A Monte Carlo simulation of Auger cascades

The energy imparted to biological tissue after the decay of incorporated Auger emitters stems from two sources: (a) energy deposition by the Auger and Coster-Kronig electrons and (b) the charge potential which remains on the multiple ionized atom after the end of the cascade. For the numerical assessment of both the kinetic energy of the released electrons and the charge potential, a new and--for purposes of microdosimetry--precise method is presented. Based on relativistic Dirac-Fock calculations and a rigorous bookkeeping, this method provides a perfect energy balance of the considered atomic system when applied to Monte Carlo simulations of Auger cascades. By comparing the results for charge distribution for krypton and iodine with experimental data and the electron spectrum of 125I with theoretical data, it can be shown that the approach followed in this work is reasonable and appropriate for the determination of the energy deposited by incorporated Auger emitters in small volumes of condensed matter. The total energy deposited by 125I in a volume of 20-nm diameter is 2.03 keV which is made up by multiple ionization (1.07 keV) and energy deposition by the emitted Auger electrons (0.96 keV).     

Polymer chromosome models and Monte Carlo simulations of radiation breaking DNA

MOTIVATION: Chromatin breakage by ionizing radiation is relevant to studies of carcinogenesis, tumor radiotherapy, biodosimetry and molecular biology. This article focuses on computer analysis of chromosome irradiation in mammlian cells. METHODS: Polymer physics and Monte Carlo numerical methods are used to develop a coarse-grained computational approach. Chromatin is modeled as a random walk on a cubic lattice, and the radiation tracks hitting the chromatin are modeled as straight lines hitting lattice sites. Each track can make a cluster of DSBs on a chromosome. RESULTS: The results obtained replace conjectured DNA fragment-size distribution functions in the recently developed RLC formalism by more mechanistically motivated distributions. The discrete lattice algorithm reproduces features of current radiation experiments relevant to chromatin on large scales. It approximates the continuous formalism and experimental data with adequate precision. It was also found that assuming either fixed chromatin with correlations among different clusters of DSBs or moving chromatin with no such correlations gives virtually identical numerical predictions.     

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.     

Combined use of Monte Carlo DNA damage simulations and deterministic repair models to examine putative mechanisms of cell killing

A kinetic repair-misrepair-fixation (RMF) model is developed to better link double-strand break (DSB) induction to reproductive cell death. Formulas linking linear-quadratic (LQ) model radiosensitivity parameters to DSB induction and repair explicitly account for the contribution to cell killing of unrejoinable DSBs, misrepaired and fixed DSBs, and exchanges formed through intra- and intertrack DSB interactions. Information from Monte Carlo simulations is used to determine the initial yields and complexity of DSBs formed by low- and high-LET radiations. Our analysis of published survival data for human kidney cells suggests that intratrack DSB interactions are negligible for low-LET radiations but increase rapidly with increasing LET. The analysis suggests that no class of DSB is intrinsically unrejoinable or that DSB reparability is not strictly determined by the number of lesions forming the DSB. For radiations with LET >110 keV/mum, the model predicts that the relative cell killing efficiency, per unit absorbed dose, should continue to increase, whereas data from published experiments indicate a reduced cell killing efficiency. This observation suggests that the Monte Carlo simulation overestimates the DSB yield beyond 110 keV/microm or that other biological phenomena not included in the model, such as proximity effects, are important. For 200-250 kVp X rays ( approximately 1.9 keV/microm), only about 1% of the one-track killing is attributed to intratrack binary misrepair interactions. The analysis indicates that the remaining 99% of the lethal damage is due to other types of one-track damage, including possible unrepairable, misrepaired and fixed damage. Compared to the analysis of the X-ray results, 48% of the one-track lethal damage caused by 5.1 MeV alpha particles (approximately 88 keV/microm) is due to intratrack DSB interactions while the remainder is due to other forms of one-track damage.     

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.     

Quantitative modelling of DNA damage using Monte Carlo track structure method

This paper presents data on modelling of DNA damage induced by electrons, protons and alpha-particles to provide an insight into factors which determine the biological effectiveness of radiations of high and low linear energy transfer (LET). These data include the yield of single- and double-strand breaks (ssb, dsb) and base damage in a cellular environment. We obtain a ratio of 4–15 for ssb:dsb for solid and cellular DNA and a preliminary ratio of about 2 for base damage to strand breakage. Data are also given on specific characteristics of damage at the DNA level in the form of clustered damage of varying complexity, that challenge the repair processes and if not processed adequately could lead to the observed biological effects. It is shown that nearly 30% of dsb are of complex form for low-LET radiation, solely by virtue of additional breaks, rising to about 70% for high-LET radiation. Inclusion of base damage increases the complex proportion to about 60% and 90% for low- and high-LET radiation, respectively. The data show a twofold increase in frequencies of complex dsb from low-LET radiation when base damage is taken into account. It is shown that most ssb induced by high-LET radiation have associated base damages, and also a substantial proportion is induced by low-energy electrons. Received: 20 September 1998 / Accepted in revised form: 15 December 1998     

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 structure and entanglements in polymer melts

Atomistic models of short chain branched (SCB) polyethylene melts have been equilibrated at 450 K using a connectivity altering Monte Carlo method. Quantities related to the chain dimensions and entanglements have been determined. The simulated tube diameters, 〈a_pp〉, of SCB melts are found to scale with the backbone weight fraction, ?, as 〈a_pp〉～?^? 0.46, close to the scaling predicted by the binary contact model, 〈a_pp〉～?^? 0.5. Similar relationships are observed experimentally for polymer solutions, and reproduced by the present methods.     

Monte Carlo simulations of the chiral recognition of fenoprofen enantiomers by cyclomaltoheptaose (beta-cyclodextrin)

Differential complexation of fenoprofen enantiomers by cyclomaltoheptaose (beta-cyclodextrin) was investigated by Monte Carlo docking simulations. The chiral discrimination of (R)- and (S)-fenoprofen by beta-cyclodextrin was discussed in terms of the difference in the interaction energies and the patterns of molecular interactions. The interaction energies between each enantiomer of fenoprofen and beta-cyclodextrin were consistent with the reported experimental results that showed that the S isomer interacted preferentially with beta-cyclodextrin and was retained longer in a separation process than the R isomer. The thermodynamic preference of inclusion complex formation of (S)-fenoprofen could be explained by the orientation of the phenyl group attached to the chiral carbon, which provided closer contact and thus more favorable intermolecular interactions between the host and guest molecule. The results presented here would be very useful for the prediction of chiral recognition ability of beta-cyclodextrin.     

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.     

Ammonium ion representation in Monte Carlo simulations of biomolecular solutions

Monte Carlo computer simulation techniques may be used to predict structural properties of solvent networks in helical fragments of nucleic acids, provided that suitable potential functions are available to describe the interactions between nucleic acid atoms, water and counterions. Previous studies have shown that simple non-bonded and point charge parameters are adequate for mononuclear ions such as sodium and calcium. In this study a model interaction potential for the polynuclear ammonium ion is evaluated. The parameters used take account of the distribution of charge over the constituent atoms in the ion. Simulations are carried out on the ammonium salt of a small nucleic acid crystal hydrate and a comparison is made between the predicted and experimental results. It is shown that the simulated structure is in reasonable agreement with experiment. It is therefore feasible to use this potential in studies of ammonium-containing bimolecular systems.     

Monte Carlo simulations of nucleotide crystal hydrates and their counter-ions

A knowledge of structural and energetic aspects of water- and ion-nucleic acid interactions is essential for the understanding of the role of solvent and counterions in stabilising the various helical forms of nucleic acids. In this study, Monte Carlo computer simulation techniques have been used to predict structural properties of solvent networks in small nucleic acid crystal hydrates containing the ions sodium, ammonium and calcium. Appropriate parameters to describe the interaction potentials of the ions are added to those previously developed for water and nucleic acid atoms. A comparison is made between the predicted and experimental results and it is concluded that the potential functions used lead to simulated solvent structure in reasonable agreement with experimental data, at least in the cases of sodium and calcium. It is now feasible to use these functions in studies of hydration of larger helical fragments of nucleic acids of more direct biological interest.     

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.     

Salt-dependent DNA superhelix diameter studied by small angle neutron scattering measurements and Monte Carlo simulations.

Using small angle neutron scattering we have measured the static form factor of two different superhelical DNAs, p1868 (1868 bp) and pUC18 (2686 bp), in dilute aqueous solution at salt concentrations between 0 and 1.5 M Na+ in 10 mM Tris at 0% and 100% D2O. For both DNA molecules, the theoretical static form factor was also calculated from an ensemble of Monte Carlo configurations generated by a previously described model. Simulated and measured form factors of both DNAs showed the same behavior between 10 and 100 mM salt concentration: An undulation in the scattering curve at a momentum transfer q = 0.5 nm-1 present at lower concentration disappears above 100 mM. The position of the undulation corresponds to a distance of approximately 10-20 nm. This indicated a change in the DNA superhelix diameter, as the undulation is not present in the scattering curve of the relaxed DNA. From the measured scattering curves of superhelical DNA we estimated the superhelix diameter as a function of Na+ concentration by a quantitative comparison with the scattering curve of relaxed DNA. The ratio of the scattering curves of superhelical and relaxed DNA is very similar to the form factor of a pair of point scatterers. We concluded that the distance of this pair corresponds to the interstrand separation in the superhelix. The computed superhelix diameter of 16.0 +/- 0.9 nm at 10 mM decreased to 9.0 +/- 0.7 nm at 100 mM salt concentration. Measured and simulated scattering curves agreed almost quantitatively, therefore we also calculated the superhelix diameter from the simulated conformations. It decreased from 18.0 +/- 1.5 nm at 10 mM to 9.4 +/- 1.5 nm at 100 mM salt concentration. This value did not significantly change to lower values at higher Na+ concentration, in agreement with results obtained by electron microscopy, scanning force microscopy imaging in aqueous solution, and recent MC simulations, but in contrast to the observation of a lateral collapse of the DNA superhelix as indicated by cryo-electron microscopy studies.     

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 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.     

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 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.