Chunguang Li

Stability of Genetic Networks With SUM Regulatory Logic: Lur'e System and LMI Approach

In this paper, we present a nonlinear model for genetic regulatory networks with SUM regulatory functions. We show that the genetic network can be transformed into Lure form. Based on the Lyapunov method and the Lure system approach, sufficient conditions for the stability of the genetic networks are derived, in particular for the cases with time delays owing to the slow processes of transcription, translation, and translocation, and for the cases with stochastic perturbations due to natural random intra- and inter-cellular fluctuations. All the stability conditions are given in terms of linear matrix inequalities (LMIs), which are very easy to be verified. To test the effectiveness of our theoretical results, several examples of genetic networks are also presented in this paper

Synchronization of coupled nonidentical genetic oscillators.

The study of the collective dynamics of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic oscillators are biochemical networks, which can generally be modelled as nonlinear dynamic systems. We show in this paper that many genetic oscillators can be transformed into Lure form by exploiting the special structure of biological systems. By using a control theory approach, we provide a theoretical method for analysing the synchronization of coupled nonidentical genetic oscillators. Sufficient conditions for the synchronization as well as the estimation of the bound of the synchronization error are also obtained. To demonstrate the effectiveness of our theoretical results, a population of genetic oscillators based on the Goodwin model are adopted as numerical examples.

Stochastic Stability of Genetic Networks With Disturbance Attenuation

Gene regulation is an intrinsically noisy process, which is subject to intracellular and extracellular noise perturbations and environment fluctuations. In this brief, we consider a stochastic nonlinear model for genetic regulatory networks with SUM regulatory functions. Based on the Lyapunov method and the Lure system approach, sufficient conditions for the stochastic stability of the genetic networks with disturbance attenuation are derived. The case with time delays owing to the slow processes of transcription, translation, and translocation is also studied. All the results are presented in terms of linear matrix inequalities (LMIs).

Stochastic synchronization of genetic oscillator networks

BackgroundThe study of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic networks are intrinsically noisy due to natural random intra- and inter-cellular fluctuations. Therefore, it is important to study the effects of noise perturbation on the synchronous dynamics of genetic oscillators. From the synthetic biology viewpoint, it is also important to implement biological systems that minimizing the negative influence of the perturbations.ResultsIn this paper, based on systems biology approach, we provide a general theoretical result on the synchronization of genetic oscillators with stochastic perturbations. By exploiting the specific properties of many genetic oscillator models, we provide an easy-verified sufficient condition for the stochastic synchronization of coupled genetic oscillators, based on the Lure system approach in control theory. A design principle for minimizing the influence of noise is also presented. To demonstrate the effectiveness of our theoretical results, a population of coupled repressillators is adopted as a numerical example.ConclusionIn summary, we present an efficient theoretical method for analyzing the synchronization of genetic oscillator networks, which is helpful for understanding and testing the synchronization phenomena in biological organisms. Besides, the results are actually applicable to general oscillator networks.

Impulsive control of stochastic systems with applications in chaos control, chaos synchronization, and neural networks

Real systems are often subject to both noise perturbations and impulsive effects. In this paper, we study the stability and stabilization of systems with both noise perturbations and impulsive effects. In other words, we generalize the impulsive control theory from the deterministic case to the stochastic case. The method is based on extending the comparison method to the stochastic case. The method presented in this paper is general and easy to apply. Theoretical results on both stability in the pth mean and stability with disturbance attenuation are derived. To show the effectiveness of the basic theory, we apply it to the impulsive control and synchronization of chaotic systems with noise perturbations, and to the stability of impulsive stochastic neural networks. Several numerical examples are also presented to verify the theoretical results.

Modeling and Analyzing Biological Oscillations in Molecular Networks

One of the major challenges for postgenomic biology is to understand how genes, proteins, and small molecules dynamically interact to form molecular networks which facilitate sophisticated biological functions. In this paper, we present a survey on recent developments on modelling molecular networks and analyzing synchronization of bio-oscillators in multicellular systems from the viewpoint of systems biology. Attention will be focused on deriving general theoretical results to understand the dynamical behaviors of biological systems based on nonlinear dynamical and control theory. Specifically, we first describe the stochastic and deterministic approaches to model molecular networks and give a brief comparison between them. Then, we explain how to construct a molecular network, in particular, a gene regulatory network with specific functions, e.g., switches and oscillators, in individual cells at the molecular level by using feedback systems, and how to model a general multicellular system with the consideration of external fluctuations and intercellular coupling to study the general cooperative behaviors for a population of bio-oscillators. Finally, as an illustrative example, a synthetic multicellular system is designed to show how synchronization is effectively achieved and how dynamics of individual cells is efficiently controlled. Some recent developments and perspectives of analysis on biological oscillations in future are also discussed.

Transient Resetting: A Novel Mechanism for Synchrony and Its Biological Examples

The study of synchronization in biological systems is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. In this paper, by using simple dynamical systems theory, we present a novel mechanism, named transient resetting, for the synchronization of uncoupled biological oscillators with stimuli. This mechanism not only can unify and extend many existing results on (deterministic and stochastic) stimulus-induced synchrony, but also may actually play an important role in biological rhythms. We argue that transient resetting is a possible mechanism for the synchronization in many biological organisms, which might also be further used in the medical therapy of rhythmic disorders. Examples of the synchronization of neural and circadian oscillators as well as a chaotic neuron model are presented to verify our hypothesis.

A Systems Biology Perspective on Signal Processing in Genetic Network Motifs [Life Sciences]

This article summarizes the characteristics and information processing roles of motifs found in gene transcription networks. The gene transcription networks are defined and the genetic network motif functions are examined. After expanding the discussion to integrated cellular network motifs, the directions for future work are outlined