5,590 research outputs found
Finite-Time Stability Analysis of Switched Genetic Regulatory Networks
This paper investigates the finite-time stability problem of switching genetic regulatory networks (GRNs) with interval time-varying delays and unbounded continuous distributed delays. Based on the piecewise Lyapunov-Krasovskii functional and the average dwell time method, some new finite-time stability criteria are obtained in the form of linear matrix inequalities (LMIs), which are easy to be confirmed by the Matlab toolbox. The finite-time stability is taken into account in switching genetic regulatory networks for the first time and the average dwell time of the switching signal is obtained. Two numerical examples are presented to illustrate the
effectiveness of our results
Recommended from our members
Filtering for nonlinear genetic regulatory networks with stochastic disturbances
In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures
Time-and event-driven communication process for networked control systems: A survey
Copyright © 2014 Lei Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany
Compositionality, stochasticity and cooperativity in dynamic models of gene regulation
We present an approach for constructing dynamic models for the simulation of
gene regulatory networks from simple computational elements. Each element is
called a ``gene gate'' and defines an input/output-relationship corresponding
to the binding and production of transcription factors. The proposed reaction
kinetics of the gene gates can be mapped onto stochastic processes and the
standard ode-description. While the ode-approach requires fixing the system's
topology before its correct implementation, expressing them in stochastic
pi-calculus leads to a fully compositional scheme: network elements become
autonomous and only the input/output relationships fix their wiring. The
modularity of our approach allows to pass easily from a basic first-level
description to refined models which capture more details of the biological
system. As an illustrative application we present the stochastic repressilator,
an artificial cellular clock, which oscillates readily without any cooperative
effects.Comment: 15 pages, 8 figures. Accepted by the HFSP journal (13/09/07
A self-organized model for cell-differentiation based on variations of molecular decay rates
Systemic properties of living cells are the result of molecular dynamics
governed by so-called genetic regulatory networks (GRN). These networks capture
all possible features of cells and are responsible for the immense levels of
adaptation characteristic to living systems. At any point in time only small
subsets of these networks are active. Any active subset of the GRN leads to the
expression of particular sets of molecules (expression modes). The subsets of
active networks change over time, leading to the observed complex dynamics of
expression patterns. Understanding of this dynamics becomes increasingly
important in systems biology and medicine. While the importance of
transcription rates and catalytic interactions has been widely recognized in
modeling genetic regulatory systems, the understanding of the role of
degradation of biochemical agents (mRNA, protein) in regulatory dynamics
remains limited. Recent experimental data suggests that there exists a
functional relation between mRNA and protein decay rates and expression modes.
In this paper we propose a model for the dynamics of successions of sequences
of active subnetworks of the GRN. The model is able to reproduce key
characteristics of molecular dynamics, including homeostasis, multi-stability,
periodic dynamics, alternating activity, differentiability, and self-organized
critical dynamics. Moreover the model allows to naturally understand the
mechanism behind the relation between decay rates and expression modes. The
model explains recent experimental observations that decay-rates (or turnovers)
vary between differentiated tissue-classes at a general systemic level and
highlights the role of intracellular decay rate control mechanisms in cell
differentiation.Comment: 16 pages, 5 figure
The stochastic behavior of a molecular switching circuit with feedback
Background: Using a statistical physics approach, we study the stochastic
switching behavior of a model circuit of multisite phosphorylation and
dephosphorylation with feedback. The circuit consists of a kinase and
phosphatase acting on multiple sites of a substrate that, contingent on its
modification state, catalyzes its own phosphorylation and, in a symmetric
scenario, dephosphorylation. The symmetric case is viewed as a cartoon of
conflicting feedback that could result from antagonistic pathways impinging on
the state of a shared component.
Results: Multisite phosphorylation is sufficient for bistable behavior under
feedback even when catalysis is linear in substrate concentration, which is the
case we consider. We compute the phase diagram, fluctuation spectrum and
large-deviation properties related to switch memory within a statistical
mechanics framework. Bistability occurs as either a first-order or second-order
non-equilibrium phase transition, depending on the network symmetries and the
ratio of phosphatase to kinase numbers. In the second-order case, the circuit
never leaves the bistable regime upon increasing the number of substrate
molecules at constant kinase to phosphatase ratio.
Conclusions: The number of substrate molecules is a key parameter controlling
both the onset of the bistable regime, fluctuation intensity, and the residence
time in a switched state. The relevance of the concept of memory depends on the
degree of switch symmetry, as memory presupposes information to be remembered,
which is highest for equal residence times in the switched states.
Reviewers: This article was reviewed by Artem Novozhilov (nominated by Eugene
Koonin), Sergei Maslov, and Ned Wingreen.Comment: Version published in Biology Direct including reviewer comments and
author responses, 28 pages, 7 figure
Fluctuations in Gene Regulatory Networks as Gaussian Colored Noise
The study of fluctuations in gene regulatory networks is extended to the case
of Gaussian colored noise. Firstly, the solution of the corresponding Langevin
equation with colored noise is expressed in terms of an Ito integral. Then, two
important lemmas concerning the variance of an Ito integral and the covariance
of two Ito integrals are shown. Based on the lemmas, we give the general
formulae for the variances and covariance of molecular concentrations for a
regulatory network near a stable equilibrium explicitly. Two examples, the gene
auto-regulatory network and the toggle switch, are presented in details. In
general, it is found that the finite correlation time of noise reduces the
fluctuations and enhances the correlation between the fluctuations of the
molecular components.Comment: 10 pages, 4 figure
- …