Monte Carlo simulation on polymer translocation in crowded environment

The effect of crowded environment with static obstacles on the translocation of a three-dimensional self-avoiding polymer through a small pore is studied using dynamic Monte Carlo simulation. The translocation time τ is dependent on polymer-obstacle interaction and obstacle concentration. The influence of obstacles on the polymer translocation is explained qualitatively by the free energy landscape. There exists a special polymer-obstacle interaction at which the translocation time is roughly independent of the obstacle concentration at low obstacle concentration, and the strength of the special interaction is roughly independent of chain length N. Scaling relation τ ~ N(1.25) is observed for strong driving translocations. The diffusion property of polymer chain is also influenced by obstacles. Normal diffusion is only observed in dilute solution without obstacles or in a crowded environment with weak polymer-obstacle attraction. Otherwise, subdiffusion behavior of polymer is observed.     

New insights into diffusion in 3D crowded media by Monte Carlo simulations: effect of size, mobility and spatial distribution of obstacles

Particle diffusion in crowded media was studied through Monte Carlo simulations in 3D obstructed lattices. Three particular aspects affecting the diffusion, not extensively treated in a three-dimensional geometry, were analysed: the relative particle-obstacle size, the relative particle-obstacle mobility and the way of having the obstacles distributed in the simulation space (randomly or uniformly). The results are interpreted in terms of the parameters that characterize the time dependence of the diffusion coefficient: the anomalous diffusion exponent (α), the crossover time from anomalous to normal diffusion regimes (τ) and the long time diffusion coefficient (D*). Simulation results indicate that there are a more anomalous diffusion (smaller α) and a lower long time diffusion coefficient (D*) when obstacle concentration increases, and that, for a given total excluded volume and immobile obstacles, the anomalous diffusion effect is less important for bigger size obstacles. However, for the case of mobile obstacles, this size effect is inverted yielding values that are in qualitatively good agreement with in vitro experiments of protein diffusion in crowded media. These results underline that the pattern of the spatial partitioning of the obstacle excluded volume is a factor to be considered together with the value of the excluded volume itself.     

Lateral diffusion of molecules in two-component lipid bilayer: a Monte Carlo simulation study

Lateral diffusion of membrane components makes possible any in-plane membrane reaction and has a key role in signaling in cell membranes. In this report the equilibrium lateral diffusion of intrinsic molecules in an equimolar DMPC/DSPC mixture is simulated using a thoroughly tested two-state model of two-component phospholipid bilayers. The model has been successful in calculating the excess heat capacity function, the most frequent center-to-center distances between DSPC clusters, and the fractal dimensions of gel clusters (Sugar, I. P., Thompson, T. E., Biltonen, R. L. Biophys. J. 1999, 76, 2099-2110). In the gel/fluid mixed phase region, a diffusing intrinsic molecule may change its state from fluid to gel (or from gel to fluid) at any time. A common characterization of the diffusion of intrinsic molecules is given by the simulated average first-passage time curves. We find that these curves can be described as power functions containing two parameters, alpha and beta, except near the percolation threshold of gel/fluid or compositional clusters. We find also that the intrinsic molecules are involved in approximately normal diffusion, i.e., beta approximately 2 in the extreme gel and fluid phase regions, while in the gel/fluid and gel/gel mixed phase regions the diffusion is anomalous, i.e., beta not equal 2. In the mixed phase regions, when the initial local state of the diffusing molecule is not specified, each component is involved in sub-diffusion (beta > 2). In the gel/fluid mixed phase region molecules situated initially inside a fluid cluster are involved in sub-diffusion, but DMPC molecules situated initially inside a gel cluster are involved in super-diffusion (beta < 2). The possibility of anomalous diffusion in membranes apparently arises because the diffusing molecule visits a variety of different environments characterized by its relative proximity to various membrane components. The diffusion is actually anomalous when the components of the bilayer are nonrandomly distributed. The deviation from random distribution is strongly correlated with beta. Similar to the results of the NMR experiments, the calculated relative diffusion coefficient continuously decreases in the gel/fluid mixed phase region with decreasing temperature. In apparent contradiction, diffusion measured by fluorescence recovery after photobleaching (FRAP) demonstrates the existence of a threshold temperature, below which long-range diffusion of FRAP probe molecules is essentially blocked. This threshold temperature is highly correlated with the percolation temperature of gel clusters.     

Nanoparticle formation in water-in-oil microemulsions: experiments, mechanism, and Monte Carlo simulation

The dynamics of nanoparticle formation in water-in-oil microemulsions via temporal size evolution has been followed from UV-visible absorption spectra of CdS nanoparticles. Existing Monte Carlo (MC) simulations of nanoparticle formation are primarily based on the mechanism of nuclei formation and their growth by coalescence-exchange of drops, which alone do not predict particles of large size as observed in some experiments. Hence, we have included an additional size enlargement process, namely coagulation of nanoparticles during drop coalescence. We find that particle coagulation, constrained by microemulsion drop size, shows very good agreement with our experimental data on CdS nanoparticle size evolution, for different drop sizes. Thus a combined approach of spectroscopy and MC simulation is helpful in elucidating the mechanism of nanoparticle formation in these confined systems, leading to prediction of size-controlled nanoparticle synthesis.     

Microscopic solvation: spectroscopic results vs. Monte Carlo simulations

Van-der-Waals clusters of carbazole (representing the ‘solute’) with up to 40 nitrogen or methane solvent molecules were characterized using two-color resonant two-photon ionization spectroscopy. Features in these spectra (redshift, homogeneous and heterogeneous broadening, etc.) are interpreted as being caused by various static and dynamic effects of the solvent shell surrounding the aromatic substrate. For a better understanding of such effects, Monte Carlo simulations of the clusters were performed: Statics: Using a Monte Carlo simulated annealing minimization procedure, minimum energy structures (local, probably global) were found for the various cluster species. Using a simple empirical additivity rule, spectral shifts are rationalized from these structures.Dynamics: Starting from these minimum configurations, canonical ensemble simulations were carried out in a temperature range from 0 to 35 K. Severalorder-disorder transitions were identified including:

1. orientational isomerization or ‘melting’
2. surface isomerization or decoupling
3. rigid → fluxional transitions
4. full cluster ‘melting’

We present some of our experimental results on the systems carbazole · (N₂) _n and carbazole · (CH₄) _n together with the corresponding simulation data.     

State of dispersion of magnetic nanoparticles in an aqueous medium: experiments and Monte Carlo simulation

Monte Carlo simulation results predicting the state of dispersion (single, dimer, trimer, and so on) of coated superparamagnetic iron oxide (Fe(3)O(4)) nanoparticles in an aqueous medium are compared with our experimental data for the same. Measured values of the volume percentage of particles in the dispersion, core particle diameter, coating-shell thickness, grafting density of the coating agent, saturation magnetization, and zeta potential for the citric acid-coated and poly(acrylic acid) [PAA]-coated particles have been used in our simulation. The simulation was performed by calculating the total interaction potential between two nanoparticles as a function of their interparticle distance and applying a criterion for the two particles to aggregate, with the criterion being that the minimum depth of the secondary minima in the total interaction potential must be at least equal to k(B)T. Simulation results successfully predicted both experimental trends-aggregates for citric acid-coated particles and an individual isolated state for PAA-coated particles. We have also investigated how this state changes for both kind of coating agents by varying the particle volume percentage from 0.01 to 25%, the particle diameter from 2 to 19 nm, the shell thickness from 1 to 14 nm, and grafting density from 10(15) to 10(22) molecules/m(2). We find that the use of a lower shell thickness and a higher particle volume percentage leads to the formation of larger aggregates. The possible range of values of these four variables, which can be used experimentally to prepare a stable aqueous dispersion of isolated particles, is recommended on the basis of predictions from our simulation.     

Monte Carlo simulation of the chain length distribution in pulsed-laser polymerization experiments in microemulsion

The Monte Carlo method has been used for numerically simulating pulsed-laser polymerization (PLP) in microemulsion, in order to establish if a shift from inflection point to peak maximum as the best measure of the propagation rate constant, k_p, will occur theoretically. Termination is assumed to be instantaneous in the simulations as droplet sizes can be very small in microemulsions. From the results of the simulations it is found that instantaneous termination indeed causes the peak maximum to become the best measure of k_p. From these results it can be deduced that in bulk it is not simply the Poisson-broadening that causes the peak maximum to yield an overestimation of k_p. This overestimation is rather caused by the fact that the termination rate is finite leading to an asymmetrical peak in the molecular weight distribution. In combination with broadening this yields the inflection point to be the best measure of k_p in the bulk.     

Monte Carlo simulation of DNA electrophoresis

This paper describes an attempt to study the electrophoresis mobility of a DNA molecule in a gel by means of a Monte Carlo simulation. We find that the electrophoresis mobility mu can be well described by the empirical equation mu v kappa 1/N + kappa 2E2 with N being the number of monomers of the model chain and E being the applied field. For small E the data can merge into the linear response result mu = kappa 1/N. The paper also discusses necessary extensions of the present approach.     

Monte Carlo simulation of osmotic equilibria

We present a Metropolis Monte Carlo simulation algorithm for the Tpπ-ensemble, where T is the temperature, p is the overall external pressure, and π is the osmotic pressure across the membrane. The algorithm, which can be applied to small molecules or sorption of small molecules in polymer networks, is tested for the case of Lennard-Jones interactions.     

Monte Carlo simulation of polymer adsorption

We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation.     

Order-parameter-based Monte Carlo simulation of crystallization

A Monte Carlo simulation method is presented for simulation of phase transitions, with emphasis on the study of crystallization. The method relies on a random walk in order parameter Phi(q(N)) space to calculate a free energy profile between the two coexisting phases. The energy and volume data generated over the course of the simulation are subsequently reweighed to identify the precise conditions for phase coexistence. The usefulness of the method is demonstrated in the context of crystallization of a purely repulsive Lennard-Jones system. A systematic analysis of precritical and critical nuclei as a function of supercooling reveals a gradual change from a bcc to a fcc structure inside the crystalline nucleus as it grows at large degrees of supercooling. The method is generally applicable and is expected to find applications in systems for which two or more coexisting phases can be distinguished through one or more order parameters.     

Monte Carlo simulation of hard spheroids

We present Monte Carlo simulations of the equation of state and radial distribution function for a model fluid composed of hard spheroids.     

Monte Carlo source simulation technique for solution of interference reactions in INAA experiments: a preliminary report

A new method using Monte Carlo source simulation of interference reactions in neutron activation analysis experiments has been developed. The neutron spectrum at the sample location has been simulated using the Monte Carlo code MCNP and the contributions of different elements to produce a specified gamma line have been determined. The produced response matrix has been used to measure peak areas and the sample masses of the elements of interest. A number of benchmark experiments have been performed and the calculated results verified against known values. The good agreement obtained between the calculated and known values suggests that this technique may be useful for the elimination of interference reactions in neutron activation analysis.     

Collective-variable Monte Carlo simulation of DNA

Monte Carlo simulations have been carried out on DNA oligomers using an internal coordinate model associated with a pseudorotational representation of sugar repuckering. It is shown that when this model is combined with the scaled collective variable approach of Noguti and Go, much more efficient simulations are obtained than with simple single variable steps. Application of this method to a DNA oligomer containing a recognition site for the TATA-box binding protein leads to striking similarities with results recently obtained from a 1-ns molecular dynamics simulation using explicit solvent and counterions. In particular, large amplitude bending fluctuations are observed directed toward the major groove. Conformational analysis of the Monte Carlo simulation shows clear base sequence effects on conformational fluctuations and also that the DNA energy hypersurface, like that of proteins, is complex with many local, conformational substates. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 2001–2011, 1997     

Monte Carlo simulation of RRKM unimolecular decomposition in molecular beam experiments. I. Basic considerations and calculational procedure

A simulation method is described for the comparison of a molecular decomposition theory, based on the fundamental RRKM theory, with crossed molecular beam experiments. In the present formulation, the method is applied to the case with long-lived collision complexes surrounded by a centrifugal barrier. The procedure uses Monte Carlo techniques to simulate the formation and decomposition of the complexes, thus effectively solving the high-dimensional integrals resulting but seldom solved in the analytical treatments. Several computational problems, like singularities in the c.m. angular distributions, have been circumvented in this procedure. Angular momentum conservation, the simultaneous interaction of several decomposition channels and strict flux conservation are included in the procedure. Dynamical features can be introduced, as will be shown in forthcoming papers.     

Monte Carlo simulation and self-consistent integral equation theory for polymers in quenched random media

The conformational properties and static structure of freely jointed hard-sphere chains in matrices composed of stationary hard spheres are studied using Monte Carlo simulations and integral equation theory. The simulations show that the chain size is a nonmonotonic function of the matrix density when the matrix spheres are the same size as the monomers. When the matrix spheres are of the order of the chain size the chain size decreases monotonically with increasing matrix volume fraction. The simulations are used to test the replica-symmetric polymer reference interaction site model (RSP) integral equation theory. When the simulation results for the intramolecular correlation functions are input into the theory, the agreement between theoretical predictions and simulation results for the pair-correlation functions is quantitative only at the highest fluid volume fractions and for small matrix sphere sizes. The RSP theory is also implemented in a self-consistent fashion, i.e., the intramolecular and intermolecular correlation functions are calculated self-consistently by combining a field theory with the integral equations. The theory captures qualitative trends observed in the simulations, such as the nonmonotonic dependence of the chain size on media fraction.     

Monte carlo simulation of macromolecular ionization by nanoelectrospray

Electrospray ionization (ESI) is commonly used in macromolecular mass spectrometry, yet the dynamics of macromolecules in ESI droplets are not well understood. In this study, a Monte Carlo based model was developed, which can predict the efficiency of electrospray ionization for macromolecules, i.e., the number of macromolecular ions produced per macromolecules electrosprayed. The model takes into account ESI droplet evaporation, macromolecular diffusion within the droplet, droplet fissions, and the statistical nature of the ESI process. Two idealized representations of macromolecular analytes were developed, describing cluster prone, droplet surface inactive macromolecules and droplet surface active macromolecules, respectively. It was found that surface active macromolecules are preferentially ionized over surface inactive cluster prone macromolecules when the initial droplet size is large and the analyte concentration in solution is high. Simulations showed that ESI efficiency decreases with increasing initial droplet size and analyte molecular weight, and is influenced by analyte surface activity, the properties of the solvent, and the variance of the droplet size distribution. Model predictions are qualitatively supported by experimental measurements of macromolecular electrospray ionization made previously. Overall, this study demonstrates the potential capabilities of Monte Carlo based ESI models. Future developments in such models will allow for more accurate predictions of macromolecular ESI intensity.     

Monte Carlo simulation of polymeric materials: Recent progress

Monte Carlo simulations are presented, dealing with phase diagrams of block copolymer melts and polymer blends, including the unmixing kinetics of the latter systems. The theoretical background is briefly reviewed: Ginzburg-type criteria reveal that in mixtures of long flexible polymers a “crossover” occurs from mean-field behavior (as described by Flory-Huggins theory) to nonclassical Ising-type behavior, and spinodal curves can be unusually sharp. This crossover is demonstrated by large scale simulations of the bond fluctuation model, and it is also shown that for symmetric mixtures the critical temperature scales with chain length as T_c α N. The prefactor in this relation is distinctly smaller than predicted by Flory-Huggins, but the Curro-Schweizer integral equation theory prediction T_c α √N is clearly ruled out. Tests of the Cahn theory on the initial stages of spinodal decomposition of polymer blends will also be reported. To conclude, the mesophase formation in block copolymers is discussed, and it is shown that the simulations agree very well with experiment. The pronounced chain stretching that already occurs in the disordered phase is compelling evidence against the validity of simple random phase approximation concepts for these systems. This shows how Monte Carlo simulations can assist in better understanding large classes of polymeric materials.     

Monte Carlo simulation of polymer mixtures: recent progress

The phase diagram of symmetrical polymer blends (A,B) confined into thin films is studied, considering both the effect of finite film thickness D and of surface forces at the confining walls that either prefer both the same species, or different species. In the case of <“>neutral<”> walls confinement enhances the compatibility of the blend. The critical temperature is depressed, the coexistence curve gets flattened (reflecting a crossover from 3‐dimensional to 2‐dimensional critical behavior). But if both walls preferentially attract species A, then also the critical composition of the blend is shifted to the A‐rich side of the phase diagram, and the coexistence curve exhibits a bulge just above the wetting transition temperature. If one wall attracts A and the other B, lateral phase separation sets in via a first order transition. Above this transition, an interface parallel to the walls is stabilized in the system.