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At least 811 records · Page 45Linked to original sources
PubMed2006

Understanding effects of matrix protease and matrix organization on directional persistence and translational speed in three-dimensional cell migration.

Recent studies have shown significant differences in migration mechanisms between two- and three-dimensional environments. While experiments have suggested a strong dependence of in vivo migration on both structure and proteolytic activity, the underlying biophysics of such dependence has not been studied adequately. In addition, the existing models of persistent random walk migration are primarily based on two-dimensional movement and do not account for the effect of proteolysis or matrix inhomogeneity. Using lattice Monte Carlo methods, we present a model to study the role of matrix metallo-proteases (MMPs) on directional persistence and speed. The simulations account for a given cell's ability to deform as well as to digest the matrix as the cell moves in three dimensions. Our results show a bimodal dependence of speed and persistence on matrix pore size and suggest high sensitivity on MMP activity, which is in very good agreement with experimental studies carried out in 3D matrices.

Cell Movement↗
PubMed2006

Improving accuracy and precision in estimating fractal dimension of animal movement paths.

It is difficult to watch wild animals while they move, so often biologists analyse characteristics of animal movement paths. One common path characteristic used is tortuousity, measured using the fractal dimension (D). The typical method for estimating fractal D, the divider method, is biased and imprecise. The bias occurs because the path length is truncated. I present a method for minimising the truncation error. The imprecision occurs because sometimes the divider steps land inside the bends of curves, and sometimes they miss the curves. I present three methods for minimising this variation and test the methods with simulated correlated random walks. The traditional divider method significantly overestimates fractal D when paths are short and the range of spatial scales is narrow. The best method to overcome these problems consists of walking the dividers forwards and backwards along the path, and then estimating the path length remaining at the end of the last divider step.

Animal Migration↗
PubMed2006

Fixation of strategies for an evolutionary game in finite populations.

A stochastic evolutionary dynamics of two strategies given by 2x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire population. The process is discussed in the framework of a random walk with site dependent hopping rates. The time of fixation is found to be identical for both strategies in any particular game. The asymptotic behavior of the fixation time and fixation probabilities in the large population size limit is also discussed. We show that fixation is fast when there is at least one pure evolutionary stable strategy (ESS) in the infinite population size limit, while fixation is slow when the ESS is the coexistence of the two strategies.

Biological Evolution↗
PubMed1980

Lateral and transversal diffusion and phase transitions in erythrocyte membranes. An excimer fluorescence study.

The lateral diffusion of the excimer-forming probe pyrene decanoic acid has been determined in erythrocyte membranes and in vesicles of the lipid extracts. The random walk of the probe molecules is characterized by their jump frequency, nu j, within the lipid matrix. At T = 35 degrees C a value of nu i = 1.6 . 10(8) s-1 is found in erythrocyte membranes. A somewhat slower mobility is determined in vesicles prepared from lipid extracts of the erythrocyte membrane. Depending on structure and change of the lipids we obtain jump frequencies between 0.8 . 10(8) s-1 and 1.5 . 10(8) s-1 at T - 35 degrees C. The results are compared with jump frequencies yielded in model membranes. The mobility of molecules perpendicular to the membrane surface (transversal diffusion) is investigated. Erythrocyte ghosts doped with pyrene phosphatidylcholine were mixed with undoped ghosts in order to study the exchange kinetics of the probe molecule. A fast transfer between the outer layers of the ghost cells tau 1/2 = 1.6 min at T = 37 degrees C) is found. The exchange process between the inner and the outer layer of one erythrocyte ghost (flip-flop process) following this fast transfer occurs with a half-life time value of t 1/2 = 100 min at T = 37 C. The application of excimer-forming probes presumes a fluid state of the membrane. Therefore we investigated the phase transition behaviour using the excimer technique. Beside a thermotropic phase transition at T = 38 degrees C and T = 33 degrees C we observed an additional fluidity change at T = 38 degrees C in erythrocyte ghost. This transition is attached to a separation of the boundary lipid layer from the intrinsic proteins. No lipid phase transition is observed in liposomes from isolated extracts of the erythrocyte membrane with our methods.

Decanoic Acids↗
PubMed1990

Statistical thermodynamics of association colloids. IV. Inhomogeneous membrane systems.

A previously developed self-consistent field theory to describe the equilibrium properties of lipid-like membranes is extended to allow the presence of inhomogeneities parallel to the membrane. Conformations of lipid molecules and foreign ('guest') molecules in the membrane are obtained by step-weighted random walk generation of the chains on a lattice, where the theory is made two-dimensional to account for the parallel inhomogeneities. No pre-assigned positions of the head groups, or other parts of the molecules, are introduced. Nearest neighbor interactions are accounted for through Flory-Huggins type interaction parameters. The theory is applied to the incorporation of trans-membrane molecules and conditions for channel formation are discussed. Lateral phase separation in membranes consisting of non-mixing lipids is also considered. Water only slightly enriches the boundary between the two lipid regions. The aliphatic chains are very well able to smoothly cover inhomogeneities in the bilayer. No indications of instability of the membrane due to the induced inhomogeneities are found.

Lipid Bilayers↗
PubMed1988

Fractals and the analysis of waveforms.

Waveforms are planar curves--ordered collections of (x, y) point pairs--where the x values increase monotonically. One technique for numerically classifying waveforms assesses their fractal dimensionality, D. For waveforms: D = log(n)/(log(n) + log(d/L], with n = number of steps in the waveform (one less than the number of (x, y) point pairs), d = planar extent (diameter) of the waveform, and L = total length of the waveform. Under this formulation, fractal dimensions range from D = 1.0, for straight lines through approximately D = 1.15 for random-walk waveforms, to D approaching 1.5 for the most convoluted waveforms. The fractal characterization may be especially useful for analyzing and comparing complex waveforms such as electroencephalograms (EEGs).

Biological Evolution↗
PubMed1969

Computer simulation of stochastic processes through model-sampling (Monte Carlo) techniques.

A simple Monte Carlo simulation program is outlined which can be used for the investigation of random-walk problems, for example in diffusion, or the movement of tracers in the blood circulation. The results given by the simulation are compared with those predicted by well-established theory, and it is shown how the model can be expanded to deal with drift, and with reflexion from or adsorption at a boundary.

Journal Article↗
PubMed1993

A model of phagosome motion within cells based on cytomagnetometric measurements.

Cytomagnetometry is the study of the intracellular movement and rheological properties of living cells by magnetic measurement. This paper summarizes the mathematics involved in the measurement and proposes a new model of phagosome motion in which a motor protein such as myosin and a protein filament such as microfilament play the role of the actomyosin system in the muscle. The rotational random walk is assumed to result from interactions of these proteins. The model makes predictions about the results of the experiments employing magnetic particles introduced into the cells by phagocytosis. The predictions are qualitatively consistent with the results of recent preliminary experiments.

Actin Cytoskeleton↗
PubMed1994

Fractal properties of ion channels and diffusion.

We focus our attention on a fractal model recently proposed by Liebovitch to account for the lack of a time scale in ion channel kinetics. We establish a connection between the dwell-time distributions and the correlation time of the ion channel signal, thereby making it possible to derive analytical predictions on the diffusion properties of a random walk constructed from the sum of the current fluctuations of ion channels. With the help of a numerical simulation of the Liebovitch model, it is shown that the Hurst analysis can provide a reliable determination of the standard (or anomalous) diffusion properties. On the basis of results of computer simulation we argue that by applying the Hurst analysis to the experimental distribution of closed times it is possible, in principle, to establish whether the Liebovitch model is valid.

Computer Simulation↗
PubMed1984

Coherent global motion percepts from stochastic local motions.

A percept of global, coherent motion results when many different localized motion vectors are combined. We studied the percept with dynamic random dot kinematograms whose elements took independent, random walks of constant step size; their directions of displacement were drawn from a uniform distribution. The tendency to see global, coherent flow along the mean of the uniform distribution varied with the range of the distribution. Psychometric functions were obtained with kinematograms having various step sizes and element densities. The changes in the psychometric function with step size and density are consistent with Ullman's "minimal map theory" of motion correspondence.

Form Perception↗
PubMed1986

Dynamical aspects of animal grouping: swarms, schools, flocks, and herds.

Grouping of animals is a natural phenomenon in which a number of animal individuals are involved in movement as forming a group. Examples are insect swarms and fish schools. In this article an attempt is made to describe the motion of grouping individuals kinematically as distinct from simple diffusion or random walk, to model the grouping on the basis of dynamics of animal motion, and to interpret the grouping from the standpoint of advection-diffusion processes. Also presented is dynamical modeling for the group size distribution as a result of amalgamation and splitting processes of groups. Examples of animal grouping are described in detail. They are insect swarms, zooplankton swarms, fish schools, bird flocks, and mammal herds. The presented mathematical models are compared with data of these animal groupings.

Animals↗
PubMed1992

Sticking coefficients of adsorbing proteins.

The protein sticking coefficient, phi, the fraction of collisions that result in adsorption, is a function of the molecular interactions between the protein and the surface. A random walk and diffusion-to-capture model was used to describe the kinetics of protein adsorption. The assumption of a constant sticking coefficient leads to a first-order model of the kinetics. A solution of the problem of adsorption from a semi-infinite medium with first-order kinetics at the boundary was obtained by numerical simulation on the computer. The results of the computer simulations match the time dependence observed experimentally. A correlation was developed to estimate phi from experimental data. phi has been found to be in the range 10(-5)-10(-8) for several protein adsorption kinetic studies reported in the literature.

Adsorption↗
PubMed1982

Kinetics of acetylthiocholine binding to electric eel acetylcholinesterase in glycerol/water solvents of increased viscosity. Evidence for a diffusion-controlled reaction.

Steady-state kinetic studies were made on the very efficient enzyme hydrolysis of acetylthiocholine by electric eel acetylcholinesterase (acetylcholine acetylhydrolase, EC 3.1.1.7) in glycerol/water solvents of increased viscosity. Determinations of the very fast minimum substrate association rate constants kmin, (2 . 10(8) M-1 . s-1 at I approximately 0.1 M and 25 degrees C) from the Michaelis parameters, V/(Km[E0]), were made at low substrate concentrations in order to obtain kmin directly. kmin was shown to be strongly dependent upon viscosity, which is characteristic of a diffusion-controlled reaction. kmin is as large or larger than plausible models for a simple diffusion-controlled reaction between a charged enzyme and substrate would suggest. Enhancement of the diffusion-controlled reaction through nonspecific binding of substrate to the highly negatively charged acetylcholinesterase followed by two-dimensional surface diffusion in a random walk to the active site may be a factor in this enzyme mechanism. Evidence for this comes from the viscosity dependence of kmin. Using the surface diffusion model it is estimated that the binding-site target area on acetylcholinesterase is effectively increased a minimum of 8-fold.

Acetylcholinesterase↗
PubMed1990

A log-linear approach to disaggregated micro-level population forecasts.

"This paper proposes the use of a log-linear model to obtain long-range micro-level population projections from the aggregative projections. The proposed model is tested using U.S. data. The total population of households is decomposed into 120 subgroups on the basis of the household's region of location, age, size and the female's employment status. The estimated number of households from the log-linear technique is compared against the random-walk and time-trend methods. A comparison of the size of the observed and estimated subgroups for the years 1960 and 1980 suggests that the log-linear technique is superior to the other two methods. Five different measures of errors are used to evaluate the projections."

Age Factors↗
PubMed1990

Simulation of interactions between migrating whales and potential oil spills.

A numerical model system was developed to quantify the probability of endangered bowhead and gray whales encountering spilled oil in Alaskan waters. Migration and diving-surfacing models for bowhead and gray whales, and an oil spill trajectory model comprise the system. The migration models were developed from conceptual considerations, then calibrated with and tested against observations. The distribution of whales is represented in space and time by discrete points, each of which may represent one or more whales. The movement of a whale point is governed by a random walk algorithm which stochastically follows a migratory pathway. Stochastic diving-surfacing models are used to stimulate surfacing behavior sequences for each species. The oil spill model accounts for oil transport and spreading in open water and in the presence of sea ice. Historical wind records and ice cover data sets provide the environmental conditions to generate stochastic oil spill scenarios. The oil spill, whale migration and diving-surfacing models are linked to provide quantitative estimates of whale-oil interactions. The model system was applied to the Alaskan Beaufort Sea to investigate the probability that bowhead whales would encounter oil spilled in this region.

Journal Article↗
PubMed1986

The uses of spatial analysis in medical geography: a review.

This paper is a review of how geographers and others have used spatial analysis to study disease and health care delivery patterns. Point, line, area and surface patterns, as well as map comparisons and relative spaces are discussed. Problems encountered in applying spatial analytic techniques in medical geography are pointed out. The paper is intended to stimulate discussion about where medical geography can and should go in this area of study. Point pattern techniques include standard distance, standard deviational ellipses, gradient analysis and space and space-time clustering. Line methods include random walks, vectors and graph theory or network analysis. Under areas, location quotients, standardized mortality ratios, Poisson probabilities, space and space-time clustering, autocorrelation measures and hierarchical clustering are discussed. Surface techniques mentioned are isolines and trend surfaces. For map comparisons, Lorenz curves, coefficients of areal correspondence and correlation coefficients have been used. Case-control matching, acquaintance networks, multidimensional scaling and cluster analysis are examples of methods that are based on relative or non-metric spaces. The review gives rise to the discussion of several general points: problems encountered in spatial analysis, theory building and verification, the appropriate role of technique and computer use. Some suggestions are made for further use of spatial analytic techniques in medical geography: Monte Carlo simulation of point patterns, network analysis to study referral systems and health care for pastoralists, geographic information systems to assess environmental risk, difference mapping for disease and risk factor map comparisons and multidimensional scaling to measure social distance.

Cross-Sectional Studies↗
PubMed1988

An analysis of the hyper-sharp phenomenon of myosin diffusion in an F-actin/ATP solution by computer simulation.

The diffusion of myosin molecules was demonstrated using schlieren optics and Rayleigh fringe optics. A hyper-sharp schlieren pattern appeared near the boundary between the upper and lower parts of the diffusion cell at a time when ATP in the lower part had almost been consumed. The mechanism underlying the appearance of the hyper-sharp peak was investigated by means of computer simulations based on random-walk theory. The schlieren pattern with the hyper-sharp peak could be reproduced on the computer with the assumptions that a myosin molecule can be detached from an actin filament only on binding of ATP and that it can then move along actin filaments or diffuse in the aqueous solution. The results of the computer simulations are in good agreement with the experimental data.

Actins↗
PubMed1995

Diffusion influenced binary reactive processes in membranes involving identical particles: a Monte Carlo study.

Simple random walk simulations on triangular lattices were performed in order to obtain a basic quantitative understanding of the kinetics of diffusion influenced binary reactive processes of membrane associated peptides or proteins within the two dimensionality of lipid bilayers. The results of the Monte Carlo simulations are compared with various formal approximate steady-state approaches, such as presented by Keizer [Acc. Chem. Res., 18 (1985) 235-241] in the context of statistical nonequilibrium thermodynamics or by Hardt [Biophys. Chem., 10 (1979) 239-243], based on the well known work of Delbrück and Adam. For diffusion controlled binary reactions of identical particles, nice agreement with the numerically simulated values is found in the low concentration limit for both Hardt's and Keizer's approach. For the latter a fluctuating steady-state particle source has to be considered. The dependence of the steady-state rate coefficient on system size is investigated, and the results are compared to the work of Swartz and Peacock-López [J. Chem. Phys., 95 (4) (1991) 2727-2731]. In order to elucidate the results, a practical application is considered. An application to a dimerization reaction on vesicles of typical experimental dimensions is given.

Journal Article↗