Time-Based Switching Control of Genetic Regulatory Networks: Toward Sequential Drug Intake for Cancer Therapy

As cancer growth and development typically involves multiple genes and pathways, combination therapy has been touted as the standard of care in the treatment of cancer. However, drug toxicity becomes a major concern whenever a patient takes 2 or more drugs simultaneously at the maximum tolerable dosage. A potential solution would be administering the drugs in a sequential or alternating manner rather than concurrently. This study therefore examines the feasibility of such an approach from a switched system control perspective. Particularly, we study how genetic regulatory systems respond to sequential (switched) drug inputs using the time-based switching mechanism. The design of the time-driven drug switching function guarantees the stability of the genetic regulatory system and the repression of the diseased genes. Simulation results using proof-of-concept models and the proliferation and survival pathways with sequential drug inputs show the effectiveness of the proposed approach.

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MODELING GENETIC REGULATORY NETWORKS: CONTINUOUS OR DISCRETE?

Journal of Biological System ◽

10.1142/s0218339006001763 ◽

2006 ◽

Vol 14 (02) ◽

pp. 219-229 ◽

Cited By ~ 30

Author(s):

IVAN IVANOV ◽

EDWARD R. DOUGHERTY

Keyword(s):

Regulatory Networks ◽

Dynamical Behavior ◽

Regulatory System ◽

Genetic Regulatory Networks ◽

Discrete Models ◽

Fine Scale ◽

Differential Equation Models ◽

Scale Models ◽

Genetic Regulatory System

Selecting an appropriate mathematical model to describe the dynamical behavior of a genetic regulatory network plays an important part in discovering gene regulatory mechanisms. Whereas fine-scale models can in principle provide a very accurate description of the real genetic regulatory system, one must be aware of the availability and quality of the data used to infer such models. Consequently, pragmatic considerations motivate the selection of a model possessing minimal complexity among those capable of capturing the level of real gene regulation being studied, particularly in relation to the prediction capability of the model. This paper compares fine-scale stochastic-differential-equation models with coarse-scale discrete models in the context of currently available data and with respect to their description of switch-like behavior among specific groups of genes.

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Effect of Leakage Delay on Stability of Neutral-Type Genetic Regulatory Networks

Abstract and Applied Analysis ◽

10.1155/2015/826020 ◽

2015 ◽

Vol 2015 ◽

pp. 1-8

Author(s):

Li Li ◽

Yongqing Yang ◽

Chuanzhi Bai

Keyword(s):

Regulatory Network ◽

Regulatory Networks ◽

Neutral Type ◽

Sufficient Conditions ◽

Functional Method ◽

Genetic Regulatory Networks ◽

Genetic Regulatory Network ◽

Leakage Delay ◽

Leakage Delays ◽

The Stability

The stability of neutral-type genetic regulatory networks with leakage delays is considered. Firstly, we describe the model of genetic regulatory network with neutral delays and leakage delays. Then some sufficient conditions are derived to ensure the asymptotic stability of the genetic regulatory network by the Lyapunov functional method. Further, the effect of leakage delay on stability is discussed. Finally, a numerical example is given to show the effectiveness of the results.

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Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Mathematical Problems in Engineering ◽

10.1155/2017/4157256 ◽

2017 ◽

Vol 2017 ◽

pp. 1-16 ◽

Cited By ~ 1

Author(s):

Fu-Dong Li ◽

Qi Zhu ◽

Hao-Tian Xu ◽

Lin Jiang

Keyword(s):

Stability Analysis ◽

Integral Inequality ◽

Regulatory Network ◽

Regulatory Networks ◽

Genetic Regulatory Networks ◽

Genetic Regulatory Network ◽

Double Integral ◽

Integral Term ◽

Double Inequality ◽

The Stability

Time delay arising in a genetic regulatory network may cause the instability. This paper is concerned with the stability analysis of genetic regulatory networks with interval time-varying delays. Firstly, a relaxed double integral inequality, named as Wirtinger-type double integral inequality (WTDII), is established to estimate the double integral term appearing in the derivative of Lyapunov-Krasovskii functional with a triple integral term. And it is proved theoretically that the proposed WTDII is tighter than the widely used Jensen-based double inequality and the recently developed Wiringter-based double inequality. Then, by applying the WTDII to the stability analysis of a delayed genetic regulatory network, together with the usage of useful information of regulatory functions, several delay-range- and delay-rate-dependent (or delay-rate-independent) criteria are derived in terms of linear matrix inequalities. Finally, an example is carried out to verify the effectiveness of the proposed method and also to show the advantages of the established stability criteria through the comparison with some literature.

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Entropy as a Robustness Marker in Genetic Regulatory Networks

Entropy ◽

10.3390/e22030260 ◽

2020 ◽

Vol 22 (3) ◽

pp. 260 ◽

Cited By ~ 1

Author(s):

Mustapha Rachdi ◽

Jules Waku ◽

Hana Hazgui ◽

Jacques Demongeot

Keyword(s):

Invariant Measure ◽

Regulatory Networks ◽

Practical Interest ◽

Genetic Network ◽

Genetic Regulatory Networks ◽

Connected Components ◽

Circular Rnas ◽

Stability Robustness ◽

The Stability ◽

Mathematical Relationships

Genetic regulatory networks have evolved by complexifying their control systems with numerous effectors (inhibitors and activators). That is, for example, the case for the double inhibition by microRNAs and circular RNAs, which introduce a ubiquitous double brake control reducing in general the number of attractors of the complex genetic networks (e.g., by destroying positive regulation circuits), in which complexity indices are the number of nodes, their connectivity, the number of strong connected components and the size of their interaction graph. The stability and robustness of the networks correspond to their ability to respectively recover from dynamical and structural disturbances the same asymptotic trajectories, and hence the same number and nature of their attractors. The complexity of the dynamics is quantified here using the notion of attractor entropy: it describes the way the invariant measure of the dynamics is spread over the state space. The stability (robustness) is characterized by the rate at which the system returns to its equilibrium trajectories (invariant measure) after a dynamical (structural) perturbation. The mathematical relationships between the indices of complexity, stability and robustness are presented in case of Markov chains related to threshold Boolean random regulatory networks updated with a Hopfield-like rule. The entropy of the invariant measure of a network as well as the Kolmogorov-Sinaï entropy of the Markov transition matrix ruling its random dynamics can be considered complexity, stability and robustness indices; and it is possible to exploit the links between these notions to characterize the resilience of a biological system with respect to endogenous or exogenous perturbations. The example of the genetic network controlling the kinin-kallikrein system involved in a pathology called angioedema shows the practical interest of the present approach of the complexity and robustness in two cases, its physiological normal and pathological, abnormal, dynamical behaviors.

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Stability of Uncertain Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delay in the Leakage Term

Abstract and Applied Analysis ◽

10.1155/2014/706720 ◽

2014 ◽

Vol 2014 ◽

pp. 1-15 ◽

Cited By ~ 2

Author(s):

Jun Li ◽

Manfeng Hu ◽

Jinde Cao ◽

Yongqing Yang ◽

Yinghua Jin

Keyword(s):

Regulatory Networks ◽

Convex Combination ◽

Genetic Regulatory Networks ◽

Time Varying ◽

Leakage Term ◽

Combination Technique ◽

Time Varying Delay ◽

The Stability ◽

Stochastic Genetic Regulatory Networks ◽

Delay Dependent

This paper is concerned with the stability problem for a class of uncertain impulsive stochastic genetic regulatory networks (UISGRNs) with time-varying delays both in the leakage term and in the regulator function. By constructing a suitable Lyapunov-Krasovskii functional which uses the information on the lower bound of the delay sufficiently, a delay-dependent stability criterion is derived for the proposed UISGRNs model by using the free-weighting matrices method and convex combination technique. The conditions obtained here are expressed in terms of LMIs whose feasibility can be checked easily by MATLAB LMI control toolbox. In addition, three numerical examples are given to justify the obtained stability results.

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DELAY-INDEPENDENT STABILITY OF GENETIC REGULATORY NETWORKS WITH TIME DELAYS

Advances in Complex Systems ◽

10.1142/s0219525909002040 ◽

2009 ◽

Vol 12 (01) ◽

pp. 3-19 ◽

Cited By ~ 21

Author(s):

FANG-XIANG WU

Keyword(s):

Time Delays ◽

Regulatory Networks ◽

Sufficient Conditions ◽

Genetic Regulatory Networks ◽

Biological Knowledge ◽

Multiple Time ◽

Zebra Fish ◽

E Coli ◽

The Stability ◽

Delay Differential

In an organism, genes encode proteins, some of which in turn regulate other genes. Such interactions work in highly structured but incredibly complex ways, and make up a genetic regulatory network. Recently, nonlinear delay differential equations have been proposed for describing genetic regulatory networks in the state-space form. In this paper, we study stability properties of genetic regulatory networks with time delays, by the notion of delay-independent stability. We first present necessary and sufficient conditions for delay-independent local stability of genetic regulatory networks with a single time delay, and then extend the main result to genetic regulatory networks with multiple time delays. To illustrate the main theory, we analyze delay-independent stability of three genetic regulatory networks in E. coli or zebra fish. For E. coli, an autoregulatory network and a repressilatory network are analyzed. The results show that these two genetic regulatory networks with parameters in the physiological range are delay-independently robustly stable. For zebra fish, an autoregulatory network for the gene her1 is analyzed. The result shows that delay-independent stability of this network depends on the initial number of protein molecules, which is in agreement with the existing biological knowledge. The theories presented in this paper provide a very useful complement to the previous work and a framework for further studying the stability of more complex genetic regulatory networks.

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Bifurcation Analysis and Impulsive Control of Genetic Regulatory Networks with Multi Delays

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2019.p0743 ◽

2019 ◽

Vol 23 (4) ◽

pp. 743-748 ◽

Cited By ~ 1

Author(s):

Feng Liu ◽

Jie Ren ◽

Ting Dong ◽

Shiqi Zheng ◽

◽

...

Keyword(s):

Numerical Simulation ◽

Hopf Bifurcation ◽

Regulatory Network ◽

Regulatory Networks ◽

Control Method ◽

Impulsive Control ◽

Genetic Regulatory Networks ◽

Genetic Regulatory Network ◽

The Stability ◽

Theoretical Results

In this study, the stability and Hopf bifurcation of a genetic regulatory network with delays are addressed. Some bifurcations may cause network oscillation and induce instability. An impulsive control method is proposed to control the bifurcations. A numerical simulation was performed to demonstrate the effectiveness of the theoretical results.

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A Less Conservative Stability Criterion for Delayed Stochastic Genetic Regulatory Networks

Mathematical Problems in Engineering ◽

10.1155/2014/768483 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11 ◽

Cited By ~ 4

Author(s):

Tingting Yu ◽

Jing Wang ◽

Xian Zhang

Keyword(s):

Stability Criterion ◽

Regulatory Networks ◽

Genetic Regulatory Networks ◽

Linear Matrix ◽

Stochastic Disturbances ◽

Mean Square Stability ◽

The Mean ◽

The Stability ◽

The One ◽

Stochastic Genetic Regulatory Networks

This paper concerns the problem of stability analysis for delayed stochastic genetic regulatory networks. By introducing an appropriate Lyapunov-Krasovskii functional and employing delay-range partition approach, a new stability criterion is given to ensure the mean square stability of genetic regulatory networks with time-varying delays and stochastic disturbances. The stability criterion is given in the form of linear matrix inequalities, which can be easily tested by the LMI Toolbox of MATLAB. Moreover, it is theoretically shown that the obtained stability criterion is less conservative than the one in W. Zhang et al., 2012. Finally, a numerical example is presented to illustrate our theory.

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Computational Approaches for Modeling Intrinsic Noise and Delays in Genetic Regulatory Networks

Handbook of Research on Computational Methodologies in Gene Regulatory Networks ◽

10.4018/978-1-60566-685-3.ch007 ◽

2010 ◽

pp. 169-197 ◽

Cited By ~ 2

Author(s):

Manuel Barrio ◽

Kevin Burrage ◽

Pamela Burrage ◽

André Leier ◽

Tatiana Márquez Lago

Keyword(s):

Regulatory Networks ◽

Computational Simulation ◽

Network Motif ◽

Regulatory System ◽

Intrinsic Noise ◽

Genetic Regulatory Networks ◽

Biological Data ◽

Protein Levels ◽

Temporal Models ◽

Oscillatory Gene Expression

This chapter focuses on the interactions and roles between delays and intrinsic noise effects within cellular pathways and regulatory networks. We address these aspects by focusing on genetic regulatory networks that share a common network motif, namely the negative feedback loop, leading to oscillatory gene expression and protein levels. In this context, we discuss computational simulation algorithms for addressing the interplay of delays and noise within the signaling pathways based on biological data. We address implementational issues associated with efficiency and robustness. In a molecular biology setting we present two case studies of temporal models for the Hes1 gene (Monk, 2003; Hirata et al., 2002), known to act as a molecular clock, and the Her1/Her7 regulatory system controlling the periodic somite segmentation in vertebrate embryos (Giudicelli and Lewis, 2004; Horikawa et al., 2006).

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The hardwiring of development: organization and function of genomic regulatory systems

Development ◽

10.1242/dev.124.10.1851 ◽

1997 ◽

Vol 124 (10) ◽

pp. 1851-1864 ◽

Cited By ~ 16

Author(s):

M.I. Arnone ◽

E.H. Davidson

Keyword(s):

Transcription Factors ◽

Regulatory Networks ◽

Regulatory System ◽

Development Organization ◽

Regulatory Systems ◽

Target Sites ◽

Transcription Factor Target ◽

Gene Regulatory ◽

Genomic Regulatory Networks ◽

And Function

The gene regulatory apparatus that directs development is encoded in the DNA, in the form of organized arrays of transcription factor target sites. Genes are regulated by interactions with multiple transcription factors and the target sites for the transcription factors required for the control of each gene constitute its cis-regulatory system. These systems are remarkably complex. Their hardwired internal organization enables them to behave as genomic information processing systems. Developmental gene regulatory networks consist of the cis-regulatory systems of all the relevant genes and the regulatory linkages amongst them. Though there is yet little explicit information, some general properties of genomic regulatory networks have become apparent. The key to understanding how genomic regulatory networks are organized, and how they work, lies in experimental analysis of cis-regulatory systems at all levels of the regulatory network.

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