Lateral Inhibition through Delta-Notch Signaling: A Piecewise Affine Hybrid Model

Ghosh, Ronojoy; Tomlin, Claire J.

doi:10.1007/3-540-45351-2_21

Cited by 98 publications

(84 citation statements)

References 13 publications

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“…Methods similar in spirit have been proposed in the hybrid systems community [22,23]. QR methods have been applied to the regulation of tryptophan synthesis [33] and phage growth [32] in E. coli, and to the regulation of the transcription factor families AP-1 and NF-B in different classes of animals [68].…”

Section: Discussionmentioning

confidence: 99%

“…On a formal level, the PL models are related to a class of asynchronous logical models proposed by Thomas and colleagues [66,67]. PL models and their logical relatives have been used for the study of a number of prokaryotic and eukaryotic regulatory networks [1,22,23,46,50,55,58,65]. In addition, they have been used for modeling food webs [53], neural networks [42], and biological computers [6].…”

Section: Introductionmentioning

confidence: 99%

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Qualitative simulation of genetic regulatory networks using piecewise-linear models

Jong

Gouzé

Hernandez

et al. 2004

Bulletin of Mathematical Biology

319

305

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In order to cope with the large amounts of data that have become available in genomics, mathematical tools for the analysis of networks of interactions between genes, proteins, and other molecules are indispensable. We present a method for the qualitative simulation of genetic regulatory networks, based on a class of piecewise-linear (PL) differential equations that has been well-studied in mathematical biology. The simulation method is well-adapted to state-of-the-art measurement techniques in genomics, which often provide qualitative and coarsegrained descriptions of genetic regulatory networks. Given a qualitative model of a genetic regulatory network, consisting of a system of PL differential equations and inequality constraints on the parameter values, the method produces a graph of qualitative states and transitions between qualitative states, summarizing the qualitative dynamics of the system. The qualitative simulation method has been implemented in Java in the computer tool Genetic Network Analyzer.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Qualitative simulation of genetic regulatory networks using piecewise-linear models

Jong

Gouzé

Hernandez

et al. 2004

Bulletin of Mathematical Biology

319

305

View full text Add to dashboard Cite

show abstract

“…Various formalisms are putting the executable biology framework into practice. For example, Petri-nets [3,7], process calculi [22,15], interacting state-machines [9,11], and hybrid automata [13,2]. In many cases, the analysis of these models includes reachability analysis and model checking in addition to traditional simulations.…”

Section: Introductionmentioning

confidence: 99%

“…For example, a similar process occurs during the formation of the wing of the Drosophila fruit fly [13]. Ghosh and Tomlin's work provides a detailed model (using hybrid automata) of this process.…”

Section: Introductionmentioning

confidence: 99%

Bounded Asynchrony: Concurrency for Modeling Cell-Cell Interactions

Fisher

Henzinger

Mateescu

et al.

Formal Methods in Systems Biology

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Abstract. We introduce bounded asynchrony, a notion of concurrency tailored to the modeling of biological cell-cell interactions. Bounded asynchrony is the result of a scheduler that bounds the number of steps that one process gets ahead of other processes; this allows the components of a system to move independently while keeping them coupled. Bounded asynchrony accurately reproduces the experimental observations made about certain cell-cell interactions: its constrained nondeterminism captures the variability observed in cells that, although equally potent, assume distinct fates. Real-life cells are not "scheduled", but we show that distributed real-time behavior can lead to component interactions that are observationally equivalent to bounded asynchrony; this provides a possible mechanistic explanation for the phenomena observed during cell fate specification.We use model checking to determine cell fates. The nondeterminism of bounded asynchrony causes state explosion during model checking, but partialorder methods are not directly applicable. We present a new algorithm that reduces the number of states that need to be explored: our optimization takes advantage of the bounded-asynchronous progress and the spatially local interactions of components that model cells. We compare our own communication-based reduction with partial-order reduction (on a restricted form of bounded asynchrony) and experiments illustrate that our algorithm leads to significant savings.

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“…In practice, logical models have proven capable of accounting for the qualitative dynamics of a variety of genetic systems [15][16][17][18][19][20][21][22][23]. Models that combine logical rules with concentration thresholds for the action of regulatory molecules, as in the French-flag model of Wolpert [24] or Glass networks more generally [25], satisfactorily describe other systems either qualitatively [26][27][28] or quantitatively [29]. Synthetic biologists have constructed gene networks that perform elementary logical operations, such as storing a bit of memory [30] or turning off and on with a fixed period [31].…”

Section: Introductionmentioning

confidence: 99%

Implementing Arithmetic and Other Analytic Operations by Transcriptional Regulation

Cory¹,

Perkins²

2005

PLoS Comput Biol

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The transcriptional regulatory machinery of a gene can be viewed as a computational device, with transcription factor concentrations as inputs and expression level as the output. This view begs the question: what kinds of computations are possible? We show that different parameterizations of a simple chemical kinetic model of transcriptional regulation are able to approximate all four standard arithmetic operations: addition, subtraction, multiplication, and division, as well as various equality and inequality operations. This contrasts with other studies that emphasize logical or digital notions of computation in biological networks. We analyze the accuracy and precision of these approximations, showing that they depend on different sets of parameters, and are thus independently tunable. We demonstrate that networks of these ''arithmetic'' genes can be combined to accomplish yet more complicated computations by designing and simulating a network that detects statistically significant elevations in a time-varying signal. We also consider the much more general problem of approximating analytic functions, showing that this can be achieved by allowing multiple transcription factor binding sites on the promoter. These observations are important for the interpretation of naturally occurring networks and imply new possibilities for the design of synthetic networks.

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Lateral Inhibition through Delta-Notch Signaling: A Piecewise Affine Hybrid Model

Cited by 98 publications

References 13 publications

Qualitative simulation of genetic regulatory networks using piecewise-linear models

Qualitative simulation of genetic regulatory networks using piecewise-linear models

Bounded Asynchrony: Concurrency for Modeling Cell-Cell Interactions

Implementing Arithmetic and Other Analytic Operations by Transcriptional Regulation

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