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Stochastic pattern formation and spontaneous polarisation: the linear noise approximation and beyond.

Alan J McKane1, Tommaso Biancalani, Tim Rogers

  • 1Theoretical Physics Division, School of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK, alan.mckane@manchester.ac.uk.

Bulletin of Mathematical Biology
|March 9, 2013
PubMed
Summary

This study details mathematical models for biological stochasticity, explaining how noise creates patterns and cell polarity. These findings advance our understanding of noise-induced phenomena in biological systems.

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Area of Science:

  • Mathematical Biology
  • Theoretical Biology
  • Systems Biology

Background:

  • Biological systems exhibit inherent randomness (stochasticity) that influences their behavior.
  • Existing macroscopic models often simplify or overlook these crucial stochastic effects.
  • Understanding stochasticity is key to accurately modeling biological processes.

Purpose of the Study:

  • To review and derive the mathematical formalism for modeling stochasticity in biological systems.
  • To apply this formalism to analyze noise-induced phenomena in biologically inspired models.
  • To provide a framework for understanding pattern formation and cell polarization driven by noise.

Main Methods:

  • Derivation of mesoscopic equations from basic constituents, generalizing macroscopic equations.
  • Application of the formalism to analyze stochastic amplification of Turing instability.
  • Analysis of spontaneous cell polarity emergence using time-scale separation.

Main Results:

  • Stochastic amplification of Turing instability leads to observable spatial and temporal patterns.
  • These patterns are explicable within the linear noise approximation.
  • Analytic progress was made in understanding cell polarity through time-scale separation.

Conclusions:

  • The derived mesoscopic formalism effectively models stochasticity in biological systems.
  • Noise is a significant factor driving pattern formation and cellular organization.
  • This work provides a foundation for further theoretical and experimental investigations into biological noise.