Convergence Properties of Monte Carlo Simulations on Fluids

Convergence properties of standard Monte Carlo simulations for various fluid systems are studied both theoretically and experimentally. It turns out that pseudo-dynamic behaviour found for homogeneous fluids with periodic boundary conditions differs substantially from that for fluids at interfaces and for other inhomogeneous, anisotropic or less than three-dimensional systems. The results are applied to the problems of error estimation and the optimum frequency of measurement of the quantities.     

Monte Carlo Study of the Buckingham Exponential-six Fluid

Abstract

In this paper we report the results of extensive Monte Carlo simulations of a pure fluid of Buckingham modified exponential-six molecules. Data are presented for the configurational energy and pressure covering a wide range of temperatures and densities. These data are interpreted using the generalized van der Waals partition function with a novel separation into free volume and mean potential terms. We find, surprisingly, that the Buckingham fluid is described by a simple van der Waals-like equation of state provided that the b parameter is temperature dependent and chosen in a theoretically correct manner.     

Thermal Properties of Supercritical Carbon Dioxide by Monte Carlo Simulations

We present simulation results for the volume expansivity, isothermal compressibility, isobaric heat capacity, Joule-Thomson coefficient and speed of sound for carbon dioxide (CO 2 ) in the supercritical region, using the fluctuation method based on Monte Carlo simulations in the isothermal-isobaric ensemble. We model CO 2 as a quadrupolar two-center Lennard-Jones fluid with potential parameters reported in the literature, derived from vapor-liquid equilibria (VLE) of CO 2 . We compare simulation results with an equation of state (EOS) for the two-center Lennard-Jones plus point quadrupole (2CLJQ) fluid and with a multiparametric EOS adjusted to represent CO 2 experimental data. It is concluded that the VLE-based parameters used to model CO 2 as a quadrupolar two-center Lennard-Jones fluid (both simulations and EOS) can be used with confidence for the prediction of thermodynamic properties, including those of industrial interest such as the speed of sound or Joule-Thomson coefficient, for CO 2 in the supercritical region, except in the extended critical region.     

Direct Sampling of Local Density Fluctuations in Monte Carlo Simulations

A novel method for accelerating Monte Carlo simulations of fluids based on a direct sampling of local density fluctuations by a multiparticle move is proposed. The method is expected to be particularly efficient for inhomogeneous pure fluids consisting of spherical or moderately nonspherical molecules which is confirmed by a sample simulation of a Lennard-Jones fluid in a slit pore. An analogous method for a mixture, a direct sampling of local concentration fluctuations by swapping particles of different species, is successfully tested on a liquid mixture of argon and nitrogen.     

Vapour-Liquid Phase Equilibria of n-alkanes by Direct Monte Carlo Simulations

Abstract

We report results of direct Monte Carlo simulations of n-pentane and n-decane at the liquidvapour interface for a number of temperatures. The intermolecular interactions are modeled using the last version of the anisotropic united atom model (AUA4). We have used the local long range correction energy and an algorithm allowing to select randomly with equal probability two different displacements. The liquid and vapour densities are in excellent agreement with experimental data and with those previously calculated using the GEMC method.     

On the Sampling Method for Grand Canonical Monte Carlo Simulations

Abstract

A bulk Lennard-Jones fluid was simulated using the grand canonical Monte Carlo method. Three different sampling methods were used in the transition matrix, namely the Metropolis, Barker and a third novel method. While it can be shown that the Metropolis method will give the most accurate ensemble averages in the limit of an infinitely long run, the new method termed “Modified Barker Sampling” (MBS), is shown to be superior for the runs of practical length for the particular system studied.     

Forced Detection Monte Carlo Algorithms for Accelerated Blood Vessel Image Simulations

Two forced detection (FD) variance reduction Monte Carlo algorithms for image simulations of tissue‐embedded objects with matched refractive index are presented. The principle of the algorithms is to force a fraction of the photon weight to the detector at each and every scattering event. The fractional weight is given by the probability for the photon to reach the detector without further interactions. Two imaging setups are applied to a tissue model including blood vessels, where the FD algorithms produce identical results as traditional brute force simulations, while being accelerated with two orders of magnitude. Extending the methods to include refraction mismatches is discussed. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Understanding Actin Organization in Cell Structure through Lattice Based Monte Carlo Simulations

Understanding the connection between mechanics and cell structure requires the exploration of the key molecular constituents responsible for cell shape and motility. One of these molecular bridges is the cytoskeleton, which is involved with intracellular organization and mechanotransduction. In order to examine the structure in cells, we have developed a computational technique that is able to probe the self-assembly of actin filaments through a lattice based Monte Carlo method. We have modeled the polymerization of these filaments based upon the interactions of globular actin through a probabilistic model encompassing both inert and active proteins. The results show similar response to classic ordinary differential equations at low molecular concentrations, but a bi-phasic divergence at realistic concentrations for living mammalian cells. Further, by introducing localized mobility parameters, we are able to simulate molecular gradients that are observed in non-homogeneous protein distributionsin vivo. The method and results have potential applications in cell and molecular biology as well as self-assembly for organic and inorganic systems.     

Thermal Stabilization of Dihydrofolate Reductase Using Monte Carlo Unfolding Simulations and Its Functional Consequences

Design of proteins with desired thermal properties is important for scientific and biotechnological applications. Here we developed a theoretical approach to predict the effect of mutations on protein stability from non-equilibrium unfolding simulations. We establish a relative measure based on apparent simulated melting temperatures that is independent of simulation length and, under certain assumptions, proportional to equilibrium stability, and we justify this theoretical development with extensive simulations and experimental data. Using our new method based on all-atom Monte-Carlo unfolding simulations, we carried out a saturating mutagenesis of Dihydrofolate Reductase (DHFR), a key target of antibiotics and chemotherapeutic drugs. The method predicted more than 500 stabilizing mutations, several of which were selected for detailed computational and experimental analysis. We find a highly significant correlation of r = 0.65–0.68 between predicted and experimentally determined melting temperatures and unfolding denaturant concentrations for WT DHFR and 42 mutants. The correlation between energy of the native state and experimental denaturation temperature was much weaker, indicating the important role of entropy in protein stability. The most stabilizing point mutation was D27F, which is located in the active site of the protein, rendering it inactive. However for the rest of mutations outside of the active site we observed a weak yet statistically significant positive correlation between thermal stability and catalytic activity indicating the lack of a stability-activity tradeoff for DHFR. By combining stabilizing mutations predicted by our method, we created a highly stable catalytically active E. coli DHFR mutant with measured denaturation temperature 7.2°C higher than WT. Prediction results for DHFR and several other proteins indicate that computational approaches based on unfolding simulations are useful as a general technique to discover stabilizing mutations.     

Thermodynamics of Long Supercoiled Molecules: Insights from Highly Efficient Monte Carlo Simulations

Supercoiled DNA polymer models for which the torsional energy depends on the total twist of molecules (Tw) are a priori well suited for thermodynamic analysis of long molecules. So far, nevertheless, the exact determination of Tw in these models has been based on a computation of the writhe of the molecules (Wr) by exploiting the conservation of the linking number, Lk = Tw + Wr, which reflects topological constraints coming from the helical nature of DNA. Because Wr is equal to the number of times the main axis of a DNA molecule winds around itself, current Monte Carlo algorithms have a quadratic time complexity, O(L²), with respect to the contour length (L) of the molecules. Here, we present an efficient method to compute Tw exactly, leading in principle to algorithms with a linear complexity, which in practice is O(L^1.2). Specifically, we use a discrete wormlike chain that includes the explicit double-helix structure of DNA and where the linking number is conserved by continuously preventing the generation of twist between any two consecutive cylinders of the discretized chain. As an application, we show that long (up to 21 kbp) linear molecules stretched by mechanical forces akin to magnetic tweezers contain, in the buckling regime, multiple and branched plectonemes that often coexist with curls and helices, and whose length and number are in good agreement with experiments. By attaching the ends of the molecules to a reservoir of twists with which these can exchange helix turns, we also show how to compute the torques in these models. As an example, we report values that are in good agreement with experiments and that concern the longest molecules that have been studied so far (16 kbp).     

Monte Carlo Simulations of the Chemical Potential and Free Energy for Trimer and Hexamer Rings

Abstract

The chemical potential of a trimer and hexamer model ring system was determined by computer simulation over a range of temperatures and densities. Such ring molecules are important as model aromatic and naphthenic hydrocarbons. Thermodynamic integration of the pressure along a reversible path, Widom's ghost particle insertion method and Kirkwood's charging parameter method were used over a molecular density range of 0.05 to 0.30. Data were obtained by Monte Carlo simulation of a 96 molecule system that was modelled with a Lennard-Jones 6-12 truncated potential. The original insertion method, which does not take into account the orientation of the molecule when it is inserted, gives results for the chemical potential which deviate from that obtained using the thermodynamic pressure integration. At high density or temperature the deviation is significant. We have modified the Widom insertion technique to account for this short range orientation and find good agreement between this technique and the thermodynamic integration method for the chemical potential. We also calculated the free energy difference between our model ring molecules and ring molecules made up of hard spheres.     

A Monte Carlo Study of the Argon Fluid Around a Benzene Molecule

Abstract

Monte Carlo simulations have been carried out for argon fluid containing one benzene molecule at the supercritical region. The purpose in this study is to examine the effect of plate-like molecule on the structure of neighboring fluid composed of simple spherical molecules of the system. In the first neighbor shell of argon from the center of benzene molecule, the average potential energy of argon atoms is confirmed to have a large density dependence. This potential energy is relatively large in the high density region. It is found that the spatial distribution of argon fluid is significantly affected by the molecular shape of benzene and it has little direct connection with the attractive interaction between benzene and argon.     

Monte Carlo Simulations for the Detection of Buried Objects Using Single Sided Backscattered Radiation

Background

Detection of buried improvised explosive devices (IEDs) is a delicate task, leading to a need to develop sensitive stand-off detection technology. The shape, composition and size of the IEDs can be expected to be revised over time in an effort to overcome increasingly sophisticated detection methods. As an example, for the most part, landmines are found through metal detection which has led to increasing use of non-ferrous materials such as wood or plastic containers for chemical based explosives being developed.

Methodology

Monte Carlo simulations have been undertaken considering three different commercially available detector materials (hyperpure-Ge (HPGe), lanthanum(III) bromide (LaBr) and thallium activated sodium iodide (NaI(Tl)), applied at a stand-off distance of 50 cm from the surface and burial depths of 0, 5 and 10 cm, with sand as the obfuscating medium. Target materials representing medium density wood and mild steel have been considered. Each detector has been modelled as a 10 cm thick cylinder with a 20 cm diameter.

Principal Findings

It appears that HPGe represents the most promising detector for this application. Although it was not the highest density material studied, its excellent energy resolving capability leads to the highest quality spectra from which detection decisions can be inferred.

Conclusions

The simulation work undertaken here suggests that a vehicle-born threat detection system could be envisaged using a single betatron and a series of detectors operating in parallel observing the space directly in front of the vehicle path. Furthermore, results show that non-ferrous materials such as wood can be effectively discerned in such remote-operated detection system, with the potential to apply a signature analysis template matching technique for real-time analysis of such data.     

Coexistence Densities of Methane and Propane by Canonical Molecular Dynamics and Gibbs Ensemble Monte Carlo Simulations

We present preliminary canonical molecular dynamics (MD) and Gibbs ensemble Monte Carlo (GEMC) results for the vapour-liquid orthobaric densities of methane and propane. Computational advantages and drawbacks of both simulation methods are discussed and future work is outlined on the application of these techniques to the calculation of transport and interfacial properties. n -Alkanes are described through the TraPPE-UA force field. We study the effect of the truncation of interactions in the Lennard-Jones potential on the accuracy of the orthobaric liquid densities for these inhomogeneous systems along the phase diagram. We observed that a cut-off of at least 5.5 times the Lennard-Jones diameter is needed to obtain accurate results for saturated liquid densities.     

Folding of Globular Proteins by Energy Minimization and Monte Carlo Simulations with Hydrophobic Surface Area Potentials

We describe an efficient method to calculate analytically the solvent accessible surface areas and their gradients in proteins for empirical force field calculations on serial and parallel computers. In an application to the small three helix bundle protein Er-10, energy minimizations and Monte Carlo simulations were performed with the empirical ECEPP/2 force field, which was extended by a protein solvent interaction term. We show that the NMR structure is stable when refined with the force field including the protein solvent interaction term, but large structural deviations are observed in energy minimization in vacuo. When we started from random structures with preformed helices and maintained the helical segments by dihedral angle constraints, the final structures with the lowest energies resembled the native form. The root-mean-square deviations for the backbone atoms of the three helices compared to the experimentally determined structure was 3 Å to 4 Å.     

Utilizing Coarse-Grained Modeling and Monte Carlo Simulations to Evaluate the Conformational Ensemble of Intrinsically Disordered Proteins and Regions

In this study, we have used the coarse-grained model developed for the intrinsically disordered saliva protein (IDP) Histatin 5, on an experimental selection of monomeric IDPs, and we show that the model is generally applicable when electrostatic interactions dominate the intra-molecular interactions. Experimental and theoretically calculated small-angle X-ray scattering data are presented in the form of Kratky plots, and discussions are made with respect to polymer theory and the self-avoiding walk model. Furthermore, the impact of electrostatic interactions is shown and related to estimations of the conformational ensembles obtained from computer simulations and “Flexible-meccano.” Special attention is given to the form factor and how it is affected by the salt concentration, as well as the approximation of using the form factor obtained under physiological conditions to obtain the structure factor.     

Investigation of the Air Separation Properties of Zeolites Types A,X and Y by Monte Carlo Simulations

Abstract

The air separation properties of zeolite types A, X, and Y have been studied using grand canonical Monte Carlo simulations of nitrogen, oxygen, and argon adsorbed in these zeolite lattices. Nitrogen is adsorbed preferentially due to the quadrupole-ion electrostatic interactions with the extra framework cations. The localization of adsorption sites for nitrogen near cations and the more diffuse distributions of oxygen and argon within zeolite cavities are clearly illustrated. Predicted nitrogen/oxygen selectivity for 5A from simulations is in good agreement with that determined experimentally. The effect of the calcium-sodium ion exchange on the predicted nitrogen/oxygen selectivity is examined, and is shown to be sensitive to the magnitude of the charges assigned to the extra framework cations.