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Precision and dissipation of a stochastic Turing pattern.

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Spontaneous pattern formation precision is maximized at intermediate thermodynamic costs. Increasing costs beyond this point reduces pattern precision, despite reduced fluctuations.

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Area of Science:

  • Molecular Biophysics
  • Theoretical Physics
  • Chemical Kinetics

Background:

  • Spontaneous pattern formation is a key problem in reaction-diffusion systems, notably studied by Turing.
  • In molecular biophysics, pattern formation often involves significant fluctuations.
  • The relationship between pattern precision and thermodynamic cost in nonequilibrium systems is underexplored.

Purpose of the Study:

  • To investigate the connection between pattern precision and thermodynamic cost in spontaneous pattern formation.
  • To analyze this relationship using a stochastic reaction-diffusion model.

Main Methods:

  • Utilized a one-dimensional Brusselator model, a standard reaction-diffusion system.
  • Analyzed the impact of varying thermodynamic costs on pattern precision.
  • Investigated the role of fluctuations in pattern formation.

Main Results:

  • Pattern precision reaches a maximum at an intermediate thermodynamic cost.
  • Higher thermodynamic costs beyond the optimum lead to decreased pattern precision.
  • Fluctuations, while diminishing with increased cost, can positively influence pattern precision.

Conclusions:

  • The precision of patterns formed via spontaneous processes is not monotonically dependent on thermodynamic cost.
  • An optimal thermodynamic cost exists for maximizing pattern precision in stochastic reaction-diffusion systems.
  • Fluctuations play a complex role, potentially enhancing precision even as they are suppressed by increasing cost.