A New Coarse-Grained Model for E. coli Cytoplasm: Accurate Calculation of the Diffusion Coefficient of Proteins and Observation of Anomalous Diffusion

A new coarse-grained model of the E. coli cytoplasm is developed by describing the proteins of the cytoplasm as flexible units consisting of one or more spheres that follow Brownian dynamics (BD), with hydrodynamic interactions (HI) accounted for by a mean-field approach. Extensive BD simulations were performed to calculate the diffusion coefficients of three different proteins in the cellular environment. The results are in close agreement with experimental or previously simulated values, where available. Control simulations without HI showed that use of HI is essential to obtain accurate diffusion coefficients. Anomalous diffusion inside the crowded cellular medium was investigated with Fractional Brownian motion analysis, and found to be present in this model. By running a series of control simulations in which various forces were removed systematically, it was found that repulsive interactions (volume exclusion) are the main cause for anomalous diffusion, with a secondary contribution from HI.     

Mesoscale Simulation and cryo-TEM of Nanoscale Drug Delivery Systems

This work sets out to study the effect of hydrophobic molecules on the morphology of aqueous solutions of amphiphilic block copolymer, which has potential drug delivery applications. The effect is studied both experimentally and by using simulations. Using cryogenic TEM observations, micelles can clearly be visualised and their core size measured. While pure polymer solutions form into spherical micelles with a narrow size distribution, addition of small amounts of hydrophobic drug molecules leads to distortions in shape, a wider size distribution, and larger average core diameter. Simulations are based on a mesoscale dynamic density functional method with Gaussian chain Hamiltonian and mean-field interactions, as implemented in the MesoDyn code. With parameters for the amphiphilic system established in earlier work, and mean-field interactions for the drug molecule derived from structure–property relationships, we obtain good agreement with the TEM observations for the effect of the hydrophobic molecules on the morphology. The simulations clearly show how increasing drug concentration leads to an increase in micelle size, a wider distribution and more elongated rather than spherical micelles.     

Modelling Diffusion in Zeolites by Molecular Dynamics Simulations

Abstract

The diffusion of molecules sorbed in zeolites is of growing interest for understanding the mechanisms of chemical processes with regard to selectivity and reactivity [1].

MD simulations give insight into physical systems on the molecular level allowing to study and visualize the motion of molecules even beyond the possibilities of experiments [2,3]. Single system parameters can easily be varied to study their influence, also those parameters that are fixed in reality (e.g., the size of particles). We present a cross section of our recent work to illustrate the capabilities of MD: The self diffusion coefficients (D) of a mixture of methane and xenon in silicalite show remarkable deviations from those of the pure species. This is shown and confirmed by PFG NMR experiments [4].

Simulating ethane in zeolite A the mechanism of diffusion has been studied. The effects of rotation on the diffusion lead to cases where D decreases with growing temperature [5].

The independence of self diffusion on lattice vibrations is proven even for zeolites with windows of guest particle size comparing simulations with rigid and vibrating zeolite lattice [6].     

Synthesis and Characterization of Templated Mesoporous Materials Using Molecular Simulation

Abstract

Lattice Monte Carlo simulations are used to calculate equilibrium properties of surfactant-solvent-silica liquid-crystal systems under no-polymerization conditions. The formation of a high-surfactant high-silica concentration phase in equilibrium with a dilute phase is observed when the surfactant-silica interactions are stronger than the surfactant-solvent interactions. Different silica structures that are similar to the M41 family are observed, depending on the overall concentration of the system. The formation of a hexagonal phase is favored at a surfactant/silica ratio of 0.2, whereas a lamellar phase is observed a surfactant/silica ratio of 1.

Argon adsorption properties on a model porous structure of the MCM-41 type prepared using this mimetic simulation protocol are calculated using grand canonical Monte Carlo simulation. Heats of adsorption are calculated from fluctuations in the energy and number of molecules [1] following the work of Nicholson and Parsonage [Computer Simulation and the Statistical Mechanics of Adsorption (Academic Press, London), 1982, p 97 8 pp]. A decrease in the heats of adsorption for coverage less than one statistical monolayer is evidence of surface heterogeneity. The results are in qualitative agreement with experimental measurements for argon on MCM-41.     

Gibbs Ensemble Calculations with an Equation of State: An Application to Vapor-Liquid Equilibria

Abstract

A new modification of the Gibbs ensemble Monte Carlo computer simulation method for fluid phase equilibria is described. The modification is based on a thermodynamic model for the vapor phase, and uses an equation of state to account for the weak interactions between the vapor phase molecules. Reductions in the computational time by 30–40% as compared to the original Gibbs ensemble method are obtained. The algorithm is applied to Lennard-Jones - (12,6) fluids and their mixtures and the results are in good agreement with results obtained from simulations using the full Gibbs ensemble method.     

Molecular Modelling of The Mechanism of Action of Organic Clay-Swelling Inhibitors

Abstract

It is well known that the sodium smectite class of clays swells macroscopically in contact with water, whereas under normal conditions the potassium form does not. In recent work using molecular simulation methods, we have provided a quantitative explanation both for the swelling behaviour of sodium smectite clays and the lack of swelling of potassium smectites [1]. In the present paper, we apply similar modelling methods to study the mechanism of inhibition of clay-swelling by a range of organic molecules.

Experimentally, it is known that polyalkylene glycols (polyethers) of intermediate to high relative molecular mass are effective inhibitors of smectite clay swelling. We use a range of atomistic simulation techniques, including Monte Carlo and molecular dynamics, to investigate the interactions between a selection of these compounds, water, and a model smectite clay mineral. These interactions occur by means of organised intercalation of water and organic molecules within the galleries between individual clay layers.

The atomic interaction potentials deployed in this work are not as highly optimised as those used in our clay-cation-water work [1]. Nevertheless, our simulations yield trends and results that are in qualitative and sometimes semi-quantitative agreement with experimental findings on similiar (but not identical) systems. The internal energy of adsorption of simple polyethers per unit mass on the model clay is not significantly different from that for water adsorption; our Monte Carlo studies indicate that entropy is the driving force for the sorption of the simpler organic molecules inside the clay layers: a single long chain polyethylene glycol can displace a large number of water molecules, each of whose translational entropy is greatly enhanced when outside the clay. Hydrophobically modified polyalkylene glycols also enjoy significant van der Waals interactions within the layers which they form within the clay galleries.

In conjunction with experimental studies, our work furnishes valuable insights into the relative effectiveness of the compounds considered and reveals the generic features that high performance clay-swelling inhibitors should possess. For optimal inhibitory activity, these compounds should be reasonably long chain linear organic molecules with localised hydrophobic and hydrophilic regions along the chain. On intercalation of these molecules within the clay layers, the hydrophobic regions provide an effective seal against ingress of water, while the hydrophilic ones enhance the binding of the sodium cations to the clay surface, preventing their hydration and the ensuing clay swelling.     

Nonadditive Monte Carlo Simulation of Liquid Hydrogen Chloride Difference Algorithm and Parallel Implementation

Abstract

This paper continues our Monte Carlo simulation study of liquid hydrogen chloride [1]. The importance of non-additive interactions is carefully analyzed. Computed atom pair correlation functions are compared to neutron scattering experiments [2]. A difference algorithm (“Δ—algorithm”) is developed, which makes non-additive Monte Carlo simulations practicable. We also report an implementation of this algorithm on a transputer network, taking advantage of the inherent parallelism of the Δ — algorithm.     

Anisotropic Site-Site Potentials in Molecular Dynamics

Abstract

This paper describes techniques for calculating the forces and torques for molecular simulations that use anisotropic site-site potentials. The general techniques are illustrated for pairs of linear and tetrahedral molecules. A technique for combining anisotropic site-site potentials with constraint dynamics is described. These ideas are tested by simulating an anisotropic site-site potential model for the non-bonded interactions in liquid butane. This model is as accurate as the all-atom Williams potential from which it is derived but can be simulated using approximately half the computer time of the all-atom potential. Anisotropic site-site potentials offer a flexible and cost-effective method of simulating a range of hydrocarbon systems.     

Molecular Dynamics as a Mathematical Mapping. I. Differentiable Force Functions

Abstract

The molecular dynamics technique can be viewed as a deterministic mathematical mapping between, on one side, the force field parameters that describe the potential energy interactions and the input macroscopic conditions, and, on the other, the calculated macroscopic properties of the bulk molecular system.

The differentiability of such a mapping in the conventional molecular dynamics calculations is affected by the discontinuities in particle positions introduced by the periodic boundary conditions and the discontinuities introduced by the minimum image convention and other methods commonly employed to approximate the calculation of interparticle potential and force.

This paper proposes an alternative molecular dynamics framework based on modified force functions which are almost everywhere continuous and differentiable, and exhibit a natural periodicity. These characteristics obviate the need for both the periodic boundary conditions and the minimum image convention, as well as for any corrections for long-range interactions. They also make it possible to apply standard methods of variational calculus for the computation of partial derivatives of the molecular dynamics mapping.

The modified framework is first introduced for the case of simple monoatomic fluids where the nature of the forces exerted between any pair of two particles is identical. A more general model describing the interactions of flexible molecules is then developed. We describe the application of this approach to mixtures of alkane molecules interacting via the NERD force field.     

Behavior of Aromatic Molecules in Silicalite by the Direct Integration of the Configurational Integral

Abstract

Adsorption data of aromatic molecules adsorbed in silicalite show highly unusual characteristics which were attributed to structural effects caused by the comparable size of molecules and pores. In this study, the interaction of aromatic compounds with silicalite are examined on the molecular level. The interactions are calculated by atom-atom approximation using Lennard-Jones potentials. The constants are calculated, without fitting, from Kirkwood-Muller formulas. Benzene and p-xylene are represented as a rigid structure of 12 and 18 atom centers. The model is anisotropic.

The diffusional behavior of molecules is examined by minimizing the potential energy in the channels which requires less computational time than Molecular Dynamics. The activation energy for the diffusion of benzene, 27.6 kJ/mol, is in excellent agreement with data, 28.8 kJ/mol. The results indicate that both molecules can enter the smaller zig-zag channels. The energetically most favorable location in the main channels is the mid-point between intersections. All rotations are restricted in the channels but the molecules can rotate in any direction (with some movement of the center) at intersections.

The Henry's law constant and internal energy of adsorption at zero coverage are calculated by direct integration of the configurational integral. Direct integration is more efficient than Monte Carlo and Molecular Dynamics simulations since the molecules are highly restricted in the pores. The predicted internal energy of adsorption, ? 54.86 and ? 75.30 kJ/mol for benzene and p-xylene is in good agreement with data of ? 50.92 and ? 62.15 kJ/mol respectively. There is appreciable difference between the predicted and experimental Henry's law constants. The agreement can be improved by fitting the Lennard-Jones constants which has not been attempted.

Although the calculations are performed at infinite dilution and entropy effects are not included, the results bring insight to the behavior of molecules in highly restricted environments such as in tight pores. Similar simplified calculations can be used to close the gap between highly idealized molecular simulations and complicated systems common in real applications.     

On the Implementation of Friedman Boundary Conditions in Liquid Water Simulations

Abstract

We have applied the image approximation to the reaction field as suggested by H.L. Friedman [Mol. Phys., 29, 1533 (1975)] by investigating appropriate cavity sizes and system parameters for use in molecular simulations. The energy of and the structure around a central simple point charge (SPC) water molecule in a dielectric cavity was found to be in good agreement with the properties of a liquid sample. To confine the water molecules within the cavity, we introduced a short-range repulsion between a real charge and its image as the Lennard-Jones repulsive potential between oxygen atoms of the SPC potential. For a system of 65 water molecules a cavity radius of 10.45 Å is appropriate; this radius is altered to 12.00 Å for a cavity surrounding 113 molecules. The effect of the boundary is restricted to the outer-most water layer which is in contact with the dielectric continuum.     

Ryanodine receptor allosteric coupling and the dynamics of calcium sparks

Puffs and sparks are localized intracellular Ca²⁺ elevations that arise from the cooperative activity of Ca²⁺-regulated inositol 1,4,5-trisphosphate receptors and ryanodine receptors clustered at Ca²⁺ release sites on the surface of the endoplasmic reticulum or the sarcoplasmic reticulum. While the synchronous gating of Ca²⁺-regulated Ca²⁺ channels can be mediated entirely though the buffered diffusion of intracellular Ca²⁺, interprotein allosteric interactions also contribute to the dynamics of ryanodine receptor (RyR) gating and Ca²⁺ sparks. In this article, Markov chain models of Ca²⁺ release sites are used to investigate how the statistics of Ca²⁺ spark generation and termination are related to the coupling of RyRs via local [Ca²⁺] changes and allosteric interactions. Allosteric interactions are included in a manner that promotes the synchronous gating of channels by stabilizing neighboring closed-closed and/or open-open channel pairs. When the strength of Ca²⁺-mediated channel coupling is systematically varied (e.g., by changing the Ca²⁺ buffer concentration), simulations that include synchronizing allosteric interactions often exhibit more robust Ca²⁺ sparks; however, for some Ca²⁺ coupling strengths the sparks are less robust. We find no evidence that the distribution of spark durations can be used to distinguish between allosteric interactions that stabilize closed channel pairs, open channel pairs, or both in a balanced fashion. On the other hand, the changes in spark duration, interspark interval, and frequency observed when allosteric interactions that stabilize closed channel pairs are gradually removed from simulations are qualitatively different than the changes observed when open or both closed and open channel pairs are stabilized. Thus, our simulations clarify how changes in spark statistics due to pharmacological washout of the accessory proteins mediating allosteric coupling may indicate the type of synchronizing allosteric interactions exhibited by physically coupled RyRs. We also investigate the validity of a mean-field reduction applicable to the dynamics of a ryanodine receptor cluster coupled via local [Ca²⁺] and allosteric interactions. In addition to facilitating parameter studies of the effect of allosteric coupling on spark statistics, the derivation of the mean-field model establishes the correct functional form for cooperativity factors representing the coupled gating of RyRs. This mean-field formulation is well suited for use in computationally efficient whole cell simulations of excitation-contraction coupling.     

Linked Lists and the Method of Lights in Molecular Dynamics Simulation - Search for the Best Method of Forces Evaluation in Sequential MD Codes

Abstract

In this paper two methods of forces evaluation used in the MD codes are presented and compared against the classical linked lists algorithm [3,4] and its modified version [5]. The first algorithm, so called the method of lights is a sequential version of the CYBER 205 vector oriented code [6]. A new algorithm of forces evaluation is also proposed, which incorporates advantages of the method of lights and the linked lists technique.     

The Calculation of 3D Solubility Parameters Using Molecular Models

Abstract

In this paper we describe the use of molecular mechanics models to examine detailed intermolecular interactions within the liquid state of a common nonionic surfactant system, nonyl phenol ethoxylate (NPE). Using constant energy molecular dynamics simulations we have studied the relative strengths of dispersive interactions versus polar interactions and have estimated three dimensional solubility parameters for NPE systems as a function of temperature and ethylene oxide content. The predictions at 300 K are in good agreement with three dimensional solubility parameters predicted using group contribution tables. Models of the amorphous liquid state were represented by single molecular structures of NPE in a periodic cell. The solubility parameters predicted with these models were in good agreement with those values derived from models having eight NPE molecules packed into a cell with the exception of the electrostatic interactions, which are the most sensitive to system size effects.     

Modeling DNA Hydration: Comparison of Calculated and Experimental Hydration Properties of Nuclic Acid Bases

Abstract

Hydration properties of individual nucleic acid bases were calculated and compared with the available experimental data. Three sets of classical potential functions (PF) used in simulations of nucleic acid hydration were juxtaposed: (i) the PF developed by Poltev and Malenkov (PM), (ii) the PF of Weiner and Kollman (WK), which together with Jorgensen's TIP3P water model are widely used in the AMBER program, and (HI) OPLS (optimized potentials for liquid simulations) developed by Jorgensen (J). The global minima of interaction energy of single water molecules with all the natural nucleic acid bases correspond to the formation of two water-base hydrogen bonds (water bridging of two hydrophilic atoms of the base). The energy values of these minima calculated via PM potentials are in somewhat better conformity with mass-spectrometric data than the values calculated via WK PF. OPLS gave much weaker water-base interactions for all compounds considered, thus these PF were not used in further computations. Monte Carlo simulations of the hydration of 9- methyladenine, 1-methyluracil and 1-methylthymine were performed in systems with 400 water molecules and periodic boundary conditions. Results of simulations with PM potentials give better agreement with experimental data on hydration energies than WK PF. Computations with PM PF of the hydration energy of keto and enol tautomers of 9-methyl- guanine can account for the shift in the tautomeric equilibrium of guanine in aqueous media to a dominance of the keto form in spite of nearly equal intrinsic stability of keto and enol tautomers. The results of guanine hydration computations are discussed in relation to mechanisms of base mispairing errors in nucleic acid biosynthesis. The data presented in this paper along with previous results on simulation of hydration shell structures in DNA duplex grooves provide ample evidence for the advantages of PM PF in studies of nucleic-acid hydration.     

MD Simulations of Liquids with Td,Oh Molecular Symmetry

Abstract

A new method is proposed for the calculation of intermolecular interactions in Molecular Dynamics simulations of liquids with T_d, O_h molecular symmetry. The new algorithm is based on the separation of the pair potential into a short-range and a long-range contribution described by a site-site and a spherical centre-centre potential model respectively using an additional cutoff distance. Test calculations for the Lennard-Jones fluids CCl₄ and SF₆ show significant savings in CPU time. We compare thermodynamic properties, pair correlation functions and a few dynamic autocorrelation functions obtained with the novel strategy with results of the commonly used algorithm for systems containing 864 molecules. Since no significant differences appear the new algorithm may be suggested as a useful contribution to the area of Molecular Dynamics simulation of liquids with these rather high molecular symmetries.     

Microstructures,interactions and dynamics properties studies of N-methyldiethanolamine + guanidinium triflate ionic liquid + water tertiary system at the standard temperature

Molecular dynamics simulations with an all-atom force field have been carried out in order to understand the phase equilibrium behaviour of ternary aqueous mixtures containing guanidinium triflate ionic liquid [gua][OTf] and water mixed with N-methyldiethanolamine (MDEA) in different function composition at the standard temperature of 298.15 K. A very good numerical agreement has been obtained for the prediction of the mixture densities. The analysis of structural and dynamic properties showed that the molecular level of ternary mixtures is slightly affected by the presence of MDEA and [gua][OTf] molar fractions. For MDEA–water interactions in [gua][OTf] media, we found that MDEA prefers to be surrounded by water molecules rather than by MDEA molecules even at a high MDEA molar fraction. While for [gua][OTf]–water interaction in MDEA media, as [gua][OTf] molar fraction increases, water molecules replace counterions in the coordination shell of both ions, thus weakening their interaction. On the other hand, for MDEA–[gua][OTf] interactions in water media, we have found that as the molar fraction of [gua][OTf] increases, a sulfonate group from anion appears to have a stronger association by making hydrogen bonding with MDEA molecules. The chemical process using ionic liquids (ILs) as solvents is commonly limited by their high viscosity. Based on their physical properties such as viscosities, these ternary solvents can be applied in natural gas industry, such as removing carbon dioxide using aqueous MDEA and IL at high pressure.     

Residue contact-count potentials are as effective as residue-residue contact-type potentials for ranking protein decoys

Background  

For over 30 years potentials of mean force have been used to evaluate the relative energy of protein structures. The most commonly used potentials define the energy of residue-residue interactions and are derived from the empirical analysis of the known protein structures. However, single-body residue 'environment' potentials, although widely used in protein structure analysis, have not been rigorously compared to these classical two-body residue-residue interaction potentials. Here we do not try to combine the two different types of residue interaction potential, but rather to assess their independent contribution to scoring protein structures.     

Phase Coexistence Curves for Off-lattice Polymer-Solvent Mixtures: Gibbs-Duhem Integration Simulations

The Gibbs-Duhem integration scheme is combined with the osmotic Gibbs-ensemble simulation method presented in previous work [Brennan, J.K. and Madden, W.G. "Phase coexistence curves for off-lattice polymer-solvent mixtures: Gibbs-ensemble simulations." Macromolecules , 2002, 35, 2827.] to calculate the phase coexistence of a polymer-solvent mixture. Gibbs-Duhem integration simulations are carried out at temperatures for which the osmotic Gibbs-ensemble method is not valid because the solvent-rich phase contains a significant amount of polymer. This combined strategy allows for the calculation of the full coexistence curve for polymer-solvent systems in the continuum. An alternative formulation of the Gibbs-Duhem integration algorithm is also presented. A major strength of the technique is that neither chain insertions nor deletions are required. The method allows for the calculation of the phase behavior of polymer-solvent mixtures containing long chains or branched and networked chains not previously possible.     

Denaturation of HIV-1 Protease (PR) Monomer by Acetic Acid: Mechanistic and Trajectory Insights from Molecular Dynamics Simulations and NMR

Abstract

Inside a living cell there can be a variety of interactions for any given protein, which serve to regulate denaturation and renaturation processes. Insights into some of them can be obtained by in vitro studies using various denaturing agents. In this study, all-atom MD simulations in explicit solvent and NMR relaxation studies were performed on HIV-1 Protease (PR) in 9 M acetic acid (AcOH) (the commonly used denaturant during PR preparation). Following previous reports that denaturation proceeds via dissociation of the dimer into monomers, unfolding of the monomer by acetic acid has been explicitly investigated here. Direct visualization of the denaturation process and evidence for the mechanism of denaturation have been presented. Our simulations reveal that the denaturation of the PR monomer is caused due to direct interaction between acetic acid molecules and PR. Autocorrelation of N-H vectors calculated from the simulations have revealed that the α-helix and the surrounding β-strands represent the sensitive regions of the PR that respond maximally to the change in the solvent environment around the PR and are prone to disruption by acetic acid. This disruption is caused due to increased penetration of the acetic acid molecules into the PR structure by formation of preferred tertiary contacts and hydrogen bonds between the PR and acetic acid molecules. Following the loss of these critical interactions, the PR follows a random and non-equilibrating path on the conformation landscape and cycles between different denatured extended and compact states.