Three-dimensional dynamic Monte Carlo simulations of elastic actin-like ratchets

We present three-dimensional dynamic Monte Carlo simulations of the growth of a semiflexible fiber against a fluctuating obstacle. The natural reference for our numerical study are the elastic and Brownian ratchet models previously analyzed semianalytically. We find that the decay of the velocity versus applied load is exponential to a good degree of accuracy, provided we include in the load the drag force felt by the moving obstacle. If the fiber and obstacle only interact via excluded volume, there are small corrections to the Brownian ratchet predictions which suggest that tip fluctuations play a minor role. If on the other hand fiber and obstacle interact via a soft potential, the corrections are much larger when the obstacle diffuses slowly. This means that microscopic assumptions can profoundly affect the dynamics. We also identify and characterize a novel "pushing catastrophe"--which is distinct from the usual fiber buckling--in which the growth of the fiber decouples from the obstacle movement. The time distribution of catastrophes can be explained via an approximate analytical treatment, and our numerics suggest that the time taken to lose propulsive force is largely dependent on the fiber incidence angle. Our results are a first step in realizing numerical polymer models for the motion of sets or networks of semiflexible fibers close to a fluctuating membrane or obstacle.     

Monte Carlo simulations of the hydrophobic effect in aqueous electrolyte solutions

The hydrophobic interaction between two methane molecules in salt-free and high salt-containing aqueous solutions and the structure in such solutions have been investigated using an atomistic model solved by Monte Carlo simulations. Monovalent salt representing NaCl and divalent salt with the same nonelectrostatic properties as the monovalent salt have been used to examine the influence of the valence of the salt species. In salt-free solution the effective interaction between the two methane molecules displayed a global minimum at close contact of the two methane molecules and a solvent-separated secondary minimum. In 3 and 5 M monovalent salt solution the potential of mean force became slightly more attractive, and in a 3 M divalent salt solution the attraction became considerably stronger. The structure of the aqueous solutions was determined by radial distribution functions and angular probability functions. The distortion of the native water structure increased with ion valence. The increase of the hydrophobic attraction was associated with (i) a breakdown of the tetrahedral structure formed by neighboring water molecules and of the hydrogen bonds between them and (i) the concomitant increase of the solution density.     

Monte Carlo simulations of single crystals from polymer solutions

A novel "anisotropic aggregation" model is proposed to simulate nucleation and growth of polymer single crystals as functions of temperature and polymer concentration in dilute solutions. Prefolded chains in a dilute solution are assumed to aggregate at a seed nucleus with an anisotropic interaction by a reversible adsorption/desorption mechanism, with temperature, concentration, and seed size being the control variables. The Monte Carlo results of this model resolve the long-standing dilemma regarding the kinetic and thermal roughenings, by producing a rough-flat-rough transition in the crystal morphology with increasing temperature. It is found that the crystal growth rate varies nonlinearly with temperature and concentration without any marked transitions among any regimes of polymer crystallization kinetics. The induction time increases with decreasing the seed nucleus size, increasing temperature, or decreasing concentration. The apparent critical nucleus size is found to increase exponentially with increasing temperature or decreasing concentration, leading to a critical nucleus diagram composed in the temperature-concentration plane with three regions of different nucleation barriers: no growth, nucleation and growth, and spontaneous growth. Melting temperatures as functions of the crystal size, heating rate, and concentration are also reported. The present model, falling in the same category of small molecular crystallization with anisotropic interactions, captures most of the phenomenology of polymer crystallization in dilute solutions.     

Monte Carlo simulations of polymer dynamics: Recent advances

A brief review is given of applications of Monte Carlo simulations to study the dynamical properties of coarse-grained models of polymer melts, emphasizing the crossover from the Rouse model toward reptation, and the glass transition. The extent to which Monte Carlo algorithms can mimic the actual chain dynamics is critically examined, and the need for the use of coarse-grained rather than fully atomistic models for such simulations is explained. It is shown that various lattice and continuum models yield qualitatively similar results, and the behavior agrees with the findings of corresponding molecular dynamics simulations and experiments, where available. It is argued that these simulations significantly enhance our understanding of the theoretical concepts on the dynamics of dense macromolecular systems. © 1997 John Wiley & Sons, Inc.     

Monte Carlo structure simulations for aqueous 1,4-dioxane solutions

Monte Carlo simulations in the NpT ensembles have been performed for the structure exploration of aqueous 1,4-dioxane solutions. Three different systems with all-atom dioxane:TIP4P water molar compositions of 2:500 (code:D2), 8:465 (D8), and 17:425 (D17) modeled solutions of 0.22, 0.88, and 1.86 mol/dm3 concentrations, respectively, at T = 298 K and p = 1 atm. The calculated solution densities increase from 0.992 to 1.002 g/cm3 with increasing dioxane concentration and approach the experimentally determined densities within 1%. This close agreement was achieved by utilizing RESP charges fitted to the in-solution IEF-PCM/B3LYP/6-31G* electrostatic potential of dioxane taken in its chair conformation and recently developed C, H steric parameters for ethers for calculations with a 12-6-1 all-atom potential. Solution structure analyses pointed out that the dioxane molecules arrange in the solutions with favorable distances of 4-8 angstroms for the ring symmetry centers. Within this range not only pairs of rings but triangular triads and tetrads have also been observed with center-center distances <8 angstroms. For the D8 system, about 25% of the sampled configurations included such a triad. In the case of the D17 model, two simulations starting from different solution configuration predicted different degrees for the dioxane aggregation in aqueous solution. In the more aggregated structure 3-21 triads are consistently maintained and 1-2 tetrads are formed in 58% of the configurations. Each dioxane oxygen forms about one hydrogen bond, on average, to a water molecule in the 0.22-1.86 molar range. The most likely O(dioxane)...H(water) hydrogen bond distance is 1.75-1.80 angstroms compared to the optimal distance of 1.72 angstroms in the isolated dimer. The optimal dioxane-water interaction energy of -5.65 kcal/mol indicates a remarkable hydrogen-bond acceptor character for dioxane.     

Avoiding unphysical kinetic traps in Monte Carlo simulations of strongly attractive particles

We introduce a "virtual-move" Monte Carlo algorithm for systems of pairwise-interacting particles. This algorithm facilitates the simulation of particles possessing attractions of short range and arbitrary strength and geometry, an important realization being self-assembling particles endowed with strong, short-ranged, and angularly specific ("patchy") attractions. Standard Monte Carlo techniques employ sequential updates of particles and can suffer from low acceptance rates when attractions are strong. In this event, collective motion can be strongly suppressed. Our algorithm avoids this problem by proposing simultaneous moves of collections (clusters) of particles according to gradients of interaction energies. One particle first executes a "virtual" trial move. We determine which of its neighbors move in a similar fashion by calculating individual bond energies before and after the proposed move. We iterate this procedure and update simultaneously the positions of all affected particles. Particles move according to an approximation of realistic dynamics without requiring the explicit computation of forces and without the step size restrictions required when integrating equations of motion. We employ a size- and shape-dependent damping of cluster movements, motivated by collective hydrodynamic effects neglected in simple implementations of Brownian dynamics. We discuss the virtual-move algorithm in the context of other Monte Carlo cluster-move schemes and demonstrate its utility by applying it to a model of biological self-assembly.     

Monte Carlo vs molecular dynamics for all-atom polypeptide folding simulations

An efficient Monte Carlo (MC) algorithm including concerted rotations is directly compared to molecular dynamics (MD) in all-atom statistical mechanics folding simulations of small polypeptides. The previously reported algorithm "concerted rotations with flexible bond angles" (CRA) has been shown to successfully locate the native state of small polypeptides. In this study, the folding of three small polypeptides (trpzip2/H1/Trp-cage) is investigated using MC and MD, for a combined sampling time of approximately 10(11) MC configurations and 8 micros, respectively. Both methods successfully locate the experimentally determined native states of the three systems, but they do so at different speed, with 2-2.5 times faster folding of the MC runs. The comparison reveals that thermodynamic and dynamic properties can reliably be obtained by both and that results from folding simulations do not depend on the algorithm used. Similar to previous comparisons of MC and MD, it is found that one MD integration step of 2 fs corresponds to one MC scan, revealing the good sampling of MC. The simplicity and efficiency of the MC method will enable its future use in folding studies involving larger systems and the combination with replica exchange algorithms.     

Three-dimensional Monte Carlo simulations of intracellular diffusion and reaction of signaling proteins

We show that the Monte Carlo technique makes it possible to perform three-dimensional simulations of intracellular protein-mediated signal transduction with realistic ratio of the rates of protein diffusion and association with genes. Specifically, we illustrate that in the simplest case when the protein degradation and phosphorylation/dephosphorylation are negligible the distribution of the first passage time for this process is close to exponential provided that the number of target genes is between 1 and 100.     

Monte Carlo simulations of fluids whose particles interact with a logarithmic potential

Monte Carlo simulations of a model fluid in which the particles interact via a continuous potential that has a logarithmic divergence at a pair separation of sigma, which we introduced in J. G. Powles et al., Proc. R. Soc. London, Ser. A 455, 3725 (1999), have been carried out. The potential has the form, phi(r)= -epsilon ln(fr), where epsilon sets the energy scale and fr=1-(sigma/r)m. The value of m chosen was 12 but the qualitative trends depend only weakly on the value of m, providing it is greater than 3. The potential is entirely repulsive and has a logarithmic divergence as approximately -ln(r/sigma-1) in the r-->sigma limit. Predictions of the previous paper that the internal energy can be computed at all temperatures using the standard statistical mechanics formula for continuous potentials are verified here. The pressure can be calculated using the usual virial expression for continuous potentials, although there are practical limitations in resolving the increasingly important contribution from the r-->sigma limit at reduced temperatures greater than approximately 5. The mean square force F2 and infinite frequency shear Ginfinity and bulk Kinfinity moduli are only finite for T*=kBT/epsilon<1. The logarithmic fluid's physical properties become increasingly more like that of the hard sphere fluid with increasing temperature, showing a sharp transition in the behavior of the mean square force and infinite frequency elastic constants at T*=1. The logarithmic fluid is shown to exhibit a solid-fluid phase transition.     

Experimental,Monte Carlo and molecular dynamics simulations to investigate corrosion inhibition of mild steel in hydrochloric acid solutions

The efficiency of three furan derivatives, namely 2-(p-toluidinylmethyl)-5-methyl furan (Inh. A), 2-(p-toluidinylmethyl)-5-nitro furan (Inh. B) and 2-(p-toluidinylmethyl)-5-bromo furan (Inh. C), as possible corrosion inhibitors for mild steel in 1.0 M HCl, has been determined by weight loss and electrochemical measurements. These compounds inhibit corrosion even at very low concentrations, and 2-(p-toluidinylmethyl)-5-methyl furan (Inh. A) is the best inhibitor. Polarization curves indicate that all compounds are mixed-type inhibitors, affecting both cathodic and anodic corrosion currents. Adsorption of furan derivatives on the mild steel surface follows the Langmuir adsorption isotherm, and the calculated Gibbs free energy values confirm the chemical nature of the adsorption. Monte Carlo simulations technique incorporating molecular mechanics and molecular dynamics can be used to simulate the adsorption of furan derivatives on mild steel surface in 1.0 M HCl.     

Macroion solutions in the cell model studied by field theory and Monte Carlo simulations

Aqueous solutions of charged spherical macroions with variable dielectric permittivity and their associated counterions are examined within the cell model using a field theory and Monte Carlo simulations. The field theory is based on separation of fields into short- and long-wavelength terms, which are subjected to different statistical-mechanical treatments. The simulations were performed by using a new, accurate, and fast algorithm for numerical evaluation of the electrostatic polarization interaction. The field theory provides counterion distributions outside a macroion in good agreement with the simulation results over the full range from weak to strong electrostatic coupling. A low-dielectric macroion leads to a displacement of the counterions away from the macroion.     

Reactive Monte Carlo and grand-canonical Monte Carlo simulations of the propene metathesis reaction system

The influence of silicalite-1 pores on the reaction equilibria and the selectivity of the propene metathesis reaction system in the temperature range between 300 and 600 K and the pressure range from 0.5 to 7 bars has been investigated with molecular simulations. The reactive Monte Carlo (RxMC) technique was applied for bulk-phase simulations in the isobaric-isothermal ensemble and for two phase systems in the Gibbs ensemble. Additionally, Monte Carlo simulations in the grand-canonical ensemble (GCMC) have been carried out with and without using the RxMC technique. The various simulation procedures were combined with the configurational-bias Monte Carlo approach. It was found that the GCMC simulations are superior to the Gibbs ensemble simulations for reactions where the bulk-phase equilibrium can be calculated in advance and does not have to be simulated simultaneously with the molecules inside the pore. The confined environment can increase the conversion significantly. A large change in selectivity between the bulk phase and the pore phase is observed. Pressure and temperature have strong influences on both conversion and selectivity. At low pressure and temperature both conversion and selectivity have the highest values. The effect of confinement decreases as the temperature increases.     

Parallel Markov chain Monte Carlo simulations

With strict detailed balance, parallel Monte Carlo simulation through domain decomposition cannot be validated with conventional Markov chain theory, which describes an intrinsically serial stochastic process. In this work, the parallel version of Markov chain theory and its role in accelerating Monte Carlo simulations via cluster computing is explored. It is shown that sequential updating is the key to improving efficiency in parallel simulations through domain decomposition. A parallel scheme is proposed to reduce interprocessor communication or synchronization, which slows down parallel simulation with increasing number of processors. Parallel simulation results for the two-dimensional lattice gas model show substantial reduction of simulation time for systems of moderate and large size.     

Monte Carlo simulations of squalane in the Gibbs ensemble

We investigate the liquid–vapour coexistence curve of 2,6,10,15,19,23-hexamethyltetracosane (squalane) near the critical point with a new Lennard–Jones parameter set and compare our results to existing simulation data as well as to recent experimental vapour pressure data. Comparison of the liquid–vapour coexistence curve to previous simulation data reveals that this new force field, which includes tail corrections to the truncation of the non-bonded interactions increases the liquid density. We determine the critical temperature to 829 K and 825 K (with roughly 1% error) for two different system sizes, 72 and 108 molecules, and the critical density to 0.211 g/cm³ and 0.228 g/cm³, respectively. We extrapolate experimental vapour pressure data by use of Antoine's law to the temperature range covered by simulation and yield good agreement between simulation and experiment. We note that the vapour pressure in simulation is essentially governed by the ideal vapour pressure.     

Three-dimensional Monte Carlo simulations of internal aggregate structures in a colloidal dispersion composed of rod-like particles with magnetic moment normal to the particle axis

We have treated a suspension composed of ferromagnetic rod-like particles with a magnetic moment normal to the particle axis in order to investigate aggregation phenomena of such a suspension by means of cluster-moving Monte Carlo simulations. In the present study, we have considered a three-dimensional mono-dispersed model system composed of such rod-like particles. Internal structures of self-assembled clusters have been discussed quantitatively in terms of radial distribution, pair correlation, orientational pair correlation functions, number distributions of clusters, and order functions. The main results obtained here are summarized as follows. Rod-like particles tend to aggregate to form raft-like clusters along the magnetic moment direction more significantly with magnetic particle-particle interactions. In such raft-like clusters, the direction of each particle axis has a tendency to incline in parallel formation, but is not so parallel as in a two-dimensional dispersion. As the volumetric fraction increases, longer raft-like clusters are formed, but such raft-like clusters do not aggregate further to form thicker clusters, which is in significantly contrast with a dispersion of spherical particles, where thicker chain-like clusters are observed under certain conditions. For the case of strong magnetic particle-particle interactions, sufficiently long raft-like clusters are formed along the magnetic field direction, even if the influence of an external magnetic field is of the same order of that of the thermal energy. However, rod-like particles in such clusters do not necessarily incline in significantly parallel formation along a certain direction. Self-assembled tube-like clusters are formed when magnetic particle-particle interactions are much more dominant than the rotational Brownian motion under circumstances of rod-like particles inclining in a certain direction.     

Configuration biased Monte Carlo and Brownian dynamics simulations of semiflexible polymers in extensional flows

Configuration Biased Monte Carlo (CBMC) and Non-Equilibrium Brownian Dynamics (NEBD) simulations are used to understand the dynamics of semi-flexible macromolecules undergoing extensional flow. The mathematical model utilizes a discretized version of the Kratky-Porod wormlike (or persistent) chain as the building block, and using kinetic theory, generalized to include flow. In steady, potential flows, the solution of the Fokker-Planck equation exists and is used in the generation of trial and acceptance moves in the CBMC scheme. For the NEBD, the Fokker-Planck equation is converted to a Stochastic Differential Equation (SDE) from which the simulation algorithm is obtained. Various conformational quantities are monitored, under both steady-state and transient conditions, with the primary independent variable being the flexibility parameter β, the bending constant of the chain. It is found that the model is able to describe qualitatively many of the experimentally observed effects in such systems. In particular, we find that there is a direct link between the molecular flexibility and its birefringence response in an elongational flow field. We are able to draw conclusions by considering the behavior of molecular-conformational quantities such as the radius of gyration and the moment of inertia.     

On the acceptance ratio in Monte Carlo computer simulations

The functional form of acceptance probabilities in Monte Carlo algorithms bears a resemblance to the distance functions which are specifically defined to be bracketed by the unit interval. This observation led us to seek the average distance between any two points on the unit interval and this by analogy resulted in a suggestion of an upper and a lower bound of 1/2 and 1/3, respectively, for the acceptance ratio or the average acceptance probability in Monte Carlo computer simulations.     

Guest-specific diffusion anisotropy in nanoporous materials: Molecular dynamics and dynamic Monte Carlo simulations

For anisotropic nanoporous materials, guest diffusion is often reflected by a diffusion tensor rather than a scalar diffusion coefficient. Moreover, the resulting diffusion anisotropy may notably differ for different guest molecules. As a particular class of such systems, we consider an array of two types of channels, mutually intersecting each other, where the rates of diffusion in the different directions depend on the nature of the guest molecules. The simultaneous adsorption of two types of guest molecules is considered, as in technical applications of porous materials such as catalysis. A case study is presented in which atomistic molecular dynamics (MD) and coarse-grained dynamic Monte Carlo (DMC) simulations are compared and shown to yield qualitatively similar results for non-steady-state diffusion. The two techniques are complementary. MD simulations are able to predict the details of molecular propagation over distances of a few unit cells, whereas the evolution of sorption profiles over distances comparable with entire crystallites can be studied with DMC simulations. Consideration of these longer length and time scales is necessary for applications of such systems in chemical separations and heterogeneous catalysis.