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Marehalli Srinivas SG, Avanzini F, Esposito M. Thermodynamics of Growth in Open Chemical Reaction Networks. PHYSICAL REVIEW LETTERS 2024; 132:268001. [PMID: 38996287 DOI: 10.1103/physrevlett.132.268001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Accepted: 04/12/2024] [Indexed: 07/14/2024]
Abstract
We identify the thermodynamic conditions necessary to observe indefinite growth in homogeneous open chemical reaction networks (CRNs) satisfying mass action kinetics. We also characterize the thermodynamic efficiency of growth by considering the fraction of the chemical work supplied from the surroundings that is converted into CRN free energy. We find that indefinite growth cannot arise in CRNs chemostatted by fixing the concentration of some species at constant values, or in continuous-flow stirred tank reactors. Indefinite growth requires a constant net influx from the surroundings of at least one species. In this case, unimolecular CRNs always generate equilibrium linear growth, i.e., a continuous linear accumulation of species with equilibrium concentrations and efficiency one. Multimolecular CRNs are necessary to generate nonequilibrium growth, i.e., the continuous accumulation of species with nonequilibrium concentrations. Pseudounimolecular CRNs-a subclass of multimolecular CRNs-always generate asymptotic linear growth with zero efficiency. Our findings demonstrate the importance of the CRN topology and the chemostatting procedure in determining the dynamics and thermodynamics of growth.
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Affiliation(s)
- Shesha Gopal Marehalli Srinivas
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Francesco Avanzini
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
- Department of Chemical Sciences, University of Padova, Via F. Marzolo, 1, I-35131 Padova, Italy
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
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2
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Marehalli Srinivas SG, Avanzini F, Esposito M. Characterizing the conditions for indefinite growth in open chemical reaction networks. Phys Rev E 2024; 109:064153. [PMID: 39020892 DOI: 10.1103/physreve.109.064153] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Accepted: 04/25/2024] [Indexed: 07/20/2024]
Abstract
The thermodynamic and dynamical conditions necessary to observe indefinite growth in homogeneous open chemical reaction networks (CRNs) satisfying mass action kinetics are presented in Srinivas et al. [Phys. Rev. Lett. 132, 268001 (2024)10.1103/PhysRevLett.132.268001]. Unimolecular CRNs can accumulate only equilibrium concentrations of species while multimolecular CRNs are needed to produce indefinite growth with nonequilibrium concentrations. Within multimolecular CRNs, pseudo-unimolecular CRNs produce nonequilibrium concentrations with zero efficiencies. Nonequilibrium growth with efficiencies greater than zero requires dynamically nonlinear CRNs. In this paper, we provide a detailed analysis supporting these results. Mathematical proofs are provided for growth in unimolecular and pseudo-unimolecular CRNs. For multimolecular CRNs, four models displaying very distinctive topological properties are extensively studied, both numerically and partly analytically.
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3
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Kumar P, Gangopadhyay G. Nonequilibrium thermodynamic signatures of collective dynamical states around chimera in a chemical reaction network. Phys Rev E 2023; 108:044218. [PMID: 37978606 DOI: 10.1103/physreve.108.044218] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2023] [Accepted: 10/03/2023] [Indexed: 11/19/2023]
Abstract
Different dynamical states ranging from coherent, incoherent to chimera, multichimera, and related transitions are addressed in a globally coupled nonlinear continuum chemical oscillator system by implementing a modified complex Ginzburg-Landau equation. Besides dynamical identifications of observed states using standard qualitative metrics, we systematically acquire nonequilibrium thermodynamic characterizations of these states obtained via coupling parameters. The nonconservative work profiles in collective dynamics qualitatively reflect the time-integrated concentration of the activator, and the majority of the nonconservative work contributes to the entropy production over the spatial dimension. It is illustrated that the evolution of spatial entropy production and semigrand Gibbs free-energy profiles associated with each state are connected yet completely out of phase, and these thermodynamic signatures are extensively elaborated to shed light on the exclusiveness and similarities of these states. Moreover, a relationship between the proper nonequilibrium thermodynamic potential and the variance of activator concentration is established by exhibiting both quantitative and qualitative similarities between a Fano factor like entity, derived from the activator concentration, and the Kullback-Leibler divergence associated with the transition from a nonequilibrium homogeneous state to an inhomogeneous state. Quantifying the thermodynamic costs for collective dynamical states would aid in efficiently controlling, manipulating, and sustaining such states to explore the real-world relevance and applications of these states.
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Affiliation(s)
- Premashis Kumar
- S. N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
| | - Gautam Gangopadhyay
- S. N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India
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4
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Aslyamov T, Avanzini F, Fodor É, Esposito M. Nonideal Reaction-Diffusion Systems: Multiple Routes to Instability. PHYSICAL REVIEW LETTERS 2023; 131:138301. [PMID: 37832019 DOI: 10.1103/physrevlett.131.138301] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2023] [Accepted: 08/30/2023] [Indexed: 10/15/2023]
Abstract
We develop a general classification of the nature of the instabilities yielding spatial organization in open nonideal reaction-diffusion systems, based on linear stability analysis. This encompasses dynamics where chemical species diffuse, interact with each other, and undergo chemical reactions driven out of equilibrium by external chemostats. We find analytically that these instabilities can be of two types: instabilities caused by intermolecular energetic interactions (E type), and instabilities caused by multimolecular out-of-equilibrium chemical reactions (R type). Furthermore, we identify a class of chemical reaction networks, containing unimolecular networks but also extending beyond them, that can only undergo E-type instabilities. We illustrate our analytical findings with numerical simulations on two reaction-diffusion models, each displaying one of the two types of instability and generating stable patterns.
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Affiliation(s)
- Timur Aslyamov
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Francesco Avanzini
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
- Department of Chemical Sciences, University of Padova, Via F. Marzolo, 1, I-35131 Padova, Italy
| | - Étienne Fodor
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Massimiliano Esposito
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
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5
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Kumar P, Gangopadhyay G. Glycolytic Wave Patterns in a Simple Reaction-diffusion System with Inhomogeneous Influx: Dynamic Transitions. Chemphyschem 2023; 24:e202200643. [PMID: 36478341 DOI: 10.1002/cphc.202200643] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2022] [Revised: 11/21/2022] [Indexed: 12/12/2022]
Abstract
An inhomogeneous profile of chemostatted species generates a rich variety of patterns in glycolytic waves depicted in a Selkov reaction-diffusion framework here. A key role played by diffusion amplitude and symmetry in the chemostatted species profile in dictating the fate of local spatial dynamics involving periodic, quasiperiodic, and chaotic patterns and transitions among them are investigated systematically. More importantly, various dynamic transitions, including wave propagation direction changes, are illustrated in interesting situations. Besides numerical results, our analytical formulation of the amplitude equation connecting complex Ginzburg-Landau and Lambda-omega representation shed light on the phase dynamics of the system. This systematic study of the glycolytic reaction-diffusion wave is in line with previous experimental results in open spatial reactor and will provide a knowledge about the dynamics that shape and control biological information processing and related phenomena.
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Affiliation(s)
- Premashis Kumar
- S. N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata, 700 106, India
| | - Gautam Gangopadhyay
- S. N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata, 700 106, India
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6
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Ohga N, Ito S. Information-geometric structure for chemical thermodynamics: An explicit construction of dual affine coordinates. Phys Rev E 2022; 106:044131. [PMID: 36397558 DOI: 10.1103/physreve.106.044131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 09/08/2022] [Indexed: 06/16/2023]
Abstract
We construct an information-geometric structure for chemical thermodynamics, applicable to a wide range of chemical reaction systems including nonideal and open systems. For this purpose, we explicitly construct dual affine coordinate systems, which completely designate an information-geometric structure, using the extent of reactions and the affinities of reactions as coordinates on a linearly constrained space of amounts of substances. The resulting structure induces a metric and a divergence (a function of two distributions of amounts), both expressed with chemical potentials. These quantities have been partially known for ideal-dilute solutions, but their extensions for nonideal solutions and the complete underlying structure are novel. The constructed geometry is a generalization of dual affine coordinates for stochastic thermodynamics. For example, the metric and the divergence are generalizations of the Fisher information and the Kullback-Leibler divergence. As an application, we identify the chemical-thermodynamic analog of the Hatano-Sasa excess entropy production using our divergence.
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Affiliation(s)
- Naruo Ohga
- Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Sosuke Ito
- Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
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7
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Penocchio E, Avanzini F, Esposito M. Information thermodynamics for deterministic chemical reaction networks. J Chem Phys 2022; 157:034110. [DOI: 10.1063/5.0094849] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
Information thermodynamics relates the rate of change of mutual information between two interacting subsystems to their thermodynamics when the joined system is described by a bipartite stochastic dynamics satisfying local detailed balance. Here, we expand the scope of information thermodynamics to deterministic bipartite chemical reaction networks, namely, composed of two coupled subnetworks sharing species but not reactions. We do so by introducing a meaningful notion of mutual information between different molecular features that we express in terms of deterministic concentrations. This allows us to formulate separate second laws for each subnetwork, which account for their energy and information exchanges, in complete analogy with stochastic systems. We then use our framework to investigate the working mechanisms of a model of chemically driven self-assembly and an experimental light-driven bimolecular motor. We show that both systems are constituted by two coupled subnetworks of chemical reactions. One subnetwork is maintained out of equilibrium by external reservoirs (chemostats or light sources) and powers the other via energy and information flows. In doing so, we clarify that the information flow is precisely the thermodynamic counterpart of an information ratchet mechanism only when no energy flow is involved.
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Affiliation(s)
- Emanuele Penocchio
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Francesco Avanzini
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
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8
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Avanzini F, Esposito M. Thermodynamics of concentration vs flux control in chemical reaction networks. J Chem Phys 2022; 156:014116. [PMID: 34998328 DOI: 10.1063/5.0076134] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate the thermodynamic implications of two control mechanisms of open chemical reaction networks. The first controls the concentrations of the species that are exchanged with the surroundings, while the other controls the exchange fluxes. We show that the two mechanisms can be mapped one into the other and that the thermodynamic theories usually developed in the framework of concentration control can be applied to flux control as well. This implies that the thermodynamic potential and the fundamental forces driving chemical reaction networks out of equilibrium can be identified in the same way for both mechanisms. By analyzing the dynamics and thermodynamics of a simple enzymatic model, we also show that while the two mechanisms are equivalent at steady state, the flux control may lead to fundamentally different regimes where systems achieve stationary growth.
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Affiliation(s)
- Francesco Avanzini
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
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9
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Zhang Z, Xu L, Huang J. Controlling Chemical Waves by Transforming Transient Mass Transfer. ADVANCED THEORY AND SIMULATIONS 2021. [DOI: 10.1002/adts.202100375] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Zeren Zhang
- Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE) Fudan University Shanghai 200438 China
| | - Liujun Xu
- Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE) Fudan University Shanghai 200438 China
| | - Jiping Huang
- Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE) Fudan University Shanghai 200438 China
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10
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Penocchio E, Rao R, Esposito M. Nonequilibrium thermodynamics of light-induced reactions. J Chem Phys 2021; 155:114101. [PMID: 34551539 DOI: 10.1063/5.0060774] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Abstract
Current formulations of nonequilibrium thermodynamics of open chemical reaction networks only consider chemostats as free-energy sources sustaining nonequilibrium behaviors. Here, we extend the theory to include incoherent light as a source of free energy. We do so by relying on a local equilibrium assumption to derive the chemical potential of photons relative to the system they interact with. This allows us to identify the thermodynamic potential and the thermodynamic forces driving light-reacting chemical systems out-of-equilibrium. We use this framework to treat two paradigmatic photochemical mechanisms describing light-induced unimolecular reactions-namely, the adiabatic and diabatic mechanisms-and highlight the different thermodynamics they lead to. Furthermore, using a thermodynamic coarse-graining procedure, we express our findings in terms of commonly measured experimental quantities, such as quantum yields.
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Affiliation(s)
- Emanuele Penocchio
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, G. D. Luxembourg
| | - Riccardo Rao
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, G. D. Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, G. D. Luxembourg
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11
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Ueltzhöffer K, Da Costa L, Cialfi D, Friston K. A Drive towards Thermodynamic Efficiency for Dissipative Structures in Chemical Reaction Networks. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1115. [PMID: 34573740 PMCID: PMC8472781 DOI: 10.3390/e23091115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/13/2021] [Revised: 08/23/2021] [Accepted: 08/25/2021] [Indexed: 11/17/2022]
Abstract
Dissipative accounts of structure formation show that the self-organisation of complex structures is thermodynamically favoured, whenever these structures dissipate free energy that could not be accessed otherwise. These structures therefore open transition channels for the state of the universe to move from a frustrated, metastable state to another metastable state of higher entropy. However, these accounts apply as well to relatively simple, dissipative systems, such as convection cells, hurricanes, candle flames, lightning strikes, or mechanical cracks, as they do to complex biological systems. Conversely, interesting computational properties-that characterize complex biological systems, such as efficient, predictive representations of environmental dynamics-can be linked to the thermodynamic efficiency of underlying physical processes. However, the potential mechanisms that underwrite the selection of dissipative structures with thermodynamically efficient subprocesses is not completely understood. We address these mechanisms by explaining how bifurcation-based, work-harvesting processes-required to sustain complex dissipative structures-might be driven towards thermodynamic efficiency. We first demonstrate a simple mechanism that leads to self-selection of efficient dissipative structures in a stochastic chemical reaction network, when the dissipated driving chemical potential difference is decreased. We then discuss how such a drive can emerge naturally in a hierarchy of self-similar dissipative structures, each feeding on the dissipative structures of a previous level, when moving away from the initial, driving disequilibrium.
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Affiliation(s)
- Kai Ueltzhöffer
- Wellcome Centre for Human Neuroimaging, Queen Square Institute of Neurology, University College London, London WC1N 3AR, UK; (L.D.C.); (K.F.)
- Department of General Psychiatry, Center of Psychosocial Medicine, Heidelberg University, 69115 Heidelberg, Germany
| | - Lancelot Da Costa
- Wellcome Centre for Human Neuroimaging, Queen Square Institute of Neurology, University College London, London WC1N 3AR, UK; (L.D.C.); (K.F.)
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK
| | - Daniela Cialfi
- Department of Philosophical, Pedagogical and Economic-Quantitative Sciences, Economic and Quantitative Methods Section, University of Studies Gabriele d’Annunzio Chieti-Pescara, 65127 Pescara, Italy;
| | - Karl Friston
- Wellcome Centre for Human Neuroimaging, Queen Square Institute of Neurology, University College London, London WC1N 3AR, UK; (L.D.C.); (K.F.)
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12
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Kumar P, Gangopadhyay G. Nonequilibrium thermodynamics of glycolytic traveling wave: Benjamin-Feir instability. Phys Rev E 2021; 104:014221. [PMID: 34412344 DOI: 10.1103/physreve.104.014221] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2021] [Accepted: 07/08/2021] [Indexed: 11/07/2022]
Abstract
Evolution of the nonequilibrium thermodynamic entities corresponding to dynamics of the Hopf instabilities and traveling waves at a nonequilibrium steady state of a spatially extended glycolysis model is assessed here by implementing an analytically tractable scheme incorporating a complex Ginzburg-Landau equation (CGLE). In the presence of self and cross diffusion, a more general amplitude equation exploiting the multiscale Krylov-Bogoliubov averaging method serves as an essential tool to reveal the various dynamical instability criteria, especially Benjamin-Feir (BF) instability, to estimate the corresponding nonlinear dispersion relation of the traveling wave pattern. The critical control parameter, wave-number selection criteria, and magnitude of the complex amplitude for traveling waves are modified by self- and cross-diffusion coefficients within the oscillatory regime, and their variabilities are exhibited against the amplitude equation. Unlike the traveling waves, a low-amplitude broad region appears for the Hopf instability in the concentration dynamics as the system phase passes through minima during its variation with the control parameter. The total entropy production rate of the uniform Hopf oscillation and glycolysis wave not only qualitatively reflects the global dynamics of concentrations of intermediate species but almost quantitatively. Despite the crucial role of diffusion in generating and shaping the traveling waves, the diffusive part of the entropy production rate has a negligible contribution to the system's total entropy production rate. The Hopf instability shows a more complex and colossal change in the energy profile of the open nonlinear system than in the traveling waves. A detailed analysis of BF instability shows a contrary nature of the semigrand Gibbs free energy with discrete and continuous wave numbers for the traveling wave. We hope the Hopf and traveling wave pattern around the BF instability in terms of energetics and dissipation will open up new applications of such dynamical phenomena.
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Affiliation(s)
- Premashis Kumar
- S. N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700 106, India
| | - Gautam Gangopadhyay
- S. N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700 106, India
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13
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Tamemoto N, Noguchi H. Reaction-diffusion waves coupled with membrane curvature. SOFT MATTER 2021; 17:6589-6596. [PMID: 34166481 DOI: 10.1039/d1sm00540e] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The reaction-diffusion waves of proteins are known to be involved in fundamental cellular functions, such as cell migration, cell division, and vesicular transportation. In some of these phenomena, pattern formation on the membranes is induced by the coupling between membrane deformation and the reaction-diffusion system through curvature-inducing proteins that bend the biological membranes. Although the membrane shape and the dynamics of the curvature-inducing proteins affect each other in these systems, the effect of such mechanochemical feedback loops on the waves has not been studied in detail. In this study, reaction-diffusion waves coupled with membrane deformation are investigated using simulations combining a dynamically triangulated membrane model with the Brusselator model extended to include the effect of membrane curvature. It is found that the propagating wave patterns change into nonpropageting patterns and spiral wave patterns due to the mechanochemical effects. Moreover, the wave speed is positively or negatively correlated with the local membrane curvature depending on the spontaneous curvature and bending rigidity. In addition, self-oscillation of the vesicle shape occurs, associated with the reaction-diffusion waves of curvature-inducing proteins. This agrees with the experimental observation of GUVs with a reconstituted Min system, which plays a key role in the cell division of Escherichia coli. The findings of this study demonstrate the importance of mechanochemical coupling in biological phenomena.
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Affiliation(s)
- Naoki Tamemoto
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan.
| | - Hiroshi Noguchi
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan.
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14
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Avanzini F, Penocchio E, Falasco G, Esposito M. Nonequilibrium thermodynamics of non-ideal chemical reaction networks. J Chem Phys 2021; 154:094114. [PMID: 33685183 DOI: 10.1063/5.0041225] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
All current formulations of nonequilibrium thermodynamics of open chemical reaction networks rely on the assumption of non-interacting species. We develop a general theory that accounts for interactions between chemical species within a mean-field approach using activity coefficients. Thermodynamic consistency requires that rate equations do not obey standard mass-action kinetics but account for the interactions with concentration dependent kinetic constants. Many features of the ideal formulations are recovered. Crucially, the thermodynamic potential and the forces driving non-ideal chemical systems out of equilibrium are identified. Our theory is general and holds for any mean-field expression of the interactions leading to lower bounded free energies.
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Affiliation(s)
- Francesco Avanzini
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Emanuele Penocchio
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Gianmaria Falasco
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
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15
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Rana S, Barato AC. Precision and dissipation of a stochastic Turing pattern. Phys Rev E 2020; 102:032135. [PMID: 33075863 DOI: 10.1103/physreve.102.032135] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2020] [Accepted: 08/28/2020] [Indexed: 11/07/2022]
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 phenomenon 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 largely unexplored. Here, we analyze this relation with a paradigmatic stochastic reaction-diffusion model, i.e., 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.
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Affiliation(s)
- Shubhashis Rana
- Department of Physics, University of Houston, Houston, Texas 77204, USA
| | - Andre C Barato
- Department of Physics, University of Houston, Houston, Texas 77204, USA
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16
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Abstract
The Turing instability is one of the most commonly studied mechanisms leading to pattern formation in reaction–diffusion systems, yet there are still many open questions on the applicability of the Turing mechanism. Although experiments on pattern formation using chemical systems have shown that temperature differences play a role in pattern formation, there is far less theoretical work concerning the interplay between temperature and spatial instabilities. We consider a thermodynamically extended reaction–diffusion system, consisting of a pair of reaction–diffusion equations coupled to an energy equation for temperature, and use this to obtain a natural extension of the Turing instability accounting for temperature. We show that thermal contributions can restrict or enlarge the set of unstable modes possible under the instability, and in some cases may be used to completely shift the set of unstable modes, strongly modifying emergent Turing patterns. Spatial heterogeneity plays a role under several experimentally feasible configurations, and we give particular consideration to scenarios involving thermal gradients, thermodynamics of chemicals transported within a flow, and thermodiffusion. Control of Turing patterns is also an area of active interest, and we also demonstrate how patterns can be modified using time-dependent control of the boundary temperature.
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Affiliation(s)
- Robert A. Van Gorder
- Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9054, New Zealand
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17
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Esposito M. Open questions on nonequilibrium thermodynamics of chemical reaction networks. Commun Chem 2020; 3:107. [PMID: 36703333 PMCID: PMC9814766 DOI: 10.1038/s42004-020-00344-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2020] [Accepted: 07/01/2020] [Indexed: 02/06/2023] Open
Affiliation(s)
- Massimiliano Esposito
- grid.16008.3f0000 0001 2295 9843Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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18
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Avanzini F, Falasco G, Esposito M. Chemical cloaking. Phys Rev E 2020; 101:060102. [PMID: 32688465 DOI: 10.1103/physreve.101.060102] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2019] [Accepted: 05/22/2020] [Indexed: 11/07/2022]
Abstract
Hiding an object in a chemical gradient requires one to suppress the distortions it would naturally cause on it. To do so, we propose a strategy based on coating the object with a chemical reaction-diffusion network which can act as an active cloaking device. By controlling the concentration of some species in its immediate surrounding, the chemical reactions redirect the gradient as if the object was not there. We also show that a substantial fraction of the energy required to cloak can be extracted from the chemical gradient itself.
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Affiliation(s)
- Francesco Avanzini
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511, Luxembourg
| | - Gianmaria Falasco
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511, Luxembourg
| | - Massimiliano Esposito
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511, Luxembourg
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Kumar P, Gangopadhyay G. Energetic and entropic cost due to overlapping of Turing-Hopf instabilities in the presence of cross diffusion. Phys Rev E 2020; 101:042204. [PMID: 32422772 DOI: 10.1103/physreve.101.042204] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2019] [Accepted: 02/28/2020] [Indexed: 11/07/2022]
Abstract
A systematic introduction to nonequilibrium thermodynamics of dynamical instabilities are considered for an open nonlinear system beyond conventional Turing pattern in presence of cross diffusion. An altered condition of Turing instability in presence of cross diffusion is best reflected through a critical control parameter and wave number containing both the self- and cross-diffusion coefficients. Our main focus is on entropic and energetic cost of Turing-Hopf interplay in stationary pattern formation. Depending on the relative dispositions of Turing-Hopf codimensional instabilities from the reaction-diffusion equation it clarifies two aspects: energy cost of pattern formation, especially how Hopf instability can be utilized to dictate a stationary concentration profile, and the possibility of revealing nonequilibrium phase transition. In the Brusselator model, to understand these phenomena, we have analyzed through the relevant complex Ginzberg-Landau equation using multiscale Krylov-Bogolyubov averaging method. Due to Hopf instability it is observed that the cross-diffusion parameters can be a source of huge change in free-energy and concentration profiles.
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Affiliation(s)
- Premashis Kumar
- S. N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700 106, India
| | - Gautam Gangopadhyay
- S. N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700 106, India
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