A continuous model for microtubule dynamics with catastrophe, rescue and nucleation processes

Microtubules are a major component of the cytoskeleton distinguished by highly dynamic behavior both in vitro and in vivo. We propose a general mathematical model that accounts for the growth, catastrophe, rescue and nucleation processes in the polymerization of microtubules from tubulin dimers. Our model is an extension of various mathematical models developed earlier formulated in order to capture and unify the various aspects of tubulin polymerization including the dynamic instability, growth of microtubules to saturation, time-localized periods of nucleation and depolymerization as well as synchronized oscillations exhibited by microtubules under various experimental conditions. Our model, while attempting to use a minimal number of adjustable parameters, covers a broad range of behaviors and has predictive features discussed in the paper. We have analyzed the resultant behaviors of the microtubules changing each of the parameter values at a time and observing the emergence of various dynamical regimes.Comment: 25 pages, 12 figure

Quantum corrections to static solutions of Nahm equation and Sin-Gordon models via generalized zeta-function

One-dimensional Yang-Mills Equations are considered from a point of view of a class of nonlinear Klein-Gordon-Fock models. The case of self-dual Nahm equations and non-self-dual models are discussed. A quasiclassical quantization of the models is performed by means of generalized zeta-function and its representation in terms of a Green function diagonal for a heat equation with the correspondent potential. It is used to evaluate the functional integral and quantum corrections to mass in the quasiclassical approximation. Quantum corrections to a few periodic (and kink) solutions of the Nahm as a particular case of the Ginzburg-Landau (phi-in-quadro) and and Sin-Gordon models are evaluated in arbitrary dimensions. The Green function diagonal for heat equation with a finite-gap potential is constructed by universal description via solutions of Hermit equation. An alternative approach based on Baker-Akhiezer functions for KP equation is proposed . The generalized zeta-function and its derivative at zero point as the quantum corrections to mass is expressed in terms of elliptic integrals.Comment: Workshop Nonlinear Physics and Experiment; Gallipoli, 200

High-Temperature Expansions of Bures and Fisher Information Priors

For certain infinite and finite-dimensional thermal systems, we obtain --- incorporating quantum-theoretic considerations into Bayesian thermostatistical investigations of Lavenda --- high-temperature expansions of priors over inverse temperature beta induced by volume elements ("quantum Jeffreys' priors) of Bures metrics. Similarly to Lavenda's results based on volume elements (Jeffreys' priors) of (classical) Fisher information metrics, we find that in the limit beta -> 0, the quantum-theoretic priors either conform to Jeffreys' rule for variables over [0,infinity], by being proportional to 1/beta, or to the Bayes-Laplace principle of insufficient reason, by being constant. Whether a system adheres to one rule or to the other appears to depend upon its number of degrees of freedom.Comment: Six pages, LaTeX. The title has been shortened (and then further modified), at the suggestion of a colleague. Other minor change

\lambda-transition in low dimensional systems with SU_q(2) symmetry

We show that $SU_q(2)$ invariant systems in one and two dimensions exhibit Bose-Einstein condensation for $q >1$. For these systems there is a $\lambda$-transition at the critical temperature. The critical temperature and the gap in the heat capacity increase more rapidly for small deviations from the standard value $q=1$, and they become approximately constant for large values of $q$. For low temperatures and $q>1$ the entropy is lower than the entropy of an ideal Bose gas.Comment: LaTeX file, 15 pages, four figures, uses epsf.st

Cellular automata modelling of slime mould actin network signalling

© 2016, The Author(s). Actin is a cytoskeletal protein which forms dense, highly interconnected networks within eukaryotic cells. A growing body of evidence suggests that actin-mediated intra- and extracellular signalling is instrumental in facilitating organism-level emergent behaviour patterns which, crucially, may be characterised as natural expressions of computation. We use excitable cellular automata modelling to simulate signal transmission through cell arrays whose topology was extracted from images of Watershed transformation-derived actin network reconstructions; the actin networks sampled were from laboratory experimental observations of a model organism, slime mould Physarum polycephalum. Our results indicate that actin networks support directional transmission of generalised energetic phenomena, the amplification and trans-network speed of which of which is proportional to network density (whose primary determinant is the anatomical location of the network sampled). Furthermore, this model also suggests the ability of such networks for supporting signal-signal interactions which may be characterised as Boolean logical operations, thus indicating that a cell’s actin network may function as a nanoscale data transmission and processing network. We conclude by discussing the role of the cytoskeleton in facilitating intracellular computing, how computation can be implemented in such a network and practical considerations for designing ‘useful’ actin circuitry

Logical gates in actin monomer

© 2017 The Author(s). We evaluate information processing capacity of a single actin molecule by calculating distributions of logical gates implemented by the molecule via propagating patterns of excitation. We represent a filamentous actin molecule as an excitable automaton network (F-actin automaton). where every atom updates its state depending on states of atoms its connected to with chemical bonds (hard neighbours) and atoms being in physical proximity to the atom (soft neighbours). A resting atom excites if a sum of its excited hard neighbours and a weighted sum of its soft neighbours belong to some specified interval. We demonstrate that F-actin automata implement OR, AND, XOR and AND-NOT gates via interacting patterns of excitation. Gate AND is the most common gate and gate XOR is the rarest. Using the architectures of gates discovered we implement one bit half-adder and controlled-not circuits in the F-actin automata. Speed and space values of the F-actin molecular computers are discussed

Analytic structure factors and pair-correlation functions for the unpolarized homogeneous electron gas

We propose a simple and accurate model for the electron static structure factors (and corresponding pair-correlation functions) of the 3D unpolarized homogeneous electron gas. Our spin-resolved pair-correlation function is built up with a combination of analytic constraints and fitting procedures to quantum Monte Carlo data, and, in comparison to previous attempts (i) fulfills more known integral and differential properties of the exact pair-correlation function, (ii) is analytic both in real and in reciprocal space, and (iii) accurately interpolates the newest, extensive diffusion-Monte Carlo data of Ortiz, Harris and Ballone [Phys. Rev. Lett. 82, 5317 (1999)]. This can be of interest for the study of electron correlations of real materials and for the construction of new exchange and correlation energy density functionals.Comment: 14 pages, 5 figures, submitted to Phys. Rev.