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 algorithm for B‐DNA

Understanding the structure–function relationship of biomolecules containing DNA has motivated experiments aimed at determining molecular structure using methods such as small‐angle X‐ray and neutron scattering (SAXS and SANS). SAXS and SANS are useful for determining macromolecular shape in solution, a process which benefits by using atomistic models that reproduce the scattering data. The variety of algorithms available for creating and modifying model DNA structures lack the ability to rapidly modify all‐atom models to generate structure ensembles. This article describes a Monte Carlo algorithm for simulating DNA, not with the goal of predicting an equilibrium structure, but rather to generate an ensemble of plausible structures which can be filtered using experimental results to identify a sub‐ensemble of conformations that reproduce the solution scattering of DNA macromolecules. The algorithm generates an ensemble of atomic structures through an iterative cycle in which B‐DNA is represented using a wormlike bead–rod model, new configurations are generated by sampling bend and twist moves, then atomic detail is recovered by back mapping from the final coarse‐grained configuration. Using this algorithm on commodity computing hardware, one can rapidly generate an ensemble of atomic level models, each model representing a physically realistic configuration that could be further studied using molecular dynamics. © 2016 Wiley Periodicals, Inc.     

Efficient implementation of periodic boundary conditions in Monte Carlo simulation

Determination of the shortest distances between particles is one of the most time-consuming parts of molecular simulation by the Monte Carlo method. In this work, we demonstrate that the use of signed-integer storage of coordinates in a scaled box allows one to skip multiple conditional statements in realization of periodic boundary conditions in cubic and rectangular boxes, which, in turn, increases the performance. Performance of the improved procedure was tested in NVT Monte Carlo simulations for liquid krypton and water. © 2018 Wiley Periodicals, Inc.     

Cassandra: An open source Monte Carlo package for molecular simulation

Cassandra is an open source atomistic Monte Carlo software package that is effective in simulating the thermodynamic properties of fluids and solids. The different features and algorithms used in Cassandra are described, along with implementation details and theoretical underpinnings to various methods used. Benchmark and example calculations are shown, and information on how users can obtain the package and contribute to it are provided. © 2017 Wiley Periodicals, Inc.     

Monte Carlo simulation of diepoxides and monoepoxides cured with amines

The diepoxide–monoepoxide–diamine curing systems are investigated with a Monte Carlo simulation. The dependence of the molecular weight distribution (MWD), gel fraction, and cycle rank of the polymers on the differences in the epoxy reactivities and the contents of the monoepoxide as a reactive diluent are discussed. Before gelation, the MWD of the curing systems with a lower content of the monoepoxide is broader than the MWD of the curing systems with a higher content, and it leads to a lower critical conversion. The gel fraction and cycle rank of the polymers decrease with an increasing amount of the diluent. Even fully cured, the system with a 0.6 epoxy molar fraction of the monoepoxide still has a large fraction of sol, about 49%. Although the various reactivities of the monoepoxide result in different ways of forming gels during curing, the final gel fractions are always near 100% as long as the epoxy molar fraction of the diluent is no more than 0.2. The profiles of the molecular weights of the polymers calculated by the model are in agreement with the experimental data. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1857–1868, 2002     

Internal coordinate density of state from molecular dynamics simulation

The vibrational density of states (DoS), calculated from the Fourier transform of the velocity autocorrelation function, provides profound information regarding the structure and dynamic behavior of a system. However, it is often difficult to identify the exact vibrational mode associated with a specific frequency if the DoS is determined based on velocities in Cartesian coordinates. Here, the DoS is determined based on velocities in internal coordinates, calculated from Cartesian atomic velocities using a generalized Wilson's B ‐matrix. The DoS in internal coordinates allows for the correct detection of free dihedral rotations that may be mistaken as hindered rotation in Cartesian DoS. Furthermore, the pronounced enhancement of low frequency modes in Cartesian DoS for macromolecules should be attributed to the coupling of dihedral and angle motions. The internal DoS, thus deconvolutes the internal motions and provides fruitful insights to the dynamic behaviors of a system. © 2015 Wiley Periodicals, Inc.     

Monte Carlo simulation on layered polymeric films

Thin films of polymer blends composed of alternating copolymer, diblock copolymer and/or homopolymer are studied using Monte Carlo simulation. A multilayer morphology is observed in the film, that is, the blended polymers assemble into individual domains arranged from interior to the surfaces of the film. The coexisting components residing throughout the neighboring domains in the film make no distinguishable interface between any neighboring domains. By this means, it forms a vertical composition gradient in the polymeric film. Being different from layer-by-layer deposition of polyelectrolyte or hydrogen bonding approach etc., the layered structure in this study is formed by polymer blending in one step. Alternating copolymers are found to be essential components to form vertical composition gradient （layered structure） in thin films.     

Wavelet-accelerated Monte Carlo sampling of polymer chains

We introduce a new method for coarse-graining polymer chains, based on the wavelet transform, a multiresolution data analysis technique. This method, which assigns a cluster of particles to a coarse-grained bead located at the center of mass of the cluster, reduces the complexity of the problem significantly by dividing the simulation into several stages, each with a small fraction of the number of beads in the overall chain. At each stage, we compute the distributions of coarse-grained internal coordinates as well as potential functions required for subsequent simulation stages. We show that, with this wavelet-accelerated Monte Carlo method, coarse-grained Gaussian and self-avoiding random walks can reproduce results obtained from atomistic simulations to a high degree of accuracy in orders of magnitude less time. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 897–910, 2005     

MCDOCK: A Monte Carlo simulation approach to the molecular docking problem

Prediction of the binding mode of a ligand (a drug molecule) to its macromolecular receptor, or molecular docking, is an important problem in rational drug design. We have developed a new docking method in which a non-conventional Monte Carlo (MC) simulation technique is employed. A computer program, MCDOCK, was developed to carry out the molecular docking operation automatically. The current version of the MCDOCK program (version 1.0) allows for the full flexibility of ligands in the docking calculations. The scoring function used in MCDOCK is the sum of the interaction energy between the ligand and its receptor, and the conformational energy of the ligand. To validate the MCDOCK method, 19 small ligands, the binding modes of which had been determined experimentally using X-ray diffraction, were docked into their receptor binding sites. To produce statistically significant results, 20 MCDOCK runs were performed for each protein–ligand complex. It was found that a significant percentage of these MCDOCK runs converge to the experimentally observed binding mode. The root-mean-square (rms) of all non-hydrogen atoms of the ligand between the predicted and experimental binding modes ranges from 0.25 to 1.84 Å for these 19 cases. The computational time for each run on an SGI Indigo2/R10000 varies from less than 1 min to 15 min, depending upon the size and the flexibility of the ligands. Thus MCDOCK may be used to predict the precise binding mode of ligands in lead optimization and to discover novel lead compounds through structure-based database searching.     

Application of combined Monte Carlo and molecular dynamics method to simulation of dipalmitoyl phosphatidylcholine lipid bilayer

We describe a new equilibration procedure for the atomic level simulation of a hydrated lipid bilayer. The procedure consists of alternating molecular dynamics trajectory calculations in a constant surface tension and temperature ensemble with configurational bias Monte Carlo moves to different regions of the configuration space of the bilayer, in a constant volume and temperature ensemble. The procedure is described in detail and is applied to a bilayer of 100 molecules of dipalmitoyl phosphatidylcholine (DPPC) and 3205 water molecules. We find that the hybrid simulation procedure enhances the equilibration of the bilayer as measured by the convergence of the area per molecule and the segmental order parameters, as compared with a simulation using only molecular dynamics (MD). Progress toward equilibration is almost three times as fast in CPU time, compared with a purely MD simulation. Equilibration is complete, as judged by the lack of energy drift in three separate 200-ps runs of continuous MD started from different initial states. Results of the simulation are presented and compared with experimental data and with other recent simulations of DPPC. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1153–1164, 1999     

Monte Carlo Simulations of Adsorbed Solutions in Heterogeneous Porous Materials

We present results of a Monte Carlo simulation study of binary mixtures of ethane and methane in silica gel. The molecular model treats the adsorbent as a matrix of silica microspheres. The adsorption isotherms, adsorption selectivities and isosteric heats of adsorption have been determined for these systems. The results are compared with predictions from the ideal adsorbed solution (IAS) theory and with experiment. The heats of adsorption are accurately described by the IAS theory. The adsorption isotherms are accurately described by the IAS theory at low bulk pressure but the IAS theory overpredicts the density at high bulk pressure. This latter effect is opposite to that observed in bulk mixtures of this type where nonidealities generally lead to a density increase on mixing. The pressure dependence of the selectivity does not exhibit a maximum at low pressure. We discuss this effect in terms of the adsorbent microstructure.     

Inverse Monte Carlo procedure for conformation determination of macromolecules

A novel numerical method for determining the conformational structure of macromolecules is applied to idealized biomacromolecules in solution. The method computes effective inter-residue interaction potentials solely from the corresponding radial distribution functions, such as would be obtained from experimental data. The interaction potentials generate conformational ensembles that reproduce thermodynamic properties of the macromolecule (mean energy and heat capacity) in addition to the target radial distribution functions. As an evaluation of its utility in structure determination, we apply the method to a homopolymer and a heteropolymer model of a three-helix bundle protein [Zhou, Y.; Karplus, M. Proc Natl Acad Sci USA 1997, 94, 14429; Zhou, Y. et al. J Chem Phys 1997, 107, 10691] at various thermodynamic state points, including the ordered globule, disordered globule, and random coil states.     

Algorithm and application of Monte Carlo simulation for multi-dispersive copolymerization system

A Monte Carlo algorithm has been established for multi-dispersive copolymerization system, based on the experimental data of copolymer molecular weight and dispersion via GPC measurement. The program simulates the insertion of every monomer unit and records the structure and microscopical sequence of every chain in various lengths. It has been applied successfully for the ring-opening copolymerization of 2,2-dimethyltrimethylene carbonate (DTC) with δ-caprolactone (δ-CL). The simulation coincides with the experimental results and provides microscopical data of triad fractions, lengths of homopolymer segments, etc., which are difficult to obtain by experiments. The algorithm presents also a uniform frame for copolymerization studies under other complicated mechanisms.     

Monte Carlo simulation of polarizable systems: Early rejection scheme for improving the performance of adiabatic nuclear and electronic sampling Monte Carlo simulations

An early rejection scheme for trial moves in adiabatic nuclear and electronic sampling Monte Carlo simulation (ANES-MC) of polarizable intermolecular potential models is presented. The proposed algorithm is based on Swendsen–Wang filter functions for prediction of success or failure of trial moves in Monte Carlo simulations. The goal was to reduce the amount of calculations involved in ANES-MC electronic moves, by foreseeing the success of an attempt before making those moves. The new method was employed in Gibbs ensemble Monte Carlo (GEMC) simulations of the polarizable simple point charge-fluctuating charge (SPC-FQ) model of water. The overall improvement in GEMC depends on the number of swap attempts (transfer molecules between phases) in one Monte Carlo cycle. The proposed method allows this number to increase, enhancing the chemical potential equalization. For a system with 300 SPC-FQ water molecules, for example, the fractions of early rejected transfers were about 0.9998 and 0.9994 at 373 and 423 K, respectively. This means that the transfer moves consume only a very small part of the overall computing effort, making GEMC almost equivalent to a simulation in the canonical ensemble.     

DNA closed nanostructures: a structural and Monte Carlo simulation study

DNA nanoconstructs are obtained in solution by using six unique 42-mer DNA oligonucleotides, whose sequences have been designed to form a pseudohexagonal structure. The required flexibility is provided by the insertion of two non-base-paired thymines in the middle of each sequence that work as flexible hinges and constitute the corners of the nanostructure when formed. We show that hexagonally shaped nanostructures of about 7 nm diameter and their corresponding linear open constructs are formed by self-assembly of the specifically designed linear oligonucleotides. The structural and dynamical characterization of the nanostructure is obtained in situ for the first time by using dynamic light scattering (DLS), a noninvasive method that provides a fast dynamic and structural analysis and allows the characterization of the different synthetic DNA nanoconstructs in solution. A validation of the LS results is obtained through Monte Carlo (MC) simulations and atomic force microscopy (AFM). In particular, a mesoscale molecular model for DNA, developed by Knotts et al., is exploited to perform MC simulations and to obtain information about the conformations as well as the conformational flexibilities of these nanostructures, while AFM provides a very detailed particle analysis that yields an estimation of the particle size and size distribution. The structural features obtained by MC and AFM are in good agreement with DLS, showing that DLS is a fast and reliable tool for characterization of DNA nanostructures in solution.     

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.     

Monte Carlo simulation of polymer welding

Monte Carlo Modelling of random polymer chains, course grained onto a cubic F lattice, provides the ability to monitor the long range relaxation processes and the dynamic parameters of chains up to 400 units long. The model, described and verified by Haire et al. (Haire KR, Carver TJ, Windle AH. A Monte Carlo model for dense polymer systems and its interlocking with molecular dynamics simulation. Computational and Theoretical Polymer Science 2000; in press), is here applied to the study of molecular parameters in the vicinity of different types of surface and also to the process of polymer welding, whereby adhesion between two adjacent surfaces is achieved by the interpenetration of chains which are across the surface.The model demonstrates that a surface distorts the conformation of chains adjacent to it to give an oblate molecular envelope, that the concentration of vacant sites and chain ends increases near to the surface and that the density of points representing the centres of mass of the chains increases in the sub-surface regions. These results confirm earlier predictions and provide additional confidence in the model.Modelling of the welding process leads to the parameter intrinsic weld time, t_w, which is the time from initial perfect contact of the surfaces to the achievement of a weld within which the chain conformation is indistinguishable from the bulk. After the initial period in which the mating surfaces roughen, the welding proceeds according to the t^1/4 law predicted by reptation theory. The time to a given level of interdiffusion across the boundary is proportional to the chain length l, a comparatively weak dependence, while t_w is proportional to l³, a strong dependence. This is the same dependence on length as for the relaxation time of the chain end-to-end vectors. In fact, the agreement between the relaxation time, measured on the model of the bulk, and t_w is surprisingly close, at least for the monodisperse polymers investigated here.     

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 the structure of mono- and bidisperse polyethylene nanocomposites

The structure of bidisperse polyethylene(PE) nanocomposite mixtures of 50:50(by mole) of long and short chains of C160H322/C80H162 and C160H322/C40H82 filled with spherical nanoparticles were investigated by a coarse-grained, on lattice Monte Carlo method using rotational isomeric state theory for short-range and Lennard-Jones for long-range energetic interactions. Simulations were performed to evaluate the effect of wall-to-wall distance between fillers(D), polymer-filler interaction(w) and polydispersity(number of short chains in the mixture) on the behavior of the long PE chains. The results indicate that long chain conformation statistics remain Gaussian regardless of the effects of confinement, interaction strength and polydispersity. The various long PE subchain structures(bridges, dangling ends, trains, and loops) are influenced strongly by confinement whereas monomer-filler interaction and polydispersity did not have any impact. In addition, the average number of subchain segments per filler in bidisperse PE nanocomposites decreased by about 50% compared to the nanocomposite system with monodisperse PE chains. The presence of short PE chains in the polymer matrix leads to a reduction of the repeat unit density of long PE chains at the interface suggesting that the interface is preferentially populated by short chains.     

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.