Multistability equivalence between gene regulatory networks of different dimensionality

Schittler, Daniella; Allgöwer, Frank; Waldherr, Steffen

doi:10.23919/ecc.2013.6669352

Cited by 2 publications

(24 citation statements)

References 11 publications

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“…The theorem was proven also in [6] under the assumption that all feedback loops in the interaction functions a.´/ can be broken by a single-input single-output loopbreaking. Such a loopbreaking was defined by [12], and it was exploited in the proof for the property (iii).…”

Section: Theoremmentioning

confidence: 90%

“…However, the restriction to single-input single-output systems means that the theorem could not be applied to many GRNs where multiple feedback loops are present. To overcome this drawback, the idea of a MIMO loopbreaking based on [6,12] was introduced by [19], where also the corresponding generalization of the proof was sketched.…”

Section: Theoremmentioning

confidence: 99%

“…In this paper, this method is generalized to networks with potentially multiple feedback loops in the interaction structure.In Section 2, we present the concept of multistability equivalence, which allows to match the stability properties of two GRN systems of different dimensionality. Then we review in Section 3 the construction method for a multistability-equivalent system [6]. In Section 4, we proof a theorem regarding the multistability equivalence, which is more general than the one shown previously [6], based on a multi-input multi-output (MIMO) loopbreaking approach.…”

mentioning

confidence: 96%

“…Mapping the lowdimensional models coming from bottom-up modeling approaches to high-dimensional topologies from top-down approaches, while preserving key dynamic properties, is thus a relevant concern for connecting qualitative models to actual experimental data.The aim of this paper is to propose construction rules for the expansion of a low-dimensional to a higher-dimensional ODE system, while ensuring multistability equivalence. For a special case of networks with a single feedback loop, a construction method was proposed earlier [6]. In this paper, this method is generalized to networks with potentially multiple feedback loops in the interaction structure.In Section 2, we present the concept of multistability equivalence, which allows to match the stability properties of two GRN systems of different dimensionality.…”

mentioning

confidence: 99%

“…The aim of this paper is to propose construction rules for the expansion of a low-dimensional to a higher-dimensional ODE system, while ensuring multistability equivalence. For a special case of networks with a single feedback loop, a construction method was proposed earlier [6]. In this paper, this method is generalized to networks with potentially multiple feedback loops in the interaction structure.…”

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confidence: 99%

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Multistability equivalence between gene regulatory networks of different dimensionality with application to a differentiation network

Schittler

Jouini

Allgöwer

et al. 2016

Intl J Robust & Nonlinear

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This paper formulates and addresses the problem of equivalence in terms of multistability properties between nonlinear models of gene regulatory systems of different dimensionality. Given a nonlinear dynamical model of a gene regulatory network and the structure of another higher-dimensional gene regulatory network, the aim is to find a dynamical model for the latter that has the same equilibria and stability properties as the former. We propose construction rules for the dynamics of a high-dimensional system, given the low-dimensional system and the high-dimensional network structure. These construction rules yield a multistability-equivalent system, as we prove in this work. We demonstrate the value of our method by applying it to an example of a multistable gene regulatory network involved in mesenchymal stem cell differentiation. Here, differentiation is described by a core motif of three genetic regulators, but the detailed network contains at least nine genes. The proposed construction method allows to transfer the multistability based differentation mechanism of the core motif to the more detailed gene regulatory network. Copyright MULTISTABILITY EQUIVALENCE BETWEEN GENE REGULATORY NETWORKS 4149 A central property of GRNs is that many of them exhibit multistability, thereby realizing the coexistence of several stable states of the system, of which a suitable one can be adopted under the respective biological circumstances ([2, 5, 7, 8]). The analysis of multistability properties of such systems is of high interest and has attracted the development of new specially suited methods [9][10][11][12].It is desired that the analysis of a conceptual, low-dimensional model should allow for conclusions about a higher-dimensional model. On the one hand, low-dimensional systems are amenable to systems-theoretic tools such as multistability and bifurcation analysis. On the other hand, a high-dimensional dynamic model might be required for fitting model dynamics to data from gene expression measurements, and thus for quantitative predictions about the real biological system. From this, the task arises how a dynamic model for a high-dimensional system can be obtained if only a core motif model of the gene regulatory dynamics, implemented as a low-dimensional ODE system, is available. Often, the structure of the high-dimensional network is known from network identification methods (or at least a small number of alternatives exist), but the dynamics in form of an ODE system are unknown and need to be constructed. The high-dimensional ODE system to be obtained should have the same number of equilibria, and each equilibrium should have the same stability properties, as the low-dimensional system. This is somewhat complementary to the fields of model reduction and model decomposition: In model reduction, one aims to reduce a high-dimensional model to a low-dimensional one [13]. The aim of model decomposition, in contrast, is to partition a high-dimensional model into weakly connected modules, which can be analyzed by systems-...

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Section: Theoremmentioning

confidence: 90%

Section: Theoremmentioning

confidence: 99%

mentioning

confidence: 96%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Multistability equivalence between gene regulatory networks of different dimensionality with application to a differentiation network

Schittler

Jouini

Allgöwer

et al. 2016

Intl J Robust & Nonlinear

Self Cite

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Generalization of the construction method for multistability-equivalent gene regulatory networks to systems with multi-input multi-output loopbreaking

Schittler,

Jouini,

Allgöwer

et al. 2013

Preprint

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The problem of equivalence in terms of multistability properties between gene regulatory network models of different dimensionality has been recently addressed by Schittler et al. (2013). The authors in that work proposed construction rules for a high-dimensional dynamical system, when given a low-dimensional dynamical system and the high-dimensional network structure. However, the proof therein was restricted to the class of systems for which all internal feedback loops can be broken by a loopbreaking approach yielding a single-input single-output (SISO) system. In this report, we present the generalization of the proof to systems with any number of internal feedback loops, which will be broken by a generalized loopbreaking approach resulting in a multi-input multi-output (MIMO) system. This generalization of the method renders the construction method applicable to a broad class of gene regulatory network models, thus promoting the transfer of results from core motif models to more realistic, high-dimensional models of gene regulation. We demonstrate the potential and value of our method by applying it to an example of a gene regulatory network in mesenchymal stem cell differentiation. * Parts of the results here have been presented in a preliminary version, Multistability equivalence between gene regulatory networks of different dimensionality, which appeared in the Proceedings of the 12th European Control Conference (ECC); see Schittler et al. (2013).

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Multistability equivalence between gene regulatory networks of different dimensionality

Cited by 2 publications

References 11 publications

Multistability equivalence between gene regulatory networks of different dimensionality with application to a differentiation network

Multistability equivalence between gene regulatory networks of different dimensionality with application to a differentiation network

Generalization of the construction method for multistability-equivalent gene regulatory networks to systems with multi-input multi-output loopbreaking

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