Understanding the Bacterial Stringent Response Using Reachability Analysis of Hybrid Systems

Belta, Călin; Finin, Peter; Habets, L.C.G.J.M.; Halász, Ádám; Imieliński, Marcin; Kumar, Rajesh; Rubin, Harvey

doi:10.1007/978-3-540-24743-2_8

Cited by 26 publications

(23 citation statements)

References 22 publications

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“…The study of these models and their generalizations has been an active research area in both mathematical biology and hybrid systems theory (e.g., [8,9,10,11,12,13]). Notwithstanding their simple mathematical form, PWA systems capture essential aspects of gene regulation, as demonstrated by several modeling studies of regulatory networks of biological interest [12,14].…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of Switching Thresholds in Piecewise-Affine Models of Genetic Regulatory Networks

Ferrari-Trecate

Jong

Viari

2006

Hybrid Systems: Computation and Control

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Abstract. Recent advances of experimental techniques in biology have led to the production of enormous amounts of data on the dynamics of genetic regulatory networks. In this paper, we present an approach for the identification of PieceWise-Affine (PWA) models of genetic regulatory networks from experimental data, focusing on the reconstruction of switching thresholds associated with regulatory interactions. In particular, our method takes into account geometric constraints specific to models of genetic regulatory networks. We show the feasibility of our approach by the reconstruction of switching thresholds in a PWA model of the carbon starvation response in the bacterium Escherichia coli.

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Section: Introductionmentioning

confidence: 99%

Reconstruction of Switching Thresholds in Piecewise-Affine Models of Genetic Regulatory Networks

Ferrari-Trecate

Jong

Viari

2006

Hybrid Systems: Computation and Control

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“…. q N ) is the corresponding rectangle (5), and the map F has a deterministic part described by (6). A transition ((q 1 .…”

Section: Rectangular Multi-affine Hybrid Systemsmentioning

confidence: 99%

“…q N ) at state x. Remark 2.2 Due to the particular shape of the invariants, a convenient way of representing a rectangular multi-affine hybrid system (6), (5) is as a simple graph with .qN ) ) and has associated dynamics (6). An edge in the graph connects nodes corresponding to adjacent rectangles, i.e., there is an edge between any pair of nodes that differ by a Hamming distance of 1.…”

Section: Rectangular Multi-affine Hybrid Systemsmentioning

confidence: 99%

Computational Techniques for Analysis of Genetic Network Dynamics

Belta

Esposito

Kim

et al. 2005

The International Journal of Robotics Research

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In this paper we propose modeling and analysis techniques for genetic networks that provide biologists with insight into the dynamics of such systems. Central to our modeling approach is the framework of hybrid systems and our analysis tools are derived from formal analysis of such systems. Given a set of states characterizing a property of biological interest P, we present the Multi-Affine Rectangular Partition (MARP) algorithm for the construction of a set of infeasible states I that will never reach P and the Rapidly Exploring Random Forest of Trees (RRFT) algorithm for the construction of a set of feasible states F that will reach P. These techniques are scalable to high dimensions and can incorporate uncertainty (partial knowledge of kinetic parameters and state uncertainty). We apply these methods to understand the genetic interactions involved in the phenomenon of luminescence production in the marine bacterium V. fischeri. Abstract In this paper we propose modeling and analysis techniques for genetic networks that provide biologists with an insight into the dynamics of the system. These techniques are scalable to high dimensions and can incorporate uncertainty (partial knowledge of kinetic parameters and state uncertainty). We are not only interested in developing mathematical models and simulating them, but in proving biologically significant properties. Central to our modeling approach is the framework of hybrid systems and our analysis tools derived from formal analysis of such systems. Given a set of states characterizing a property of interest P, we present the MultiAffine Rectangular Partition (MARP) algorithm for the construction of a set of infeasible states I that will never reach P and the Rapidly Exploring Random Forest of Trees (RRFT) algorithm for the construction of a set of feasible states F that will reach P. We apply these methods to understand the genetic interactions involved in the phenomenon of luminescence production in the marine bacterium V. fischeri.

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“…Similarity between engineering design principles and the organization of a biological system has been investigated in [2]. Hybrid systems theory has been applied to multi-cellular networks by Ghosh and Tomlin [3], and genetic networks by Batt et al [4] as well as [5]. Stochastic hybrid systems were used to study genetic networks by Hespanha and Singh [6].…”

Section: Introductionmentioning

confidence: 99%

Finite state abstraction of a stochastic model of the lactose regulation system of Escherichia coli

Julius

Halász

Kumar

et al. 2006

Proceedings of the 45th IEEE Conference on Decision and Control

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, "Finite state abstraction of a stochastic model of the lactose regulation system of Escherichia coli" (2006). Departmental Papers (MEAM). 151. http://repository.upenn.edu/meam_papers/151Finite state abstraction of a stochastic model of the lactose regulation system of Escherichia coli AbstractThis paper focuses on the lactose regulation system in Escherichia coli bacteria, one of the most extensively studied examples of positive feedback in a naturally occurring gene network. State-of-the-art nonlinear dynamical system models predict a bi-stability phenomenon that is confirmed in experiments. However, such deterministic models fail to explain experimental observations of spontaneous transition between the two stable states in the system and the simultaneous occurrence of both steady states in a population of cells. In this paper, we propose a stochastic model that explains this phenomenon. Furthermore, we also extract a coarser two-state continuous-time Markov chain as a higher level abstraction of this model, and show that macroscopic properties are retained in the abstraction. Comments Copyright 2006 IEEE. Reprinted from Proceedings of the 45th IEEE Conference on Decision & Control 2006.This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/151 Abstract-This paper focuses on the lactose regulation system in Escherichia coli bacteria, one of the most extensively studied examples of positive feedback in a naturally occurring gene network. State-of-the-art nonlinear dynamical system models predict a bi-stability phenomenon that is confirmed in experiments. However, such deterministic models fail to explain experimental observations of spontaneous transition between the two stable states in the system and the simultaneous occurrence of both steady states in a population of cells. In this paper, we propose a stochastic model that explains this phenomenon. Furthermore, we also extract a coarser two-state continuous-time Markov chain as a higher level abstraction of this model, and show that macroscopic properties are retained in the abstraction.

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Understanding the Bacterial Stringent Response Using Reachability Analysis of Hybrid Systems

Cited by 26 publications

References 22 publications

Reconstruction of Switching Thresholds in Piecewise-Affine Models of Genetic Regulatory Networks

Reconstruction of Switching Thresholds in Piecewise-Affine Models of Genetic Regulatory Networks

Computational Techniques for Analysis of Genetic Network Dynamics

Finite state abstraction of a stochastic model of the lactose regulation system of Escherichia coli

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