Monte Carlo simulations of supercoiled DNAs confined to a plane.

Recent advances in atomic force microscopy (AFM) have enabled researchers to obtain images of supercoiled DNAs deposited on mica surfaces in buffered aqueous milieux. Confining a supercoiled DNA to a plane greatly restricts its configurational freedom, and could conceivably alter certain structural properties, such as its twist and writhe. A program that was originally written to perform Monte Carlo simulations of supercoiled DNAs in solution was modified to include a surface potential. This potential flattens the DNAs to simulate the effect of deposition on a surface. We have simulated transfers of a 3760-basepair supercoiled DNA from solution to a surface in both 161 and 10 mM ionic strength. In both cases, the geometric and thermodynamic properties of the supercoiled DNAs on the surface differ significantly from the corresponding quantities in solution. At 161 mM ionic strength, the writhe/twist ratio is 1.20-1.33 times larger for DNAs on the surface than for DNAs in solution and significant differences in the radii of gyration are also observed. Simulated surface structures in 161 mM ionic strength closely resemble those observed by AFM. Simulated surface structures in 10 mM ionic strength are similar to a minority of the structures observed by AFM, but differ from the majority of such structures for unknown reasons. In 161 mM ionic strength, the internal energy (excluding the surface potential) decreases substantially as the DNA is confined to the surface. Evidently, supercoiled DNAs in solution are typically deformed farther from the minimum energy configuration than are the corresponding surface-confined DNAs. Nevertheless, the work (Delta A(int)) done on the internal coordinates, which include uniform rotations at constant configuration, during the transfer is positive and 2.6-fold larger than the decrease in internal energy. The corresponding entropy change is negative, and its contribution to Delta A(int) is positive and exceeds the decrease in internal energy by 3.6 fold. The work done on the internal coordinates during the solution-to-surface transfer is directed primarily toward reducing their entropy. Evidently, the number of configurations available to the more deformed solution DNA is vastly greater than for the less deformed surface-confined DNA.     

Monte Carlo simulations of ionic channel selectivity

Monte Carlo simulations have been developed to study the selectivityof ionic channels in biological membranes. The channel is consideredto be in either of two possible states: (i) densely packed withions, the ions moving in single file in one direction, or alternatively,(ii) sparsely packed, where holes could appear at any particulartime thereby allowing bidirectional movement of ions. The twomodels enable us to envisage a quantitative flux of permeableions in the presence of smaller sized ions, taking into considerationtheir concentrations in the bulk solutions, the ion-channelinteractions and probability with which they fill up the channel.The programs are written in FORTRAN-77 (MS-FORTRAN) for an IBM-compatiblepersonal computer. From the simulation results we observe anenzymatic function of the channel and also note that the smallersized ions tend to block the movement of permeable ions. Thesimulations represent a technique for visualization of the factorsthat decide ionic permeability and help in manipulating theireffects with ease and speed which would otherwise involve intricateexperimental setups. Received on September 7, 1990; accepted on January 14, 1991     

Monte Carlo implementation of supercoiled double-stranded DNA

Metropolis Monte Carlo simulation is used to investigate the elasticity of torsionally stressed double-stranded DNA, in which twist and supercoiling are incorporated as a natural result of base-stacking interaction and backbone bending constrained by hydrogen bonds formed between DNA complementary nucleotide bases. Three evident regimes are found in extension versus torsion and force versus extension plots: a low-force regime in which over- and underwound molecules behave similarly under stretching; an intermediate-force regime in which chirality appears for negatively and positively supercoiled DNA and extension of underwound molecule is insensitive to the supercoiling degree of the polymer; and a large-force regime in which plectonemic DNA is fully converted to extended DNA and supercoiled DNA behaves quite like a torsionless molecule. The striking coincidence between theoretic calculations and recent experimental measurement of torsionally stretched DNA (Strick et al., Science. 271:1835, 1996; Biophys. J. 74:2016, 1998) strongly suggests that the interplay between base-stacking interaction and permanent hydrogen-bond constraint takes an important role in understanding the novel properties of elasticity of supercoiled DNA polymer.     

Monte Carlo simulations of supercoiling free energies for unknotted and trefoil knotted DNAs.

A new Monte Carlo (MC) algorithm is proposed for simulating inextensible circular chains with finite twisting and bending rigidity. This new algorithm samples the relevant Riemann volume elements in a uniform manner, when the constraining potential vanishes. Simulations are performed for filaments comprising 170 subunits, each containing approximately 28 bp, which corresponds to a DNA length of 4770 bp. The bending rigidity is chosen to yield a persistence length, P = 500 A, and the intersubunit potential is taken to be a hard-cylinder potential with diameter d = 50 A. This value of d yields the same second virial coefficient as the electrostatic potential obtained by numerical solution of the Poisson-Boltzmann equation for 150 mM salt. Simulations are performed for unknotted circles and also for trefoil knotted circles using two different values of the torsional rigidity, C = (2.0 and 3.0) x 10(-19) dyne cm2. In the case of unknotted circles, the simulated supercoiling free energy varies practically quadratically with linking difference delta l. The simulated twist energy parameter ET, its slope dET/dT, and the mean reduced writhe <w>/delta l for C = 3 x 10(-19) dyne cm2 all agree well with recent simulations for unknotted circles using the polygon-folding algorithm with identical P, d, and C. The simulated ET vs. delta l data for C = 2.0 x 10(-19) dyne cm2 agree rather well with recent experimental data for p30 delta DNA (4752 bp), for which the torsional rigidity, C = 2.07 x 10(-19) dyne cm2, was independently measured. The experimental data for p30 delta are enormously more likely to have arisen from C = 2.0 x 10(-19) than from C = 3.0 x 10(-19) dyne cm2. Serious problems with the reported experimental assessments of ET for pBR322 and their comparison with simulated data are noted. In the case of a trefoil knotted DNA, the simulated value, (ET)tre, exceeds that of the unknotted DNA, (ET)unk, by approximately equal to 1.40-fold at magnitude of delta l = 1.0, but declines to a plateau about 1.09-fold larger than (ET)unk when magnitude of delta l > or = 15. Although the predicted ratio, (ET)tre/(ET)unk approximately equal to 1.40, agrees fairly well with recent experimental measurements on a 5600-bp DNA, the individual measured ET values, like some of those reported for pBR322, are so large that they cannot be simulated using P = 500 A, d = 50 A, and any previous experimental estimate of C.     

Monte Carlo simulations of peptide solvation

To increase our understanding of peptide–water interactions, we are simulating the behavior of water molecules in the intermolecular channels of [Phe⁴Val⁶]antamanide dododecahydrate crystals. There is good overall agreement between the positions predicted using two alternative potential functions and those that have been observed by x-ray diffraction. Detailed differences between the predictions for the two potential functions are discussed.     

Grazers and grass: Monte Carlo simulations

To illustrate the interplay between grazers and grass, we present a novel Monte Carlo model including grass-island growth, consumption of grass by grazers, and birth, migration and death of grazers. The rates of the former and three latter processes are assumed to depend on the environment so that the conventional mean-field approximation does not hold (in particular, the model takes into account that grass grows on the grass-island boundaries, and grazers are mobile and prefer to stay on the areas covered by grass). Due to the feedback between various processes, as expected, the model predicts stable regimes and irregular oscillations of the area of the grass islands and grazer population. The patterns observed are however different compared to those predicted by conventional Monte Carlo prey-predator models. Specifically, there is no tendency for grazers and grass to segregate. The mean-field version of the model is briefly discussed as well.     

Monte Carlo simulations on marker grouping and ordering

Four global algorithms, maximum likelihood (ML), sum of adjacent LOD score (SALOD), sum of adjacent recombinant fractions (SARF) and product of adjacent recombinant fraction (PARF), and one approximation algorithm, seriation (SER), were used to compare the marker ordering efficiencies for correctly given linkage groups based on doubled haploid (DH) populations. The Monte Carlo simulation results indicated the marker ordering powers for the five methods were almost identical. High correlation coefficients were greater than 0.99 between grouping power and ordering power, indicating that all these methods for marker ordering were reliable. Therefore, the main problem for linkage analysis was how to improve the grouping power. Since the SER approach provided the advantage of speed without losing ordering power, this approach was used for detailed simulations. For more generality, multiple linkage groups were employed, and population size, linkage cutoff criterion, marker spacing pattern (even or uneven), and marker spacing distance (close or loose) were considered for obtaining acceptable grouping powers. Simulation results indicated that the grouping power was related to population size, marker spacing distance, and cutoff criterion. Generally, a large population size provided higher grouping power than small population size, and closely linked markers provided higher grouping power than loosely linked markers. The cutoff criterion range for achieving acceptable grouping power and ordering power differed for varying cases; however, combining all situations in this study, a cutoff criterion ranging from 50 cM to 60 cM was recommended for achieving acceptable grouping power and ordering power for different cases.     

Monte Carlo simulations of plasma membrane corral-induced EGFR clustering

Experimental evidence suggests that the cell membrane is a highly organized structure that is compartmentalized by the underlying membrane cytoskeleton (MSK). The interaction between the cell membrane and the cytoskeleton led to the “picket-fence” model, which was proposed to explain certain aspects of membrane compartmentalization. This model assumes that the MSK hinders and confines the motion of receptors and lipids to compartments in the membrane. However, the impact of the MSK on receptor clustering, aggregation, and downstream signaling remains unclear. For example, some evidence suggests that the MSK enhances dimerization, while other evidence suggests decreased dimerization and signaling. Herein, we use computational Monte Carlo simulations to examine the effects of MSK density and receptor concentration on receptor dimerization and clustering. Preliminary results suggest that the MSK may have the potential to induce receptor clustering, which is a function of both picket-fence density and receptor concentration.     

Lipid-cholesterol interactions. Monte Carlo simulations and theory.

Results of Monte Carlo calculations of order parameter profiles of lipid chains interacting with cholesterol are presented. Cholesterol concentrations in the simulations are sufficiently large that it is possible to analyze profiles for chains which are near neighbors of two or more cholesterol molecules, chains which are neighbors to a single cholesterol, and chains which are not near any cholesterol molecules. The profiles, show that cholesterol acts to significantly decrease the ability of neighboring chains to undergo trans-gauche isomeric rotations, although these chains are not all forced into all-trans conformations. The effect is significantly greater for chains which are neighbors to more than one cholesterol. The Monte Carlo results are next used as a guide to develop a theoretical model for lipid-cholesterol mixtures. The properties of this model and the phase diagram which it predicts are described. The phase diagram is then compared with experimentally determined phase diagrams. The model calculations and the computer simulations upon which they are based yield a molecular mechanism for several of the observed phases exhibited by lipid-cholesterol mixtures. The theoretical model predicts that at low temperatures the system should exhibit solid phase immiscibility.     

Monte Carlo simulations of voltage-driven translocation of a signal sequence

CD1d-deficient (CD1d-/-) mouse lymphocytes were analyzed to classify the natural killer T (NKT) cells without reactivity to CD1d. The cells bearing a V(alpha)19.1-J(alpha)26 (AV19-AJ33) invariant TCR alpha chain, originally found in the peripheral blood lymphocytes, were demonstrated to be abundant in the NK1.1+ but not NK1.1- T cell population isolated from CD1d-/- mice. Moreover, more than half (11/21) of the hybrid cell lines established from CD1d-/- NKT cells expressed the V(alpha)19.1-J(alpha)26 invariant TCR alpha chain. The expression of the invariant V(alpha)19.1-J(alpha)26 mRNA was absent in beta2-microglobulin-deficient mice. Collectively, the present findings suggest the presence of a second NKT cell repertoire characterized by an invariant TCR alpha chain (V(alpha)19.1-J(alpha)26) that is selected by an MHC class I-like molecule other than CD1d.     

The flexibility of locally melted DNA

Protein-bound duplex DNA is often bent or kinked. Yet, quantification of intrinsic DNA bending that might lead to such protein interactions remains enigmatic. DNA cyclization experiments have indicated that DNA may form sharp bends more easily than predicted by the established worm-like chain (WLC) model. One proposed explanation suggests that local melting of a few base pairs introduces flexible hinges. We have expanded this model to incorporate sequence and temperature dependence of the local melting, and tested it for three sequences at temperatures from 23°C to 42°C. We find that small melted bubbles are significantly more flexible than double-stranded DNA and can alter DNA flexibility at physiological temperatures. However, these bubbles are not flexible enough to explain the recently observed very sharp bends in DNA.     

Monte Carlo simulations of VEGF binding to cell surface receptors in vitro

The vascular endothelial growth factor (VEGF) family binds multiple endothelial cell surface receptors. Our goal is to build comprehensive models of these interactions for the purpose of simulating angiogenesis. In view of low concentrations of growth factors in vivo and in vitro, stochastic modeling of molecular interactions may be necessary. Here, we compare Monte Carlo simulations of the stochastic binding of VEGF and two of its major receptors on cells in vitro to equivalent deterministic simulations. In the range of typical VEGF concentrations, the stochastic and deterministic models are in agreement. However, we observe significant variability in receptor binding, which may be linked to biological stochastic events, e.g., blood vessel sprout initiation. We study patches of cell surface of varying sizes to investigate spatial integration of the signal by the cell, which impacts directly the variability of binding, and find significant variability up to the single-cell level. Dimerization of VEGF receptors does not significantly alter the variability in ligand binding. A 'sliding window' approach demonstrated no reduction in the variability of binding by temporal integration. The variability is expected to be more prominent in in vivo situations where the number of ligand molecules available for binding is less.     

Numerical and Monte Carlo simulations of phenolic polymerizations catalyzed by peroxidase

Numerical and Monte Carlo simulations of horseradish peroxidase-catalyzed phenolic polymerizations have been performed. Kinetic constants for the simulations were fit to data from the oxidation and polymerization of bisphenol A. Simulations of peroxidase-catalyzed phenolic polymerization were run as a function of enzyme concentration and radical transfer and radical coupling rate constants. Predictions were performed with respect to conversion vs. time and number average molecular weight and polydispersity vs. conversion. It is shown that the enzymatic polymerization of phenols can be optimized with respect to high molecular weights by employing low enzyme concentrations and phenols with low radical coupling rate constants coupled with relatively high radical transfer rate constants. Such phenols may be identified by using linear free energy relationships that relate radical reactivity to electron donating/withdrawing potential of the phenolic substituent. (c) 1993 John Wiley & Sons, Inc.     

Monte Carlo simulations of receptor dynamics: Insights into cell signaling

Many receptor-level processes involve the diffusion and reaction of receptors with other membrane-localized molecules. Monte Carlo simulation is a powerful technique that allows us to track the motions and discrete reactions of individual receptors, thus simulating receptor dynamics and the early events of signal transduction. In this paper, we discuss simulations of two receptor processes, receptor dimerization and G-protein activation. Our first set of simulations demonstrates how receptor dimerization can create clusters of receptors via partner switching and the relevance of this clustering for receptor cross-talk and integrin signaling. Our second set of simulations investigates the activation and desensitization of G-protein coupled receptors when either a single agonist or both an agonist and an antagonist are present. For G-protein coupled receptor systems in the presence of an agonist alone, the dissociation rate constant of agonist is predicted to affect the ratio of G-protein activation to receptor phosphorylation. Similarly, this ratio is affected by the antagonist dissociation rate constant when both agonist and antagonist are present. The relationship of simulation predictions to experimental findings and potential applications of our findings are also discussed.     

Monte Carlo simulations of tBid association with the mitochondrial outer membrane

Bid, a BH3-only pro-apoptopic member of the BCL-2 protein family, regulates cell death at the level of mitochondrial cytochrome c efflux. Bid consists of 8 α-helices (H1–H8, respectively) and is soluble cytosolic protein in its native state. Proteolysis of the N-terminus (encompassing H1 and H2) of Bid by caspase 8 in apoptosis yields activated “tBid” (truncated Bid), which translocates to the mitochondria and induces the efflux of cytochrome c. The release of cytochrome c from mitochondria to the cytosol constitutes a critical control point in apoptosis that is regulated by interaction of tBid protein with mitochondrial membrane. tBid displays structural homology to channel-forming bacterial toxins, such as colicins or transmembrane domain of diphtheria toxin. By analogy, it has been hypothesized that tBid would unfold and insert into the lipid bilayer of the mitochondria outer membrane (MOM) upon membrane association. However, it has been shown recently that unlike colicins and the transmembrane domain of diphtheria toxin, tBid binds to the lipid bilayer maintaining α-helical conformation of its helices without adopting a transmembrane orientation by them. Here, the mechanism of the association of tBid with the model membrane mimicking the mitochondrial membrane is studied by Monte Carlo simulations, taking into account the underlying energetics. A novel two-stage hierarchical simulation protocol combining coarse-grained discretization of conformational space with subsequent refinements was applied which was able to generate the protein conformation and its location in the membrane using modest computational resources. The simulations show that starting from NMR-established conformation in the solution, the protein associates with the membrane without adopting the transmembrane orientation. The configuration (conformation and location) of tBid providing the lowest free energy for the system protein/membrane/solvent has been obtained. The simulations reveal that tBid upon association with the membrane undergoes significant conformational changes primarily due to rotations within the loops between helices H4 and H5, H6 and H7, H7 and H8. It is established that in the membrane-bound state of tBid-monomer helices H3 and H5 have the locations exposed to the solution, helices H6 and H8 are partly buried and helices H4 and H7 are buried into the membrane at shallow depth. The average orientation of tBid bound to the membrane in the most stable configuration reported here is in satisfactory agreement with the evaluations obtained by indirect experimental means. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Monte Carlo simulation of DNA strand-break induction in supercoiled plasmid pBR322 DNA from indirect effects

We present a new Monte Carlo simulation code system (DBREAK) of the detailed events that occur when ionizing radiation interacts with water and DNA molecules. The model treats the initial energy deposition by radiation, the formation of chemically active species, subsequent diffusion-controlled chemical reactions, and induction of DNA strand breaks. DBREAK assumes one-hit single-strand break (SSB) and two-hit double-strand break (DSB) mechanisms. A high-resolution model of plasmid DNA structure has been introduced. The calculated results are compared with the results of previously performed experiments of the same type. Under aerobic conditions, 89.4% of the DNA damage was attributed to OH-radical and 10.5% and 0.1% to e^– _aq and H, respectively. We also compared the differences between liquid-water track structure and gas-phase-water track structure. The calculated yield of SSBs by liquid-water track structure exceeded that of gas-phase-water track structure by a factor of 1.2. Received: 13 February 1997 / Accepted in revised form: 26 August 1997     

Monte Carlo docking simulations of cyclomaltoheptaose and dimethyl cyclomaltoheptaose with paclitaxel

The molecular basis for the remarkable enhancement of the solubility of paclitaxel by O-dimethylcyclomaltoheptaose (DM-beta-CD) over cyclomaltoheptaose (beta-cyclodextrin, beta-CD) was investigated with Monte Carlo docking-minimization simulation. As possible guests of inclusion complexation for the host cyclic oligosaccharides, two functional moieties of the suggested solution structure of paclitaxel were used where one is the C-3'N benzoyl moiety (B-ring) and the other is a hydrophobic (HP) cluster site among the C-3' phenyl (C-ring), C-2 benzoate (A-ring), and C-4 acetoxy moieties. The energetic preference of inclusion complexation of DM-beta-CD over beta-CD was analyzed on the basis of more efficient partitioning process of DM-beta-CD into the hydrophobic cluster site of the paclitaxel.