Information Thermodynamics of Turing Patterns

Falasco, Gianmaria; Rao, Riccardo; Esposito, Massimiliano

doi:10.1103/physrevlett.121.108301

Cited by 75 publications

(71 citation statements)

References 52 publications

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“…Whether anything similar occurs for multistable models, and how this interacts with dynamical biases and phase transitions, shall be a very interesting question for a future work. We might also ask similar questions for systems that exhibit instabilities leading to Turing patterns [58].…”

Section: Discussionmentioning

confidence: 99%

Large deviations and dynamical phase transitions in stochastic chemical networks

Lazarescu

Cossetto

Falasco

et al. 2019

The Journal of Chemical Physics

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Chemical reaction networks offer a natural nonlinear generalisation of linear Markov jump processes on a finite state-space. In this paper, we analyse the dynamical large deviations of such models, starting from their microscopic version, the chemical master equation. By taking a largevolume limit, we show that those systems can be described by a path integral formalism over a Lagrangian functional of concentrations and chemical fluxes. This Lagrangian is dual to a Hamiltonian, whose trajectories correspond to the most likely evolution of the system given its boundary conditions.The same can be done for a system biased on time-averaged concentrations and currents, yielding a biased Hamiltonian whose trajectories are optimal paths conditioned on those observables. The appropriate boundary conditions turn out to be mixed, so that, in the long time limit, those trajectories converge to well-defined attractors. We are then able to identify the largest value that the Hamiltonian takes over those attractors with the scaled cumulant generating function of our observables, providing a non-linear equivalent to the well-known Donsker-Varadhan formula for jump processes.On that basis, we prove that chemical reaction networks that are deterministically multistable generically undergo first-order dynamical phase transitions in the vicinity of zero bias. We illustrate that fact through a simple bistable model called the Schlögl model, as well as multistable and unstable generalisations of it, and we make a few surprising observations regarding the stability of deterministic fixed points, and the breaking of ergodicity in the large-volume limit. arXiv:1902.08416v1 [cond-mat.stat-mech]

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Section: Discussionmentioning

confidence: 99%

Large deviations and dynamical phase transitions in stochastic chemical networks

Lazarescu

Cossetto

Falasco

et al. 2019

The Journal of Chemical Physics

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“…denotes the elements of the inverse of the matrix whose entries are l λ b αy b (see Ref. [14] for details). The moieties represent the concentration of parts of molecules which are exchanged with the environment through the chemostats since their time evolution is determined only by the external currents,…”

Section: Reaction-diffusion Systemsmentioning

confidence: 99%

“…First, we recapitulate the global thermodynamic theory developed in Ref. [14] and then we generalize it to a local formulation. The global second law of thermodynamics for open RDSs can be stated as the following balance equation…”

Section: Reaction-diffusion Systemsmentioning

confidence: 99%

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Thermodynamics of chemical waves

Avanzini

Falasco

Esposito

2019

The Journal of Chemical Physics

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Chemical waves constitute a known class of dissipative structures emerging in reaction-diffusion systems. They play a crucial role in biology, spreading information rapidly to synchronize and coordinate biological events. We develop a rigorous thermodynamic theory of reaction-diffusion systems to characterize chemical waves. Our main result is the definition of the proper thermodynamic potential of the local dynamics as a nonequilibrium free energy density and establishing its balance equation. This enables us to identify the dynamics of the free energy, of the dissipation, and of the work spent to sustain the wave propagation. Two prototypical classes of chemical waves are examined. From a thermodynamic perspective, the first is sustained by relaxation towards equilibrium and the second by nonconservative forces generated by chemostats. We analytically study step-like waves, called wavefronts, using the Fisher-Kolmogorov equation as representative of the first class and oscillating waves in the Brusselator model as representative of the second. Given the fundamental role of chemical waves as message carriers in biosystems, our thermodynamic theory constitutes an important step toward an understanding of information transfers and processing in biology. :1904.08874v1 [cond-mat.stat-mech] arXiv

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“…Among other topics the link between dissipation and prediction has been explored, again showing that long term prediction requires energy expenditure [ 35 , 47 ], and the non-predictive part of the information about past fluctuations is linked to dissipation [ 35 ]. Most recently, the links between information and dissipation have been studied in spatial systems [ 52 ].…”

Section: Introductionmentioning

confidence: 99%

Dissipation in Non-Steady State Regulatory Circuits

Szymańska-Rożek

Villamaina

Miękisz

et al. 2019

Entropy

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In order to respond to environmental signals, cells often use small molecular circuits to transmit information about their surroundings. Recently, motivated by concrete examples in signaling and gene regulation, a body of work has focused on the properties of circuits that function out of equilibrium and dissipate energy. We briefly review the probabilistic measures of information and dissipation and use simple models to discuss and illustrate trade-offs between information and dissipation in biological circuits. We find that circuits with non-steady state initial conditions can transmit more information at small readout delays than steady state circuits. The dissipative cost of this additional information proves marginal compared to the steady state dissipation. Feedback does not significantly increase the transmitted information for out of steady state circuits but does decrease dissipative costs. Lastly, we discuss the case of bursty gene regulatory circuits that even in the fast switching limit function out of equilibrium.

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Information Thermodynamics of Turing Patterns

Cited by 75 publications

References 52 publications

Large deviations and dynamical phase transitions in stochastic chemical networks

Large deviations and dynamical phase transitions in stochastic chemical networks

Thermodynamics of chemical waves

Dissipation in Non-Steady State Regulatory Circuits

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