Phase Transitions Induced by Diversity and Examples in Biological Systems

Tesis leída en l'Universitat de les Illes Balears en diciembre de 2010The present thesis covers various topics that range over di erent aspects of scientific research. On one end there is the specific analysis of a precise form that models some experimental observations. A good theoretical understanding of the mathematics that describe the observations can be a guide to the experimentalist and help estimate the validity of the measurements. On the other end there are abstract models whose relation to physical systems seem far but they are prototypic for a broad range of di erent systems and the drawn conclusions tend to be quite general. Depending on the abstraction and on the simplifications in use the distinction between both ends might not be sharp. The ordering of the research results presented in part II of this thesis somehow reflects the seamless transition from one end to the other. To introduce the reader into the context of the genuine results we provide introductory material in the chapters of the present part I.Peer reviewe

Synchronization and entrainment of coupled circadian oscillators

Circadian rhythms in mammals are controlled by the neurons located in the suprachiasmatic nucleus of the hypothalamus. In physiological conditions, the system of neurons is very efficiently entrained by the 24-hour light-dark cycle. Most of the studies carried out so far emphasize the crucial role of the periodicity imposed by the light dark cycle in neuronal synchronization. Nevertheless, heterogeneity as a natural and permanent ingredient of these cellular interactions is seemingly to play a major role in these biochemical processes. In this paper we use a model that considers the neurons of the suprachiasmatic nucleus as chemically-coupled modified Goodwin oscillators, and introduce non-negligible heterogeneity in the periods of all neurons in the form of quenched noise. The system response to the light-dark cycle periodicity is studied as a function of the interneuronal coupling strength, external forcing amplitude and neuronal heterogeneity. Our results indicate that the right amount of heterogeneity helps the extended system to respond globally in a more coherent way to the external forcing. Our proposed mechanism for neuronal synchronization under external periodic forcing is based on heterogeneity-induced oscillators death, damped oscillators being more entrainable by the external forcing than the self-oscillating neurons with different periods.Comment: 17 pages, 7 figure

Order parameter expansion study of synchronous firing induced by quenched noise in the active rotator model

We use a recently developed order parameter expansion method to study the transition to synchronous firing occuring in a system of coupled active rotators under the exclusive presence of quenched noise. The method predicts correctly the existence of a transition from a rest state to a regime of synchronous firing and another transition out of it as the intensity of the quenched noise increases and leads to analytical expressions for the critical noise intensities in the large coupling regime. It also predicts the order of the transitions for different probability distribution functions of the quenched variables. We use numerical simulations and finite size scaling theory to estimate the critical exponents of the transitions and found values which are consistent with those reported in other scalar systems in the exclusive presence of additive static disorder

Advantages of Hopping on a Zig-zag Course

We investigate self-moving particles which prefer to hop with a certain turning angle equally distributed to the right or left. We assume this turning angle distribution to be given by a double Gaussian distribution. Based on the model of Active Brownian particles and we calculate the diffusion coefficient in dependence on the mean and the dispersion of the turning angles. It is shown that bounded distribution of food in patches will be optimally consumed by the objects if they hop preferably with a given angle and not straight forwardly.Comment: 10 pages, 3 figures, accepted to be published in Physica

Drug absorption through a cell monolayer: a theoretical work on a non-linear three-compartment model

The subject of analysis is a non-linear three-compartment model, widely used in pharmacological absorption studies. It has been transformed into a general form, thus leading automatically to an appropriate approximation. This made the absorption profile accessible and expressions for absorption times, apparent permeabilities and equilibrium values were given. These findings allowed a profound analysis of results from non-linear curve fits and delivered the dependencies on the systems' parameters over a wide range of values. The results were applied to an absorption experiment with multidrug transporter-affected antibiotic CNV97100 on Caco-2 cell monolayers.Comment: 21 pages, 8 figures (v4: detailed definition of the treated model - additional information about limitations

Critical behavior of a Ginzburg-Landau model with additive quenched noise

We address a mean-field zero-temperature Ginzburg-Landau, or \phi^4, model subjected to quenched additive noise, which has been used recently as a framework for analyzing collective effects induced by diversity. We first make use of a self-consistent theory to calculate the phase diagram of the system, predicting the onset of an order-disorder critical transition at a critical value {\sigma}c of the quenched noise intensity \sigma, with critical exponents that follow Landau theory of thermal phase transitions. We subsequently perform a numerical integration of the system's dynamical variables in order to compare the analytical results (valid in the thermodynamic limit and associated to the ground state of the global Lyapunov potential) with the stationary state of the (finite size) system. In the region of the parameter space where metastability is absent (and therefore the stationary state coincide with the ground state of the Lyapunov potential), a finite-size scaling analysis of the order parameter fluctuations suggests that the magnetic susceptibility diverges quadratically in the vicinity of the transition, what constitutes a violation of the fluctuation-dissipation relation. We derive an effective Hamiltonian and accordingly argue that its functional form does not allow to straightforwardly relate the order parameter fluctuations to the linear response of the system, at odds with equilibrium theory. In the region of the parameter space where the system is susceptible to have a large number of metastable states (and therefore the stationary state does not necessarily correspond to the ground state of the global Lyapunov potential), we numerically find a phase diagram that strongly depends on the initial conditions of the dynamical variables.Comment: 8 figure

Phase transitions induced by microscopic disorder: a study based on the order parameter expansion

Based on the order parameter expansion, we present an approximate method which allows us to reduce large systems of coupled differential equations with diverse parameters to three equations: one for the global, mean field, variable and two which describe the fluctuations around this mean value. With this tool we analyze phase-transitions induced by microscopic disorder in three prototypical models of phase-transitions which have been studied previously in the presence of thermal noise. We study how macroscopic order is induced or destroyed by time independent local disorder and analyze the limits of the approximation by comparing the results with the numerical solutions of the self-consistency equation which arises from the property of self-averaging. Finally, we carry on a finite-size analysis of the numerical results and calculate the corresponding critical exponents

Stochastic and Non-linear effects in Biological Systems

Memoria de investigación presentada por Niko Komin, en el Departamento de Física de la UIB, el 22 de octubre 2008.This work deals with two different fields of research. The first is dedicated to the modelling of motion found in biology. We will give a short introduction to the topic and present two possible ways to describe biological motion. Both were inspired by the research on swarming in the Humboldt University Berlin and applied to model the motion of the water flea (Daphnia). One of them is presented in more detail in chapter 2. The second field of research is related to the work at the IFISC (UIB-CSIC) within the BioSim network. It is about drug absorption through cell monolayers. In this introduction we will introduce some aspects of biological research at the level of dynamical systems and present the results from the analysis of a drug absorption model in chapter 3Peer reviewe

How to address cellular heterogeneity by distribution biology

Cellular heterogeneity is an immanent property of biological systems that covers very different aspects of life ranging from genetic diversity to cell-to-cell variability driven by stochastic molecular interactions, and noise induced cell differentiation. Here, we review recent developments in characterizing cellular heterogeneity by distributions and argue that understanding multicellular life requires the analysis of heterogeneity dy- namics at single cell resolution by integrative approaches that combine methods from non-equilibrium statistical physics, in- formation theory and omics biology