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PubMed2001

Methods of peptide conformation studies.

In solution most of the peptides assume multiple flexible conformations. Determination of the dominant conformers and evaluation of their populations is the aim of peptide conformation studies, in which theoretical and experimental methods play complementary roles. Molecular dynamics or Monte Carlo methods are quite effective in searching the conformational space accessible to a peptide but they are not able to estimate, precisely enough, the populations of various conformations. Therefore, they must be supplemented by experimental data. In this paper, a short review of the experimental methods, most widely used in peptide conformational studies, is presented. Among them NMR plays the leading role. Valuable information is also obtained from hydrogen exchange, fluorescence resonance energy transfer, and circular dichroism measurements. The advantages and shortcomings of these methods are discussed.

Circular Dichroism↗

PubMed1997

Testing for heterogeneity among phenotypic correlations: a comparison of methods using Monte Carlo simulations.

Heterogeneous phenotypic correlations may be suggestive of underlying changes in genetic covariance among life-history, morphology, and behavioural traits, and their detection is therefore relevant to many biological studies. Two new statistical tests are proposed and their performances compared with existing methods. Of all tests considered, the existing approximate test of homogeneity of product-moment correlations provides the greatest power to detect heterogeneous correlations, when based on Hotelling's z*-transformation. The use of this transformation and test is recommended under conditions of bivariate normality. A new distribution-free randomisation test of homogeneity of Spearman's rank correlations is described and recommended for use when the bivariate samples are taken from populations with non-normal or unknown distributions. An alternative randomisation test of homogeneity of product-moment correlations is shown to be a useful compromise between the approximate tests and the randomisation tests on Spearman's rank correlations: it is not as sensitive to departures from normality as the approximate tests, but has greater power than the rank correlation test. An example is provided that shows how choice of test will have a considerable influence on the conclusions of a particular study.

Journal Article↗

PubMed2006

Effects of randomization methods on statistical inference in disease cluster detection.

Monte Carlo methods are commonly used to assess the statistical significance of disease clusters. This usually involves permuting the observed outcome measure, such as the rate of disease, across the geographic units within the study area. When the variance of the disease rates is heterogeneous, however, randomizing the disease rate across the geographic units results in over-estimating the p-values in areas of low variance and under-estimating the p-values in areas of high variance. This bias results in under-ascertainment of clusters in urban areas and over-ascertainment of clusters in rural areas. As an alternative, randomizing the number of cases of disease or deaths proportional to the population at risk preserves the variance structure of the study area, therefore resulting in unbiased statistical inference. We compare results from randomizing rates with those from randomizing case counts, using county-level prostate cancer mortality data for the United States and ZIP-Code level prostate cancer incidence data for New York State, using the local Moran's I statistic.

Bias↗

PubMed2005

Grand potential, helmholtz free energy, and entropy calculation in heterogeneous cylindrical pores by the grand canonical Monte Carlo simulation method.

The adsorption of fluids in porous media is still an open area of research, since no model is able to explain all experimental features. The difficulties rise from the complexity of the real porous materials which present surface heterogeneities, large pore size distributions, and complex networks of interconnected pores. In parallel to experimental efforts trying to produce more ordered porous materials, theoreticians try to introduce more disorder in their models, with the help of molecular simulation for instance. This grand canonical Monte Carlo simulation study concentrates on the adsorption of a simple Lennard-Jones fluid in three porous substrates, to compare the effect of purely geometric heterogeneity (spatial deformation of the external potential) as opposed to purely chemical heterogeneity (amplitude variations of the external potential). This separation is unrealistic, since geometric fluctuations of a real pore diameter along its axis generally induce variations in the amplitude of the external potential created by the pore. However it enables one to compare both effects. In this paper, a thermodynamic integration scheme is applied to a complete set of adsorption/desorption isotherms. The grand potential, free energy, and entropy are calculated, which allows one to discuss the features of the phase diagrams. It is shown that a purely geometric deformation (undulation) of the external potential does not affect the thermodynamic characteristics of the confined fluid. On the other hand, amplitude modulation of the external potential (chemical heterogeneity) strongly distorts the phase diagram. This heterogeneity is actually able to stabilize a "bridgelike" phase which corresponds to an accumulation of molecules in the most attractive region of the pore.

Journal Article↗

PubMed1999

Dimensional reduction in a model with infinitely many absorbing states.

Using the Monte Carlo method, we study a two-dimensional model with infinitely many absorbing states. Our estimation of the critical exponent beta is approximately equal to 0.273(5) suggests that the model belongs to the (1+1) rather than to (2+1) directed-percolation universality class. We also show that for a large class of absorbing states the dynamic Monte Carlo method leads to spurious dynamical transitions.

Journal Article↗

PubMed1989

Recognition in cell adhesion. A comparative study of the conformations of RGD-containing peptides by Monte Carlo and NMR methods.

Many of the proteins that mediate cell adhesion processes processes-fibronectin, fibrinogen, vitronectin, von Willebrand factor, osteopontin, laminin and various collagens--contain the amino acid sequence Arg-Gly-Asp. Short peptides that include this sequence have been shown to inhibit the interactions of cell adhesion proteins with their receptors and to have dramatic effects on developmental processes involving cellular recognition. In order to determine which conformations are accessible to Arg-Gly-Asp containing peptides, we analyzed tri-, tetra- and pentapeptides using molecular mechanics and Monte Carlo methods, and studied the solution conformations of the pentapeptide Gly-Arg-Gly-Asp-Ser using nuclear magnetic resonance techniques. The Monte Carlo method was used to: (a) identify the low energy conformations of the peptides and (b) evaluate their thermodynamic properties. In the case of the pentapeptide Gly-Arg-Gly-Asp-Gly, the four stable conformations include three with reverse turns and one open structure. The conformations found in this analysis are compatible with the nuclear magnetic resonance (nuclear Overhauser effect) data.

Amino Acid Sequence↗

PubMed2004

Monte Carlo calculations of output factors for clinically shaped electron fields.

We report on the use of the EGS4/BEAM Monte Carlo technique to predict the output factors for clinically relevant, irregularly shaped inserts as they intercept a linear accelerator's electron beams. The output factor for a particular combination--energy, cone, insert, and source-to-surface distance (SSD)--is defined in accordance with AAPM TG-25 as the product of cone correction factor and insert correction factor, evaluated at the depth of maximum dose. Since cone correction factors are easily obtained, we focus our investigation on the insert correction factors (ICFs). An analysis of the inserts used in routine clinical practice resulted in the identification of a set of seven "idealized" shapes characterized by specific parameters. The ICFs for these shapes were calculated using a Monte Carlo method (EGS4/BEAM) and measured for a subset of them using an ion chamber and well-established measurement methods. Analytical models were developed to predict the Monte Carlo-calculated ICF values for various electron energies, cone sizes, shapes, and SSDs. The goodness-of-fit between predicted and Monte Carlo-calculated ICF values was tested using the Kolmogorov-Smirnoff statistical test. Results show that Monte Carlo-calculated ICFs match the measured values within 2.0% for most of the shapes considered, except for few highly elongated fields, where deviations up to 4.0% were recorded. Predicted values based on analytical modeling agree with measured ICF values within 2% to 3% for all configurations. We conclude that the predicted ICF values based on modeling of Monte Carlo-calculated values could be introduced in clinical use.

Body Burden↗

PubMed2003

Developing the molecular modelling of diffusion in zeolites as a high throughput catalyst screening technique.

Molecular modelling techniques have been used to screen zeolite catalysts for their suitability for organic synthesis. For example, we have used these techniques to study the alkylation of aromatic molecules which are important in the fine-chemical and drug industries. A survey of all such efforts is reviewed in this article. The application of molecular modelling techniques in a systematic manner is an efficient first step in the design of zeolite catalysts. As a qualitative screening tool, molecular graphics is used to visualize how well the reactant and product molecules fit inside the pores of the zeolites. Using a hybrid of several molecular modelling methods, which combines molecular dynamics (MD) and Monte Carlo methods with energy minimization, it is possible to determine the minimum energy locations of the molecules inside the zeolites cages. The minimum energy configurations determined by this hybrid method are taken as a starting point for diffusion of the molecules through the zeolite channels. When a molecule is allowed to diffuse through zeolite channel, the molecule attains some maxima and minima in its diffusion energy profile. From the differences between a maximum and a minimum energy configuration, the diffusion energy barrier for the molecule can be calculated in the zeolites. By comparing the diffusion energy barriers for various isomers of a molecule in different zeolites, it is possible to find out the most suitable zeolite for achieving the required shape-selectivity. In addition, factors influencing the diffusivity of the molecules and consequently the shape selectivity are derived. The list of factors and their relative importance are analysed to derive valuable guidelines to design shape-selective zeolite catalysts for a given reaction. Thus, the ultimate aim of these studies is to develop a high throughput computational screening process for the selection of shape-selective zeolite catalysts for various reactions. The dynamic behaviour of molecules inside the pores of zeolites can be studied using MD methods. Since MD is computationally time consuming, it is more efficient to screen the possible zeolite catalysts by energy minimization methods and then perform MD in specific zeolites. More accurate values of diffusivity of the molecules can be calculated using MD methods, and these values can be correlated with the shape-selectivity observed experimentally and /or derived from diffusion energy barrier calculations.

Catalysis↗

PubMed1996

Light distributions in a port wine stain model containing multiple cylindrical and curved blood vessels.

BACKGROUND AND OBJECTIVES: Knowledge of the light distribution in skin tissue is important for the understanding, prediction, and improvement of the clinical results in laser treatment of port wine stains (PWS). The objective of this study is to improve modelling of PWS treated by laser using an improved and more realistic PWS model. STUDY DESIGN/MATERIALS AND METHODS: Light distributions are calculated by the Monte Carlo method for various PWS blood vessel configurations, such as single and multiple vessels oriented horizontally, curved vessels, and "vertically" oriented vessels. Various vessel sizes and wavelengths are used. RESULTS: Our modelling confirms the concept of selective photothermolysis; 577nm laser light gives maximal deposited energy at the top side of the blood vessels closest to the skin surface and 585nm gives a more uniform energy distribution in the vessel. In the distribution of deposited energy multiple vessels mutually influence each other, because of "shadowing" of diffuse light. CONCLUSION: Modelling PWS laser treatments with multiple vessels confirms the need for successive treatments of vessels layer by layer. The use of different wavelengths affects the local deposited energy profiles in the blood vessels. It predicts that the significance of 585nm laser light lies in the uniform energy distribution in the vessels rather than in gain in energy deposition with depth. The calculated light distributions provide a more realistic input for modelling thermal damage effects in PWS laser treatment and modelling of the epidermal response in thermal imaging of the PWS blood vessel structure.

Blood Vessels↗

PubMed2005

Rapidly decorrelating velocity-field model as a tool for solving one-point Fokker-Planck equations for probability density functions of turbulent reactive scalars.

Light is shed upon Eulerian Monte Carlo methods and their application to the simulation of turbulent reactive flows. A rapid decorrelating velocity-field model is used to derive stochastic partial differential equations (SPDE's) stochastically equivalent to the modeled one-point joint probability density function of turbulent reactive scalars. Those SPDE's are shown to be hyperbolic, advection-reaction equations. They are dealt with in a generalized sense, so that discontinuities in the scalar fields can be treated. A numerical analysis is proposed and numerical tests are carried out. In particular, a comparison with the Lagrangian Monte Carlo method is performed.

Journal Article↗

PubMed1990

Dose-rate dependent stochastic effects in radiation cell-survival models.

When cells are subjected to ionizing radiation the specific energy rate (microscopic analog of dose-rate) varies from cell to cell. Within one cell, this rate fluctuates during the course of time; a crossing of a sensitive cellular site by a high energy charged particle produces many ionizations almost simultaneously, but during the interval between events no ionizations occur. In any cell-survival model one can incorporate the effect of such fluctuations without changing the basic biological assumptions. Using stochastic differential equations and Monte Carlo methods to take into account stochastic effects we calculated the dose-survival relationships in a number of current cell survival models. Some of the models assume quadratic misrepair; others assume saturable repair enzyme systems. It was found that a significant effect of random fluctuations is to decrease the theoretically predicted amount of dose-rate sparing. In the limit of low dose-rates neglecting the stochastic nature of specific energy rates often leads to qualitatively misleading results by overestimating the surviving fraction drastically. In the opposite limit of acute irradiation, analyzing the fluctuations in rates merely amounts to analyzing fluctuations in total specific energy via the usual microdosimetric specific energy distribution function, and neglecting fluctuations usually underestimates the surviving fraction. The MOnte Carlo methods interpolate systematically between the low dose-rate and high dose-rate limits. As in other approaches, the slope of the survival curve at low dose-rates is virtually independent of dose and equals the initial slope of the survival curve for acute radiation.

Cell Survival↗

PubMed1986

Ring closure probabilities for DNA fragments by Monte Carlo simulation.

The rate of ligation of DNA molecules into circular forms depends on the ring closure probability, commonly called the j-factor, which is a sensitive measure of the extent to which thermal fluctuations contribute to bending and twisting of DNA molecules in solution. We present a theoretical treatment of the cyclization equilibria of DNA that employs a special Monte Carlo method for generating large ensembles of model DNA chains. Using this method, the chain length dependence of the j-factor was calculated for molecules. in the size range 250 to 2000 base-pairs. The Monte Carlo results are compared with recent analytical theory and experimental data. We show that a value of 475 A for the persistence length of DNA, close to values measured by a number of other methods, is in excellent agreement with the cyclization results. Preliminary applications of the Monte Carlo method to the problem of systematically bent DNA molecules are presented. The calculated j-factor is shown to be very sensitive to the amount of bending in these fragments. This fact suggests that ligase closure measurements of systematically bent DNA molecules should be a useful method for studying sequence-directed bending in DNA.

Cyclization↗

PubMedDate not supplied

A convolution method of calculating dose for 15-MV x rays.

Arrays were generated using the Monte Carlo method representing the energy absorbed throughout waterlike phantoms from charged particles and scatter radiation set in motion by primary interactions at one location. The resulting "dose spread arrays" were normalized to the collision fraction of the kinetic energy released by the primary photons. These arrays are convolved with the relative primary fluence interacting in a phantom to obtain three-dimensional dose distributions. The method gives good agreement for the 15-MV x-ray dose in electronic disequilibrium situations, such as the buildup region, near beam boundaries, and near low-density heterogeneities.

Humans↗

PubMed2004

Flexible dose-response models for Japanese atomic bomb survivor data: Bayesian estimation and prediction of cancer risk.

Generalised absolute risk models were fitted to the latest Japanese atomic bomb survivor cancer incidence data using Bayesian Markov Chain Monte Carlo methods, taking account of random errors in the DS86 dose estimates. The resulting uncertainty distributions in the relative risk model parameters were used to derive uncertainties in population cancer risks for a current UK population. Because of evidence for irregularities in the low-dose dose response, flexible dose-response models were used, consisting of a linear-quadratic-exponential model, used to model the high-dose part of the dose response, together with piecewise-linear adjustments for the two lowest dose groups. Following an assumed administered dose of 0.001 Sv, lifetime leukaemia radiation-induced incidence risks were estimated to be 1.11 x 10(-2) Sv(-1) (95% Bayesian CI -0.61, 2.38) using this model. Following an assumed administered dose of 0.001 Sv, lifetime solid cancer radiation-induced incidence risks were calculated to be 7.28 x 10(-2) Sv(-1) (95% Bayesian CI -10.63, 22.10) using this model. Overall, cancer incidence risks predicted by Bayesian Markov Chain Monte Carlo methods are similar to those derived by classical likelihood-based methods and which form the basis of established estimates of radiation-induced cancer risk.

Algorithms↗

PubMed2003

Adaptive anisotropic diffusion filtering of Monte Carlo dose distributions.

The Monte Carlo method is the most accurate method for radiotherapy dose calculations, if used correctly. However, any Monte Carlo dose calculation is burdened with statistical noise. In this paper, denoising of Monte Carlo dose distributions with a three-dimensional adaptive anisotropic diffusion method was investigated. The standard anisotropic diffusion method was extended by changing the filtering parameters adaptively according to the local statistical noise. Smoothing of dose distributions with different noise levels in an inhomogeneous phantom, a conventional and an IMRT treatment case is shown. The resultant dose distributions were analysed using several evaluating criteria. It is shown that the adaptive anisotropic diffusion method can reduce statistical noise significantly (two to five times, corresponding to the reduction of simulation time by a factor of up to 20), while preserving important gradients of the dose distribution well. The choice of free parameters of the method was found to be fairly robust.

Anisotropy↗

PubMed1983

Electron beam dose planning using Gaussian beams. Improved radial dose profiles.

The Gaussian solution of the transport equation for electrons in a medium omits the large angle single scattering events. These events have been included by using Monte Carlo calculated radial dose profiles for point monodirectional beams. A sum of three Gaussian functions with different relative weights and widths have been fitted to the Monte Carlo calculated radial dose profiles. These profiles have been confirmed by measurements in an almost point monodirectional beam, and the importance of an adequate experimental set-up for determination of radial dose profiles is discussed. The analytic treatment when using three different functions in the Gaussian formalism is presented. Central axis depth dose curves for 10 MeV and 20 MeV have finally been calculated and compared with depth dose curves calculated using Monte Carlo technique and a single Gaussian function. Considerable errors (20-30%) result with the single Gaussian function at small field sizes whereas three components give good agreement with the Monte Carlo method.

Computers↗

PubMed1998

Theoretical treatment of human haemopoietic stem cell survival following irradiation by alpha particles.

PURPOSE: To calculate survival of human haemopoietic stem cells irradiated by alpha particles from 149Tb (initial energy 3.97 MeV) and 211At (average initial energy 6.87 MeV). METHODS: Following as closely as possible radiobiological data, Monte Carlo methods were used to calculate passages of alpha particles (originating in three geometries) through the nuclei of haemopoietic stem cells. Survival of stem cell populations was calculated from the probability of surviving each passage (a function of LET). RESULTS: For decays targeted to the surface of individual cells 37% survival was found at 1.3 passages per nucleus for 149Tb and 6.5 for 211At/Po decays. For decays distributed in a large volume the D0 doses were 0.81 and 0.87 for 149Tb and 211At respectively. When 36% of the marrow is occupied by fat cells alphas from 149Tb are more effective with a D0 of 0.68Gy compared to 0.82Gy for the 211At/Po combination. CONCLUSIONS: When the isotopes are targeted to the cell, in terms of passages, 149Tb is five times more effective at cell killing than 211At, which when expressed in terms of dose, increases to a factor of 9. When the isotopes are broadly distributed (such as in marrow or in vitro) the differences are considerably reduced.

Alpha Particles↗

PubMed2003

On how the conformation of biliverdins influences their reduction to bilirubins: a biological and molecular modeling study.

The cyclic 2,18-bridged biliverdin (2) is excreted in rat bile without reduction to the corresponding bilirubin. Conformational analysis, employing an optimized Monte Carlo method and a mixed Monte Carlo/stochastic dynamics, reveals that biliverdin IXalpha (1) and the cyclic analogue 2 adopt 'lock washer' conformations, stabilized by the presence of intramolecular hydrogen bonds between N23...H22N and, to a lesser extent, between N23...H24N. Although 2 is very similar in overall shape to 1, the former adopts a 'locked lock washer' conformation unable to undergo fluctuations, thus possibly hampering a proper recognition by biliverdin reductase.

Animals↗