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Modeling delayed processes in biological systems.

Jingchen Feng1, Stuart A Sevier2, Bin Huang3

  • 1Department of Bioengineering and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77251-1892, USA.

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Summary
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Delay differential equations (DDEs) may inaccurately model biological delays. Explicitly modeling intermediate steps reveals differences in equilibrium distributions and dynamics, highlighting DDE limitations for stochastic biological systems.

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Area of Science:

  • Mathematical Biology
  • Systems Biology
  • Computational Biology

Background:

  • Delayed processes are common in biological systems.
  • Delay differential equations (DDEs) are frequently used to model these processes, often incorporating stochastic effects.
  • DDEs typically use an average delay time, omitting explicit intermediate states.

Purpose of the Study:

  • To investigate the validity of using DDEs for systems with significant delays.
  • To compare the predictions of DDEs with deterministic delay values against models that explicitly incorporate intermediate steps.
  • To identify potential ambiguities and inaccuracies in DDE-based modeling of biological delays.

Main Methods:

  • Development of explicit models that incorporate intermediate steps for delayed biological processes.
  • Comparison of equilibrium distributions and transition times between explicit models and traditional DDEs.
  • Analysis of model dynamics to identify discrepancies and potential ambiguities.

Main Results:

  • Explicit models yield significantly different equilibrium distributions and transition times compared to DDEs with deterministic delays.
  • Different explicit models with distinct dynamics can result in the same DDE, indicating inherent ambiguities.
  • DDE predictions of oscillatory behavior may not hold true for the corresponding explicit models.

Conclusions:

  • Traditional DDEs may oversimplify biological systems with significant delays.
  • Explicitly modeling intermediate steps is crucial for accurately capturing system dynamics and equilibrium states.
  • The use of DDEs in biological modeling requires careful consideration of their limitations, especially for systems exhibiting complex dynamics or oscillatory behavior.