Phase Transition in the Aldous-Shields Model of Growing Trees

We study analytically the late time statistics of the number of particles in a growing tree model introduced by Aldous and Shields. In this model, a cluster grows in continuous time on a binary Cayley tree, starting from the root, by absorbing new particles at the empty perimeter sites at a rate proportional to c^{-l} where c is a positive parameter and l is the distance of the perimeter site from the root. For c=1, this model corresponds to random binary search trees and for c=2 it corresponds to digital search trees in computer science. By introducing a backward Fokker-Planck approach, we calculate the mean and the variance of the number of particles at large times and show that the variance undergoes a `phase transition' at a critical value c=sqrt{2}. While for c>sqrt{2} the variance is proportional to the mean and the distribution is normal, for c<sqrt{2} the variance is anomalously large and the distribution is non-Gaussian due to the appearance of extreme fluctuations. The model is generalized to one where growth occurs on a tree with $m$ branches and, in this more general case, we show that the critical point occurs at c=sqrt{m}.Comment: Latex 17 pages, 6 figure

Ryanodine Receptor Adaptation

In the heart, depolarization during the action potential activates voltage-dependent Ca2+ channels that mediate a small, localized Ca2+ influx (ICa). This small Ca2+ signal activates specialized Ca2+ release channels, the ryanodine receptors (RyRs), in the sarcoplasmic reticulum (SR). This process is called Ca2+-induced Ca2+ release (CICR). Intuitively, the CICR process should be self-regenerating because the Ca2+ released from the SR should feedback and activate further SR Ca2+ release. However, the CICR process is precisely controlled in the heart and, consequently, some sort of negative control mechanism(s) must exist to counter the inherent positive feedback of the CICR process. Defining the nature of this negative control has been a focus of investigation for decades. Several mechanisms have been suggested including all of the following: Ca2+-dependent inactivation, adaptation, stochastic attrition, “fateful” inactivation, SR Ca2+ depletion, and coupled RyR gating. These mechanisms are generally regarded as being mutually exclusive (i.e., alternative). An emerging and more sophisticated view is that the required negative control is probably provided by a synergy of mechanisms, not a single mechanism. In this perspective, we focus on the origin of Ca2+-dependent inactivation and adaptation of single cardiac RyR channels. Specific concerns about the adaptation phenomenon are addressed and a comprehensive unifying view of RyR Ca2+ regulation is forwarded. We conclude that the steady-state Ca2+ dependence, high Ca2+ inactivation and low Ca2+ adaptation are three distinct manifestations of the same underlying mechanism, Ca2+-dependent modal RyR channel gating

Time-resolved x-ray spectroscopy of optical-field-ionized plasmas

The time-dependent soft X-ray emission of helium and nitrogen plasmas generated by optical-field ionization is reported. The experiments were carried out by focusing pulses of the high-power Ti:sapphire laser of the Lund Institute of Technology (lambda = 796 nm, pulse duration 150 fs, pulse energy 150 mJ) to a 50-mu m diameter spot close to a nozzle, using He and N-2 as target gases. The emission on He+, N4+, and N3+ resonance lines was recorded by means of a flat-field grating spectrometer coupled to an X-ray streak camera. A pronounced difference in the temporal shape of the emission of the Lyman-alpha line of hydrogen-like helium and of the 2p-3d resonance lines of lithium-like and beryllium-like nitrogen was observed. The helium line exhibited an initial spike followed by a slow revival of the emission, whereas the nitrogen lines showed a slow decay after a fast initial rise. These observations are explained with the help of simulations

First Passage Properties of the Erdos-Renyi Random Graph

We study the mean time for a random walk to traverse between two arbitrary sites of the Erdos-Renyi random graph. We develop an effective medium approximation that predicts that the mean first-passage time between pairs of nodes, as well as all moments of this first-passage time, are insensitive to the fraction p of occupied links. This prediction qualitatively agrees with numerical simulations away from the percolation threshold. Near the percolation threshold, the statistically meaningful quantity is the mean transit rate, namely, the inverse of the first-passage time. This rate varies non-monotonically with p near the percolation transition. Much of this behavior can be understood by simple heuristic arguments.Comment: 10 pages, 9 figures, 2-column revtex4 forma

Exact field ionization rates in the barrier suppression-regime from numerical TDSE calculations

Numerically determined ionization rates for the field ionization of atomic hydrogen in strong and short laser pulses are presented. The laser pulse intensity reaches the so-called "barrier suppression ionization" regime where field ionization occurs within a few half laser cycles. Comparison of our numerical results with analytical theories frequently used shows poor agreement. An empirical formula for the "barrier suppression ionization"-rate is presented. This rate reproduces very well the course of the numerically determined ground state populations for laser pulses with different length, shape, amplitude, and frequency. Number(s): 32.80.RmComment: Enlarged and newly revised version, 22 pages (REVTeX) + 8 figures in ps-format, submitted for publication to Physical Review A, WWW: http://www.physik.tu-darmstadt.de/tqe

Exact eigenvalue spectrum of a class of fractal scale-free networks

The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine all the eigenvalues and their degeneracies. We then use these eigenvalues to evaluate the closed-form solution to the eigentime for random walks on the networks under consideration. Through the connection between the spectrum of transition matrix and the number of spanning trees, we corroborate the obtained eigenvalues and their multiplicities.Comment: Definitive version accepted for publication in EPL (Europhysics Letters

Ligand sensitivity of type-1 inositol 1,4,5-trisphosphate receptor is enhanced by the D2594K mutation.

Inositol 1,4,5-trisphosphate receptor (IP3R) and ryanodine receptor (RyR) are homologous cation channels that mediate release of Ca2+ from the endoplasmic/sarcoplasmic reticulum (ER/SR) and thereby are involved in many physiological processes. In previous studies, we determined that when the D2594 residue, located at or near the gate of the IP3R type 1, was replaced by lysine (D2594K), a gain of function was obtained. This mutant phenotype was characterized by increased IP3 sensitivity. We hypothesized the IP3R1-D2594 determines the ligand sensitivity of the channel by electrostatically affecting the stability of the closed and open states. To test this possibility, the relationship between the D2594 site and IP3R1 regulation by IP3, cytosolic, and luminal Ca2+ was determined at the cellular, subcellular, and single-channel levels using fluorescence Ca2+ imaging and single-channel reconstitution. We found that in cells, D2594K mutation enhances the IP3 ligand sensitivity. Single-channel IP3R1 studies revealed that the conductance of IP3R1-WT and -D2594K channels is similar. However, IP3R1-D2594K channels exhibit higher IP3 sensitivity, with substantially greater efficacy. In addition, like its wild type (WT) counterpart, IP3R1-D2594K showed a bell-shape cytosolic Ca2+-dependency, but D2594K had greater activity at each tested cytosolic free Ca2+ concentration. The IP3R1-D2594K also had altered luminal Ca2+ sensitivity. Unlike IP3R1-WT, D2594K channel activity did not decrease at low luminal Ca2+ levels. Taken together, our functional studies indicate that the substitution of a negatively charged residue by a positive one at the channels' pore cytosolic exit affects the channel's gating behavior thereby explaining the enhanced ligand-channel's sensitivity.The authors received the support of research grants from the National Institutes of Health grant/award numbers R01GM111397 to S. R. W. Chen, M. Fill, and J. Ramos‐Franco, R01HL057832 to M. Fill and by the Canadian Institutes of Health Research, grant/award number PJT‐173352. S. R. W. Chen holds the Heart and Stroke Foundation Chair in Cardiovascular Research (END611955). A. Tambeaux was supported by the Graduate College of Rush University Medical Center.S