Ionization-cluster distributions of α-particles in nanometric volumes of propane: measurement and calculation

The probability of the formation of ionization clusters by primary alpha-particles at 5.4 MeV in nanometric volumes of propane was studied experimentally and by Monte Carlo simulation, as a function of the distance between the center line of the particle beam and the center of the target volume. The volumes were of cylindrical shape, 3.7 mm in diameter and height. As the investigations were performed at gas pressures of 300 Pa and 350 Pa, the dimensions of the target volume were equivalent to 20.6 nm or 24.0 nm in a material of density 1.0 g/cm(3). The dependence of ionization-cluster formation on distance was studied up to values equivalent to about 70 nm. To validate the measurements, a Monte Carlo model was developed which allows the experimental arrangement and the interactions of alpha-particles and secondary electrons in the counter gas to be properly simulated. This model is supplemented by a mathematical formulation of cluster size formation in nanometric targets. The main results of our study are (i) that the mean ionization-cluster size in the delta-electron cloud of an alpha-particle track segment, decreases as a function of the distance between the center line of the alpha-particle beam and the center of the sensitive target volume to the power of 2.6, and (ii) that the mean cluster size in critical volumes and the relative variance of mean cluster size due to delta-electrons are invariant at distances greater than about 20 nm. We could imagine that the ionization-cluster formation in nanometric volumes might in future provide the physical basis for a redefinition of radiation quality.     

Formation of ionization clusters in nanometric structures of propane-based tissue-equivalent gas or liquid water by electrons and alpha-particles

Despite the importance of ionization yield formation in sub-cellular structures a few nanometres in size, with regard to radiation damage our present knowledge in this respect is almost exclusively based on Monte Carlo simulations which in turn are based on cross section sets for water vapour or liquid water. Experimental data, although urgently needed, are still missing because the direct measurement of ionization yields in sub-cellular structures or, at least, in nanometric volumes of liquid water, is not yet possible. The best feasible way to overcome this problem of measurement at present, is the use of highly sophisticated counters filled with gases at low operating pressure to simulate target volumes a few nanometres in diameter at unit density. An indispensable prerequisite of the reliability of such measurements is, however, a check of the equivalence of the ionization yield produced in a specified target gas and the yield to be expected in liquid water or biological material. For this purpose, the ionization yield formation by electrons and alpha-particles in liquid water was simulated using the Monte Carlo method and compared with that produced in propane-based tissue-equivalent gas (composition by volume 55% C3H8, 39.6% CO2, 5.4% N2). After a short summary of the most important physical aspects of ionization cluster formation, new results are presented and discussed from the point of view of radiation physics and radiation biology.     

Study of Clustering in Nonideal Ion Plasma by a Combined Open Ensemble Monte Carlo - Cluster Expansion Method

The chemical potential and Gibbs free energy of ion clusters are obtained by Monte Carlo method combined with a cluster expansion in a wide range of pressures. Gibbs free energy and configurational energy of the symmetric ion plasma is calculated by Frenkel-Band cluster expansion. The energy is compared with Monte Carlo data for a periodic system.     

Absorbed fraction of alpha-particles emitted in bifurcation regions of the human tracheo-bronchial tree

A model for bifurcation regions of the human tracheo-bronchial tree was developed. Equations for the surfaces are given to enable calculations of doses from alpha-particles emitted in these regions. It has been found that a bifurcation region is well approximated by a quasi-ellipsoid. The absorbed fractions of alpha-particles emitted in bifurcation regions were calculated by the Monte Carlo method. The average absorbed fraction under the bifurcation geometry is close to that found under the cylindrical geometry in the bronchial region. In the bronchiolar region, the absorbed fractions under the bifurcation geometry are up to 20% larger than those under the cylindrical geometry.     

Distribution of the coulomb microfield inside an ion cluster

The microfield distribution function in clusters is investigated numerically by the molecular dynamics and Monte Carlo methods. The results obtained are compared with the microfield distribution in an unbounded plasma. The calculated distributions are shown to have the same asymptotic forms. The position of the maximum and the existence of additional extrema depend on the size and type of cluster. The dependence of the probabilistic average and dispersion of the microfield distribution function on the number of particles in the cluster is studied.     

Microdosimetric analysis of various mammography spectra: lineal energy distributions and ionization cluster analysis

In view of recent recommendations on the frequency and the starting age of mammography screening in healthy women, it is desirable to quantify the enhanced relative biological effectiveness (RBE) of mammography X rays compared to hard X rays. While there is little doubt that the former are more potent in inducing biological damage than the latter, the magnitude of the effect is still hotly debated in the literature. We used Monte Carlo simulations and track structure analysis in micrometer and nanometer volumes to investigate differences in distributions of lineal energy and ionization clusters for a range of mammography X-ray qualities. Dose-averaged lineal energies, (yD), in breast tissue for various mammography qualities were found to result in quality factors about 40% higher than unity. Among the various mammography qualities studied, the popular molybdenum/molybdenum target/filter combination was found to have the highest (yD) in 1-microm spheres (about 5.0 keV/microm near the entrance surface of breast tissue). In 10-nm radius spheres, the mean ionization cluster order was found to be about 35% higher in mammography X rays compared to 300 keV electrons (roughly representing 60Co or 192Ir photon radiation). In even smaller spheres (2 nm radius), no significant differences were observed for the mean ionization cluster order between mammography X rays and 300 keV electrons. We conclude that the potential of mammography X rays to induce biological damage is probably not much higher than a factor of two compared to hard X rays.     

“Trion” code for radiation action calculations and its application in microdosimetry and radiobiology

A code for calculations of electron, ion and photon radiation action on tissue-equivalent matter (water vapor) by the Monte Carlo technique is presented. The new fluctuation detector method is efficient in evaluating of probability distributions and moments of absorbed energy and number of ionizations in small sites. Spatial and energy distributions of particles fluences and fluctuation characteristics of radiation action on spherical and thread-like sites of nanometer diameter are compared with various experimental and theoretical data and discussed. Non-equivalence of energy absorption and ionization events and consequences of that non-equivalence are numerically analysed. As an example of radiobiological application the yield of single- and double-strand breaks of DNA is calculated in a threshold model.     

Discrimination of near-native structures in protein-protein docking by testing the stability of local minima

Fast Fourier transform (FFT) correlation methods of protein-protein docking, combined with the clustering of low energy conformations, can find a number of local minima on the energy surface. For most complexes, the locations of the near-native structures can be constrained to the 30 largest clusters, each surrounding a local minimum. However, no reliable further discrimination can be obtained by energy measures because the differences in the energy levels between the minima are comparable with the errors in the energy evaluation. In fact, no current scoring function accounts for the entropic contributions that relate to the width rather than the depth of the minima. Since structures at narrow minima loose more entropy, some of the nonnative states can be detected by determining whether or not a local minimum is surrounded by a broad region of attraction on the energy surface. The analysis is based on starting Monte Carlo Minimization (MCM) runs from random points around each minimum, and observing whether a certain fraction of trajectories converge to a small region within the cluster. The cluster is considered stable if such a strong attractor exists, has at least 10 convergent trajectories, is relatively close to the original cluster center, and contains a low energy structure. We studied the stability of clusters for enzyme-inhibitor and antibody-antigen complexes in the Protein Docking Benchmark. The analysis yields three main results. First, all clusters that are close to the native structure are stable. Second, restricting considerations to stable clusters eliminates around half of the false positives, that is, solutions that are low in energy but far from the native structure of the complex. Third, dividing the conformational space into clusters and determining the stability of each cluster, the combined approach is less dependent on a priori information than exploring the potential conformational space by Monte Carlo minimizations.     

Structures and Energetics of Platinum–Cobalt Bimetallic Clusters

Platinum–cobalt bimetallic clusters (N=11–15) were modeled by a many-body Sutton-Chen (SC) potential. The basin-hopping algorithm and Monte Carlo (MC) energy minimization were used to determine the global minima of bimetallic clusters. The structural changes with cluster size were observed. Most of the structures had built on icosahedral packing. Second energy difference analyzes were performed to investigate the relative stability of a cluster with respect to its size and composition. The dependence of energetics and structures on size and composition is discussed.     

Dynamic properties of water bound to matrices of natural DNA and model complexes

From experimental data on the hydration energetics of nucleic acids obtained by differential scanning calorimetry under isothermal conditions, dielectric relaxation time tau d and "free volume" Vf occupied by water molecules in hydration shells of natural DNA and model polyribonucleotides were calculated. In addition, systems consisting of dinucleotides ApA, TpT, UpU, TpU, UpT and water clusters of various sizes (from 20 to 400 water molecules) were studied by Monte Carlo computer simulation. It was shown that, as water content in systems increases, the dynamic characteristics of bound water obtained with both methods approached the values for bulk water.     

Size and composition of membrane protein clusters predicted by Monte Carlo analysis

Biological membranes contain a high density of protein molecules, many of which associate into two-dimensional microdomains with important physiological functions. We have used Monte Carlo simulations to examine the self-association of idealized protein species in two dimensions. The proteins have defined bond strengths and bond angles, allowing us to estimate the size and composition of the aggregates they produce at equilibrium. With a single species of protein, the extent of cluster formation and the sizes of individual clusters both increase in non-linear fashion, showing a phase change with protein concentration and bond strength. With multiple co-aggregating proteins, we find that the extent of cluster formation also depends on the relative proportions of participating species. For some lattice geometries, a stoichiometric excess of particular species depresses cluster formation and moreover distorts the composition of clusters that do form. Our results suggest that the self-assembly of microdomains might require a critical level of subunits and that for optimal co-aggregation, proteins should be present in the membrane in the correct stoichiometric ratios.     

Structural basis of hierarchical multiple substates of a protein. II: Monte Carlo simulation of native thermal fluctuations and energy minimization

Conformational fluctuations in a globular protein, bovine pancreatic trypsin inhibitor, in the time range between picoseconds and nanoseconds are studied by a Monte Carlo simulation method. Multiple energy minima are derived from sampled conformations by minimizing their energy. They are distributed in clusters in the conformational space. A hierarchical structure is observed in the simulated dynamics. In the time range between 10(-14) and 10(-10) seconds dynamics is well represented by a superposition of vibrational motions within an energy well with transitions among minima within each cluster. Transitions among clusters take place in the time range of nanoseconds or longer.     

A Monte Carlo simulation of hydration of xanthine-derivatives and their stacked forms.

Results on a Monte Carlo simulation of the hydration of monomer and possible stacked dimer forms of a purine alkaloid series in 200- and 400-water molecule clusters are presented. Investigation of different purine stacked dimers in a 200-water molecule cluster reveals that for caffeine there exists one, for theophylline two and for theobromine four dimers are energetically favorable. For caffeine, the same energetically favored stacked dimer form is observed in both the 200- and 400-water molecule cluster. The main factor stabilizing the preferred dimer stacks is the change in the interaction between water molecules of the monomer cluster and those water molecules in the dimer cluster.     

Experimental and theoretical study of the near IR emission of xenon excited by a fast electron beam

Emission of xenon excited by a 120-keV electron beam at gas pressures of 100, 200, 500, and 760 Torr nm was studied experimentally and theoretically. More than 30 spectral lines were identified in the wavelength range of 750–1000 nm. A self-consistent kinetic model is developed to calculate the emission intensity of xenon atoms in the near IR range. The model includes balance equations for the number densities of electrons, ions and excimer molecules; equations for the populations of electron levels; and the Boltzmann equation for the low-energy part of the electron energy distribution function with a source of slow electrons. Excitation and ionization rates of xenon by the beam electrons and the energy spectrum of slow electrons are calculated by the Monte Carlo method. It is shown that, under these conditions, the main mechanism of xenon atom excitation is dissociative recombination of Xe₃ ⁺ ions.     

Stochastic model of central synapses: slow diffusion of transmitter interacting with spatially distributed receptors and transporters.

A detailed mathematical analysis of the diffusion process of neurotransmitter inside the synaptic cleft is presented and the spatio-temporal concentration profile is calculated. Using information about the experimentally observed time course of glutamate in the cleft the effective diffusion coefficient Dnet is estimated as Dnet approximately 20-50 nm(2) microseconds(-1), implying a strong reduction compared with free diffusion in aqueous solution. The tortuosity of the cleft and interactions with transporter molecules are assumed to affect the transmitter motion. We estimate the transporter density to be 5170 to 8900 micrometer(-2) in the synaptic cleft and its vicinity, using the experimentally observed time constant of glutamate. Furthermore a theoretical model of synaptic transmission is presented, taking the spatial distribution of post-synaptic (AMPA-) receptors into account. The transmitter diffusion and receptor dynamics are modeled by Monte Carlo simulations preserving the typically observed noisy character of post-synaptic responses. Distributions of amplitudes, rise and decay times are calculated and shown to agree well with experiments. Average open probabilities are computed from a novel kinetic model and are shown to agree with averages over many Monte Carlo runs. Our results suggest that post-synaptic currents are only weakly potentiated by clustering of post-synaptic receptors, but increase linearly with the total number of receptors. Distributions of amplitudes and rise times are used to discriminate between different morphologies, e.g. simple and perforated synapses. A skew in the miniature amplitude distribution can be caused by multiple release of pre-synaptic vesicles at perforated synapses.     

Visualizing "greengold" clusters in the STEM.

"Greengold" is a large metallic cluster thought to contain 75 gold atoms in a compact 1.4-nm-diameter core surrounded by an organic shell. Scanning transmission electron microscope imaging shows uniform mass and size distributions with an apparent mass of 24 kDa, unaffected by radiation damage. The signal-to-noise ratio is adequate for visualization at low dose and in the presence of a relatively thick biological matrix. Under some conditions these clusters have a slight tendency to form linear chains and 2-D hexagonal arrays with a spacing of 2.6 nm. The parameters presented permit estimation of the feasibility of proposed labeling experiments.     

Simulated self-assembly of the HIV-1 capsid: protein shape and native contacts are sufficient for two-dimensional lattice formation

We report Monte Carlo simulations of the initial stages of self-assembly of the HIV-1 capsid protein (CA), using a coarse-grained representation that mimics the CA backbone structure and intermolecular contacts observed experimentally. A simple representation of N-terminal domain/N-terminal domain and N-terminal domain/C-terminal domain interactions, coupled with the correct protein shape, is sufficient to drive formation of an ordered lattice with the correct hexagonal symmetry in two dimensions. We derive an approximate concentration/temperature phase diagram for lattice formation, and we investigate the pathway by which the lattice develops from initially separated CA dimers. Within this model, lattice formation occurs in two stages: 1), condensation of CA dimers into disordered clusters; and 2), nucleation of the lattice by the appearance of one hexamer unit within a cluster. Trimers of CA dimers are important early intermediates, and pentamers are metastable within clusters. Introduction of a preformed hexamer at the beginning of a Monte Carlo run does not directly seed lattice formation, but does facilitate the formation of large clusters. We discuss possible connections between these simulations and experimental observations concerning CA assembly within HIV-1 and in vitro.     

Energy deposition by protons and alpha particles in spherical sites of nanometer to micrometer diameter

Summary Monte Carlo simulated proton- and alpha-particle tracks in water vapor were used to develop an analytical function for calculating number distributions of ionizations induced in spherical sites. For charged particles crossing the site, Fermi-like functions were used to approximate the ionization distributions. Ionization event distributions due to particles passing outside the site were approximated with an exponentially decreasing function. The function parameters were calculated for protons and alpha particles in the energy range 0.3–5.0 MeV/ amu and for site diameters of 1 to 1000 nm. The quality of fit obtained is very good for the particles, energy range and site diameters considered.On leave from the Institute of Nuclear Physics, ul. Radzikowskiego 152, PL-31342 Kraków, Poland     

A Latent Model to Detect Multiple Clusters of Varying Sizes

Summary This article develops a latent model and likelihood‐based inference to detect temporal clustering of events. The model mimics typical processes generating the observed data. We apply model selection techniques to determine the number of clusters, and develop likelihood inference and a Monte Carlo expectation–maximization algorithm to estimate model parameters, detect clusters, and identify cluster locations. Our method differs from the classical scan statistic in that we can simultaneously detect multiple clusters of varying sizes. We illustrate the methodology with two real data applications and evaluate its efficiency through simulation studies. For the typical data‐generating process, our methodology is more efficient than a competing procedure that relies on least squares.