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PubMed2005

Protein folding stabilizing time measurement: a direct folding process and three-dimensional random walk simulation.

Protein particles undergo Brownian motion and collisions in solution. The diffusive collisions may lead to aggregation. For proteins to fold successfully the process has to occur quickly and before significant collision takes place. The speed of protein folding was deduced by studying the correlation time of a lysozyme refolding process from autocorrelation function analysis of the mean collision time and aggregation/soluble ratio of protein. It is a measure of time before which an aggregate can be formed and also is the time measure for a protein to fold into a stable state. We report on the protein folding stabilizing time of a lysozyme system to be 25.5-27.5 micros (<+/-4%) between 295 and 279K via direct folding experimental studies, supported by a three-dimensional random walk simulation of diffusion-limited aggregation model. Aggregation is suppressed when the protein is folded to a stable form. Spontaneous folding and diffusion-limited aggregation are antagonistic in nature. Meanwhile, the resultant aggresome, suggested by Raman and mass spectroscopy, may be formed by cross-linkages of disulfide bonds and hydrophobic interactions.

Binding Sites↗
PubMed2005

Entropic sampling via Wang-Landau random walks in dominant energy subspaces.

Dominant energy subspaces of statistical systems are defined with the help of restrictive conditions on various characteristics of the energy distribution, such as the probability density and the fourth order Binder's cumulant. Our analysis generalizes the ideas of the critical minimum energy subspace (CRMES) technique, applied previously to study the specific heat's finite-size scaling. Here, we illustrate alternatives that are useful for the analysis of further finite-size anomalies and the behavior of the corresponding dominant subspaces is presented for the two-dimensional (2D) Baxter-Wu and the 2D and 3D Ising models. In order to show that a CRMES technique is adequate for the study of magnetic anomalies, we study and test simple methods which provide the means for an accurate determination of the energy-order-parameter (E,M) histograms via Wang-Landau random walks. The 2D Ising model is used as a test case and it is shown that high-level Wang-Landau sampling schemes yield excellent estimates for all magnetic properties. Our estimates compare very well with those of the traditional Metropolis method. The relevant dominant energy subspaces and dominant magnetization subspaces scale as expected with exponents alpha/nu and gamma/nu, respectively. Using the Metropolis method we examine the time evolution of the corresponding dominant magnetization subspaces and we uncover the reasons behind the inadequacy of the Metropolis method to produce a reliable estimation scheme for the tail regime of the order-parameter distribution.

Journal Article↗
PubMed1983

A random-walk model for helix bending in B-DNA.

The double-helical B-DNA dodecamer of sequence d(C-G-C-G-A-A-T-T-C-G-C-G) has been refined independently from x-ray crystal structure analyses in five different variants: d(C-G-C-G-A-A-T-T-C-G-C-G) at 16 K, at room temperature, and with bound cis-diamminedichloroplatinum(II), and d(C-G-C-G-A-A-T-T-brC-G-C-G) in 60% 2-methyl-2,4-pentanediol at 20 degrees C and 7 degrees C. These helices display overall axial bends of 22 degrees, 18 degrees, 17 degrees, 14 degrees, and 3 degrees, respectively, providing an opportunity to investigate the nature of the bending process in B-DNA. Bending from one base pair to the next is best described as a stochastic or random-walk process, having forward, retrograde, and sidewise individual steps, but with an overall sense of bending. Individual steps almost always involve rolling of adjacent base pairs over one another along their long axes, not a tilting or wedge displacement that lifts neighboring base pairs apart at one end. A slight preference is observed for bending the double helix in a direction that compresses the major groove rather than the minor, and this is intuitively reasonable in view of the narrowness of the minor groove and its occupation by the spine of hydration that stabilizes the B form of DNA. This model predicts that, when DNA is wound around the nucleosome core, it should not be smoothly curved but should exhibit discrete bends every five base pairs as proposed by Zhurkin et al. [Zhurkin, V.B., Lysov, Y. P. & Ivanov, V. I. (1979) Nucleic Acids Res. 6, 1081-1096)]. Sharper bends may occur at alternate positions, where the major groove faces the nucleosome core.

Base Sequence↗
PubMed2003

Random walks with non-Gaussian step-size distributions and the folding of random polymer chains.

In this paper, we study a random walker whose step-size distribution is of non-Gaussian bimodal form due to the addition of a quartic term in the exponential. By the central limit theorem, we know that in the limit of a large number of steps, the probability distribution representing the distance the walker has traveled becomes Gaussian. We investigate the nature of this convergence both numerically and analytically. We obtain a scaling relation describing the number of steps required for convergence in terms of the width and separation of the peaks of the step-size distribution. We assume in the concluding section that our model is well suited for the application of the folding of a random polymer chain.

Journal Article↗
PubMedDate not supplied

A randomized walking trial in postmenopausal women: effects on physical activity and health 10 years later.

BACKGROUND: It is important to determine if permanent lifestyle changes may result from physical activity interventions and whether health may be affected by these changes. OBJECTIVE: To conduct a 10-year follow-up of physical activity and self-reported health status in participants of a randomized clinical trial of walking intervention. METHODS: Of the original 229 volunteer postmenopausal women who participated in the original clinical trial, 196 (N = 96 intervention and 100 controls) completed the 10-year follow-up telephone interview. The interview protocol included questions on self-reported walking for exercise and purposes other than exercise, the Paffenbarger sport and exercise index, functional status, and various chronic diseases and conditions. RESULTS: The median values for both usual walking for exercise and total walking were significantly higher for walkers compared with controls (for both, P = .01), with median differences of 706 and 420 kcal/wk, respectively. After excluding women who reported heart disease during the original trial, 2 women in the walking group (2%) and 11 women in the control group (12%) reported physician-diagnosed heart disease over the last 10 years (P = .07). There were also fewer hospitalizations, surgeries, and falls among women in the walking group, although these differences were not statistically significant (P>.05). CONCLUSIONS: Although limited by self-report, this study may be the first to demonstrate long-term exercise compliance to a randomized control trial in older women and to suggest that health benefits may have ensued as a result of these increased activity levels.

Aged↗
PubMed1999

Analytical results for random walks in the presence of disorder and traps.

In this paper, we study the dynamics of a random walker diffusing on a disordered one-dimensional lattice with random trappings. The distribution of escape probabilities is computed exactly for any strength of the disorder. These probabilities do not display any multifractal properties, contrary to previous numerical claims. The explanation for this apparent multifractal behavior is given, and our conclusions are supported by numerical calculations. These exact results are exploited to compute the large time asymptotics of the survival probability (or the density) which is found to decay as exp[-Ct(1/3)ln(2/3)(t)]. An exact lower bound for the density is found to decay in a similar way.

Journal Article↗
PubMed2001

Radiation breakage of DNA: a model based on random-walk chromatin structure.

Monte Carlo computer software, called DNAbreak, has recently been developed to analyze observed non-random clustering of DNA double strand breaks in chromatin after exposure to densely ionizing radiation. The software models coarse-grained configurations of chromatin and radiation tracks, small-scale details being suppressed in order to obtain statistical results for larger scales, up to the size of a whole chromosome. We here give an analytic counterpart of the numerical model, useful for benchmarks, for elucidating the numerical results, for analyzing the assumptions of a more general but less mechanistic "randomly-located-clusters" formalism, and, potentially, for speeding up the calculations. The equations characterize multi-track DNA fragment-size distributions in terms of one-track action; an important step in extrapolating high-dose laboratory results to the much lower doses of main interest in environmental or occupational risk estimation. The approach can utilize the experimental information on DNA fragment-size distributions to draw inferences about large-scale chromatin geometry during cell-cycle interphase.

Animals↗
PubMed2006

Random walks with shrinking steps: first-passage characteristics.

We study the mean first-passage time of a one-dimensional random walker with step sizes decaying exponentially in discrete time. That is step sizes go like lambda(n) with lambda< or =1. We also present, for pedagogical purposes, a continuum system with a diffusion constant decaying exponentially in continuous time. Qualitatively both systems are alike in their global properties. However, the discrete case shows very rich mathematical structure, depending on the value of the shrinking parameter, such as self-repetitive and fractal-like structure for the first-passage characteristics. The results we present show that the most important quantitative behavior of the discrete case is that the support of the distribution function evolves in time in a rather complicated way in contrast to the time independent lattice structure of the ordinary random walker. We also show that there are critical values of lambda defined by the equation lambda(K) + 2lambda(P)-2=0 with {K,N}[formula: see text] where the mean first-passage time undergoes transitions.

Journal Article↗
PubMed2005

A non-random walk through the genome.

Recent publications on a wide range of eukaryotes indicate that genes showing particular expression patterns are not randomly distributed in the genome but are clustered into contiguous regions that we call neighborhoods. It seems probable that this organization is related to chromatin and the structure of the nucleus.

Animals↗
PubMed1977

A random walk model of cellular kinetics.

The sorting out of biological cell mixtures into clusters of one cell type is modelled as a consequence of random cell and cluster motion, during which cells of like type cohere upon collision. After a description of the model and its motility rules, the results of several computer simulation studies are analysed and compared with both laboratory data and certain theoretical predictions. The model is found to be more biologically realistic than previous models with similar results. Suggestions for further reserach are discussed. An Appendix contains details about the data structures and algorithms employed in the simulation.

Cell Adhesion↗
PubMed2000

Random walks in logarithmic and power-law potentials, nonuniversal persistence, and vortex dynamics in the two-dimensional XY model

The Langevin equation for a particle ("random walker") moving in d-dimensional space under an attractive central force and driven by a Gaussian white noise is considered for the case of a power-law force, F(r) approximately -r(-sigma). The "persistence probability," P0(t), that the particle has not visited the origin up to time t is calculated for a number of cases. For sigma>1, the force is asymptotically irrelevant (with respect to the noise), and the asymptotics of P0(t) are those of a free random walker. For sigma<1, the noise is (dangerously) irrelevant and the asymptotics of P0(t) can be extracted from a weak noise limit within a path-integral formalism employing the Onsager-Machlup functional. The case sigma=1, corresponding to a logarithmic potential, is most interesting because the noise is exactly marginal. In this case, P0(t) decays as a power law, P0(t) approximately t(-straight theta) with an exponent straight theta that depends continuously on the ratio of the strength of the potential to the strength of the noise. This case, with d=2, is relevant to the annihilation dynamics of a vortex-antivortex pair in the two-dimensional XY model. Although the noise is multiplicative in the latter case, the relevant Langevin equation can be transformed to the standard form discussed in the first part of the paper. The mean annihilation time for a pair initially separated by r is given by t(r) approximately r(2) ln(r/a) where a is a microscopic cutoff (the vortex core size). Implications for the nonequilibrium critical dynamics of the system are discussed and compared to numerical simulation results.

Journal Article↗
PubMed1982

The random walk description for isotope exchange in a polypeptide.

Isotope exchange in a polypeptide is considered from the point of view in which the boundary point between helix and coil regions of a polypeptide behaves like a weakly asymmetric random walker. We assume that the boundary point is reflected completely at the ends of a polypeptide. The equilibrium fraction of helix region is obtained under this assumption, and this is also confirmed by computer simulation. The experimental results of isotope exchange can be explained in this situation. On the other hand. the rate constant of exchange of a residue given by experiments can also be explained by another assumption, as considered before (M. Fujiwara and N. Saitô, Polym. J. 9 (1977) 625.), in which the nucleations of coil states take place in the helix region. Which of the two is of major importance is left to further studies.

Journal Article↗
PubMed2006

Random walks for image segmentation.

A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with user-defined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a high-quality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs.

Algorithms↗
PubMed2001

Random walk in an eddy and tube formation from fine particles.

Tubular shape formation of an ensemble of ultrafine particles, captured by microscopic eddies in a fluid or gaseous medium, is investigated. In the circulation flow of the eddy, the small particles are driven by the deterministic hydrodynamical forces and the random forces of Brownian motion. The conditions for dynamically/statistically stable tube formation and the resulting tube parameters are obtained by analytic calculations and computer simulations, respectively. The model yields striking similarities to the characteristics of nanotube formation observed in turbulent media such as the carbon arc, and throws some light on tubular formation observed in fluid media. (c) 2001 American Institute of Physics.

Journal Article↗
PubMed2005

Random walks, diffusion limited aggregation in a wedge, and average conformal maps.

We investigate diffusion-limited aggregation (DLA) in a wedge geometry. Arneodo and collaborators have suggested that the ensemble average of DLA cluster density should be close to the noise-free selected Saffman-Taylor finger. We show that a different, but related, ensemble average, that of the conformal maps associated with random clusters, yields a nontrivial shape which is also not far from the Saffman-Taylor finger. However, we have previously demonstrated that the same average of DLA in a channel geometry is not the Saffman-Taylor finger. This casts doubt on the idea that the average of noisy diffusion-limited growth is governed by a simple transcription of noise-free results.

Cluster Analysis↗
PubMed2003

Random walks with thin filaments: application of in vitro motility assay to the study of actomyosin regulation.

The in vitro motility devised by Kron and Spudich (Kron and Spudich, 1986; Kron et al., 1991) has proved a very valuable technique for studying the motor properties of myosin of all kinds but it is equally useful for the study of the thin filaments of muscle and their regulation. The movement of a population of thin filaments over immobilised myosin appears to be random but it does in fact yield a large amount of information about contractility and its regulation. The key to extracting useful information from in vitro motility assay experiments is the logical and comprehensive analysis of filament movements.

Actin Cytoskeleton↗
PubMed2006

T-cell motility in the early stages of the immune response modeled as a random walk amongst targets.

The transport process by which a T cell makes high-frequency encounters with antigen-presenting cells following infection is an important element of adaptive immunity. Recent experimental work has allowed in vivo cell motility to be characterized in detail. On the basis of experimental data we develop a quantitative model for encounters between T cells and antigen-presenting cells. We model this as a transport-limited chemical reaction with the dynamics dependent on physical contact between randomly moving reactants. We use asymptotic methods to calculate a time distribution which characterizes the delay before a T cell is activated and use Monte Carlo simulations to verify the analysis. We find that the density of antigen-primed dendritic cells within the lymph node paracortex must be greater than 35 cells/mm3 for a T cell to have a more than 50% chance of encountering a dendritic cell within 24 h. This density is much larger than existing estimates based on calculations which neglect the transport process. We also use simulations to compare a T cell which re-orients isotropically with a T cell which turns according to an experimentally observed distribution and find that the effects of anisotropy on the solution are small.

Animals↗
PubMed2006

Critical behavior of an even-offspringed branching and annihilating random-walk cellular automaton with spatial disorder.

A stochastic cellular automaton exhibiting a parity-conserving class transition has been investigated in the presence of quenched spatial disorder by large-scale simulations. Numerical evidence has been found that weak disorder causes irrelevant perturbation for the universal behavior of the transition and the absorbing phase of this model. This opens up the possibility for experimental observation of the critical behavior of a nonequilibrium phase transition to absorbing state. For very strong disorder the model breaks up into blocks with exponential-size distribution and continuously changing critical exponents are observed. For strong disorder the randomly distributed diffusion walls introduce another transition within the inactive phase of the model, in which residual particles survive the extinction. The critical dynamical behavior of this transition has been explored.

Journal Article↗