Lattice structures that parameterize regulatory network dynamics
We consider two types of models of regulatory network dynamics: Boolean maps and systems of switching ordinary differential equations. Our goal is to construct all models in each category that are compatible with the directed signed graph that describe the network interactions. This leads to conside...
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| Published in: | Mathematical biosciences Vol. 374; p. 109225 |
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| Language: | English |
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01.08.2024
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| ISSN: | 0025-5564, 1879-3134, 1879-3134 |
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| Abstract | We consider two types of models of regulatory network dynamics: Boolean maps and systems of switching ordinary differential equations. Our goal is to construct all models in each category that are compatible with the directed signed graph that describe the network interactions. This leads to consideration of lattice of monotone Boolean functions (MBF), poset of non-degenerate MBFs, and a lattice of chains in these sets. We describe explicit inductive construction of these posets where the induction is on the number of inputs in MBF.
Our results allow enumeration of potential dynamic behavior of the network for both model types, subject to practical limitation imposed by the size of the lattice of MBFs described by the Dedekind number.
•Regulatory networks are modeled using both Boolean and ODE models.•There are finite ensembles of Boolean and switching ODE models compatible with network structure.•Capacity of network to support dynamics is given by its prevalence in the ensemble.•.We present iterative algorithms that construct ensembles of the network models. |
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| AbstractList | We consider two types of models of regulatory network dynamics: Boolean maps and systems of switching ordinary differential equations. Our goal is to construct all models in each category that are compatible with the directed signed graph that describe the network interactions. This leads to consideration of lattice of monotone Boolean functions (MBF), poset of non-degenerate MBFs, and a lattice of chains in these sets. We describe explicit inductive construction of these posets where the induction is on the number of inputs in MBF.
Our results allow enumeration of potential dynamic behavior of the network for both model types, subject to practical limitation imposed by the size of the lattice of MBFs described by the Dedekind number.
•Regulatory networks are modeled using both Boolean and ODE models.•There are finite ensembles of Boolean and switching ODE models compatible with network structure.•Capacity of network to support dynamics is given by its prevalence in the ensemble.•.We present iterative algorithms that construct ensembles of the network models. We consider two types of models of regulatory network dynamics: Boolean maps and systems of switching ordinary differential equations. Our goal is to construct all models in each category that are compatible with the directed signed graph that describe the network interactions. This leads to consideration of lattice of monotone Boolean functions (MBF), poset of non-degenerate MBFs, and a lattice of chains in these sets. We describe explicit inductive construction of these posets where the induction is on the number of inputs in MBF. Our results allow enumeration of potential dynamic behavior of the network for both model types, subject to practical limitation imposed by the size of the lattice of MBFs described by the Dedekind number. We consider two types of models of regulatory network dynamics: Boolean maps and systems of switching ordinary differential equations. Our goal is to construct all models in each category that are compatible with the directed signed graph that describe the network interactions. This leads to consideration of lattice of monotone Boolean functions (MBF), poset of non-degenerate MBFs, and a lattice of chains in these sets. We describe explicit inductive construction of these posets where the induction is on the number of inputs in MBF. Our results allow enumeration of potential dynamic behavior of the network for both model types, subject to practical limitation imposed by the size of the lattice of MBFs described by the Dedekind number.We consider two types of models of regulatory network dynamics: Boolean maps and systems of switching ordinary differential equations. Our goal is to construct all models in each category that are compatible with the directed signed graph that describe the network interactions. This leads to consideration of lattice of monotone Boolean functions (MBF), poset of non-degenerate MBFs, and a lattice of chains in these sets. We describe explicit inductive construction of these posets where the induction is on the number of inputs in MBF. Our results allow enumeration of potential dynamic behavior of the network for both model types, subject to practical limitation imposed by the size of the lattice of MBFs described by the Dedekind number. |
| ArticleNumber | 109225 |
| Author | Gedeon, Tomáš |
| Author_xml | – sequence: 1 givenname: Tomáš orcidid: 0000-0001-5555-6741 surname: Gedeon fullname: Gedeon, Tomáš email: tgedeon@montana.edu organization: Montana State University, Bozeman, 59717, MT, USA |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/38866065$$D View this record in MEDLINE/PubMed |
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| Keywords | Regulatory network dynamics Switching systems Boolean systems Monotone Boolean functions |
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| SubjectTerms | Boolean systems Monotone Boolean functions Regulatory network dynamics Switching systems |
| Title | Lattice structures that parameterize regulatory network dynamics |
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