Abstract
Boolean networks have been used in a variety of settings, as models for general complex systems as well as models of specific systems in diverse fields, such as biology, engineering, and computer science. Traditionally, their properties as dynamical systems have been studied through simulation studies, due to a lack of mathematical structure. This paper uses a common mathematical technique to identify a class of Boolean networks with a “simple” structure and describes an algorithm to construct arbitrary extensions of a collection of simple Boolean networks. In this way, all Boolean networks can be obtained from a collection of simple Boolean networks as building blocks. The paper furthermore provides a formula for the number of extensions of given simple networks and, in some cases, provides a parametrization of those extensions. This has potential applications to the construction of networks with particular properties, for instance in synthetic biology, and can also be applied to develop efficient control algorithms for Boolean network models.
| Original language | English |
|---|---|
| Article number | 134278 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 468 |
| DOIs | |
| State | Published - Nov 2024 |
Bibliographical note
Publisher Copyright:© 2024 Elsevier B.V.
Funding
Author Matthew Wheeler was supported by The American Association of Immunologists through an Intersect Fellowship for Computational Scientists and Immunologists, United States. This work was further supported by the Simons foundation, United States [grant numbers 712537 (to C.K.), 850896 (to D.M.), 516088 (to A.V.)]; the National Institute of Health [grant number 1 R01 HL169974-01 (to R.L.)]; and the Defense Advanced Research Projects Agency, United States [grant number HR00112220038 (to R.L.)]. The authors also thank the Banff International Research Station, United States for support through its Focused Research Group program during the week of May 29, 2022 (22frg001), which was of great help in framing initial ideas of this paper. Author Matthew Wheeler was supported by The American Association of Immunologists through an Intersect Fellowship for Computational Scientists and Immunologists . This work was further supported by the Simons foundation [grant numbers 712537 (to C.K.), 850896 (to D.M.), 516088 (to A.V.)]; the National Institute of Health [grant number 1 R01 HL169974-01 (to R.L.)]; and the Defense Advanced Research Projects Agency [grant number HR00112220038 (to R.L.)]. The authors also thank the Banff International Research Station for support through its Focused Research Group program during the week of May 29, 2022 (22frg001), which was of great help in framing initial ideas of this paper.
| Funders | Funder number |
|---|---|
| American Association of Immunologists | |
| University of California Institute for Mexico and the United States | |
| National Institutes of Health (NIH) | 1 R01 HL169974-01 |
| National Institutes of Health (NIH) | |
| Simons Foundation | 850896, 712537, 516088 |
| Simons Foundation | |
| Defense Advanced Research Projects Agency | 22frg001, HR00112220038 |
| Defense Advanced Research Projects Agency |
Keywords
- Boolean network
- Decomposition theory
- Enumeration
- Gene regulatory network
- Modularity
- Nested canalizing function
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics