A mathematical framework for describing and analysing gene regulatory networks

Mestl, Thomas; Plahte, Erik; Omholt, Stig W.

doi:10.1006/jtbi.1995.0199

Cited by 234 publications

(149 citation statements)

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“…Another frequently used type of model (Snoussi and Thomas, 1993;Mestl et al, 1995aMestl et al, , 1996Plahte et al, 1998) that describes gene networks is:…”

Section: 2mentioning

confidence: 99%

“…In recent work that focuses on analytic determination of steady states and periodic orbits in equations (2), the generic threshold functions S i have been taken as: (1) step functions, generating piecewise-linear (PL) differential equations (Snoussi and Thomas, 1993;Mestl et al, 1996), (2) logoid functions, which rise linearly from 0 to 1 over a defined range of the effector (Mestl et al, 1995a), or (3) steep sigmoidal functions . In most of this work each S i is a function of only one gene product concentration.…”

Section: 2mentioning

confidence: 99%

“…Indeed, such dynamics should probably be avoided if consistency of response to external or internal stimuli is desired. Differential equations using logoids have been suggested to be superior to PL equations because they can incorporate non-additivity of the effects of multiple TFs in a way that appears more biochemically reasonable (Mestl et al, 1995a). For these equations, the steady states can also be determined analytically (Mestl et al, 1995a) and progress has been made in locating periodic solutions (Mestl et al, 1995b).…”

Section: 2mentioning

confidence: 99%

“…Differential equations using logoids have been suggested to be superior to PL equations because they can incorporate non-additivity of the effects of multiple TFs in a way that appears more biochemically reasonable (Mestl et al, 1995a). For these equations, the steady states can also be determined analytically (Mestl et al, 1995a) and progress has been made in locating periodic solutions (Mestl et al, 1995b). For differential equations using steep sigmoids, an analytic method for determining the steady states has recently been developed (Plahte et al, 1994.…”

Section: 2mentioning

confidence: 99%

“…In the future, computerized versions of the methods of Plahte et al (1998), Mestl et al (1996), Mestl et al (1995a), or Snoussi and Thomas (1993) could prove a valuable adjunct to numerical simulations. These methods could make tentative identifications, subject to experimental confirmation, of steady and periodic dynamic solutions for gene product concentrations in specific genetic regulatory systems.…”

Section: 2mentioning

confidence: 99%

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Mathematical models are useful for providing a framework for integrating data and gaining insights into the static and dynamic behavior of complex biological systems such as networks of interacting genes. We review the dynamic behaviors expected from model gene networks incorporating common biochemical motifs, and we compare current methods for modeling genetic networks. A common modeling technique, based on simply modeling genes as ON-OFF switches, is readily implemented and allows rapid numerical simulations. However, this method may predict dynamic solutions that do not correspond to those seen when systems are modeled with a more detailed method using ordinary differential equations. Until now, the majority of gene network modeling studies have focused on determining the types of dynamics that can be generated by common biochemical motifs such as feedback loops or protein oligomerization. For example, these elements can generate multiple stable states for gene product concentrations, state-dependent responses to stimuli, circadian rhythms and other oscillations, and optimal stimulus frequencies for maximal transcription. In the future, as new experimental techniques increase the ease of characterization of genetic networks, qualitative modeling will need to be supplanted by quantitative models for specific systems.

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“…Another frequently used type of model (Snoussi and Thomas, 1993;Mestl et al, 1995aMestl et al, , 1996Plahte et al, 1998) that describes gene networks is:…”

Section: 2mentioning

confidence: 99%