Precision and dissipation of a stochastic Turing pattern

Abstract

Spontaneous pattern formation is a fundamental scientific problem that has received much attention since the seminal theoretical work of Turing on reaction-diffusion systems. In molecular biophysics, this phenomena often takes place under the influence of large fluctuations. It is then natural to inquire about the precision of such pattern. In particular, spontaneous pattern formation is a nonequilibrium phenomenon, and the relation between the precision of a pattern and the thermodynamic cost associated with it remains unexplored. Here, we analyze this relation with a paradigmatic stochastic reaction-diffusion model, the Brusselator in one spatial dimension. We find that the precision of the pattern is maximized for an intermediate thermodynamic cost, i.e., increasing the thermodynamic cost beyond this value makes the pattern less precise. Even though fluctuations get less pronounced with an increase in thermodynamic cost, we argue that larger fluctuations can also have a positive effect on the precision of the pattern.

arXiv comment7 pages, 8 figures

References in corpus (25)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Thermodynamic uncertainty relation for biomolecular processes
• The Energetic Costs of Cellular Computation
• The free energy cost of accurate biochemical oscillations
• Efficiency of cellular information processing
• Stochastic Turing patterns in the Brusselator model
• Robust ecological pattern formation induced by demographic noise
• Fluctuation-driven Turing patterns
• Quasi-cycles in a spatial predator-prey model
• Information Thermodynamics of Turing Patterns
• Nonequilibrium thermodynamics of coupled molecular oscillators: The energy cost and optimal design for synchronization
• Entropy production in the majority-vote model
• Giant amplification of noise in fluctuation-induced pattern formation
• Coherence of Biochemical Oscillations is Bounded by Driving Force and Network Topology
• Biochemical machines for the interconversion of mutual information and work
• The Thermodynamic Uncertainty Relation in Biochemical Oscillations
• Phase transition in thermodynamically consistent biochemical oscillators
• Thermodynamics of Chemical Waves
• Critical behavior of entropy production and learning rate: Ising model with an oscillating field
• High chemical affinity increases the robustness of biochemical oscillations
• Quantifying fluctuations in reversible enzymatic cycles and clocks
• Error-speed correlations in biopolymer synthesis
• Entropy production of a bound nonequilibrium interface
• Robust oscillations in multi-cyclic models of biochemical clocks
• Stochastic thermodynamics of chemical reactions coupled to finite reservoirs: A case study for the Brusselator

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• Nonequilibrium fluctuations of chemical reaction networks at criticality: The Schlögl model as paradigmatic case
• Geometric thermodynamics of reaction-diffusion systems: Thermodynamic trade-off relations and optimal transport for pattern formation
• Irreversibility in Non-reciprocal Chaotic Systems
• Positional information trade-offs in boundary-driven reaction-diffusion systems
• Phase coexistence in a weakly stochastic reaction-diffusion system
• Limits to positional information in boundary-driven systems
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