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1.
Network motifs hold a very important
status in genetic regulatory networks. This paper aims to analyse
the dynamical property of the network motifs in genetic regulatory
networks. The main result we obtained is that the dynamical
property of a single motif is very simple with only an
asymptotically stable equilibrium point, but the combination of
several motifs can make more complicated dynamical properties
emerge such as limit cycles. The above-mentioned result shows that
network motif is a stable substructure in genetic regulatory
networks while their combinations make the genetic regulatory
network more complicated. 相似文献
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Weiming Ye 《Physics letters. A》2010,374(25):2521-4755
Recently, self-sustained oscillations in complex networks consisting of non-oscillatory nodes have attracted great interest in diverse natural and social fields. Oscillatory genomic regulatory networks are one of the most typical examples of this kind. Given an oscillatory genomic network, it is important to reveal the central structure generating the oscillation. However, if the network consists of large numbers of genes and interactions, the oscillation generator is deeply hidden in the complicated interactions. We apply the dominant phase-advanced driving path method proposed in Qian et al. (2010) [1] to reduce complex genomic regulatory networks to one-dimensional and unidirectionally linked network graphs where negative regulatory loops are explored to play as the central generators of the oscillations, and oscillation propagation pathways in the complex networks are clearly shown by tree branches radiating from the loops. Based on the above understanding we can control oscillations of genomic networks with high efficiency. 相似文献
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Qiang Lai 《Chinese Journal of Physics (Taipei)》2018,56(3):1064-1073
This paper studies the stability and bifurcation of three cases of bidirectional gene regulatory networks with negative feedback loops and time delays. The uniqueness of the positive equilibrium point of the gene regulatory networks is verified. The delay independent stability conditions of the networks are established by analyzing their corresponding characteristic equations. The existence of the Hopf bifurcation of the networks with or without time delays is presented. Numerical simulations demonstrate the correctness of the obtained theoretical results. 相似文献
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This paper investigates the stability of the equilibria of the piecewise-linear models of genetic regulatory networks on the intersection of the thresholds of all variables. It first studies circling trajectories and derives some stability conditions by quantitative analysis in the state transition graph. Then it proposes a common Lyapunov function for convergence analysis of the piecewise-linear models and gives a simple sign condition. All the obtained conditions are only related to the constant terms on the right-hand side of the differential equation after bringing the equilibrium to zero. 相似文献
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Acknowledging the expanding role of complex networks in numerous scientific contexts, we examine significant functional and topological differences between bridge and brick motifs for predicting network behaviors and functions. After observing similarities between social networks and their genetic, ecological, and engineering counterparts, we identify a larger number of brick motifs in social networks and bridge motifs in the other three types. We conclude that bridge and brick motif content analysis can assist researchers in understanding the small-world and clustering properties of network structures when investigating network functions and behaviors. 相似文献
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More and more experiments show that small RNAs regulate gene expression by repressing translation of messenger RNAs (mRNAs) or degrading mRNAs. In this paper, we incorporate the small RNAs into a simple gene regulatory network and investigate its dynamical behaviors. In addition, we also derive the theoretical results of globally asymptotic stability and provide the sufficient conditions for the oscillation of the simple gene regulatory network, and further demonstrate that the amplitudes against the change of delay in the gene regulatory network are robust. 相似文献
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The effect of delay, nonlinearity and noise on oscillatory motion is of permanent interest for theoretical and experimental research. Here we explore a negative feedback loop between p53 and Mdm2 with a time delay, which is a key circuit in the response of cells to damage. This circuit shows noisy sustained oscillations in individual human cells following DNA damage, and damped oscillations at the cell population level. We demonstrate the effect of delay on the oscillation, and the correlation in time course. In a multi-species system, the events at different time points which span a time delay are coupled even when the delay is large compared with the other characteristic times of the system. We also clarify that the dynamics at the single-cell level appears to be coherent resonance, and the origin of the damped oscillation at the macroscopic level out of the sustained ones at the single-cell level can be ascribed to the dephasing process which is induced by the interplay between nonlinearity and noise. The findings are consistent with experimental observations and advance our understanding of the dynamics of the p53 network. 相似文献
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Axel Hutt 《Contemporary Physics》2013,54(1):3-16
The brain is a complex system and exhibits various subsystems on different spatial and temporal scales. These subsystems are recurrent networks of neurons or populations that interact with each other. The single neurons are microscopic objects and evolve on a different time scale than macroscopic neural populations. To understand the dynamics of the brain, however, it is necessary to understand the dynamics of the brain network both on the microscopic and the macroscopic level and the interaction between the levels. The presented work introduces one to the major properties of single neurons and their interactions. The physical aspects of some standard mathematical models are discussed in some detail. The work shows that both single neurons and neural populations are excitable in the sense that small differences in an initial short stimulation may yield very different dynamical behaviour of the system. To illustrate the power of the neural population model discussed, the work applies the model to explain experimental activity in the delayed feedback system in weakly electric fish and the electroencephalogram (EEG). 相似文献
10.
Statistical analysis of gene regulatory networks reconstructed from gene expression data of lung cancer 总被引:1,自引:0,他引:1
Recently, inferring gene regulatory network from large-scale gene expression data has been considered as an important effort to understand the life system in whole. In this paper, for the purpose of getting further information about lung cancer, a gene regulatory network of lung cancer is reconstructed from gene expression data. In this network, vertices represent genes and edges between any two vertices represent their co-regulatory relationships. It is found that this network has some characteristics which are shared by most cellular networks of health lives, such as power-law, small-world behaviors. On the other hand, it also presents some features which are obviously different from other networks, such as assortative mixing. In the last section of this paper, the significance of these findings in the context of biological processes of lung cancer is discussed. 相似文献
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This Letter is concerned with the robust state estimation problem for uncertain time-delay Markovian jumping genetic regulatory networks (GRNs) with SUM logic, where the uncertainties enter into both the network parameters and the mode transition rate. The nonlinear functions describing the feedback regulation are assumed to satisfy the sector-like conditions. The main purpose of the problem addressed is to design a linear estimator to approximate the true concentrations of the mRNA and protein through available measurement outputs. By resorting to the Lyapunov functional method and some stochastic analysis tools, it is shown that if a set of linear matrix inequalities (LMIs) is feasible, the desired state estimator, that can ensure the estimation error dynamics to be globally robustly asymptotically stable in the mean square, exists. The obtained LMI conditions are dependent on both the lower and the upper bounds of the delays. An illustrative example is presented to demonstrate the feasibility of the proposed estimation schemes. 相似文献
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SHEN Jian-Wei 《理论物理通讯》2011,55(3):465-472
Bacterial quorum sensing (QS) has attracted much interests and it is an important process of cell communication. Recently, Bassler et al. studied the phenomena of QS regulated by small RNAs and the experimental data showed that small RNAs played important role in the QS of Vibrio harveyi and it can permit the fine-tuningof gene regulation and maintenance of homeostasis. According to Michaelis-Menten kinetics and mass action law in this paper, we construct a mathematical model to investigate the mechanism induced QS by coexist of small RNA and signal molecular (AI) and show that there are periodic oscillation when the time delay and Hill coefficient exceed a critical value and the periodic oscillation produces the change of concentration and induces QS. These results are fit to the experimental results. In the meanwhile, we also get some theoretical value of Hopf Bifurcation on time deday. In addition, we also find this network is robust against noise. 相似文献
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Living cells can maintain their internal states, react to changing environments, grow, differentiate, divide, etc. All these processes are tightly controlled by what can be called a regulatory program. The logic of the underlying control can sometimes be guessed at by examining the network of influences amongst genetic components. Some associated gene regulatory networks have been studied in prokaryotes and eukaryotes, unveiling various structural features ranging from broad distributions of out-degrees to recurrent “motifs”, that is small subgraphs having a specific pattern of interactions. To understand what factors may be driving such structuring, a number of groups have introduced frameworks to model the dynamics of gene regulatory networks. In that context, we review here such in silico approaches and show how selection for phenotypes, i.e., network function, can shape network structure. 相似文献
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A measure of the correlation between two earthquakes is used to link events to their aftershocks, generating a growing network structure. In this framework one can quantify whether an aftershock is close or far, from main shocks of all magnitudes. We find that simple network motifs involving links to far aftershocks appear frequently before the three biggest earthquakes of the last 16 years in Southern California. Hence, networks could be useful to detect symptoms typically preceding major events. 相似文献
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Stability analysis of delayed genetic regulatory networks with stochastic disturbances 总被引:1,自引:0,他引:1
This Letter considers the problem of stability analysis of a class of delayed genetic regulatory networks with stochastic disturbances. The delays are assumed to be time-varying and bounded. By utilizing Itô's differential formula and Lyapunov-Krasovskii functionals, delay-range-dependent and rate-dependent (rate-independent) stability criteria are proposed in terms of linear matrices inequalities. An important feature of the proposed results is that all the stability conditions are dependent on the upper and lower bounds of the delays. Another important feature is that the obtained stability conditions are less conservative than certain existing ones in the literature due to introducing some appropriate free-weighting matrices. A simulation example is employed to illustrate the applicability and effectiveness of the proposed methods. 相似文献