The logical analysis of continuous, non-linear biochemical control networks

Glass, Leon; Kauffman, Stuart

doi:10.1016/0022-5193(73)90208-7

Cited by 844 publications

(688 citation statements)

References 21 publications

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“…Although a steady state of a Boolean representation of a genetic system will correspond, qualitatively, to an analogous steady state in the 'continuous' representation with ordinary differential equations, the converse is not necessarily true. Not all steady states of the continuous representation are required to appear as steady solutions in the Boolean representation (Glass and Kauffman, 1973). Also, periodic solutions in the Boolean representation may not correspond to periodic solutions in the continuous system.…”

Section: 3mentioning

confidence: 99%

“…Also, periodic solutions in the Boolean representation may not correspond to periodic solutions in the continuous system. Several examples are given in Glass and Kauffman (1973) and Bagley and Glass (1996). For example, Glass and Kauffman (1973) considered the simple feedback loop in which X 1 induces the production of X 2 and conversely X 2 represses the production of X 1 .…”

Section: 3mentioning

confidence: 99%

“…Several examples are given in Glass and Kauffman (1973) and Bagley and Glass (1996). For example, Glass and Kauffman (1973) considered the simple feedback loop in which X 1 induces the production of X 2 and conversely X 2 represses the production of X 1 . Using 1 to refer to a gene being ON and 0 to refer to a gene being OFF, the Boolean representation of this system has four possible states: (1,0), (0,1), (1,1) and (0,0).…”

Section: 3mentioning

confidence: 99%

“…Only if an additional complication is added (i.e., if X 1 and X 2 are assumed to be synthesized in separate compartments) is a stable limit cycle found for some parameter values. Glass and Kauffman (1973) gave a procedure for determining whether limit cycles in low-dimensional (2-4 variable) Boolean systems are 'spurious' in the sense that they would not be seen in the continuous representation. However, no such procedure appears to have been developed for higher-dimensional systems.…”

Section: 3mentioning

confidence: 99%

See 3 more Smart Citations

Modeling Transcriptional Control in Gene Networks—Methods, Recent Results, and Future Directions

Smolen

Baxter

Byrne

2000

Bulletin of Mathematical Biology

280

161

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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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Section: 3mentioning

confidence: 99%

Section: 3mentioning

confidence: 99%

Section: 3mentioning

confidence: 99%

Section: 3mentioning

confidence: 99%

See 2 more Smart Citations

Modeling Transcriptional Control in Gene Networks—Methods, Recent Results, and Future Directions

Smolen

Baxter

Byrne

2000

Bulletin of Mathematical Biology

280

161

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“…A number of theoretical studies characterise the relationships between Boolean and continuous models (Glass and Kauffman 1973;Wilds and Glass 2009;Wittmann et al 2009;Jamshidi et al 2012). Indeed, while different mathematical frameworks are considered to model molecular networks (de Jong 2002), it is important to understand, for example, how properties of a given model translate to another framework.…”

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confidence: 99%

Logical Modelling of Regulatory Networks, Methods and Applications

Chaouiya

Rémy

2013

Bull Math Biol

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About 40 years ago, seminal work by S. Kauffman (1969) and R. Thomas (1973) paved the way to the establishment of a coarse-grained, "logical" modelling of gene regulatory networks. This gave rise to an increasingly active field of research, which ranges from theoretical studies to models of networks controlling a variety of cellular processes (Bornholdt 2008;Glass and Siegelmann 2010). Briefly, in these models, genes (or regulatory components) are assigned discrete values that account for their functional levels of expression (or activity). A regulatory function defines the evolution of the gene level, depending on the levels of its regulators. This abstracted representation of molecular mechanisms is very convenient for handling large networks for which precise kinetic data are lacking.Within the logical framework, one can distinguish several approaches that differ in the way of defining a model and its behaviour. In random Boolean networks, first introduced by S. Kauffman, the components are randomly assigned a set of regulators and a regulatory function that drives their evolution, depending on these regulators (Kauffman 1969). In threshold Boolean networks, the function is derived from a given regulatory structure as a sum of the input signals, possibly considering a threshold (Bornholdt 2008;Li et al. 2004). In the generalised logical approach introduced by R. Thomas, the logical functions are general, but are constrained by the regulatory graph. Whenever necessary or useful, the formalism supports multi-valued variables C. Chaouiya ( )

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Logical Description, Analysis, and Synthesis of Biological and Other Networks Comprising Feedback Loops

Thomas¹

1994

Advances in Chemical Physics

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The logical analysis of continuous, non-linear biochemical control networks

Cited by 844 publications

References 21 publications

Modeling Transcriptional Control in Gene Networks—Methods, Recent Results, and Future Directions

Modeling Transcriptional Control in Gene Networks—Methods, Recent Results, and Future Directions

Logical Modelling of Regulatory Networks, Methods and Applications

Logical Description, Analysis, and Synthesis of Biological and Other Networks Comprising Feedback Loops

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