Molecular dynamics studies of a DNA-binding protein: 2. An evaluation of implicit and explicit solvent models for the molecular dynamics simulation of the Escherichia coli trp repressor.

Although aqueous simulations with periodic boundary conditions more accurately describe protein dynamics than in vacuo simulations, these are computationally intensive for most proteins. Trp repressor dynamic simulations with a small water shell surrounding the starting model yield protein trajectories that are markedly improved over gas phase, yet computationally efficient. Explicit water in molecular dynamics simulations maintains surface exposure of protein hydrophilic atoms and burial of hydrophobic atoms by opposing the otherwise asymmetric protein-protein forces. This properly orients protein surface side chains, reduces protein fluctuations, and lowers the overall root mean square deviation from the crystal structure. For simulations with crystallographic waters only, a linear or sigmoidal distance-dependent dielectric yields a much better trajectory than does a constant dielectric model. As more water is added to the starting model, the differences between using distance-dependent and constant dielectric models becomes smaller, although the linear distance-dependent dielectric yields an average structure closer to the crystal structure than does a constant dielectric model. Multiplicative constants greater than one, for the linear distance-dependent dielectric simulations, produced trajectories that are progressively worse in describing trp repressor dynamics. Simulations of bovine pancreatic trypsin were used to ensure that the trp repressor results were not protein dependent and to explore the effect of the nonbonded cutoff on the distance-dependent and constant dielectric simulation models. The nonbonded cutoff markedly affected the constant but not distance-dependent dielectric bovine pancreatic trypsin inhibitor simulations. As with trp repressor, the distance-dependent dielectric model with a shell of water surrounding the protein produced a trajectory in better agreement with the crystal structure than a constant dielectric model, and the physical properties of the trajectory average structure, both with and without a nonbonded cutoff, were comparable.     

Decomposition of protein experimental compressibility into intrinsic and hydration shell contributions

The experimental determination of protein compressibility reflects both the protein intrinsic compressibility and the difference between the compressibility of water in the protein hydration shell and bulk water. We use molecular dynamics simulations to explore the dependence of the isothermal compressibility of the hydration shell surrounding globular proteins on differential contributions from charged, polar, and apolar protein-water interfaces. The compressibility of water in the protein hydration shell is accounted for by a linear combination of contributions from charged, polar, and apolar solvent-accessible surfaces. The results provide a formula for the deconvolution of experimental data into intrinsic and hydration contributions when a protein of known structure is investigated. The physical basis for the model is the variation in water density shown by the surface-specific radial distribution functions of water molecules around globular proteins. The compressibility of water hydrating charged atoms is lower than bulk water compressibility, the compressibility of water hydrating apolar atoms is somewhat larger than bulk water compressibility, and the compressibility of water around polar atoms is about the same as the compressibility of bulk water. We also assess whether hydration water compressibility determined from small compound data can be used to estimate the compressibility of hydration water surrounding proteins. The results, based on an analysis from four dipeptide solutions, indicate that small compound data cannot be used directly to estimate the compressibility of hydration water surrounding proteins.     

Studying pressure denaturation of a protein by molecular dynamics simulations

Many globular proteins unfold when subjected to several kilobars of hydrostatic pressure. This “unfolding‐up‐on‐squeezing” is counter‐intuitive in that one expects mechanical compression of proteins with increasing pressure. Molecular simulations have the potential to provide fundamental understanding of pressure effects on proteins. However, the slow kinetics of unfolding, especially at high pressures, eliminates the possibility of its direct observation by molecular dynamics (MD) simulations. Motivated by experimental results—that pressure denatured states are water‐swollen, and theoretical results—that water transfer into hydrophobic contacts becomes favorable with increasing pressure, we employ a water insertion method to generate unfolded states of the protein Staphylococcal Nuclease (Snase). Structural characteristics of these unfolded states—their water‐swollen nature, retention of secondary structure, and overall compactness—mimic those observed in experiments. Using conformations of folded and unfolded states, we calculate their partial molar volumes in MD simulations and estimate the pressure‐dependent free energy of unfolding. The volume of unfolding of Snase is negative (approximately ?60 mL/mol at 1 bar) and is relatively insensitive to pressure, leading to its unfolding in the pressure range of 1500–2000 bars. Interestingly, once the protein is sufficiently water swollen, the partial molar volume of the protein appears to be insensitive to further conformational expansion or unfolding. Specifically, water‐swollen structures with relatively low radii of gyration have partial molar volume that are similar to that of significantly more unfolded states. We find that the compressibility change on unfolding is negligible, consistent with experiments. We also analyze hydration shell fluctuations to comment on the hydration contributions to protein compressibility. Our study demonstrates the utility of molecular simulations in estimating volumetric properties and pressure stability of proteins, and can be potentially extended for applications to protein complexes and assemblies. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Simulation of the diffusion-controlled reaction between superoxide and superoxide dismutase. II. Detailed models

A two-stage Brownian dynamics simulation method is used to study the diffusion-influenced bimolecular reaction between superoxide and superoxide dismutase (SOD). The crystal structure of the dimeric enzyme is used in constructing detailed topographical and electrostatic models. Several electrostatic models are considered. In the most realistic, the excluded volume of the protein, which is impermeable to penetration by mobile ions, is assigned a dielectric constant of 2 and the surrounding “solvent” is assigned a value of 78. A finite difference method is used to solve the linearized Poisson–Boltzmann equation. For native SOD, the simulations reproduce the pronounced salt dependence of the rate constant observed experimentally. This salt dependence is attributed to electrostatic interactions between enzyme and substrate that are inherently attractive and amplified by the low dielectric constant of the protein interior. The simulation method is also applied to a modified enzyme, acylated SOD.     

Computational Soft Nanotechnology with Mesodyn

The simulation of microstructures on a scale 1–1000?nm is a typical problem in colloid and polymer science, and this is also the realm of modern computational “soft nanotechnology”. Accordingly, computational methods rely heavily on time-honoured approaches for calculating the thermodynamical stability of complex mixtures. We describe such approaches in the framework of MesoDyn, a general purpose software package for field-based simulations methods, such as the polymer mean-field model for microphase formation and the Poisson–Boltzmann model for electrostatic interactions. The paper concludes with a small review of examples of application: the formation of microscopic structures in block copolymer bulk solutions, block copolymer melt structures on surfaces (thin films) and structure formation in tiny polymer surfactant droplets (polymersomes). The method works quite well in all cases where a mean-field model is appropriate, but it is a challenge to extend the simulations to systems in which specific correlations are important.     

Use of Probability Weighted Moments in the Analysis of Means

In the analysis of means the estimate of σ is usually calculated using range. In this study it is proposed that the linear estimate of σ based on probability weighted moments should be used. A simulation study based on 1000 values suggested that the linear estimate of σ using probability weighted moments is more close to the original value. In the simulations different distributions such as normal, t, Cauchy and exponential were assumed.     

The origin and impact of bound water around intrinsically disordered proteins

Proteins and water couple dynamically over a wide range of time scales. Motivated by their central role in protein function, protein-water dynamics and thermodynamics have been extensively studied for structured proteins, where correspondence to structural features has been made. However, properties controlling intrinsically disordered protein (IDP)-water dynamics are not yet known. We report results of megahertz-to-terahertz dielectric spectroscopy and molecular dynamics simulations of a group of IDPs with varying charge content along with structured proteins of similar size. Hydration water around IDPs is found to exhibit more heterogeneous rotational and translational dynamics compared with water around structured proteins of similar size, yielding on average more restricted dynamics around individual residues of IDPs, charged or neutral, compared with structured proteins. The on-average slower water dynamics is found to arise from excess tightly bound water in the first hydration layer, which is related to greater exposure to charged groups. The more tightly bound water to IDPs correlates with the smaller hydration shell found experimentally, and affects entropy associated with protein-water interactions, the contribution of which we estimate based on the dielectric measurements and simulations. Water-IDP dynamic coupling at terahertz frequencies is characterized by the dielectric measurements and simulations.     

The enzymatic mechanism of carboxypeptidase: A molecular dynamics study

An MD simulation of the system carboxypeptidase A (CPA) with the tetrapeptide Val-Leu-Phe-Phe has been performed in order to learn about the substrate disposition just prior to nucleophilic attack. We have explored the model in which the substrate does not substitute the zinc-coordinated water (the “water” mechanism). The simulations do suggest as feasible that the Zn-OH₂ group performs a nucleophilic attack on the Phe-Phe peptidic bond. We have also investigated the model in which the carbonyl oxygen displaces the zinc-coordinated water. In this case the substrate and Glu-270 orient themselves to allow an anhydride intermediate during the peptidic bond cleavage (the “anhydride” mechanism). Based on the results of the simulations, both “water” and “anhydride” mechanisms are structurally feasible, although the former model seems more probable on chemical grounds. © 1994 John Wiley & Sons, Inc.     

Adaptive glenoid bone remodeling simulation

Glenoid prosthesis loosening is the most common cause for revision total shoulder arthroplasty. Stress-induced bone remodeling may compromise long-term prosthesis fixation and significantly contribute to loosening. Realistic, robust analysis of bone-prosthesis constructs need to look beyond initial post-implantation mechanics provided by static finite element (FE) simulation. Adaptive bone remodeling simulations based on Wolff's law are needed for evaluating long-term glenoid prostheses fixation. The purpose of this study was to take a first step towards this goal and create and validate two-dimensional FE simulations, using the intact glenoid, for computing subject-specific adaptive glenoid remodeling. Two-dimensional glenoid FE models were created from scapulae computed tomography images. Two distinct processes, “element” and “node” simulations, used the forward-Euler method to compute bone remodeling. Initial bone density was homogeneous. Center and offset load combinations were iteratively applied. To validate the simulations we performed location-specific statistical comparisons between predicted and actual bone density, load combinations, and “element” and “node” processes. Visually and quantitatively “element” simulations produced better results (p>0.22), and correlation coefficients ranged 0.51–0.69 (p<0.001). Having met this initial work's goals, we expect subject-specific FE glenoid bone remodeling simulations together with static FE stress analyses to be effective tools for designing and evaluating glenoid prostheses.     

A simulation study of three methods for estimating selective values and survival rates from recapture data

The methods ofManly (1973),Manly (1975) andManly (1977) for estimating survival rates and relative survival rates from recapture data have been compared by computer simulation. In the simulations batches of two types of animal were “released” at one point in “time” and recapture samples were taken at “daily” intervals from then on. The various methods of estimation were then used to estimate, the daily survival rates of type 1 and type 2 animals, and also the survival rate of the type 2 animals relative to the type 1 animals. Simulation experiments were designed to examine (a) the bias in estimates, (b) the relative precision of different methods of estimation, (c) the validity of confidence intervals for true parameter values, and (d) the effect on estimates of the failure of certain assumptions.     

Model for the conformational analysis of hydrated peptides. Effect of hydration on the conformational stability of the terminally blocked residues of the 20 naturally occurring amino acids

The effects of hydration are included in empirical conformational energy computations on oligopeptides by means of a modified hydration-shell model. Free energy terms are introduced to account for “specific hydration” due to water–solute hydrogen bonding and for “nonspecific hydration” describing the interaction of the solute with water molecules in a first-neighbor shell. The dielectric constant has been doubled (over the value used for calculations in the absence of water) to take into account the presence of solvent. Computations were carried out for the N-acetyl-N′-methylamides of the 20 naturally occurring amino acids. Conformational energy maps are compared with similar maps calculated in the absence of hydration. Minimum-energy conformations are located and compared with the corresponding minima for unhydrated peptides in terms of ordering with respect to potential energy, the dihedral angles at the minima, and the presence of intramolecular hydrogen bonds. The Boltzmann factors for various conformational regions are altered significantly on hydration in some cases. These changes can be explained in terms of differences in the hydration free energy terms for various conformations.     

Point Charges Optimally Placed to Represent the Multipole Expansion of Charge Distributions

We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA) retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance the extent of the charge distribution–the mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 Å from the oxygen atom), is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 Å ) is half that of the point multipole expansion up to the octupole order.     

Microbial expansion–collision dynamics promote cooperation and coexistence on surfaces

Microbes colonizing a surface often experience colony growth dynamics characterized by an initial phase of spatial clonal expansion followed by collision between neighboring colonies to form potentially genetically heterogeneous boundaries. For species with life cycles consisting of repeated surface colonization and dispersal, these spatially explicit “expansion‐collision dynamics” generate periodic transitions between two distinct selective regimes, “expansion competition” and “boundary competition,” each one favoring a different growth strategy. We hypothesized that this dynamic could promote stable coexistence of expansion‐ and boundary‐competition specialists by generating time‐varying, negative frequency‐dependent selection that insulates both types from extinction. We tested this experimentally in budding yeast by competing an exoenzyme secreting “cooperator” strain (expansion–competition specialists) against nonsecreting “defectors” (boundary–competition specialists). As predicted, we observed cooperator–defector coexistence or cooperator dominance with expansion–collision dynamics, but only defector dominance otherwise. Also as predicted, the steady‐state frequency of cooperators was determined by colonization density (the average initial cell–cell distance) and cost of cooperation. Lattice‐based spatial simulations give good qualitative agreement with experiments, supporting our hypothesis that expansion–collision dynamics with costly public goods production is sufficient to generate stable cooperator–defector coexistence. This mechanism may be important for maintaining public–goods cooperation and conflict in microbial pioneer species living on surfaces.     

Spherical tensor multipolar electrostatics and smooth particle mesh Ewald summation: a theoretical study

The point-charge approximation, typically used by classical molecular mechanics force-fields, can be overcome by a multipolar expansion. For decades multipole moments were only used in the context of the rigid body approximation but recently it has become possible to combine multipolar electrostatics with molecular flexibility. The program DL_MULTI, which is derived from DL_POLY_2, includes efficient multipolar Ewald functionality up to the hexadecapole moment but the code is restricted to rigid bodies. The incorporation of flexibility into DL_MULTI would cause too large an impact on its architecture whereas the package DL_POLY_4 offers a more attractive and sustainable route to handle multipolar electrostatics. This package inherently handles molecular flexibility, which warrants sufficiently transferable atoms or atoms that are “knowledgeable” about their chemical environment (as made possible by quantum chemical topology and machine learning). DL_MULTI uses the spherical multipole formalism, which is mathematically more involved than the Cartesian one but which is more compact. DL_POLY_4 uses the computationally efficient method of smooth particle mesh Ewald (SPME) summation, which has also been parallellized by others. Therefore, combining the strengths of DL_POLY_4 and DL_MULTI poses the challenge of merging SPME with multipolar electrostatics by spherical multipole. In an effort to recast as clearly as possible the principles behind DL_MULTI, its key equations have been reformulated by the more streamlined route involving the algebra of complex numbers, and some of these equations’ peculiarities clarified. This article explores theoretically the repercussions of the merging of SPME with spherical multipole electrostatics (as implemented in DL_MULTI). Difficulties in design and implementation of possible future code are discussed.     

Finite element modeling of shell shape in the freshwater turtle Pseudemys concinna reveals a trade‐off between mechanical strength and hydrodynamic efficiency

Aquatic species can experience different selective pressures on morphology in different flow regimes. Species inhabiting lotic regimes often adapt to these conditions by evolving low‐drag (i.e., streamlined) morphologies that reduce the likelihood of dislodgment or displacement. However, hydrodynamic factors are not the only selective pressures influencing organismal morphology and shapes well suited to flow conditions may compromise performance in other roles. We investigated the possibility of morphological trade‐offs in the turtle Pseudemys concinna. Individuals living in lotic environments have flatter, more streamlined shells than those living in lentic environments; however, this flatter shape may also make the shells less capable of resisting predator‐induced loads. We tested the idea that “lotic” shell shapes are weaker than “lentic” shell shapes, concomitantly examining effects of sex. Geometric morphometric data were used to transform an existing finite element shell model into a series of models corresponding to the shapes of individual turtles. Models were assigned identical material properties and loaded under identical conditions, and the stresses produced by a series of eight loads were extracted to describe the strength of the shells. “Lotic” shell shapes produced significantly higher stresses than “lentic” shell shapes, indicating that the former is weaker than the latter. Females had significantly stronger shell shapes than males, although these differences were less consistent than differences between flow regimes. We conclude that, despite the potential for many‐to‐one mapping of shell shape onto strength, P. concinna experiences a trade‐off in shell shape between hydrodynamic and mechanical performance. This trade‐off may be evident in many other turtle species or any other aquatic species that also depend on a shell for defense. However, evolution of body size may provide an avenue of escape from this trade‐off in some cases, as changes in size can drastically affect mechanical performance while having little effect on hydrodynamic performance. J. Morphol. 2011. © 2011 Wiley‐Liss, Inc.     

Folding polypeptide α-carbon backbones by distance geometry methods

Polypeptide α-carbon backbones were modeled as freely rotating chains made up of spherical monomers. The monomers were assigned an abstract binary “hydrophobicity” property that could be either present or absent. Under the assumption that “hydrophobic” residues tend to cluster together, away from the polar solvent, three-dimensional conformations of random copolymers of “hydrophobic” and “hydrophilic” monomers were calculated by a novel algorithm based on distance geometry techniques. The simulated molecules were globular and compact, in shape, and possessed distinct hydrophobic cores, indicating that our method was capable of reproducing some of the important global features of real polypeptides. © 1994 John Wiley & Sons, Inc.     

Thermal Excitations of Hydrated Macromolecules: The Effects of Hydration on the Mössbauer Absorption and Scattering Spectra

Abstract

The spectra of Rayleigh scattering of Mössbauer radiation (RSMR) and Mössbauer absorption by globular macromolecules are calculated. The dependence of the spectra parameters on hydration is modeled with the account for thermal low-frequency vibrations of the particles constituting the globule. Deformational motions of the macromolecule fragments leading to deviations from its equilibrium spherical shape are considered introducing collective dynamical variables governed by Langevin equations with random sources of external forces. The macromolecule is modeled by a double-layered sphere: a rigid (elastic) core is surrounded by a porous hydration shell filled with fluid. The dynamical properties of the bound water inside the shell are described by the Debye-Brinkman equations. The degree of hydration is introduced by means of a combination of the mass coefficients of the porous shell with fluid and the mass coefficients in the limiting cases when the flow inside the shell is “frozen” and in the case of free flow. The hydration-dependent Lamb-Mössbauer factor and the elastic fraction of the RSMR are calculated and compared with experimental data from the literature.     

Vectorial insertion of a β-helical peptide into membrane: a theoretical study on polytheonamide B

Spontaneous unidirectional, or vectorial, insertion of transmembrane peptides is a fundamental biophysical process for toxin and viral actions. Polytheonamide B (pTB) is a potent cytotoxic peptide with a β^6.3-helical structure. Previous experimental studies revealed that the pTB inserts into the membrane in a vectorial fashion and forms a channel with its single molecular length long enough to span the membrane. Also, molecular dynamics simulation studies demonstrated that the pTB is prefolded in aqueous solution. These are unique features of pTB because most of the peptide toxins form channels through oligomerization of transmembrane helices. Here, we performed all-atom molecular dynamics simulations to examine the dynamic mechanism of the vectorial insertion of pTB, providing underlying elementary processes of the membrane insertion of a prefolded single transmembrane peptide. We find that the insertion of pTB proceeds with only the local lateral compression of the membrane in three successive phases: “landing,” “penetration,” and “equilibration” phases. The free energy calculations using the replica-exchange umbrella sampling simulations present an energy cost of 4.3 kcal/mol at the membrane surface for the membrane insertion of pTB from bulk water. The trajectories of membrane insertion revealed that the insertion process can occur in two possible pathways, namely “trapped” and “untrapped” insertions; in some cases, pTB is trapped in the upper leaflet during the penetration phase. Our simulations demonstrated the importance of membrane anchoring by the hydrophobic N-terminal blocking group in the landing phase, leading to subsequent vectorial insertion.     

Influences of transect relocation errors on line-point estimates of plant cover

The line-point transect method has been used to estimate plant cover for about nine decades. In particular, the method is often used to determine baseline plant cover and monitor for changes in plant cover over time. In such cases, detection of change requires both the initial transect starting position and angle of orientation are exact in relocation without error. A study was conducted on influences of errors in basal cover estimates that resulted from inexact relocation and orientation of a resample transect. Simulation studies of actual field data showed that variation in plant cover estimates from relocated line-point transects increased with each source of error and combinations of these errors. Relocated transects resulted in unbiased estimates of total-plant cover only when means over all transects are used to detect changes over time. Substantial errors were observed when the mean cover of individually relocated transect was compared to its original transect.