Cited by 242Gene Regulatory Network AnalysisAdvanced Differential Equations and Dynamical SystemsNonlinear Dynamics and Pattern Formation

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Multistationarity, the basis of cell differentiation and memory. II. Logical analysis of regulatory networks in terms of feedback circuits

Thomas, R., Kaufman, M.·2001·Chaos: An Interdisciplinary Journal of Nonlinear Science

DOI 10.1063/1.1349893

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Abstract

Circuits and their involvement in complex dynamics are described in differential terms in Part I of this work. Here, we first explain why it may be appropriate to use a logical description, either by itself or in symbiosis with the differential description. The major problem of a logical description is to find an adequate way to involve time. The procedure we adopted differs radically from the classical one by its fully asynchronous character. In Sec. II we describe our “naive” logical approach, and use it to illustrate the major laws of circuitry (namely, the involvement of positive circuits in multistationarity and of negative circuits in periodicity) and in a biological example. Already in the naive description, the major steps of the logical description are to: (i) describe a model as a set of logical equations, (ii) derive the state table from the equations, (iii) derive the graph of the sequences of states from the state table, and (iv) determine which of the possible pathways will be actually followed in terms of time delays. In the following sections we consider multivalued variables where required, the introduction of logical parameters and of logical values ascribed to the thresholds, and the concept of characteristic state of a circuit. This generalized logical description provides an image whose qualitative fit with the differential description is quite remarkable. A major interest of the generalized logical description is that it implies a limited and often quite small number of possible combinations of values of the logical parameters. The space of the logical parameters is thus cut into a limited number of boxes, each of which is characterized by a defined qualitative behavior of the system. Our analysis tells which constraints on the logical parameters must be fulfilled in order for any circuit (or combination of circuits) to be functional. Functionality of a circuit will result in multistationarity (in the case of a positive circuit) or in a cycle (in the case of a negative circuit). The last sections deal with “more about time delays” and “reverse logic,” an approach that aims to proceed rationally from facts to models.

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Self-citation

Authors: Thomas, R., & Kaufman, M.
Affiliations: Université Libre de Bruxelles (BE)
Venue: Chaos: An Interdisciplinary Journal of Nonlinear Science
Publisher: AIP Publishing
Published: 2001-03-01
Volume: 11
Issue: 1
Pages: 180-195
ISSN: 1054-1500 (ISSN-L)
1089-7682
DOI: 10.1063/1.1349893
OpenAlex: W2065782501
Cited by: 242
References: 35
Citations by year: 2026: 7 · 2025: 1 · 2024: 5 · 2023: 10 · 2022: 10 · 2021: 6 · 2020: 11 · 2019: 10 · 2018: 15 · 2017: 11 · 2016: 9 · 2015: 7 · 2014: 13 · 2013: 12 · 2012: 5
FWCI: 1.85
Type: journal article
Language: en
Open access: closed
Locations: Chaos An Interdisciplinary Journal of Nonlinear Science (publishedVersion)
PubMed (publishedVersion)
Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) (submittedVersion)
Topics: Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Equations and Dynamical Systems
Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Dynamics and Pattern Formation
Keywords: multistationarity, feedback circuits, cell differentiation, cellular memory, periodicity, time delay, asynchronous logic, state tables, gene regulatory networks

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Multistationarity, the basis of cell differentiation and memory. II. Logical analysis of regulatory networks in terms of feedback circuits

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