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At least 451 records · Page 25Linked to original sources
PubMed2000

Multiscale random-walk algorithm for simulating interfacial pattern formation.

We present a novel computational method to simulate accurately a wide range of interfacial patterns whose growth is limited by a large-scale diffusion field. To illustrate the computational power of this method, we demonstrate that it can be used to simulate three-dimensional dendritic growth in a previously unreachable range of low undercoolings that is of direct experimental relevance.

Algorithms↗
PubMed2003

Absorbing phase transitions of branching-annihilating random walks.

The phase transitions to absorbing states of the branching-annihilating reaction-diffusion processes mA-->(m+k)A, nA-->(n-l)A are studied systematically in one space dimension within a new family of models. Four universality classes of nontrivial critical behavior are found. This provides, in particular, the first evidence of universal scaling laws for pair and triplet processes.

Journal Article↗
PubMed2005

First-passage times for random walks in bounded domains.

We present a novel computational method of first-passage times between a starting site and a target site of regular bounded lattices. We derive accurate expressions for all the moments of this first-passage time, validated by numerical simulations. Their range of validity is discussed. We also consider the case of a starting site and two targets. In addition, we present the extension to continuous Brownian motion. These results are of great relevance to any system involving diffusion in confined media.

Journal Article↗
PubMed1988

Exact random-walk models in crystallographic statistics. IV. P.d.f.'s of [E] allowing for atoms in special positions.

The effect of scatterers, located in variable special positions, on the probability density function of the magnitude of the normalized structure factor has been investigated. Exact characteristic functions have been obtained for all the statistically different variable special positions in triclinic, monoclinic and ortho-rhombic space groups except in Fdd2 and in the space groups based on the point group 222, and the probability density functions have been evaluated from their Fourier or Fourier-Bessel series expansions. It is seen that the effect of heavy scatterers, located in the special positions investigated, is very marked and should be accounted for in cases of space-group ambiguities.

Crystallography↗
PubMed1990

Exact random-walk models in crystallographic statistics. V. Non-symmetrically bounded distributions of structure-factor magnitudes.

Derivations of exactly formulated Fourier-series representations of probability density functions (p.d.f.'s) of the magnitude of the structure factor are based on the fact that the structure factor and its real and imaginary parts are bounded. In some situations the bounds of the real and imaginary parts of the structure factor are different, and this gives rise to modified forms of the p.d.f.'s. Three physical examples that call for such modifications are investigated: (i) effect of dispersive scatterers on the p.d.f. of a centrosymmetric structure factor, (ii) effect of the presence of a centrosymmetric fragment in the asymmetric unit of a non-centrosymmetric space group, and (iii) effect of heavy scatterers in special positions of a non-centrosymmetric space group, where the imaginary part of the trigonometric structure factor for these special positions vanishes by symmetry. The general form of an exact Fourier p.d.f., taking account of such modifications, is derived, and expressions for Fourier coefficients are obtained for selected examples of the above three situations. It is seen that the effects of pseudocentrosymmetry may be most pronounced and those of dispersion are significant mainly in the range of small values of the structure factor.

Data Interpretation, Statistical↗
PubMed1991

Exact random-walk models in crystallographic statistics. VI. P.D.F.'s of magnitude of [E] for all plane groups and most space groups.

An exact calculation of the probability density function (p.d.f.) of magnitude of [E], the magnitude of the normalized structure factor, can be developed in terms of Fourier and Fourier-Bessel series whose coefficients can be expressed in terms of the characteristic function. This article provides the formulae for atomic contributions to such characteristic functions. The results presented in this study are applicable to all the plane groups and to 206 three dimensional space groups. Only the space groups isomorphous to the cubic point groups 432, 43m and m3m were omitted due to the complexity of the resulting expressions and the small deviations of the corresponding densities from the central-limit-theorem approximation, which have been observed in simulations for extreme atomic heterogeneities. Representative derivations illustrating the problems and techniques of their solution are provided. All the theoretical results have been computed numerically and compared with simulated distributions. Some results of these computations are illustrated in the accompanying paper, Part VII of this series [Rabinovich, Shmueli, Stein, Shashua & Weiss (1991). Acta Cryst. A47, 336-340].

Fourier Analysis↗
PubMed1991

Exact random-walk models in crystallographic statistics. VII. An all-space-group study of the effects of atomic heterogeneity on the P.D.F.'s of magnitude of [E].

Exact expressions have been found for the probability density functions (p.d.f.'s) of the magnitude of the normalized structure factor for all the two-dimensional and most three-dimensional space groups [Part VI: Rabinovich, Shmueli, Stein, Shashua & Weiss (1991). Acta Cryst. A47, 328-335]. The results of that investigation are used in the present article to examine some effects of atomic heterogeneity, in the various space-group symmetries, on the p.d.f.'s. Some typical comparisons are made between p.d.f.'s based on the central limit theorem and p.d.f.'s computed from exact formulae. In addition, the exact results are compared to histograms of simulated values of magnitude of [E]. It is found that the p.d.f.'s for some space groups are influenced rather strongly by the presence of outstandingly heavy scatters, but they are quite insensitive to the presence of such scatterers in other space groups. The often made general statement 'The presence of outstandingly heavy scatterers may invalidate the indications of Wilson's statistics' is made more precise here, insofar as it depends on the particular space group.

Fourier Analysis↗
PubMed2001

A random walk through models of nonlinear clustering.

A few simple models of the mass function of collapsed objects are presented. The emphasis is on apparently unrelated models which end up giving the same answer for the number density and merger histories of virialized clumps. Models of the spatial distribution of the clumps and how they can be used to model the spatial distribution of the mass are briefly discussed.

Journal Article↗
PubMed2005

Modeling the signaling endosome hypothesis: why a drive to the nucleus is better than a (random) walk.

BACKGROUND: Information transfer from the plasma membrane to the nucleus is a universal cell biological property. Such information is generally encoded in the form of post-translationally modified protein messengers. Textbook signaling models typically depend upon the diffusion of molecular signals from the site of initiation at the plasma membrane to the site of effector function within the nucleus. However, such models fail to consider several critical constraints placed upon diffusion by the cellular milieu, including the likelihood of signal termination by dephosphorylation. In contrast, signaling associated with retrogradely transported membrane-bounded organelles such as endosomes provides a dephosphorylation-resistant mechanism for the vectorial transmission of molecular signals. We explore the relative efficiencies of signal diffusion versus retrograde transport of signaling endosomes. RESULTS: Using large-scale Monte Carlo simulations of diffusing STAT-3 molecules coupled with probabilistic modeling of dephosphorylation kinetics we found that predicted theoretical measures of STAT-3 diffusion likely overestimate the effective range of this signal. Compared to the inherently nucleus-directed movement of retrogradely transported signaling endosomes, diffusion of STAT-3 becomes less efficient at information transfer in spatial domains greater than 200 nanometers from the plasma membrane. CONCLUSION: Our model suggests that cells might utilize two distinct information transmission paradigms: 1) fast local signaling via diffusion over spatial domains on the order of less than 200 nanometers; 2) long-distance signaling via information packets associated with the cytoskeletal transport apparatus. Our model supports previous observations suggesting that the signaling endosome hypothesis is a subset of a more general hypothesis that the most efficient mechanism for intracellular signaling-at-a-distance involves the association of signaling molecules with molecular motors that move along the cytoskeleton. Importantly, however, cytoskeletal association of membrane-bounded complexes containing ligand-occupied transmembrane receptors and downstream effector molecules provides the ability to regenerate signals at any point along the transmission path. We conclude that signaling endosomes provide unique information transmission properties relevant to all cell architectures, and we propose that the majority of relevant information transmitted from the plasma membrane to the nucleus will be found in association with organelles of endocytic origin.

Animals↗
PubMed2004

Anomalous diffusion in a gel-fluid lipid environment: a combined solid-state NMR and obstructed random-walk perspective.

Lateral diffusion is an essential process for the functioning of biological membranes. Solid-state nuclear magnetic resonance (NMR) is, a priori, a well-suited technique to study lateral diffusion within a heterogeneous environment such as the cell membrane. Moreover, restriction of lateral motions by lateral heterogeneities can be used as a means to characterize their geometry. The goal of this work is to understand the advantages and limitations of solid-state NMR exchange experiments in the study of obstructed lateral diffusion in model membranes. For this purpose, simulations of lateral diffusion on a sphere with varying numbers and sizes of immobile obstacles and different percolation properties were performed. From the results of these simulations, two-dimensional 31P NMR exchange maps and time-dependent autocorrelation functions were calculated. The results indicate that the technique is highly sensitive to percolation properties, total obstacle area, and, within certain limits, obstacle size. A practical example is shown, namely the study of the well-characterized DMPC-DSPC binary mixture. The comparison of experimental and simulated results yielded obstacle sizes in the range of hundreds of nanometers, therefore bridging the gap between previously published NMR and fluorescence recovery after photobleaching results. The method could also be applied to the study of membrane protein lateral diffusion in model membranes.

Algorithms↗