Dynamics of molecular diffusion of rhodamine 6G in silica nanochannels.

We describe a method to study diffusion of rhodamine 6G dye in single silica nanochannels using arrays of silica nanochannels. Dynamics of the molecules inside single nanochannel is found from the change of the dye concentration in solution with time. A 10(8) decrease in the dye diffusion coefficient relative to water was observed. In comparison to single fluorescent molecule studies, the presented method does not require fluorescence of the diffusing molecules.

Alternatively spliced isoforms of a novel stromal RNA regulating factor.

Bone marrow stromal cells (MSC) are pluripotent cells that possess a unique capacity to differentiate under appropriate conditions into various lineages. The MSC differentiation is dependent on factors that can switch on and maintain a relevant genetic program to make a particular cell type. The present study describes the cloning and molecular analysis of a novel gene, SRRF (Stromal RNA Regulating Factor), suggested to be involved in RNA processing in MSC. We cloned two alternatively spliced isoforms of this gene, transcripts A and B, from the marrow stromal cells expression library. Differential expression analysis demonstrated a restricted expression of the transcripts to MSC, while other spliced forms of this gene were detected in other tissues. The bioinformatic analysis of the two isoforms revealed RNA binding motifs (RRM), protein-protein and protein-DNA interaction motifs. Participation of SRRF isoforms in post-transcriptional events in MSC is believed to govern the tissue specificity of RNA transcription and to have an important role in regulation of the RNA expression that directs the MSC differentiation pathway.

Percolation in directed scale-free networks.

Many complex networks in nature have directed links, a property that affects the network's navigability and large-scale topology. Here we study the percolation properties of such directed scale-free networks with correlated in and out degree distributions. We derive a phase diagram that indicates the existence of three regimes, determined by the values of the degree exponents. In the first regime we regain the known directed percolation mean field exponents. In contrast, the second and third regimes are characterized by anomalous exponents, which we calculate analytically. In the third regime the network is resilient to random dilution, i.e., the percolation threshold is p(c)-->1.

Correlation functions for diffusion-limited annihilation, A+A-->0.

The full hierarchy of multiple-point correlation functions for diffusion-limited annihilation, A+A-->0, is obtained analytically and explicitly, following the method of intervals. In the long-time asymptotic limit, the correlation functions of annihilation are identical to those of coalescence, A+A-->A, despite differences between the two models in other statistical measures, such as the interparticle distribution function.

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.

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.

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.

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.

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 alpha0.99.

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.

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.

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.

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.