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Gedeon T. Lattice structures that parameterize regulatory network dynamics. Math Biosci 2024; 374:109225. [PMID: 38866065 DOI: 10.1016/j.mbs.2024.109225] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2024] [Revised: 05/13/2024] [Accepted: 05/29/2024] [Indexed: 06/14/2024]
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.
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Affiliation(s)
- Tomáš Gedeon
- Montana State University, Bozeman, 59717, MT, USA.
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Hari K, Duncan W, Ibrahim MA, Jolly MK, Cummins B, Gedeon T. Assessing biological network dynamics: comparing numerical simulations with analytical decomposition of parameter space. NPJ Syst Biol Appl 2023; 9:29. [PMID: 37400474 DOI: 10.1038/s41540-023-00289-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2022] [Accepted: 06/14/2023] [Indexed: 07/05/2023] Open
Abstract
Mathematical modeling of the emergent dynamics of gene regulatory networks (GRN) faces a double challenge of (a) dependence of model dynamics on parameters, and (b) lack of reliable experimentally determined parameters. In this paper we compare two complementary approaches for describing GRN dynamics across unknown parameters: (1) parameter sampling and resulting ensemble statistics used by RACIPE (RAndom CIrcuit PErturbation), and (2) use of rigorous analysis of combinatorial approximation of the ODE models by DSGRN (Dynamic Signatures Generated by Regulatory Networks). We find a very good agreement between RACIPE simulation and DSGRN predictions for four different 2- and 3-node networks typically observed in cellular decision making. This observation is remarkable since the DSGRN approach assumes that the Hill coefficients of the models are very high while RACIPE assumes the values in the range 1-6. Thus DSGRN parameter domains, explicitly defined by inequalities between systems parameters, are highly predictive of ODE model dynamics within a biologically reasonable range of parameters.
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Affiliation(s)
- Kishore Hari
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore, 560012, India
| | - William Duncan
- Department of Mathematical Sciences, Montana State University, Bozeman, MT, 59717, USA
| | - Mohammed Adil Ibrahim
- Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Hyderabad, 502285, India
| | - Mohit Kumar Jolly
- Centre for BioSystems Science and Engineering, Indian Institute of Science, Bangalore, 560012, India.
| | - Breschine Cummins
- Department of Mathematical Sciences, Montana State University, Bozeman, MT, 59717, USA.
| | - Tomas Gedeon
- Department of Mathematical Sciences, Montana State University, Bozeman, MT, 59717, USA.
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Cummins B, Motta FC, Moseley RC, Deckard A, Campione S, Gameiro M, Gedeon T, Mischaikow K, Haase SB. Experimental guidance for discovering genetic networks through hypothesis reduction on time series. PLoS Comput Biol 2022; 18:e1010145. [PMID: 36215333 PMCID: PMC9584434 DOI: 10.1371/journal.pcbi.1010145] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Revised: 10/20/2022] [Accepted: 09/05/2022] [Indexed: 11/19/2022] Open
Abstract
Large programs of dynamic gene expression, like cell cyles and circadian rhythms, are controlled by a relatively small "core" network of transcription factors and post-translational modifiers, working in concerted mutual regulation. Recent work suggests that system-independent, quantitative features of the dynamics of gene expression can be used to identify core regulators. We introduce an approach of iterative network hypothesis reduction from time-series data in which increasingly complex features of the dynamic expression of individual, pairs, and entire collections of genes are used to infer functional network models that can produce the observed transcriptional program. The culmination of our work is a computational pipeline, Iterative Network Hypothesis Reduction from Temporal Dynamics (Inherent dynamics pipeline), that provides a priority listing of targets for genetic perturbation to experimentally infer network structure. We demonstrate the capability of this integrated computational pipeline on synthetic and yeast cell-cycle data.
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Affiliation(s)
- Breschine Cummins
- Department of Mathematical Sciences, Montana State University, Bozeman, Montana, United States of America
- * E-mail:
| | - Francis C. Motta
- Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, Florida, United States of America
| | - Robert C. Moseley
- Department of Biology, Duke University, Durham, North Carolina, United States of America
| | - Anastasia Deckard
- Geometric Data Analytics, Durham, North Carolina, United States of America
| | - Sophia Campione
- Department of Biology, Duke University, Durham, North Carolina, United States of America
| | - Marcio Gameiro
- Department of Mathematics, Rutgers University, New Brunswick, New Jersey, United States of America
- Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, São Paulo, Brazil
| | - Tomáš Gedeon
- Department of Mathematical Sciences, Montana State University, Bozeman, Montana, United States of America
| | - Konstantin Mischaikow
- Department of Mathematics, Rutgers University, New Brunswick, New Jersey, United States of America
| | - Steven B. Haase
- Department of Biology, Duke University, Durham, North Carolina, United States of America
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Fox E, Cummins B, Duncan W, Gedeon T. Modeling Transport Regulation in Gene Regulatory Networks. Bull Math Biol 2022; 84:89. [PMID: 35831627 DOI: 10.1007/s11538-022-01035-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2022] [Accepted: 05/26/2022] [Indexed: 12/01/2022]
Abstract
A gene regulatory network summarizes the interactions between a set of genes and regulatory gene products. These interactions include transcriptional regulation, protein activity regulation, and regulation of the transport of proteins between cellular compartments. DSGRN is a network modeling approach that builds on traditions of discrete-time Boolean models and continuous-time switching system models. When all interactions are transcriptional, DSGRN uses a combinatorial approximation to describe the entire range of dynamics that is compatible with network structure. Here we present an extension of the DGSRN approach to transport regulation across a boundary between compartments, such as a cellular membrane. We illustrate our approach by searching a model of the p53-Mdm2 network for the potential to admit two experimentally observed distinct stable periodic cycles.
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Affiliation(s)
- Erika Fox
- Department of Mathematics, University of Nevada, Reno, NV, USA
| | - Bree Cummins
- Department of Mathematical Sciences, Montana State University, Bozeman, MT, USA
| | - William Duncan
- Department of Mathematical Sciences, Montana State University, Bozeman, MT, USA
| | - Tomáš Gedeon
- Department of Mathematical Sciences, Montana State University, Bozeman, MT, USA.
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Gameiro M, Gedeon T, Kepley S, Mischaikow K. Rational design of complex phenotype via network models. PLoS Comput Biol 2021; 17:e1009189. [PMID: 34324484 PMCID: PMC8354484 DOI: 10.1371/journal.pcbi.1009189] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Revised: 08/10/2021] [Accepted: 06/17/2021] [Indexed: 11/18/2022] Open
Abstract
We demonstrate a modeling and computational framework that allows for rapid screening of thousands of potential network designs for particular dynamic behavior. To illustrate this capability we consider the problem of hysteresis, a prerequisite for construction of robust bistable switches and hence a cornerstone for construction of more complex synthetic circuits. We evaluate and rank most three node networks according to their ability to robustly exhibit hysteresis where robustness is measured with respect to parameters over multiple dynamic phenotypes. Focusing on the highest ranked networks, we demonstrate how additional robustness and design constraints can be applied. We compare our results to more traditional methods based on specific parameterization of ordinary differential equation models and demonstrate a strong qualitative match at a small fraction of the computational cost. A major challenge in the domains of systems and synthetic biology is an inability to efficiently predict function(s) of complex networks. This work demonstrates a modeling and computational framework that allows for a mathematically justifiable rigorous screening of thousands of potential network designs for a wide variety of dynamical behavior. We screen all 3-node genetic networks and rank them based on their ability to act as an inducible bistable switch. Our results are summarized in a searchable database that can be used to construct robust switches. The ability to quickly screen thousands of designs significantly reduces the set of viable designs and allows synthetic biologists to focus their experimental and more traditional modeling tools to this much smaller set.
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Affiliation(s)
- Marcio Gameiro
- Department of Mathematics, Rutgers, The State University of New Jersey, Piscataway, New Jersey, United States of America.,Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, São Paulo, Brazil
| | - Tomáš Gedeon
- Department of Mathematical Sciences, Montana State University, Bozeman, Montana, United States of America
| | - Shane Kepley
- Department of Mathematics, Rutgers, The State University of New Jersey, Piscataway, New Jersey, United States of America
| | - Konstantin Mischaikow
- Department of Mathematics, Rutgers, The State University of New Jersey, Piscataway, New Jersey, United States of America
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