Elementary derivation of Spitzer's asymptotic law for Brownian windings and some of its physical applications

A simple derivation of Spitzer'z asymptotic law for Brownian windings [Trans.Am.Math.Soc.87,187 (1958)]is presented along with its generalizations >.These include the cases of planar Brownian walks interacting with a single puncture and Brownian walks on a single truncated cone with variable conical angle interacting with the truncated conical tip.Such situations are typical in the theories of quantum Hall effect and 2+1 quantum gravity, respectively .They also have some applications in polymer physic

Conformational transformations induced by the charge-curvature interaction at finite temperature

The role of thermal fluctuations on the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular aggregates may undergo transformation to polygonal shape. The transition occurs both in the case of hardening and softening charge-bending interaction. In the former case the charge and curvature are smoothly distributed along the chain while in the latter spontaneous kink formation is initiated. The transition to a non-circular conformation is analogous to the phase transition of the second kind.Comment: 23 pages (Latex), 10 figures (Postscript), 2 biblio file (bib-file and bbl-file

Veneziano Amplitudes, Spin Chains and String Models

In a series of recently published papers we reanalyzed the existing treatments of Veneziano and Veneziano-like amplitudes and the models associated with these amplitudes. In this work we demonstrate that the already obtained new partition function for these amplitudes can be exactly mapped into that for the Polychronakos-Frahm (P-F) spin chain model. This observation allows us to recover many of the existing string-theoretic models, including the most recent ones.Comment: 38 page

Generating functional analysis of complex formation and dissociation in large protein interaction networks

We analyze large systems of interacting proteins, using techniques from the non-equilibrium statistical mechanics of disordered many-particle systems. Apart from protein production and removal, the most relevant microscopic processes in the proteome are complex formation and dissociation, and the microscopic degrees of freedom are the evolving concentrations of unbound proteins (in multiple post-translational states) and of protein complexes. Here we only include dimer-complexes, for mathematical simplicity, and we draw the network that describes which proteins are reaction partners from an ensemble of random graphs with an arbitrary degree distribution. We show how generating functional analysis methods can be used successfully to derive closed equations for dynamical order parameters, representing an exact macroscopic description of the complex formation and dissociation dynamics in the infinite system limit. We end this paper with a discussion of the possible routes towards solving the nontrivial order parameter equations, either exactly (in specific limits) or approximately.Comment: 14 pages, to be published in Proc of IW-SMI-2009 in Kyoto (Journal of Phys Conference Series

Positional Information Generated by Spatially Distributed Signaling Cascades

The temporal and stationary behavior of protein modification cascades has been extensively studied, yet little is known about the spatial aspects of signal propagation. We have previously shown that the spatial separation of opposing enzymes, such as a kinase and a phosphatase, creates signaling activity gradients. Here we show under what conditions signals stall in the space or robustly propagate through spatially distributed signaling cascades. Robust signal propagation results in activity gradients with long plateaus, which abruptly decay at successive spatial locations. We derive an approximate analytical solution that relates the maximal amplitude and propagation length of each activation profile with the cascade level, protein diffusivity, and the ratio of the opposing enzyme activities. The control of the spatial signal propagation appears to be very different from the control of transient temporal responses for spatially homogenous cascades. For spatially distributed cascades where activating and deactivating enzymes operate far from saturation, the ratio of the opposing enzyme activities is shown to be a key parameter controlling signal propagation. The signaling gradients characteristic for robust signal propagation exemplify a pattern formation mechanism that generates precise spatial guidance for multiple cellular processes and conveys information about the cell size to the nucleus

Bimodal distribution function of a 3d wormlike chain with a fixed orientation of one end

We study the distribution function of the three dimensional wormlike chain with a fixed orientation of one chain end using the exact representation of the distribution function in terms of the Green's function of the quantum rigid rotator in a homogeneous external field. The transverse 1d distribution function of the free chain end displays a bimodal shape in the intermediate range of the chain lengths ($1.3L_{p},...,3.5L_{p}$). We present also analytical results for short and long chains, which are in complete agreement with the results of previous studies obtained using different methods.Comment: 6 pages, 3 figure

Guest charges in an electrolyte: renormalized charge, long- and short-distance behavior of the electric potential and density profile

We complement a recent exact study by L. Samaj on the properties of a guest charge $Q$ immersed in a two-dimensional electrolyte with charges $+1/-1$. In particular, we are interested in the behavior of the density profiles and electric potential created by the charge and the electrolyte, and in the determination of the renormalized charge which is obtained from the long-distance asymptotics of the electric potential. In Samaj's previous work, exact results for arbitrary coulombic coupling $\beta$ were obtained for a system where all the charges are points, provided $\beta Q<2$ and $\beta < 2$. Here, we first focus on the mean field situation which we believe describes correctly the limit $\beta\to 0$ but $\beta Q$ large. In this limit we can study the case when the guest charge is a hard disk and its charge is above the collapse value $\beta Q>2$. We compare our results for the renormalized charge with the exact predictions and we test on a solid ground some conjectures of the previous study. Our study shows that the exact formulas obtained by Samaj for the renormalized charge are not valid for $\beta Q>2$, contrary to a hypothesis put forward by Samaj. We also determine the short-distance asymptotics of the density profiles of the coions and counterions near the guest charge, for arbitrary coulombic coupling. We show that the coion density profile exhibit a change of behavior if the guest charge becomes large enough ($\beta Q\geq 2-\beta$). This is interpreted as a first step of the counterion condensation (for large coulombic coupling), the second step taking place at the usual Manning--Oosawa threshold $\beta Q=2$

Quantifying gene network connectivity in silico: Scalability and accuracy of a modular approach

Large, complex data sets that are generated from microarray experiments, create a need for systematic analysis techniques to unravel the underlying connectivity of gene regulatory networks. A modular approach, previously proposed by Kholodenko and co-workers, helps to scale down the network complexity into more computationally manageable entities called modules. A functional module includes a gene\u27s mRNA, promoter and resulting products, thus encompassing a large set of interacting states. The essential elements of this approach are described in detail for a three-gene model network and later extended to a ten-gene model network, demonstrating scalability. The network architecture is identified by analysing in silico steady-state changes in the activities of only the module outputs, communicating intermediates, that result from specific perturbations applied to the network modules one at a time. These steady-state changes form the system response matrix, which is used to compute the network connectivity or network interaction map. By employing a known biochemical network, the accuracy of the modular approach and its sensitivity to key assumptions are evaluated

A Hidden Feedback in Signaling Cascades Is Revealed

Cycles involving covalent modification of proteins are key components of the intracellular signaling machinery. Each cycle is comprised of two interconvertable forms of a particular protein. A classic signaling pathway is structured by a chain or cascade of basic cycle units in such a way that the activated protein in one cycle promotes the activation of the next protein in the chain, and so on. Starting from a mechanistic kinetic description and using a careful perturbation analysis, we have derived, to our knowledge for the first time, a consistent approximation of the chain with one variable per cycle. The model we derive is distinct from the one that has been in use in the literature for several years, which is a phenomenological extension of the Goldbeter-Koshland biochemical switch. Even though much has been done regarding the mathematical modeling of these systems, our contribution fills a gap between existing models and, in doing so, we have unveiled critical new properties of this type of signaling cascades. A key feature of our new model is that a negative feedback emerges naturally, exerted between each cycle and its predecessor. Due to this negative feedback, the system displays damped temporal oscillations under constant stimulation and, most important, propagates perturbations both forwards and backwards. This last attribute challenges the widespread notion of unidirectionality in signaling cascades. Concrete examples of applications to MAPK cascades are discussed. All these properties are shared by the complete mechanistic description and our simplified model, but not by previously derived phenomenological models of signaling cascades