1,290 research outputs found
Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response
We investigate a stochastic version of a simple enzymatic reaction which
follows the generic Michaelis-Menten kinetics. At sufficiently high
concentrations of reacting species, the molecular fluctuations can be
approximated as a realization of a Brownian dynamics for which the model
reaction kinetics takes on the form of a stochastic differential equation.
After eliminating a fast kinetics, the model can be rephrased into a form of a
one-dimensional overdamped Langevin equation. We discuss physical aspects of
environmental noises acting in such a reduced system, pointing out the
possibility of coexistence of dynamical regimes where noise-enhanced stability
and resonant activation phenomena can be observed together.Comment: 18 pages, 11 figures, published in Physical Review E 74, 041904
(2006
Markovian Dynamics on Complex Reaction Networks
Complex networks, comprised of individual elements that interact with each
other through reaction channels, are ubiquitous across many scientific and
engineering disciplines. Examples include biochemical, pharmacokinetic,
epidemiological, ecological, social, neural, and multi-agent networks. A common
approach to modeling such networks is by a master equation that governs the
dynamic evolution of the joint probability mass function of the underling
population process and naturally leads to Markovian dynamics for such process.
Due however to the nonlinear nature of most reactions, the computation and
analysis of the resulting stochastic population dynamics is a difficult task.
This review article provides a coherent and comprehensive coverage of recently
developed approaches and methods to tackle this problem. After reviewing a
general framework for modeling Markovian reaction networks and giving specific
examples, the authors present numerical and computational techniques capable of
evaluating or approximating the solution of the master equation, discuss a
recently developed approach for studying the stationary behavior of Markovian
reaction networks using a potential energy landscape perspective, and provide
an introduction to the emerging theory of thermodynamic analysis of such
networks. Three representative problems of opinion formation, transcription
regulation, and neural network dynamics are used as illustrative examples.Comment: 52 pages, 11 figures, for freely available MATLAB software, see
http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.htm
Exclusion processes: short range correlations induced by adhesion and contact interactions
We analyze the out-of-equilibrium behavior of exclusion processes where
agents interact with their nearest neighbors, and we study the short-range
correlations which develop because of the exclusion and other contact
interactions. The form of interactions we focus on, including adhesion and
contact-preserving interactions, is especially relevant for migration processes
of living cells. We show the local agent density and nearest-neighbor two-point
correlations resulting from simulations on two dimensional lattices in the
transient regime where agents invade an initially empty space from a source and
in the stationary regime between a source and a sink. We compare the results of
simulations with the corresponding quantities derived from the master equation
of the exclusion processes, and in both cases, we show that, during the
invasion of space by agents, a wave of correlations travels with velocity v(t)
~ t^(-1/2). The relative placement of this wave to the agent density front and
the time dependence of its height may be used to discriminate between different
forms of contact interactions or to quantitatively estimate the intensity of
interactions. We discuss, in the stationary density profile between a full and
an empty reservoir of agents, the presence of a discontinuity close to the
empty reservoir. Then, we develop a method for deriving approximate
hydrodynamic limits of the processes. From the resulting systems of partial
differential equations, we recover the self-similar behavior of the agent
density and correlations during space invasion
Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm.
International audienceABSTRACT: Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. BACKGROUND: There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2) and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different) biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. RESULTS: Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be translated in a set of ordinary differential equations on probability distributions. We developed a C++ software, MaBoSS, that is able to simulate such a system by applying Kinetic Monte-Carlo (or Gillespie algorithm) on the Boolean state space. This software, parallelized and optimized, computes the temporal evolution of probability distributions and estimates stationary distributions. CONCLUSIONS: Applications of the Boolean Kinetic Monte-Carlo are demonstrated for three qualitative models: a toy model, a published model of p53/Mdm2 interaction and a published model of the mammalian cell cycle. Our approach allows to describe kinetic phenomena which were difficult to handle in the original models. In particular, transient effects are represented by time dependent probability distributions, interpretable in terms of cell populations
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