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At least 703 records · Page 39Linked to original sources
PubMed2005

Convergence of continuous-time quantum walks on the line.

The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time , converges (as tends to infinity) to a probability distribution that depends on the initial state of the particle. This convergence behavior has recently been demonstrated for the simplest continuous-time random walk [N. Konno, Phys. Rev. E 72, 026113 (2005)]. In this Brief Report, we use a different technique to establish the same convergence for a very large class of continuous-time quantum walks, and we identify the limit distribution in the general case.

Journal Article↗
PubMed2006

Superdiffusion in a honeycomb billiard.

We investigate particle transport in the honeycomb billiard which consists of connected channels placed on the edges of a honeycomb structure. The spreading of particles is superdiffusive due to the existence of ballistic trajectories which we term perfect paths. Simulations give a time exponent of 1.72 for the mean-square displacement and a starlike, i.e., anisotropic, particle distribution. We present an analytical treatment based on the formalism of continuous-time random walks and explain the anisotropic distribution under the assumption that the perfect paths follow the directions of the six lattice axes. Furthermore, we derive a relation between the time exponent and the exponent of the distribution function for trajectories close to a perfect path. In billiards with randomly distributed channels, conventional diffusion is always observed in the long-time limit, although for small disorder transient superdiffusional behavior exists. Our simulation results are again supported by an analytical analysis.

Journal Article↗
PubMed2005

Cell population dynamics modulate the rates of tissue growth processes.

The development and testing of a discrete model describing the dynamic process of tissue growth in three-dimensional scaffolds is presented. The model considers populations of cells that execute persistent random walks on the computational grid, collide, and proliferate until they reach confluence. To isolate the effect of population dynamics on tissue growth, the model assumes that nutrient and growth factor concentrations remain constant in space and time. Simulations start either by distributing the seed cells uniformly and randomly throughout the scaffold, or from an initial condition designed to simulate the migration and cell proliferation phase of wound healing. Simulations with uniform seeding show that cell migration enhances tissue growth by counterbalancing the adverse effects of contact inhibition. This beneficial effect, however, diminishes and disappears completely for large migration speeds. By contrast, simulations with the "wound" seeding mode show a continual enhancement of tissue regeneration rates with increasing cell migration speeds. We conclude that cell locomotory parameters and the spatial distribution of seed cells can have profound effects on the dynamics of the process and, consequently, on the pattern and rates of tissue growth. These results can guide the design of experiments for testing the effectiveness of biomimetic modifications for stimulating tissue growth.

Algorithms↗
PubMed2006

Sources of anomalous diffusion on cell membranes: a Monte Carlo study.

A stochastic random walk model of protein molecule diffusion on a cell membrane was used to investigate the fundamental causes of anomalous diffusion in two-dimensional biological media. Three different interactions were considered: collisions with fixed obstacles, picket fence posts, and capture by, or exclusion from, lipid rafts. If motion is impeded by randomly placed, fixed obstacles, we find that diffusion can be highly anomalous, in agreement with previous studies. In contrast, collision with picket fence posts has a negligible effect on the anomalous exponent at realistic picket fence parameters. The effects of lipid rafts are more complex. If proteins partition into lipid rafts there is a small to moderate effect on the anomalous exponent, whereas if proteins are excluded from rafts there is a large effect on the anomalous exponent. In combination, these mechanisms can explain the level of anomaly in experimentally observed membrane diffusion, suggesting that anomalous diffusion is caused by multiple mechanisms whose effects are approximately additive. Finally, we show that the long-range diffusion rate, D(macro), estimated from fluorescence recovery after photobleaching studies, can be much smaller than D(micro), the small-scale diffusion rate, and is highly sensitive to obstacle densities and other impeding structures.

Cell Membrane↗
PubMed2000

Interactions of disparate scales in drift-wave turbulence

Renormalized statistical theory is used to calculate the interactions between short scales (wave vector k) and long scales (wave vector q<<k) in the Hasegawa-Mima model of drift-wave turbulence (generalized to include proper nonadiabatic response for k( ||)=0 fluctuations). The calculations include the zonal-flow growth rate as a special case, but also describe long-wavelength fluctuations with q oriented at an arbitrary angle to the background gradient. The results are fully renormalized. They are subtly different from those of previous authors, in both mathematical form and physical interpretation. A term arising in previous treatments that is related to the propagation of short-scale wave packets is shown to be a higher-order effect that must consistently be neglected to lowest order in a systematic expansion in q/k. Rigorous functional methods are used to show that the long-wavelength growth rate gamma(q) is related to second-order functional variations of the short-wavelength energy and to derive a heuristic algorithm. The principal results are recovered from simple estimates involving the first-order wave-number distension rate gamma;((1))(k)equals, single dot abovek small middle dotnablaOmega;(k)/k(2), where Omega;(k) is a nonlinear random advection frequency. Fokker-Planck analysis involving gamma;((1))(k) is used to heuristically recover the evolution equation for the small scales, and a random-walk flux argument that relates gamma;((1))(k) to an effective autocorrelation time is used to give an independent calculation of gamma(q). Both the rigorous and heuristic derivations demonstrate that the results do not depend on, and cannot be derived from, properties of linear normal modes; they are intrinsically nonlinear. The importance of random-Galilean-invariant renormalization is stressed.

Journal Article↗
PubMed1994

Nonrandomness in protein sequences: evidence for a physically driven stage of evolution?

The sequences, or primary structures, of existing biopolymers--in particular, proteins--are believed to be a product of evolution. Are the sequences random? If not, what is the character of this nonrandomness? To explore the statistics of protein sequences, we use the idea of mapping the sequence onto the trajectory of a random walk, originally proposed by Peng et al. [Peng, C.-K., Buldyrev, S. V., Goldberger, A. L., Havlin, S., Sciortino, F., Simons, M. & Stanley, H. E. (1992) Nature (London) 356, 168-170] in their analysis of DNA sequences. Using three different mappings, corresponding to three basic physical interactions between amino acids, we found pronounced deviations from pure randomness, and these deviations seem directed toward minimization of the energy of the three-dimensional structure. We consider this result as evidence for a physically driven stage of evolution.

Amino Acid Sequence↗
PubMed1990

Lateral diffusivity of lipid analogue excimeric probes in dimyristoylphosphatidylcholine bilayers.

The lateral mobility of pyrenyl phospholipid probes in dimyristoylphosphatidylcholine (DMPC) vesicles was determined from the dependence of the pyrene monomeric and excimeric fluorescence yields on the molar probe ratio. The analysis of the experimental data makes use of the milling crowd model for two-dimensional diffusivity and the computer simulated random walks of probes in an array of lipids. The fluorescence yields for 1-palmitoyl-2-(1'-pyrenedecanoyl)phosphatidylcholine (py10PC) in DMPC bilayers are well fitted by the model both below and above the fluid-gel phase transition temperature (Tc) and permit the evaluation of the probe diffusion rate (f), which is the frequency with which probes take random steps of length L, the host membrane lipid-lipid spacing. The lateral diffusion coefficient is then obtained from the relationship D = fL2/4. In passing through the fluid-gel phase transition of DMPC (Tc = 24 degrees C), the lateral mobility of py10PC determined in this way decrease only moderately, while D measured by fluorescence photobleaching recovery (FPR) experiments is lowered by two or more orders of magnitude in gel phase. This difference in gel phase diffusivities is discussed and considered to be related either to (a) the diffusion length in FPR experiments being about a micrometer or over 100 times greater than that of excimeric probes (approximately 1 nm), or (b) to nonrandomicity in the distribution of the pyrenyl probes in gel phase DMPC. At 35 degrees C, in fluid DMPC vesicles, the diffusion rate is f = 1.8 x 10(8) s-1, corresponding to D = 29 microns2 s-1, which is about three times larger than the value obtained in FPR experiments. The activation energy for lateral diffusion in fluid DMPC was determined to be 8.0 kcal/mol.

Dimyristoylphosphatidylcholine↗
PubMed2003

Measurement and analysis of non-Fickian dispersion in heterogeneous porous media.

Contaminant breakthrough behavior in a variety of heterogeneous porous media was measured in laboratory experiments, and evaluated in terms of both the classical advection-dispersion equation (ADE) and the continuous time random walk (CTRW) framework. Heterogeneity can give rise to non-Fickian transport patterns, which are distinguished by "anomalous" early arrival and late time tails in breakthrough curves. Experiments were conducted in two mid-scale laboratory flow cells packed with clean, sieved sand of specified grain sizes. Three sets of experiments were performed, using a "homogeneous" packing, a randomly heterogeneous packing using sand of two grain sizes, and an exponentially correlated structure using sand of three grain sizes. Concentrations of sodium chloride tracer were monitored at the inflow reservoir and measured at the outflow reservoir. Breakthrough curves were then analyzed by comparison to fitted solutions from the ADE and CTRW formulations. In all three systems, including the "homogeneous" one, subtle yet measurable differences between Fickian and non-Fickian transport were observed. Quantitative analysis demonstrated that the CTRW theory characterized the full shape of the breakthrough curves far more effectively than the ADE.

Chemical Phenomena↗
PubMed2002

Evaluating sequential values using time-adjusted biological variation.

One can compare the difference between two sequential values with the biological variation. Biological variation is a measure of the random disturbances of an analyte's value, measured at different times. When the difference > Z square root 2 SD(BV) then the difference is due to an underlying disease process or physiologic change. A Z value of 1.96 yields a 95% confidence limit. When using multiple sequential values or time periods exceeding that for the empirically derived biological variance, a random walk model allows one to estimate the spread of the variance. For a difference, (delta) to be significant, delta > Z square root 2n SD(BV), where n is the ratio of time reflecting the longer time period divided by the shorter time period. Not all variances grow to this degree over time, because restoring forces diminish the extent of random disturbances. The relationship between a biological variance measured over a longer time period to the one measured over a shorter period can be expressed in terms of this restoring force as SD2 BV,n = SD2 BV,1 sigma(n) j=1 e(-2)(j-1)phi, where n is the ratio of time periods. One can calculate phi using this formula and a spreadsheet. From phi one can calculate the biological variance for any time period, within experimental limits, and compare the difference in sequential values with it. Test intervals can be calculated based on these biological variances.

Analysis of Variance↗
PubMed2003

Coding DNA sequences: statistical distributions.

The base distributions in coding DNA sequences (CDS) are investigated. We explore the scaling properties of the 4-dimensional directed random walk and compare them with that for the DNA sequences. Inference from these observation are, however, contradicted by alternate analysis using factorial moments. To resolve this conflict we look directly at the nucleotide base distributions. In all the cases the base distributions change from gaussian to non-gaussian as the scale size is increased. The CDS, therefore, have nucleotide distributions different from the random.

Animals↗
PubMed1993

Directional selection and the evolution of sex and recombination.

Models of the evolutionary advantages of sex and genetic recombination due to directional selection on a quantitative trait are analysed. The models assume that the trait is controlled by many additive genes. A nor-optimal selection function is used, in which the optimum either moves steadily in one direction, follows an autocorrelated linear Markov process or a random walk, or varies cyclically. The consequences for population mean fitness of a reduction in genetic variance, due to a shift from sexual to asexual reproduction are examined. It is shown that a large reduction in mean fitness can result from such a shift in the case of a steadily moving optimum, under light conditions. The conditions are much more stringent with a cyclical or randomly varying environment, especially if the autocorrelation for a random environment is small. The conditions for spread of a rare modifier affecting the rate of genetic recombination are also examined, and the strength of selection on such a modifier determined. Again, the case of a steadily moving optimum is most favourable for the evolution of increased recombination. The selection pressure on a recombination modifier when a trait is subject to strong truncation selection is calculated, and shown to be large enough to account for observed increases in recombination associated with artificial selection. Theoretical and empirical evidence relevant to evaluating the importance of this model for the evolution of sex and recombination is discussed.

Biological Evolution↗
PubMed1979

Preaggregative cell motion in Dictyostelium.

The motions of a large number (495) of preaggregative D. discoideum NC-4 cells in sparse fields are recorded on time-lapse film and analysed using a specially constructed computer graphics system. All films are produced under a standard set of conditions, so that the range of cell behaviours under given conditions can be characterized. The mean velocity of pre-aggregative D. discoideum NC-4 is 7.19 micrometers/min. The mean velocity time course has a significant early peak at about 3 h. The distribution of mean velocities is fairly broad with a long high velocity tail. A modified random walk model using the parameters diffusion constant and persistence time describes well the changes in cell direction with time. Persistence can be described as an exponentially distributed 'memory' of movement direction, with a mean of 4.89 min. High velocity cells never have long persistence times, and persistence time shows no relationship with age. A nearest neighbour model of cell spacing shows that cells are randomly (Poisson) distributed at low densities. Measurements of cell contacts are compared to a simple model of contact frequency based on the kinetic theory of gases to show that cells at low densities have an affinity for making collisions. The length of contact durations is indicative of some mechanical adhesion between cells, and cells in contact move significantly though not dramatically slower. A cross-correlation analysis shows that the various parameters of motion are significantly interrelated in numerous ways. Finally mutants and strains related to D. discoideum NC-4 exhibit a number of new behaviours, suggesting that motion is a distinctive characteristic of cell type.

Agglutination↗
PubMed1995

Video light microscopy of 670-kb DNA in a hanging drop: shape of the envelope of DNA.

Although its conformation has not been observed directly, double-stranded DNA in solution is usually assumed to be randomly coiled at the level of the DNA double helix. By video light microscopy of ethidium-stained DNA at equilibrium in a nonturbulent hanging drop, in the present study, the 670 kb linear bacteriophage G DNA is found to form a flexible filament that has on average 17 double helical segments across its width. This flexible filament 1) has both asymmetry and dimensions expected of a random coil and 2) has ends that move according to the statistics expected of a random walk. After unraveling the flexible filament-associated DNA double helix near the surface of a hanging drop, recompaction occurs without perceptible rotation of the DNA. Both conformational change and intermolecular tangling of the DNA are observed when G DNA undergoes nondiffusive motion in a hanging drop. The characteristics of the G DNA flexible filament are explained by the assumption that the flexible filament is a random coil of double helical segments that are unperturbed by motion of the suspending medium.

Bacteriophages↗
PubMed2001

Extrapolation of the dna fragment-size distribution after high-dose irradiation to predict effects at low doses.

The patterns of DSBs induced in the genome are different for sparsely and densely ionizing radiations: In the former case, the patterns are well described by a random-breakage model; in the latter, a more sophisticated tool is needed. We used a Monte Carlo algorithm with a random-walk geometry of chromatin, and a track structure defined by the radial distribution of energy deposition from an incident ion, to fit the PFGE data for fragment-size distribution after high-dose irradiation. These fits determined the unknown parameters of the model, enabling the extrapolation of data for high-dose irradiation to the low doses that are relevant for NASA space radiation research. The randomly-located-clusters formalism was used to speed the simulations. It was shown that only one adjustable parameter, Q, the track efficiency parameter, was necessary to predict DNA fragment sizes for wide ranges of doses. This parameter was determined for a variety of radiations and LETs and was used to predict the DSB patterns at the HPRT locus of the human X chromosome after low-dose irradiation. It was found that high-LET radiation would be more likely than low-LET radiation to induce additional DSBs within the HPRT gene if this gene already contained one DSB.

DNA↗
PubMed2006

Nonrandom movement behavior at habitat boundaries in two butterfly species: implications for dispersal.

We observed meadow brown (Maniola jurtina) and gatekeeper (Pyronia tithonus) butterflies at habitat boundaries and observed spontaneous movements out of suitable habitat in order to investigate such movements in relation to dispersal. We found that butterflies of both species were aware of the position of a highly permeable habitat boundary without needing to cross it. Nevertheless, a considerable proportion of butterflies close to the boundary left their habitat (25-43%). Butterflies that crossed the boundary, and moved substantial distances into unsuitable habitat (up to 350 m in M. jurtina and 70 m in P. tithonus), usually returned to their original habitat patch (98-100%). Movement trajectories, at least in M. jurtina, were significantly different from, and more directed and systematic than, a correlated random walk. Approximately 70-80% of spontaneous movements into unsuitable habitat in both species were "foray" loops comparable to those described in mammals and birds. We conclude that, since migrants seemed to have considerable control over leaving their patch and over their subsequent movement trajectories, chance encounter rates with habitat boundaries, and indeed habitat leaving rates, might be less crucial in determining dispersal rates than is usually assumed. In addition, random dispersal trajectories should not be taken for granted in population or evolution models.

Animals↗
PubMed2005

Survival and relaxation time, pore size distribution moments, and viscous permeability in random unidirectional fiber structures.

Computer simulation results are presented for the mean survival time, principal relaxation time, mean pore size, and mean square pore size, for random porous structures consisting of parallel nonoverlapping or partially overlapping fibers. The numerical procedure is based on a discrete step-by-step random walk mechanism simulating the Brownian diffusion trajectories of molecules in the porous media. Numerical results on the viscous permeability of these structures are computed with a method based on electrical conduction principles and compared to a variational bound derived from the mean survival time. The results show that nonoverlapping fiber structures exhibit lower values of the dimensionless mean survival time, principal relaxation time, mean pore size, and mean square pore size than randomly overlapping fiber structures of the same porosity, while partially overlapping fiber structures show behavior intermediate to those of the two extreme cases. The mean square pore size (second moment of the pore size distribution) is found to be a very good predictor of the mean survival time for non-, partially, and randomly overlapping fiber structures. Dimensionless groups representing the deviation of variational bounds from our simulation results vary in practically the same range as the corresponding values reported earlier for beds of spherical particles. A universal scaling expression of the literature relating the mean survival time to structural properties [S. Torquato and C. L. Y. Yeong, J. Chem. Phys. 106, 8814 (1997)] agrees very well with our results for all examined fiber structures, thus validated for the first time for porous media formed by partially overlapping particles. The permeability behavior of partially overlapping fiber structures resembles that of nonoverlapping fiber structures for flow parallel to the fibers, but not for transverse flow, where percolation phenomena prevail. The permeability results for beds of unidirectional partially overlapping fibers of moderate and low hard-core porosity compliment successfully earlier numerical data on the permeability of similar structures originating from high-porosity beds of nonoverlapping fibers.

Journal Article↗
PubMed2004

Nonlinear effects in the torsional adjustment of interacting DNA.

DNA molecules in solution, having negatively charged phosphates and countercations readsorbed on its surface, possess a distinct charge separation motif to interact electrostatically. If their double-helical structure were ideal, duplexes in parallel juxtaposition could choose azimuthal alignment providing attraction, or at least a reduction of repulsion, between them. But duplexes are not perfect staircases and the distortions of their helical structure correlate with their base pair texts. If the patterns of distortions on the opposing molecules are uncorrelated, the mismatch will accumulate as a random walk and attraction vanishes. Based on this idea, a model of recognition of homologous sequences has been proposed [A. A. Kornyshev and S. Leikin, Phys. Rev. Lett. 86, 3666 (2001)]. But DNA has torsional elasticity. How will this help to relax a mismatch between the charge distributions on two nonhomologous DNA's? In the same work, the solution of this problem has been mapped onto a frustrated sine Gordon equation in a nonlocal random field (where the latter represents a pattern of twist angle distortions on the opposing molecules), but the results had been obtained in the limit of torsionally rigid molecules. In the present paper, by solving this equation numerically, we find a strongly nonlinear relaxation mechanism which utilizes static kink-soliton modes triggered by the "random field." In the range of parameters where the solitons do not emerge, we find good agreement with the results of a variational study [A. G. Cherstvy, A. A. Kornyshev, and S. Leikin, J. Phys. Chem. B (to be published)]. We reproduce the first-order transitions in the interaxial separation dependence, but detect also second-order or weak first-order transitions for shorter duplexes. The recognition energy between two nonhomologous DNA sequences is calculated as a function of interaxial separation and the length of juxtaposition. The soliton-caused kinky length dependence is discussed in connection with plots of recombination frequency as a function of the length of homology.

Binding Sites↗
PubMed2003

Distance, dissimilarity index, and network community structure.

We address the question of finding the community structure of a complex network. In an earlier effort [H. Zhou, Phys. Rev. E 67, 041908 (2003)], the concept of network random walking is introduced and a distance measure defined. Here we calculate, based on this distance measure, the dissimilarity index between nearest-neighboring vertices of a network and design an algorithm to partition these vertices into communities that are hierarchically organized. Each community is characterized by an upper and a lower dissimilarity threshold. The algorithm is applied to several artificial and real-world networks, and excellent results are obtained. In the case of artificially generated random modular networks, this method outperforms the algorithm based on the concept of edge betweenness centrality. For yeast's protein-protein interaction network, we are able to identify many clusters that have well defined biological functions.

Algorithms↗