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Biomedical subjects

D ben-Avraham

Publications and source records attributed to D ben-Avraham.

At least 19 recordsLinked to original sources
PubMed2001

Continuously variable survival exponent for random walks with movable partial reflectors.

We study a one-dimensional lattice random walk with an absorbing boundary at the origin and a movable partial reflector. On encountering the reflector at site x, the walker is reflected (with probability r) to x-1 and the reflector is simultaneously pushed to x+1. Iteration of the transition matrix, and asymptotic analysis of the probability generating function show that the critical exponent delta governing the survival probability varies continuously between 1/2 and 1 as r varies between 0 and 1. Our study suggests a mechanism for nonuniversal kinetic critical behavior, observed in models with an infinite number of absorbing configurations.

Journal Article↗
PubMed2001

Solution of the modified Helmholtz equation in a triangular domain and an application to diffusion-limited coalescence.

A new transform method for solving boundary value problems for linear and integrable nonlinear partial differential equations recently introduced in the literature is used here to obtain the solution of the modified Helmholtz equation q(xx)(x,y)+q(yy)(x,y)-4 beta(2)q(x,y)=0 in the triangular domain 0< or =x< or =L-y< or =L, with mixed boundary conditions. This solution is applied to the problem of diffusion-limited coalescence, A+A<==>A, in the segment (-L/2,L/2), with traps at the edges.

Journal Article↗
PubMed2001

Method of intervals for the study of diffusion-limited annihilation, A+A-->0.

We introduce a method of intervals for the analysis of diffusion-limited annihilation, A+A-->0, on the line. The method leads to manageable diffusion equations whose interpretation is intuitively clear. As an example, we treat the following cases: (a) annihilation in the infinite line and in infinite (discrete) chains; (b) annihilation with input of single particles, adjacent particle pairs, and particle pairs separated by a given distance; (c) annihilation, A+A-->0, along with the birth reaction A-->3A, on finite rings, with and without diffusion.

Journal Article↗
PubMed2001

Breakdown of the internet under intentional attack.

We study the tolerance of random networks to intentional attack, whereby a fraction p of the most connected sites is removed. We focus on scale-free networks, having connectivity distribution P(k) approximately k(-alpha), and use percolation theory to study analytically and numerically the critical fraction p(c) needed for the disintegration of the network, as well as the size of the largest connected cluster. We find that even networks with alpha < or = 3, known to be resilient to random removal of sites, are sensitive to intentional attack. We also argue that, near criticality, the average distance between sites in the spanning (largest) cluster scales with its mass, M, as square root of [M], rather than as log (k)M, as expected for random networks away from criticality.

Computer Security↗
PubMed2000

Resilience of the internet to random breakdowns

A common property of many large networks, including the Internet, is that the connectivity of the various nodes follows a scale-free power-law distribution, P(k) = ck(-alpha). We study the stability of such networks with respect to crashes, such as random removal of sites. Our approach, based on percolation theory, leads to a general condition for the critical fraction of nodes, p(c), that needs to be removed before the network disintegrates. We show analytically and numerically that for alpha</=3 the transition never takes place, unless the network is finite. In the special case of the physical structure of the Internet (alpha approximately 2.5), we find that it is impressively robust, with p(c)>0.99.

Journal Article↗
PubMed2000

Trafficking and signaling through the cytoskeleton: a specific mechanism.

A specific mechanism for the intracellular translocation of nonvesicle-associated proteins is proposed. This movement machinery is based on the assumption that the cytoskeleton represents an interconnected network of filamentous macromolecules, which extends over the entire cytoplasm. Diffusion along the filaments provides an efficient way for movement and with this, for signal transduction, between various intracellular compartments. We calculate the First Passage Time (FPT), the average time it takes a signaling molecule, diffusing along the cytoskeleton, to arrive from the cell surface to the nucleus for the first time. We compare our results with the FPT of free diffusion and of diffusion in the permeating cytoplasm. The latter is hindered by intracellular organelles and the cytoskeleton itself. We find that for filament concentrations even below physiological values, the FPT along cytoskeletal filaments converges to that for free diffusion. When filaments are considered as obstacles, the FPT grows steadily with filament concentration. At realistic filament concentrations the FPT is insensitive to local modifications in the cytoskeletal network, including bundle formation. We conclude that diffusion along cytoskeletal tracks is a reliable alternative to other established ways of intracellular trafficking and signaling, and therefore provides an additional level of cell function regulation.

Actin Cytoskeleton↗
PubMed1995

Normal modes as refinement parameters for the F-actin model.

The slow normal modes of G-actin were used as structural parameters to refine the F-actin model against 8-A resolution x-ray fiber diffraction data. The slowest frequency normal modes of G-actin pertain to collective rearrangements of domains, motions that are characterized by correlation lengths on the order of the resolution of the fiber diffraction data. Using a small number of normal mode degrees of freedom (< or = 12) improved the fit to the data significantly. The refined model of F-actin shows that the nucleotide binding cleft has narrowed and that the DNase I binding loop has twisted to a lower radius, consistent with other refinement techniques and electron microscopy data. The methodology of a normal mode refinement is described, and the results, as applied to actin, are detailed.

Actins↗
PubMed1995

Dynamic and elastic properties of F-actin: a normal-modes analysis.

We examine the dynamic, elastic, and mechanical consequences of the proposed atomic models of F-actin, using a normal mode analysis. This initial analysis is done in vacuo and assumes that all monomers are rigid and equivalent. Our computation proceeds from the atomic level and, relying on a single fitting parameter, reproduces various experimental results, including persistence lengths, elastic moduli, and contact energies. The computations reveal modes of motion characteristic to all polymers, such as longitudinal pressure waves, torsional waves, and bending, as well as motions unique to F-actin. Motions typical to actin include a "groove-swinging" motion of the two long-pitch helices, as well as an axial slipping motion of the two strands. We prepare snapshots of thermally activated filaments and quantify the accumulation of azimuthal angular "disorder," variations in cross-over lengths, and various other fluctuations. We find that the orientation of a small number of select residues has a surprisingly large effect on the filament flexibility and elasticity characteristics.

Actins↗
PubMed1993

Normal mode analysis of G-actin.

We undertook a normal mode analysis of the G-actin monomer bound with ADP and Ca2+, in order to better understand the internal modes of this protein. The internal co-ordinates consisted of 1373 single bond torsions, plus an additional 11 torsions to parameterize the motion of the nucleotide and cation with respect to the protein. A generalized eigenvalue problem was solved to yield a complete description of the motion in the 0.1 to 17.0 picosecond time range. The modes were visualized using an interactive graphics routine. The softest, slowest modes include a propeller-like twisting of the large and small domain about the phosphate binding loops, a rolling of subdomain 4 about an alpha-helix axis and a scissor-type opening and closing of the ADP-binding cleft. The computed temperature factors agree well with experimental ones. A comparable analysis done on G-actin-ATP shows that the softest modes are almost identical.

Actins↗