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Thermodynamics of Concentration vs Flux Control in Chemical Reaction Networks
TL;DR: In this paper, the thermodynamic implications of two control mechanisms of open chemical reaction networks were investigated, i.e., the first controls the concentrations of the species that are exchanged with the surroundings, while the other controls the exchange fluxes.
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 a steady state, the flux control may lead to fundamentally different regimes where systems achieve stationary growth.
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TL;DR: In this article , the authors extend the scope of information thermodynamics to deterministic bipartite chemical reaction networks, composed of two coupled subnetworks sharing species but not reactions.
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.
12 citations
TL;DR: This work provides a rigorous definition of free-energy transduction and its efficiency in arbitrary-linear or nonlinear-open chemical reaction networks operating at a steady state and relates the fundamental currents to metabolic pathways and discusses the efficiency with which they can transduce free energy.
Abstract: We provide a rigorous definition of free-energy transduction and its efficiency in arbitrary-linear or nonlinear-open chemical reaction networks (CRNs) operating at a steady state. Our method is based on the knowledge of the stoichiometric matrix and the chemostatted species (i.e., the species maintained at a constant concentration by the environment) to identify the fundamental currents and forces contributing to the entropy production. Transduction occurs when the current of a stoichiometrically balanced process is driven against its spontaneous direction (set by its force), thanks to other processes flowing along their spontaneous direction. In these regimes, open CRNs operate as thermodynamic machines. After exemplifying these general ideas using toy models, we analyze central energy metabolism. We relate the fundamental currents to metabolic pathways and discuss the efficiency with which they can transduce free energy.
7 citations
TL;DR: In this paper , the authors propose a circuit theory for chemical reaction networks, where chemical reactions are grouped into chemical modules solely characterized by their current-concentration characteristic, as electrical devices by their I-V curve in electronic circuit theory.
Abstract: We lay the foundation of a circuit theory for chemical reaction networks. Chemical reactions are grouped into chemical modules solely characterized by their current-concentration characteristic, as electrical devices by their current-voltage (I-V) curve in electronic circuit theory. This, combined with the chemical analog of Kirchhoff's current and voltage laws, provides a powerful tool to predict reaction currents and dissipation across complex chemical networks. The theory can serve to build accurate reduced models of complex networks as well as to design networks performing desired tasks.
4 citations
TL;DR: In this article , an information-geometric structure for chemical thermodynamics, applicable to a wide range of chemical reaction systems including nonideal and open systems, was constructed, using the extent of reactions and the affinities of reactions as coordinates on a linearly constrained space of amounts of substances.
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.
1 citations
TL;DR: In this article , the dual master equation, which has the same steady state as the chemical master equation but with inverted reaction currents, still describes a chemical process and the answer depends on the topological property of the underlying chemical reaction network known as deficiency.
Abstract: Stochastic chemical processes are described by the chemical master equation satisfying the law of mass-action. We first ask whether the dual master equation, which has the same steady state as the chemical master equation, but with inverted reaction currents, satisfies the law of mass-action and, hence, still describes a chemical process. We prove that the answer depends on the topological property of the underlying chemical reaction network known as deficiency. The answer is yes only for deficiency-zero networks. It is no for all other networks, implying that their steady-state currents cannot be inverted by controlling the kinetic constants of the reactions. Hence, the network deficiency imposes a form of non-invertibility to the chemical dynamics. We then ask whether catalytic chemical networks are deficiency-zero. We prove that the answer is no when they are driven out of equilibrium due to the exchange of some species with the environment.
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TL;DR: Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
Abstract: Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation–dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production. (Some figures may appear in colour only in the online journal) This article was invited by Erwin Frey.
2,834 citations
TL;DR: The reason we never observe violations of the second law of thermodynamics is in part a matter of statistics: when ∼1023 degrees of freedom are involved, the odds are overwhelmingly stacked against the possibility of seeing significant deviations away from the mean behavior.
Abstract: The reason we never observe violations of the second law of thermodynamics is in part a matter of statistics: When ∼1023 degrees of freedom are involved, the odds are overwhelmingly stacked against the possibility of seeing significant deviations away from the mean behavior. As we turn our attention to smaller systems, however, statistical fluctuations become more prominent. In recent years it has become apparent that the fluctuations of systems far from thermal equilibrium are not mere background noise, but satisfy strong, useful, and unexpected properties. In particular, a proper accounting of fluctuations allows us to rewrite familiar inequalities of macroscopic thermodynamics as equalities. This review describes some of this progress, and argues that it has refined our understanding of irreversibility and the second law.
1,008 citations
TL;DR: A new method for discriminating between networks that have the capacity for multiple equilibria and those that do not is suggested and can be implemented using standard computer algebra software and gives answers for many reaction networks for which previous methods give no information.
Abstract: The capacity for multiple equilibria in an isothermal homogeneous continuous flow stirred tank reactor is determined by the reaction network. Examples show that there is a very delicate relationship between reaction network structure and the possibility of multiple equilibria. We suggest a new method for discriminating between networks that have the capacity for multiple equilibria and those that do not. Our method can be implemented using standard computer algebra software and gives answers for many reaction networks for which previous methods give no information.
355 citations
TL;DR: In this article, the authors revisited stochastic thermodynamics for a system with discrete energy states in contact with a heat and particle reservoir, and showed that it is possible to solve the problem with a convex geometry.
Abstract: We revisit stochastic thermodynamics for a system with discrete energy states in contact with a heat and particle reservoir.
332 citations
TL;DR: The fluctuation theorem is derived for stochastic nonequilibrium reactions ruled by the chemical master equation and verified in the Schlögl model of far-from-equilibrium bistability.
Abstract: A fluctuation theorem is derived for stochastic nonequilibrium reactions ruled by the chemical master equation. The theorem is expressed in terms of the generating and large-deviation functions characterizing the fluctuations of a quantity which measures the loss of detailed balance out of thermodynamic equilibrium. The relationship to entropy production is established and discussed. The fluctuation theorem is verified in the Schlogl model of far-from-equilibrium bistability.
238 citations