[Paper Review] Free-Energy Transduction in Chemical Reaction Networks: from Enzymes to Metabolism

Artur Wachtel, Riccardo Rao+1 more|arXiv (Cornell University)|Feb 2, 2022

Advanced Thermodynamics and Statistical Mechanics32 references36 citations

TL;DR

This paper presents a general thermodynamic framework for free-energy transduction in arbitrary open chemical reaction networks (CRNs), using stoichiometric matrix and chemostated species to identify fundamental thermodynamic forces and currents. It demonstrates that metabolic pathways like glycolysis and the TCA cycle function as thermodynamic machines, with efficiency quantified via transduction of free energy from high-potential donors to ATP and other work-converting processes.

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 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.

Motivation & Objective

• To develop a rigorous, general framework for free-energy transduction in open chemical reaction networks beyond elementary reactions.
• To overcome limitations of traditional thermodynamics and existing models that assume linear kinetics or elementary steps.
• To identify fundamental thermodynamic forces and currents in nonlinear, non-elementary CRNs using network topology.
• To apply the framework to central metabolic pathways and quantify their energy transduction efficiency.
• To establish a systematic method for analyzing energy conversion in complex biological systems like glycolysis, TCA cycle, and electron transport chain.

Proposed method

• Uses the stoichiometric matrix to define net production of species in each reaction.
• Identifies chemostated species (held at constant concentration) to define environmental reservoirs.
• Derives fundamental thermodynamic forces from chemical potential differences across reactions.
• Defines fundamental currents as net flows of stoichiometrically balanced processes.
• Applies network-theoretic methods (e.g., spanning trees, cycle bases) to decompose fluxes into independent thermodynamic cycles.
• Computes entropy production via the product of forces and currents, enabling efficiency quantification.

Experimental results

Research questions

• RQ1 How can free-energy transduction be rigorously defined in arbitrary, nonlinear open CRNs?
• RQ2 What are the fundamental thermodynamic forces and currents that govern energy dissipation and transduction in such networks?
• RQ3 How do metabolic pathways like glycolysis and the TCA cycle function as thermodynamic machines?
• RQ4 What is the efficiency of free-energy transduction in central metabolism, and how is it related to underlying network topology?
• RQ5 Can this framework be systematically applied to any CRN, including complex metabolic networks?

Key findings

• The framework successfully identifies fundamental thermodynamic forces and currents in nonlinear, non-elementary CRNs using only the stoichiometric matrix and chemostated species.
• Metabolic pathways such as glycolysis, the TCA cycle, and the electron transport chain are shown to operate as thermodynamic machines driven by free-energy transduction.
• The theory quantifies transduction efficiency by relating ATP synthesis to the driving forces from high-potential donors like NADH and pyruvate.
• In ethanol fermentation, the emergent cycle transduces free energy from pyruvate to ethanol and NAD+ with a net balance consistent with thermodynamic constraints.
• For cellular respiration, the full network cycle (glycolysis + TCA + ETC) is shown to sustain a coherent transduction pathway with defined energy flow from glucose to ATP and CO2.
• The method enables a systematic, graph-theoretic decomposition of complex metabolic networks into thermodynamically independent cycles, allowing for precise efficiency analysis.