Nonlinear delay differential equations and their application to modeling biological network motifs
David S Glass1, Xiaofan Jin2, Ingmar H Riedel-Kruse3
1Department of Molecular Cell Biology, Weizmann Institute of Science, Rehovot, Israel.
Nature Communications
|March 20, 2021
Summary
Incorporating time delays into biological network models simplifies their complex dynamics. Explicit-delay modeling reveals universal behaviors and aids in discovering new functional motifs in biological systems.
Area of Science:
- Systems biology
- Theoretical biology
- Computational neuroscience
Background:
- Biological regulatory systems exhibit complex dynamics.
- Network motif models offer insights but often neglect time delays.
- Time delays are inherent in biological processes and multi-step interactions.
Purpose of the Study:
- To systematically examine explicit-delay versions of common network motifs using delay differential equations (DDEs).
- To provide analytical and numerical insights into the impact of time delays on biological network behavior.
- To explore how DDE models can simplify the phenomenology of biological networks.
Main Methods:
- Development and analysis of delay differential equation (DDE) models for common network motifs.
- Analytical derivations for parameter reduction and ODE-DDE conversions.
- Numerical simulations to explore phase space, universal behaviors, and conditions for oscillations/chaos.
Main Results:
- Identified parameter reduction opportunities compared to ordinary differential equation (ODE) models.
- Established analytical relations for converting between ODE and DDE models.
- Determined criteria for when time delays can be disregarded in modeling.
- Characterized the complete phase space for autoregulation and universal behaviors of feedforward loops.
- Developed a unified Hill-function logic framework and identified conditions for oscillations and chaos.
Conclusions:
- Explicit-delay modeling offers a simplified yet comprehensive approach to understanding biological networks.
- This modeling strategy can aid in the discovery of novel functional motifs.
- Time delays are crucial factors that influence the dynamics and behavior of biological systems.
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