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PubMed2004

Feasibility of diffusion-NMR surface-to-volume measurements tested by calculations and computer simulations.

It has been demonstrated previously that the surface-to-volume ratio S/V can be determined from the derivative of the time-dependent diffusion coefficient D(t), in the limit t --> 0. Several questions arise concerning the practicality of determining S/V by NMR. In particular, how large are the errors generated by (1) working outside the t --> 0 limit and (2) measuring D outside the b --> 0 limit, both for narrow and full-width gradient pulses? Here b is gamma2G2delta2Delta for narrow pulses and gamma2G2t3/12 for broad pulses. These questions are addressed by random-walk computer simulations and numerical calculations in geometries relevant to small-airways of lung. The results demonstrate that one can work well outside the t --> 0 and b --> 0 limits, provided 10-20% accuracy in the measured S/V is sufficient. Emphasis is placed on the useful range of times t for which NMR determinations of lung S/V are feasible.

Algorithms↗
PubMed2006

Observation of anomalous diffusion in excised tissue by characterizing the diffusion-time dependence of the MR signal.

This report introduces a novel method to characterize the diffusion-time dependence of the diffusion-weighted magnetic resonance (MR) signal in biological tissues. The approach utilizes the theory of diffusion in disordered media where two parameters, the random walk dimension and the spectral dimension, describe the evolution of the average propagators obtained from q-space MR experiments. These parameters were estimated, using several schemes, on diffusion MR spectroscopy data obtained from human red blood cell ghosts and nervous tissue autopsy samples. The experiments demonstrated that water diffusion in human tissue is anomalous, where the mean-square displacements vary slower than linearly with diffusion time. These observations are consistent with a fractal microstructure for human tissues. Differences observed between healthy human nervous tissue and glioblastoma samples suggest that the proposed methodology may provide a novel, clinically useful form of diffusion MR contrast.

Algorithms↗
PubMed2005

Dynamics of replication foci in early S phase as visualized by cross-correlation function.

To monitor gradual changes in the replication foci distribution during early S phase, different segments of newly synthesized DNA were visualized by immunocytochemical mapping of two consecutively incorporated deoxythymidine analogs in pulse-chase-pulse experiments in HeLa cells. The resulting dual-labeled fluorescence images were evaluated using cross-correlation function (CCF) analysis. General changes of CCF shape due to image deterioration caused by blur, noise, and lateral sampling (pixel size) were also discussed. Using CCF analysis of model images simulating either random initiation of new replication foci, or the firing of new foci in close proximity to completed ones, we were able to ascribe the changes in the early S replication foci distribution to the latter mechanism. In contrast to the data published previously, we monitored the dynamics of all replication foci for up to 3 h. In addition, we showed that the replication foci dynamics is well described by random walk model, so that the average de-localization of individual foci is proportional to square root of the applied chase.

DNA↗
PubMed2004

Apparent 2-D diffusivity in a ruffled cell membrane.

Most biological cell membranes have a microtopology that increases their surface area, including a highly ruffled surface in the case of leukocytes. Thus, molecular membrane diffusivities as measured by fluorescence recovery after photobleaching or other methods are decreased when projected onto a plane. We use a two-dimensional crested cycloid as a parameterized surface to simulate the random-walk diffusion of a molecule within a ruffled membrane. The apparent 2-D diffusivity was then calculated when the ruffled membrane is projected onto a plane. It is shown that the apparent diffusivity decreases as a function of the membrane area, to the -1.4 power.

Animals↗
PubMed2004

A mathematical model of tumour angiogenesis, regulated by vascular endothelial growth factor and the angiopoietins.

Angiogenesis--the growth of new blood vessels from existing ones--is a prerequisite for the growth of solid tumours beyond a diameter of approximately 2 mm. In recent years, the angiopoietins have emerged as important regulators of angiogenesis. They mediate a delicate balance between vascular quiescence, regression and new growth, but their mechanism of action is not fully understood. This work attempts to provide a mathematical description of the role of the angiopoietins in angiogenesis. The model is formulated within the framework of reinforced random walks, which allows easy transition between the continuum (macroscopic) and discrete (microscopic) forms. Model predictions are in qualitative agreement with experimental observations, and may have implications for anti-cancer therapies based on the prevention of angiogenesis.

Angiopoietins↗
PubMed2006

Inferring resource distributions from Atlantic bluefin tuna movements: an analysis based on net displacement and length of track.

We use observed movement tracks of Atlantic bluefin tuna in the Gulf of Maine and mathematical modeling of this movement to identify possible resource patches. We infer bounds on the overall sizes and distribution of such patches, even though they are difficult to quantify by direct observation in situ. To do so, we segment individual fish tracks into intervals of distinct motion types based on the ratio of net displacement to length of track (DeltaD/DeltaL) over a time window Deltat. To find the best segmentation, we optimize the fit of a random-walk movement model to each motion type. We compare results from two distinct movement models: biased turning and biased speed, to check the model-dependence of our inferences, and find that uncertainty in choice of movement model dominates the uncertainties of our conclusions. We find that our data are best described using two motion types: "localized" (DeltaD/DeltaL small) and "long-ranged" (DeltaD/DeltaL large). The biased turning model leads to significantly better resolution of localized movement intervals than the biased speed model. We hypothesize that localized movement corresponds to exploitation of resource patches. Comparison with visual behavior observations made during tracking suggests that many inferred intervals of localized motion do indeed correspond to feeding activity. From our analysis, we estimate that, on average, bluefin tuna in the Gulf of Maine encounter a resource patch every 2h, that those patches have an average radius of 0.7-1.2 km, and that, overall, there are at most 5-9 such patches per 100 km(2) in the region studied.

Animals↗
PubMed2006

The movement of oil under non-breaking waves.

The combined effects of wave kinematics, turbulent diffusion, and buoyancy on the transport of oil droplets at sea were investigated in this work using random walk techniques in a Monte Carlo framework. Six hundred oil particles were placed at the water surface and tracked for 500 wave periods. A dimensionless formulation was presented that allowed reporting distances in terms of the wave length and times in terms of the wave period. Stokes' drift was, expectedly, the major mechanism for horizontal transport. It was also found that plumes that have large terminal rise velocities move faster forward but spread less than those that have small terminal rise velocities. The increase in wave slope (or wave steepness) caused an increase in transport and spreading of the plume. Our results supported treating the oil as completely mixed vertically in a layer near the surface. In the horizontal direction, buoyant plumes had spreading coefficients that are essentially constant after about 200 wave periods. But neutrally buoyant plumes had horizontal spreading coefficients that increased with time (for the simulation time of 500 wave periods). Techniques for generalizing the results for a wide range of wave parameters were presented.

Biomechanical Phenomena↗
PubMed2005

A comparison of experimental and simulated propagators in porous media using confocal laser scanning microscopy, lattice Boltzmann hydrodynamic simulations and nuclear magnetic resonance.

Confocal laser scanning microscopy has been used to obtain 3D optical image stacks of packings of glass ballotini in various fluorescent dye-containing fluids inside a 3D micromodel. The fluids' refractive index was matched to that of the glass ballotini so that clear images at an appreciable depth (approximately 400 microm) inside the packings were obtained. The lattice Boltzmann method was then used to produce 3D velocity fields through the 3D image stacks of the packed ballotini. These have been used in conjunction with a stochastic random-walk algorithm to produce simulated displacement propagators, which have been shown to be in qualitative agreement with experimental propagators, obtained using nuclear magnetic resonance, of water flowing through the exact same micromodel.

Algorithms↗
PubMed2006

Differential learning algorithms for decorrelation and independent component analysis.

Decorrelation and its higher-order generalization, independent component analysis (ICA), are fundamental and important tasks in unsupervised learning, that were studied mainly in the domain of Hebbian learning. In this paper we present a variation of the natural gradient ICA, differential ICA, where the learning relies on the concurrent change of output variables. We interpret the differential learning as the maximum likelihood estimation of parameters with latent variables represented by the random walk model. In such a framework, we derive the differential ICA algorithm and, in addition, we also present the differential decorrelation algorithm that is treated as a special instance of the differential ICA. Algorithm derivation and local stability analysis are given with some numerical experimental results.

Acoustic Stimulation↗
PubMed2005

A Bayesian approach to modeling dynamic effective connectivity with fMRI data.

A state-space modeling approach for examining dynamic relationship between multiple brain regions was proposed in Ho, Ombao and Shumway (Ho, M.R., Ombao, H., Shumway, R., 2005. A State-Space Approach to Modelling Brain Dynamics to Appear in Statistica Sinica). Their approach assumed that the quantity representing the influence of one neuronal system over another, or effective connectivity, is time-invariant. However, more and more empirical evidence suggests that the connectivity between brain areas may be dynamic which calls for temporal modeling of effective connectivity. A Bayesian approach is proposed to solve this problem in this paper. Our approach first decomposes the observed time series into measurement error and the BOLD (blood oxygenation level-dependent) signals. To capture the complexities of the dynamic processes in the brain, region-specific activations are subsequently modeled, as a linear function of the BOLD signals history at other brain regions. The coefficients in these linear functions represent effective connectivity between the regions under consideration. They are further assumed to follow a random walk process so to characterize the dynamic nature of brain connectivity. We also consider the temporal dependence that may be present in the measurement errors. ML-II method (Berger, J.O., 1985. Statistical Decision Theory and Bayesian Analysis (2nd ed.). Springer, New York) was employed to estimate the hyperparameters in the model and Bayes factor was used to compare among competing models. Statistical inference of the effective connectivity coefficients was based on their posterior distributions and the corresponding Bayesian credible regions (Carlin, B.P., Louis, T.A., 2000. Bayes and Empirical Bayes Methods for Data Analysis (2nd ed.). Chapman and Hall, Boca Raton). The proposed method was applied to a functional magnetic resonance imaging data set and results support the theory of attentional control network and demonstrate that this network is dynamic in nature.

Attention↗
PubMed2005

Diffusional screening in real 3D human acini--a theoretical study.

Gas exchange at the acinar level involves several physico-chemical phenomena within a complex geometry. A gas transport model, which takes into account both the diffusion into the acinus and the diffusion across the alveolar membrane, is used to understand gas mixing in realistic systems. It is first shown that the behaviour of the system, computed on model geometries in 3D, only depends on the topological structure of the acinus. Taking advantage of this property, a new efficient method based on random walks on a lattice is used to compute gas diffusion in structures taken from real morphological data. This approach shows that, at rest, the human acinus efficiency is only 30-40%. These results provide a new evidence of the existence of diffusional screening at the acinar level. This implies permanent spatial inhomogeneity of oxygen and carbon dioxide partial pressure. The notion of an "alveolar gas" is reinterpreted as a spatial average of the gas distribution. This model casts new light on the respiratory properties of other gas mixtures, such as helium-oxygen.

Cell Membrane Permeability↗
PubMed2006

Migration of fallout radiocaesium in a grassland soil from 1986 to 2001. Part II: evaluation of the activity-depth profiles by transport models.

The vertical migration of (134)Cs, deposited by the Chernobyl fallout (1986), and (137)Cs, deposited by the Chernobyl and the global fallout, in the soil of an undisturbed Bavarian grassland in Germany was investigated from 1986 to 2001. The activity-depth profiles of both isotopes at ten sampling dates were evaluated by the classical convection-dispersion equation and a random walk particle model. In both models, the apparent migration velocity v and the apparent dispersion coefficient D were assumed to be independent of time. However, optimized values of v and D were significantly different for the different locations sampled at different times. If nevertheless constant values of v and D were used, the simulated activity densities per soil layer were out of the range of the spatial variability of the observed activity densities determined in 2001. It is concluded that without further simultaneous investigations e.g. on bioturbation at the study site, migration parameters of radiocaesium determined by classical transport models based on convection and dispersion during the first years after the deposition of the activity cannot be used for predictive purposes.

Cesium Radioisotopes↗
PubMed2006

Modeling observation error and its effects in a random walk/extinction model.

This paper examines the consequences of observation errors for the "random walk with drift", a model that incorporates density independence and is frequently used in population viability analysis. Exact expressions are given for biases in estimates of the mean, variance and growth parameters under very general models for the observation errors. For other quantities, such as the finite rate of increase, and probabilities about population size in the future we provide and evaluate approximate expressions. These expressions explain the biases induced by observation error without relying exclusively on simulations, and also suggest ways to correct for observation error. A secondary contribution is a careful discussion of observation error models, presented in terms of either log-abundance or abundance. This discussion recognizes that the bias and variance in observation errors may change over time, the result of changing sampling effort or dependence on the underlying population being sampled.

Analysis of Variance↗
PubMed2001

Kinetics of diffusion-assisted reactions in microheterogeneous systems.

This review is focused on the basic theory of diffusion-assisted reactions in microheterogeneous systems, from porous solids to self-organized colloids and biomolecules. Rich kinetic behaviors observed experimentally are explained in a unified fashion using simple concepts of competing distance and time scales of the reaction and the embedding structure. We mainly consider pseudo-first-order reactions, such as luminescence quenching, described by the Smoluchowski type of equation for the reactant pair distribution function with a sink term defined by the reaction mechanism. Microheterogeneity can affect the microscopic rate constant. It also enters the evolution equation through various spatial constraints leading to complicated boundary conditions and, possibly, to the reduction of dimensionality of the diffusion space. The reaction coordinate and diffusive motion along this coordinate are understood in a general way, depending on the problem at hand. Thus, the evolution operator can describe translational and rotational diffusion of molecules in a usual sense, it can be a discrete random walk operator when dealing with hopping of adsorbates in solids, or it can correspond to conformational fluctuations in proteins. Mathematical formulation is universal but physical consequences can be different. Understanding the principal features of reaction kinetics in microheterogeneous systems enables one to extract important structural and dynamical information about the host environments by analyzing suitably designed experiments, it helps building effective strategies for computer simulations, and ultimately opens possibilities for designing systems with controllable reactivity properties.

Animals↗
PubMed2000

Biophysical aspects of intra-protein proton transfer.

The passage of proton trough proteins is common to all membranal energy conserving enzymes. While the routes differ among the various proteins, the mechanism of proton propagation is based on the same chemical-physical principles. The proton progresses through a sequence of dissociation association steps where the protein and water molecules function as a solvent that lowers the energy penalty associated with the generation of ions in the protein. The propagation of the proton in the protein is a random walk, between the temporary proton binding sites that make the conducting path, that is biased by the intra-protein electrostatic potential. Kinetic measurements of proton transfer reactions, in the sub-ns up to micros time frame, allow to monitor the dynamics of the partial reactions of an overall proton transfer through a protein.

Arylsulfonates↗
PubMed2001

Anomalous subdiffusion in fluorescence photobleaching recovery: a Monte Carlo study.

Anomalous subdiffusion is hindered diffusion in which the mean-square displacement of a diffusing particle is proportional to some power of time less than one. Anomalous subdiffusion has been observed for a variety of lipids and proteins in the plasma membranes of a variety of cells. Fluorescence photobleaching recovery experiments with anomalous subdiffusion are simulated to see how to analyze the data. It is useful to fit the recovery curve with both the usual recovery equation and the anomalous one, and to judge the goodness of fit on log-log plots. The simulations show that the simplest approximate treatment of anomalous subdiffusion usually gives good results. Three models of anomalous subdiffusion are considered: obstruction, fractional Brownian motion, and the continuous-time random walk. The models differ significantly in their behavior at short times and in their noise level. For obstructed diffusion the approach to the percolation threshold is marked by a large increase in noise, a broadening of the distribution of diffusion coefficients and anomalous subdiffusion exponents, and the expected abrupt decrease in the mobile fraction. The extreme fluctuations in the recovery curves at and near the percolation threshold result from extreme fluctuations in the geometry of the percolation cluster.

Diffusion↗
PubMed2002

Gauging of the PhoE channel by a single freely diffusing proton.

In the present study we combined a continuum approximation with a detailed mapping of the electrostatic potential inside an ionic channel to define the most probable trajectory for proton propagation through the channel (propagation along a structure-supported trajectory (PSST)). The conversion of the three-dimensional diffusion space into propagation along a one-dimensional pathway permits reconstruction of an ion motion by a short calculation (a few seconds on a state-of-the-art workstation) rather than a laborious, time-consuming random walk simulations. The experimental system selected for testing the accuracy of this concept was the reversible dissociation of a proton from a single pyranine molecule (8-hydroxypyrene-1,2,3-trisulfonate) bound by electrostatic forces inside the PhoE ionic channel of the Escherichia coli outer membrane. The crystal structure coordinates were used for calculation of the intra-cavity electrostatic potential, and the reconstruction of the observed fluorescence decay curve was carried out using the dielectric constant of the intra-cavity space as an adjustable parameter. The fitting of past experimental observations (Shimoni, E., Y. Tsfadia, E. Nachliel, and M. Gutman. 1993. Biophys. J. 64:472-479) was carried out by a modified version of the Agmon geminate recombination program (Krissinel, E. B., and N. Agmon. 1996. J. Comp. Chem. 17:1085-1098), where the gradient of the electrostatic potential and the entropic terms were calculated by the PSST program. The best-fitted reconstruction of the observed dynamics was attained when the water in the cavity was assigned epsilon </= 55, corroborating the theoretical estimation of Sansom (Breed, J. R., I. D. Kerr, and M. S. P. Sansom. 1996. Biophys. J. 70:1643-1661). The dielectric constant calculated for reversed micelles of comparable size (Cohen, B., D. Huppert, K. M. Solntsev, Y. Tsfadia, E. Nachliel, and M. Gutman. 2002. JACS. 124:7539-7547) allows us to set a margin of epsilon = 50 +/- 5.

Arylsulfonates↗
PubMed2002

Quantitative analysis of actin patch movement in yeast.

To investigate the mechanism of cortical actin patch movement in yeast, we implement a method for computer tracking the motion of the patches. Digital images from fluorescence microscope movies of living cells are fed into an image-processing program, which generates two-dimensional patch coordinates in the plane of focus for each movie frame via an algorithm based on detection of rapid intensity variations. The patch coordinates in neighboring frames are connected by a minimum-distance algorithm. The method is used to analyze control cells and cells treated with the actin-depolymerizing agent latrunculin. The motion of the patches in both cases, as analyzed by mean-square patch displacements, is found to be a random walk on average, with a much lower diffusion coefficient for the latrunculin-treated cells. The mean-squared patch travel distances for all of the latrunculin-treated cells are lower than those for all of the control cells. The patches move independently of one another. We develop a quantitative criterion for the presence of directed motion, and show that numerous patches in the control cells display directed motion to a very high degree of certainty. A small number of patches in the latrunculin-treated cells display directed motion.

Actins↗