Bistable Biological Systems: A Characterization Through Local Compact Input-to-State Stability

Chaves, Madalena; Eissing, T.; Allgöwer, Frank

doi:10.1109/tcsi.2007.911328

Cited by 35 publications

(47 citation statements)

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“…This property is known as hysteresis, and refers to the ability of a bistable system to "remember" that the input stimulus was above T1 long after that stimulus is removed, until it falls below T0 [48]. The lac operon network in E. Coli, the Wee1-Cdc2 network, the N F κβ response in an apoptosis network and the cell cycle oscillator in Xenopus laevis are among the many naturally occurring biological networks whose responses have been modeled as bistable switches [48][49][50]. In some cases, the lower threshold T0 does not exist, which makes the transition from A to B irreversible.…”

Section: The Role Of Each P53 Network Configuration In Determining Swmentioning

confidence: 99%

The evolution of p53 network behavior

Sivakumar

Hespanha

Roh

et al. 2017

Preprint

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We study the evolution of the p53 core regulation network across the taxonomic span of humans to protozoans and nematodes. We introduce a new model for the core regulation network in mammalian cells, and conduct a formal analysis of the different network configurations that emerge in the evolutionary path to complexity. Solving the high dimensional equations associated with this model is typically challenging, and we develop a novel algorithm to overcome this problem. A key technical tool used is the representation of the distinct pathways in the core regulation networks as "modules", such that the behavior of the composite of two or more modules can be inferred from the characteristics of each of the individual modules. Apart from simplifying the complexity of the algorithm, this modular representation also allows us to qualitatively compare the distinct types of switching behaviors each network can exhibit. This then allows us to demonstrate how our model for the core regulation network in mammalian cells matches experimentally observed phenomena, and contrast this with the plausible behaviors admitted by the network configurations in putative primordial organisms. We show that the complexity of the p53 core regulation network in vertebrates permits a range of behaviors that can bring about distinct cell fate decisions not possible in the putative primordial organisms. p53 | evolution | modularity | bifurcationsA major cause for the emergence of tumors is genetic mutations that occur when the cellular DNA is damaged and not repaired to its original state. When the mutations interfere with the normal regulation of cell division, then cell proliferation could cause the tumor to become cancerous [1]. While there is abundant evidence that exposure to chemical carcinogens and radiation has had an impact on cancer rates [2], there is also evidence that cancer is a general feature of multi-cellular organisms that has presented a long-standing evolutionary challenge [3].A key component of the DNA damage response mechanism is the T P 53 gene which expresses the p53 tumor suppressor protein, the so-called "guardian of the genome" [4]. p53 and its ancestors have been protecting metazoans from mutations arising from DNA damage for over one billion years [5]. Recent research has shown that p53 plays this role by first sensing DNA damage, and then mediating various downstream processes in response. p53 can promote cell survival by upregulating genes that bring about cell-cycle arrest or DNA repair. However, p53 can also promote cell inactivation or death by bringing about permanent cell-cycle arrest or cell death [6][7][8][9]. How p53 levels and dynamics determine different cell fates in response to DNA damage is a crucial component of an organism's tumor suppression mechanism [10][11][12][13]. It is therefore no surprise that a mutation in p53 is implicated in over 50% of human cancers [14].One of the oldest known mechanisms cells employ in response to DNA damage is programmed cell death, also known as apoptosis [15]. Cell...

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Section: The Role Of Each P53 Network Configuration In Determining Swmentioning

confidence: 99%

The evolution of p53 network behavior

Sivakumar

Hespanha

Roh

et al. 2017

Preprint

View full text Add to dashboard Cite

show abstract

“…For this case the stability notions have to be significantly modified and relaxed as, in particular, it has been done in Efimov (2012) and further in Angeli andEfimov (2013, 2015) for the ISS case. See also Angeli (2004); Angeli and Praly (2011);Chaves et al (2008) for other results on robust stability analysis of multistable systems. The main result of Angeli and Efimov (2015) provides necessary and sufficient conditions under which a system is stable with respect to multiple invariant solutions, which belong to a decomposable set (see Definition 3 below).…”

Section: Introductionmentioning

confidence: 99%

Relaxing the conditions of ISS for multistable periodic systems

et al. 2017

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The input-to-state stability property of nonlinear dynamical systems with multiple invariant solutions is analyzed under the assumption that the system equations are periodic with respect to certain state variables. It is shown that stability can be concluded via a signindefinite function, which explicitly takes the systems' periodicity into account. The presented approach leverages some of the difficulties encountered in the analysis of periodic systems via positive definite Lyapunov functions proposed in Angeli and Efimov (2013, 2015). The new result is established based on the framework of cell structure introduced in Leonov (1974) and illustrated via the global analysis of a nonlinear pendulum with a constant persistent input.

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“…The main attention is paid to local or global stability of equilibriums or trajectories [11,13,14,17,24], set stability [16], stability with respect to part of variables [23,34], robust stability in presence of exogenous inputs [27,30,29] and oscillation analysis [4,8,31]. An interest to multi-stability is also growing during the last decade [1,2,3,7,22]. Multi-stable systems include bistable ones (the class of systems with at least two stable equilibriums), almost globally stable systems (which have one attracting invariant set and the rest are repellers) and nonlinear systems with generic invariant sets.…”

Section: Introductionmentioning

confidence: 99%

“…In the papers [7,31] bistable systems are considered for a particular form of equations, which have two stable invariant sets with right hand sides described by a full state linear negative feedback plus bounded nonlinearities, each stable set is characterized by local input-to-state stability. In the paper [21] a Lyapunov density based notion of almost everywhere stability is introduced.…”

Section: Introductionmentioning

confidence: 99%

Global Lyapunov Analysis of Multistable Nonlinear Systems

Efimov¹

2012

SIAM J. Control Optim.

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Abstract. A new type of stability is introduced and its equivalent Lyapunov characterization is presented. The problem of global stability for the compact set composed of all invariant solutions of a nonlinear system (several equilibriums, for instance) is studied. Such problem statement allows us to analyze global stability properties for multi-stable systems. It is shown that several well-known multi-stable systems satisfy this new stability property.

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Bistable Biological Systems: A Characterization Through Local Compact Input-to-State Stability

Cited by 35 publications

References 0 publications

The evolution of p53 network behavior

The evolution of p53 network behavior

Relaxing the conditions of ISS for multistable periodic systems

Global Lyapunov Analysis of Multistable Nonlinear Systems

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