginosa, a homolog of OmpA from Escherichia coli. The N-terminal domains of both proteins have been demonstrated to form low conductance channels in lipid bilayers. Homology models, consisting of an eight-stranded beta-barrel, of the N-terminal domain OprF have been constructed based on the crystal structure of the corresponding domain from E. coli OmpA. OprF homology models have been evaluated via a set (6 x 10 ns) of simulations of the beta-barrel embedded within a solvated dimyristoyl-phosphatidylcholine (DMPC) bilayer. The conformational stability of the models is similar to that of the crystal structure of OmpA in comparable simulations. There is a degree of water penetration into the pore-like center of the OprF barrel. The presence of an acidic/basic (E8/K121) side-chain interaction within the OprF barrel may form a "gate" able to close/open a central pore. Lipid-protein interactions within the simulations were analyzed and revealed that aromatic side-chains (Trp, Tyr) of OprF interact with lipid headgroups. Overall, the behavior of the OprF model in simulations supports the suggestion that this molecule is comparable to OmpA. The simulations help to explain the mechanism of formation of low conductance pores within the outer membrane.     

Effect of charge redistribution on the binding of DNA nucleotide to carbon nanotube in molecular dynamics

All-atom molecular dynamics (MD) simulations are performed to study the binding of DNA nucleotides with two carbon nanotubes (CNTs) with similar diameters but different chiralities. Two schemes for assigning partial atomic charges (PACs) are adopted: (I) using PACs obtained from isolated DNA nucleotide and CNT optimised in vacuum, and (II) using PACs obtained from optimising nucleotide-CNT hybrid in solution. The former approach is what most MD simulations have used in the study of DNA-CNT hybrids, while in the latter approach, a redistribution of the PACs has occurred upon the hybridisation. Our results show that the charge redistribution has a profound effect on the dynamics of binding. In particular, PACs obtained from (II) lead to more stable binding structures in the MD simulations. The findings suggest that care should be taken in simulating DNA-CNT interactions using the classical force field approach.