Nonlinear delay differential equations and their application to modeling biological network motifs

David S Glass; Xiaofan Jin; Ingmar H Riedel-Kruse

doi:10.1038/s41467-021-21700-8

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Nonlinear delay differential equations and their application to modeling biological network motifs

Journal article

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Nonlinear delay differential equations and their application to modeling biological network motifs

David S Glass, Xiaofan Jin and Ingmar H Riedel-Kruse

Nature communications, Vol.12(1), 1788

19/Mar/2021

DOI: https://doi.org/10.1038/s41467-021-21700-8

PMID: 33741909

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Abstract

Biological regulatory systems, such as cell signaling networks, nervous systems and ecological webs, consist of complex dynamical interactions among many components. Network motif models focus on small sub-networks to provide quantitative insight into overall behavior. However, such models often overlook time delays either inherent to biological processes or associated with multi-step interactions. Here we systematically examine explicit-delay versions of the most common network motifs via delay differential equation (DDE) models, both analytically and numerically. We find many broadly applicable results, including parameter reduction versus canonical ordinary differential equation (ODE) models, analytical relations for converting between ODE and DDE models, criteria for when delays may be ignored, a complete phase space for autoregulation, universal behaviors of feedforward loops, a unified Hill-function logic framework, and conditions for oscillations and chaos. We conclude that explicit-delay modeling simplifies the phenomenology of many biological networks and may aid in discovering new functional motifs.

Computational Biology - methods

Feedback, Physiological

Animals

Humans

Gene Expression Regulation

Models, Genetic

Signal Transduction - genetics

Gene Regulatory Networks

Algorithms

Nonlinear Dynamics

Details

Title: Nonlinear delay differential equations and their application to modeling biological network motifs
Creators: David S Glass - 972WIS_INST___122
Xiaofan Jin - Gladstone Institutes
Ingmar H Riedel-Kruse (Corresponding Author) - University of Arizona
Resource Type: Journal article
Publication Details: Nature communications, Vol.12(1), 1788
Number of pages: 19
Publisher: England
Language: English
DOI: https://doi.org/10.1038/s41467-021-21700-8
PMID: 33741909
Grant note: We would like to thank A. Choksi, J. Prine, M. Aktas, Y. Yang, A. Mayo, A. Woller, U. Alon, and the Riedel-Kruse lab for their feedback and discussions. This work was supported in part by the Davies Family Engineering Fellowship, the Bio-X Bowes Graduate Student Fellowship, and the NSERC PGS fellowship. D.S.G is currently a member of the Zuckerman Postdoctoral Scholars Program. Author contributions - D.S.G., X.J., and I.H.R.K. all contributed to conception, analysis, and writing of this manuscript.
Record Identifier: 993265437903596

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