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Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems.

Thomas E Woolley1, Ruth E Baker, Eamonn A Gaffney

  • 1Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB, United Kingdom. woolley@maths.ox.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
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Summary

Stochasticity may reduce patterning time in delayed Turing systems, but does not entirely remove sensitivity to delays. Intrinsic noise can ameliorate delay effects in specific gene expression models.

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Area of Science:

  • Computational biology
  • Systems biology
  • Biophysics

Background:

  • Cellular gene expression involves complex, time-consuming processes like DNA transcription and mRNA translation.
  • Kinetic delays in reaction-diffusion systems can significantly impact pattern formation, questioning Turing mechanisms for gene expression.
  • Deterministic models show delays can drastically increase patterning time.

Purpose of the Study:

  • To investigate if intrinsic stochasticity can shorten patterning timescales in delayed Turing systems.
  • To assess the interplay between stochasticity and delays in biological pattern formation.
  • To determine if stochasticity can mitigate the negative effects of delays on Turing patterning.

Main Methods:

  • Stochastic simulations of delayed Turing systems.
  • Analysis of four distinct Turing systems with two delay forms.
  • Comparison of patterning times in stochastic versus deterministic simulations.

Main Results:

  • Stochasticity partially mitigates, but does not eliminate, the sensitivity of Turing patterning to delays.
  • The ameliorating effect of stochasticity on delays is system-specific.
  • Patterning time scales in delayed systems can be reduced by intrinsic noise in certain cases.

Conclusions:

  • Intrinsic noise can ameliorate the impact of kinetic delays on Turing pattern formation in gene expression.
  • The effectiveness of stochasticity in mitigating delays is dependent on the specific biological system and delay characteristics.
  • Further research is needed to fully understand the role of noise and delays in biological pattern formation.