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.     

A New Version of the Insertion Particle Method for Determining the Chemical Potential by Monte Carlo Simulation

A new version of the test particle method for determining the chemical potential by Monte Carlo simulations is proposed. The method, applicable to any fluid at any density, combines the Widom's test particle insertion method with the ideas of the scaled particle theory, gradual insertion method and multistage sampling. Its applicability is exemplified by evaluating the chemical potential of the hard sphere fluid at a very high density in semi-grand-canonical and grand-canonical ensembles. A theory estimating the efficiency (i.e. statistical errors) of the method is proposed and the results are compared with the Widom's and gradual insertion methods, and the analytic results.     

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.     

Monte Carlo simulation of the double layer at an electrode including the effect of a dielectric boundary

Monte Carlo values of the density profiles and related properties of the double layer formed by an electrolyte near a charged electrode are reported for the cases where the electrode has a dielectric coefficient greater, equal, and smaller than that of the electrolyte that causes a surface polarization that can be represented by electrostatic images. As expected, compared to the case where there is no dielectric boundary the ions near the electrode are attracted or repelled by the electrode if the dielectric coefficient is greater or smaller, respectively, than that of the electrolyte. This effect is most pronounced near the electrode and is stronger for 2:2 electrolytes than for 1:1 electrolytes. For both monovalent and divalent ions the effect of the dielectric boundary is stronger at low concentrations.     

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.     

Spherical Boundary Conditions: A Finite and System Size Independent Geometry for Simulations of Electrolytic Liquids

The system size dependence of the thermodynamic properties of electrolytic systems in "Spherical Boundary Conditions" (SBC) have been examined in this work. Coulombic systems were simulated with different system sizes (N ) for a wide range of concentrations, different ionic charges and solvent permittivities. The effects of system size upon the mean internal energy ?U? and mean ionic activity coefficient ?γ _±? values were determined. Our results indicated that there was no dependence of the thermodynamic properties upon system size in the non-Euclidean geometry. Different methods of extrapolating the thermodynamic properties to infinite numbers were studied in detail. In contrast to the Euclidean geometry, the method of extrapolating ?U? or ?γ _±? versus N ^-1, N ^-2/3 and N ^-1/3 was not statistically justifiable nor advantageous. Therefore, SBC is well suited to simulating systems involving long-range electrostatic interactions because the results do not dependent upon system size.     

Simulations of NMR-detected diffusion in suspensions of red cells: the effects of variation in membrane permeability and observation time

Monte Carlo random-walk simulations of diffusion in virtual lattices of cells have been used to study and characterize diffusion-coherence phenomena that arise when pulsed field-gradient spin-echo (PGSE) nuclear magnetic resonance (NMR) experiments are conducted on human red blood cell (RBC; erythrocytes) suspensions. These coherence effects are manifest as diffraction-like patterns when the normalized PGSE signal intensities are plotted as a function of the spatial wave vector q in so-called q-space plots. q-Space analysis is sensitive to small changes in cell morphology, cell size, membrane transport rates, hematocrit, and packing arrangement. In the present study we used simulations to predict the effect of varying the time over which diffusion is measured (the "observation time" or "diffusion time") and the permeability of the membrane on the form of q-space plots. Thus we predict that inhibiting water exchange across the human RBC membrane, such that the value of the permeability coefficient is reduced by approximately an order of magnitude below the normal physiological value, will effectively render the membrane impermeable on the timescale of the PGSE NMR experiment; further inhibition will therefore result in negligible reduction in the measured root-mean-square displacement (r.m.s.d.) of diffusing water as a function of the observation time. The work also underscores the importance of using an appropriate experimental observation time if q-space data are to be used to estimate compartment dimensions and interbarrier spacing, and illustrates an expeditious method for determining this value.     

Human Exposure to Malathion during a Possible Vector-Control Intervention against West Nile Virus. II: Evaluation of the Toxicological Risks Using a Probabilistic Approach

In order to prevent the propagation of West Nile Virus (WNV), insecticide sprayings have been carried out in several locations in North America since 1999 with the objective of controlling the mosquito populations that transmit this pathogen. An attempt to quantitatively compare the risk of developing a health response to WNV infection with the toxicological risk of insecticides is presented here. First, the acute and subchronic environmental concentrations resulting from repeated spraying events were modeled according to a reasonable worst-case spraying sequence established in an intervention program proposed by the Government of Quebec (Canada). Second, probability density functions (PDF) were established for some exposure parameters according to the data for the concerned population, when feasible. Monte Carlo analyses were performed by incorporating these PDF into the equations used to calculate the daily absorbed doses resulting from the exposure scenarios presented in the companion article (this issue). The results showed that for a significant proportion of the population, aerial and, to a lesser extent, ground sprayings of malathion can generate acute and subchronic exposure that may exceed some levels of toxicological concern based on the USEPA's reference values. Indeed, in the case of acute exposure following aerial spraying for infants, toddlers, and children, these proportions were respectively 37.1%, 59.5%, and 32.8% of the individuals, and 27.3%, 41.3%, and 24.9% following subchronic exposure. For ground spraying, these values were 12.5%, 24.2%, 8.8%; and 9.8%, 16.5%, and 7.4%. These results allowed the comparison of the probability of exceeding a level of toxicological concern for malathion exposure with the probability of developing WNV symptoms. This comparison shows that in some circumstances, the toxicological risk of malathion may exceed the infectious risk of WNV.     

Dosimetric characterization of the 60Co BEBIG Co0.A86 high dose rate brachytherapy source using PENELOPE

⁶⁰Co sources are being used as an alternative to ¹⁹²Ir sources in high dose rate brachytherapy treatments. In a recent document from AAPM and ESTRO, a consensus dataset for the ⁶⁰Co BEBIG (model Co0.A86) high dose rate source was prepared by using results taken from different publications due to discrepancies observed among them. The aim of the present work is to provide a new calculation of the dosimetric characteristics of that ⁶⁰Co source according to the recommendations of the AAPM and ESTRO report. Radial dose function, anisotropy function, air-kerma strength, dose rate constant and absorbed dose rate in water have been calculated and compared to the results of previous works. Simulations using the two different geometries considered by other authors have been carried out and the effect of the cable density and length has been studied.     

Atomistic simulations of the effects of polyglutamine chain length and solvent quality on conformational equilibria and spontaneous homodimerization

Aggregation of expanded polyglutamine tracts is associated with nine different neurodegenerative diseases, including Huntington's disease. Experiments and computer simulations have demonstrated that monomeric forms of polyglutamine molecules sample heterogeneous sets of collapsed structures in water. The current work focuses on a mechanistic characterization of polyglutamine homodimerization as a function of chain length and temperature. These studies were carried out using molecular simulations based on a recently developed continuum solvation model that was designed for studying conformational and binding equilibria of intrinsically disordered molecules such as polyglutamine systems. The main results are as follows: Polyglutamine molecules form disordered, collapsed globules in aqueous solution. These molecules spontaneously associate at conditions approaching those of typical in vitro experiments for chains of length N ≥ 15. The spontaneity of these homotypic associations increases with increasing chain length and decreases with increasing temperature. Similar and generic driving forces govern both collapse and spontaneous homodimerization of polyglutamine in aqueous milieus. Collapse and dimerization maximize self-interactions and reduce the interface between polyglutamine molecules and the surrounding solvent. Other than these generic considerations, there do not appear to be any specific structural requirements for either chain collapse or chain dimerization; that is, both collapse and dimerization are nonspecific in that disordered globules form disordered dimers. In fact, it is shown that the driving force for intermolecular associations is governed by spontaneous conformational fluctuations within monomeric polyglutamine. These results suggest that polyglutamine aggregation is unlikely to follow a homogeneous nucleation mechanism with the monomer as the critical nucleus. Instead, the results support the formation of disordered, non-β-sheet-like soluble molten oligomers as early intermediates—a proposal that is congruent with recent experimental data.     

Development of Dual Ensemble Monte Carlo Program and its Application to the CO2/N2 Separation

Abstract

A novel Monte Carlo simulation named as Dual Ensemble Monte Carlo (DEMC) method is developed for the investigation of the membrane separation process. In this method the spatial combination of Grand Canonical MC and Canonical MC techniques is employed. The DEMC method can be used to calculate the separation factor at a specific chemical potential gradient. At first, a check on the accuracy of the DEMC method is made by generating gas density gradient between two reservoir regions. Thereafter, we applied this method to CO₂/N₂ gas separation by inorganic membranes and calculated the separation factor dependence on the size of micropore in membranes.     

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.     

Solution structure of the chicken skeletal muscle troponin complex via small-angle neutron and X-ray scattering

Troponin is a Ca2+-sensitive switch that regulates the contraction of vertebrate striated muscle by participating in a series of conformational events within the actin-based thin filament. Troponin is a heterotrimeric complex consisting of a Ca2+-binding subunit (TnC), an inhibitory subunit (TnI), and a tropomyosin-binding subunit (TnT). Ternary troponin complexes have been produced by assembling recombinant chicken skeletal muscle TnC, TnI and the C-terminal portion of TnT known as TnT2. A full set of small-angle neutron scattering data has been collected from TnC-TnI-TnT2 ternary complexes, in which all possible combinations of the subunits have been deuterated, in both the +Ca2+ and -Ca2+ states. Small-angle X-ray scattering data were also collected from the same troponin TnC-TnI-TnT2 complex. Guinier analysis shows that the complex is monomeric in solution and that there is a large change in the radius of gyration of TnI when it goes from the +Ca2+ to the -Ca2+ state. Starting with a model based on the human cardiac troponin crystal structure, a rigid-body Monte Carlo optimization procedure was used to yield models of chicken skeletal muscle troponin, in solution, in the presence and in the absence of regulatory calcium. The optimization was carried out simultaneously against all of the scattering data sets. The optimized models show significant differences when compared to the cardiac troponin crystal structure in the +Ca2+ state and provide a structural model for the switch between +Ca2+ and -Ca2+ states. A key feature is that TnC adopts a dumbbell conformation in both the +Ca2+ and -Ca2+ states. More importantly, the data for the -Ca2+ state suggest a long extension of the troponin IT arm, consisting mainly of TnI. Thus, the troponin complex undergoes a large structural change triggered by Ca2+ binding.     

The influence of the medical care on the human life expectancy in 20th century and the Penna ageing model

Summary The expression of many genetic defects may be suppressed by proper medical care or even by changing the environmental conditions. We have used the Penna model of ageing to show that such efFects may be responsible for increasing the human life expectancy during the 20 ^th century. This effect is equivalent to the shift of the threshold (T) in the Penna model, which determines how many deleterious, expressed mutations kill an organism. For long genomes, the shift of T changes the age distribution significantly with negligible relative changes in the maximum life span, while for short genomes, the shift of T changes both, the age distribution as well as the maximum age. Unfortunately the same simulations show that the strategy of enhancing the medical care requires more and more effort to keep the mortality rate of our populations at the same lower level and that some new defects could be exposed to selection.     

A semi-analytical model for calculating the penetration depth of a high energy electron beam in a water phantom with a magnetic field

PurposeAs an electron beam is incident on a uniform water phantom in the presence of a lateral magnetic field, the depth-dose distribution of the electron beam changes significantly and forms the well-known ‘Bragg peak’, with a depth-dose distribution similar to that of heavy ions. This phenomenon has pioneered a new field in the clinical application of electron beams. For such clinical applications, evaluating the penetration depth of electron beams quickly and accurately is the critical problem.MethodsThis paper describes a model for calculating the penetration depth of an electron beam rapidly and correctly in a water phantom under the influence of a magnetic field. The model was used to calculate the penetration depths under different conditions: the energies of electron beams of 6, 8, 12 and 15 MeV and the magnetic induction intensities of 0.75, 1.0, 1.5, 2.0 and 3.0 T. In addition, the calculation results were compared with the results of a Monte Carlo simulation.ResultsThe comparison results indicate that the difference between the two calculation methods was less than 0.5 cm. Moreover, the computing time of the calculation model was less than a second.ConclusionsThe semi-analytical model proposed in the present study enables the penetration depth of the electron beam in the presence of a magnetic field to be obtained with a computational efficiency higher than that of the Monte Carlo approach; thus, the proposed model has high potential for application.     

Computational exploration of the gas adsorption on the iron tetracarboxylate metal-organic framework MIL-102

Density functional theory calculations have been combined with forcefield-based grand canonical Monte Carlo simulations to explore the adsorption of CO₂, N₂, CH₄ and H₂ on the small one-dimensional channel MIL-102, a naphthalene tetracarboxylate-based metal-organic framework (MOF) built up from a connection of trimers of trivalent iron. A detailed analysis is provided on the preferential arrangement of the confined adsorbates as well as the energetics of the host/guest interactions. The co-adsorption properties of this solid for the elimination of CO₂ from hydrogen, natural and flue gases are then revealed. The so-predicted performances are further compared with those reported so far for a diverse series of MOFs.     

A study on the minimum number of loci required for genetic evaluation using a finite locus model

For a finite locus model, Markov chain Monte Carlo (MCMC) methods can be used to estimate the conditional mean of genotypic values given phenotypes, which is also known as the best predictor (BP). When computationally feasible, this type of genetic prediction provides an elegant solution to the problem of genetic evaluation under non-additive inheritance, especially for crossbred data. Successful application of MCMC methods for genetic evaluation using finite locus models depends, among other factors, on the number of loci assumed in the model. The effect of the assumed number of loci on evaluations obtained by BP was investigated using data simulated with about 100 loci. For several small pedigrees, genetic evaluations obtained by best linear prediction (BLP) were compared to genetic evaluations obtained by BP. For BLP evaluation, used here as the standard of comparison, only the first and second moments of the joint distribution of the genotypic and phenotypic values must be known. These moments were calculated from the gene frequencies and genotypic effects used in the simulation model. BP evaluation requires the complete distribution to be known. For each model used for BP evaluation, the gene frequencies and genotypic effects, which completely specify the required distribution, were derived such that the genotypic mean, the additive variance, and the dominance variance were the same as in the simulation model. For lowly heritable traits, evaluations obtained by BP under models with up to three loci closely matched the evaluations obtained by BLP for both purebred and crossbred data. For highly heritable traits, models with up to six loci were needed to match the evaluations obtained by BLP.     

Structure and stability of a model three-helix-bundle protein on tailored surfaces

The interaction of protein molecules with surfaces is important in numerous applications. Theoretical work on protein adsorption has been limited. In particular, it is difficult to obtain quantitative predictions about the structure and stability of proteins on surfaces. In this study, density-of-states-based simulations were performed on a Gō-like model of a three-helix-bundle fragment from protein A (PDB ID: 1bdd). Both mechanical and thermal stability were investigated on neutral and attractive surfaces and compared to that in the absence of a surface. It was found that attaching the peptide to any type of surface decreases its melting temperature by as much as 9 K, depending upon orientation. Calorimetric cooperativity, as measured by van't Hoff to calorimetric enthalpy ratios, similarly decreased. It was also found that the mechanical strength of the peptide attached to surfaces is degraded to varying extents, depending upon the surface type and protein orientation. A comparison of mechanical and thermal stability showed that the two are not synonymous, but occur through different pathways, and that system configurations that are more thermally stable are not always so mechanically.     

Modeling of peptides and proteins in a membrane environment: I. A solvation model mimicking a lipid bilayer

A theoretical solvation model of peptides and proteins that mimics the heterogeneous membrane-water system was proposed. Our approach is based on the combined use of atomic parameters of solvation for water and hydrocarbons, which approximates the hydrated polar groups and acyl chains of lipids, respectively. This model was tested in simulations of several peptides: a nonpolar 20-mer polyleucine, a hydrophobic peptide with terminal polar groups, and a strongly amphiphilic peptide. The conformational space of the peptides in the presence of the membrane was studied by the Monte Carlo method. Unlike a polar solvent and vacuum, the membrane-like environment was shown to stabilize the α-helical conformation: low-energy structures have a helicity index of 100% in all cases. At the same time, the energetically most favorable orientations of the peptides relative to the membrane depend on their hydrophobic properties: nonpolar polyleucine is entirely immersed in the bilayer and the hydrophobic peptide with polar groups at the termini adopts a transbilayer orientation, whereas the amphiphilic peptide lies at the interface parallel to the membrane plane. The results of the simulations agree well with the available experimental data for these systems. In the following communications of this series, we plan to describe applications of the solvation model to membrane-bound proteins and peptides with biologically important functional activities.