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Living systems operate out of equilibrium, continuously consuming energy to sustain organised, functional states. Their emergent behaviour usually relies on a set of interconnected chemical reaction networks (CRNs) driven by external fluxes…

Statistical Mechanics · Physics 2026-02-03 Shiling Liang , Paolo De Los Rios , Daniel Maria Busiello

Understanding the emergent behavior of chemical reaction networks (CRNs) is a fundamental aspect of biology and its origin from inanimate matter. A closed CRN monotonically tends to thermal equilibrium, but when it is opened to external…

Molecular Networks · Quantitative Biology 2024-05-16 Masanari Shimada , Pegah Behrad , Eric De Giuli

Chemical reaction networks (CRNs) are prototypical complex systems because reactions are nonlinear and connected in intricate ways, and they are also essential to understand living systems. Here, I discuss how recent developments in…

Statistical Mechanics · Physics 2020-12-23 Massimiliano Esposito

A chemical reaction network (CRN) is composed of reactions that can be seen as interactions among entities called species, which exist within the system. Endowed with kinetics, CRN has a corresponding set of ordinary differential equations…

Dynamical Systems · Mathematics 2021-04-20 Bryan S. Hernandez , Ralph John L. De la Cruz

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…

Molecular Networks · Quantitative Biology 2024-12-05 Shesha Gopal Marehalli Srinivas , Francesco Avanzini , Massimiliano Esposito

At the microscopic scale, open chemical reaction networks are described by stochastic reactions that follow mass-action kinetics and are coupled to chemostats. We show that closed chemical reaction networks -- with specific stoichiometries…

Molecular Networks · Quantitative Biology 2025-06-30 Benedikt Remlein , Massimiliano Esposito , Francesco Avanzini

In this and a companion paper we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first…

Chemical Physics · Physics 2014-10-22 Matteo Polettini , Massimiliano Esposito

Chemical reaction networks (CRNs) provide a convenient language for modelling a broad variety of biological systems. These models are commonly studied with respect to the time series they generate in deterministic or stochastic simulations.…

Molecular Networks · Quantitative Biology 2019-07-11 Ozan Kahramanoğulları

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…

Molecular Networks · Quantitative Biology 2022-06-15 Artur Wachtel , Riccardo Rao , Massimiliano Esposito

All current formulations of nonequilibrium thermodynamics of open chemical reaction networks rely on the assumption of non-interacting species. We develop a general theory which accounts for interactions between chemical species within a…

Statistical Mechanics · Physics 2021-03-09 Francesco Avanzini , Emanuele Penocchio , Gianmaria Falasco , Massimiliano Esposito

Chemical reaction networks (CRNs) exhibit complex dynamics governed by their underlying network structure. In this paper, we propose a novel approach to study the dynamics of CRNs by representing them on species graphs (S-graphs). By…

Molecular Networks · Quantitative Biology 2024-04-24 Keisuke Sugie , Dimitri Loutchko , Tetsuya J. Kobayashi

Motivation: A Chemical Reaction Network (CRN) is a set of chemical reactions, which can be very complex and difficult to analyze. Indeed, dynamical properties of CRNs can be described by a set of non-linear differential equations that…

Computational Engineering, Finance, and Science · Computer Science 2021-07-02 Lucia Nasti , Roberta Gori , Paolo Milazzo , Federico Poloni

Much of the theory on chemical-reaction networks (CRNs) has been developed in the ideal-solution limit, where interactions between the solutes are negligible. However, there is a large variety of phenomena in biological cells and…

Biological Physics · Physics 2022-12-09 Ander Movilla Miangolarra , Michele Castellana

Previous studies have primarily focused on the nonequilibrium thermodynamics of chemical reaction networks (CRNs) occurring in closed systems. In contrast, CRNs in open systems exhibit much richer nonequilibrium phenomena due to sustained…

Chemical Physics · Physics 2025-04-14 Xinyu Zhang , Haiyang Jia , Liangrong Peng , Liu Hong

The thermodynamic and dynamical conditions necessary to observe indefinite growth in homogeneous open chemical reaction networks (CRNs) satisfying mass action kinetics were presented in Srinivas et al. (2023): Unimolecular CRNs can only…

Molecular Networks · Quantitative Biology 2024-12-05 Shesha Gopal Marehalli Srinivas , Francesco Avanzini , Massimiliano Esposito

We develop a thermodynamic framework for closed and open chemical networks applicable to non-elementary reactions that do not need to obey mass action kinetics. It only requires the knowledge of the kinetics and of the standard chemical…

Statistical Mechanics · Physics 2020-09-16 Francesco Avanzini , Gianmaria Falasco , Massimiliano Esposito

We formulate a nonequilibrium thermodynamic description for open chemical reaction networks (CRN) described by a chemical master equation. The topological properties of the CRN and its conservation laws are shown to play a crucial role.…

Statistical Mechanics · Physics 2019-01-14 Riccardo Rao , Massimiliano Esposito

Chemical reactions that couple to systems that phase separate have been implicated in diverse contexts from biology to materials science. However, how a particular set of chemical reactions (chemical reaction network, CRN) would affect the…

Soft Condensed Matter · Physics 2024-04-25 Dino Osmanovic , Elisa Franco

We extend the traditional framework of steady state energy transduction -- typically characterized by a single input and output -- to multi-resource transduction in open chemical reaction networks (CRNs). Transduction occurs when…

Molecular Networks · Quantitative Biology 2025-07-24 Massimo Bilancioni , Massimiliano Esposito

The dynamics of a chemical reaction network (CRN) is often modelled under the assumption of mass action kinetics by a system of ordinary differential equations (ODEs) with polynomial right-hand sides that describe the time evolution of…

Dynamical Systems · Mathematics 2023-01-05 Radek Erban , Hye-Won Kang
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