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Fixed and Distributed Gene Expression Time Delays in Reaction-Diffusion Systems.

Alec Sargood1, Eamonn A Gaffney1, Andrew L Krause2,3

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Summary
This summary is machine-generated.

Time delays in gene expression impact pattern formation in reaction-diffusion systems. These delays affect Turing space size and pattern formation time, with effects robust across various conditions.

Keywords:
Linear instability analysisPattern formationTime delay

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Area of Science:

  • Mathematical Biology
  • Systems Biology
  • Biophysics

Background:

  • Time delays in intracellular gene expression influence reaction-diffusion system dynamics.
  • Previous studies indicate delays can shrink the Turing space and prolong pattern formation times.

Purpose of the Study:

  • To analyze the impact of fixed and distributed time delays on reaction-diffusion models of gene expression.
  • To investigate how delay location and distribution affect pattern formation dynamics.
  • To determine the robustness of delay effects under varying conditions.

Main Methods:

  • Systematic linear instability analysis.
  • Numerical simulations across diverse reaction kinetics.
  • Analysis of fixed and distributed time delays, including skewed Gaussian distributions.

Main Results:

  • Distributed time delays with complex kernels have minimal impact compared to fixed delays with the same mean.
  • Delay location significantly alters Turing space size, which can increase or decrease with mean delay.
  • Pattern formation time scales linearly with mean time delay and is robust to initial/boundary conditions.

Conclusions:

  • Gene expression time delays play a crucial role in reaction-diffusion patterning.
  • Delay location is a key factor influencing pattern formation dynamics.
  • The findings provide a clearer understanding of delay effects and guide future modeling efforts.