Thermodynamics of concentration vs flux control in chemical reaction networks

Thermodynamics of Growth in Open Chemical Reaction Networks

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.

Characterizing the conditions for indefinite growth in open chemical reaction networks

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.

Calcium oscillations optimize the energetic efficiency of mitochondrial metabolism

Energy transduction is central to living organisms, but the impact of enzyme regulation and signaling on its thermodynamic efficiency is generally overlooked. Here, we analyze the efficiency of ATP production by the tricarboxylic acid cycle and oxidative phosphorylation, which generate most of the chemical energy in eukaryotes. Calcium signaling regulates this pathway and can affect its energetic output, but the concrete energetic impact of this cross-talk remains elusive. Calcium enhances ATP production by activating key enzymes of the tricarboxylic acid cycle while calcium homeostasis is ATP-dependent. We propose a detailed kinetic model describing the calcium-mitochondria cross-talk and analyze it using nonequilibrium thermodynamics: after identifying the effective reactions driving mitochondrial metabolism out of equilibrium, we quantify the mitochondrial thermodynamic efficiency for different conditions. Calcium oscillations, triggered by extracellular stimulation or energy deficiency, boost the thermodynamic efficiency of mitochondrial metabolism, suggesting a compensatory role of calcium signaling in mitochondrial bioenergetics.

Nonideal Reaction-Diffusion Systems: Multiple Routes to Instability

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.

Random walks on modular chains: Detecting structure through statistics

We study kinetic transport through one-dimensional modular networks consisting of alternating domains using both analytical and numerical methods. We demonstrate that the mean velocity is insensitive to the local structure of the network, and it depends only on global, structural-averaged properties. However, by examining high-order cumulants characterizing the kinetics, we reveal information on the degree of inhomogeneity of blocks and the size of repeating units in the network. Specifically, in unbiased diffusion, the kurtosis is the first transport coefficient that exposes structural information, whereas in biased chains, the diffusion coefficient already reveals structural motifs. Nevertheless, this latter dependence is weak, and it disappears at both low and high biasing. Our study demonstrates that high-order moments of the population distribution over sites provide information about the network structure that is not captured by the first moment (mean velocity) alone. These results are useful towards deciphering mechanisms and determining architectures underlying long-range charge transport in biomolecules and biological and chemical reaction networks.

Information-geometric structure for chemical thermodynamics: An explicit construction of dual affine coordinates

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.

Information thermodynamics for deterministic chemical reaction networks

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.

Free-Energy Transduction in Chemical Reaction Networks: from Enzymes to Metabolism

We provide a rigorous definition of free-energy transduction and its efficiency in arbitrary---linear or nonlinear---open chemical reaction networks (CRNs) operating at steady state. Our method is based on the knowledge of the stoichiometric matrix and of the chemostatted species (i.e. the species maintained at 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 are able to transduce free energy.