A thermodynamically consistent approach to modelling epithelial solute and water transport in the proximal convoluted tubule

This study presents a novel approach to modeling ion and fluid transport in the renal nephron’sproximal convoluted tubule (PCT) using bond graph framework. Bond graphs provide a robust framework for analyzing complex systems by representing thermodynamic processes within an extended circuit-theoretic approach, enabling the explicit depiction of multi-domain energy exchange. Applications of bond graphs to physiological processes have primarily focused on solute transport, whereas our work distinguishes itself by also incorporating solvent dynamics and their interplay with solute transport, offering a more complete representation of the key physiological processes within the PCT. Leveraging the modular nature of bond graphs, we first defined resistive modules representing membranes and capacitive modules representing solution-filled compartments, before coupling them together using circuit theory. Critically, our novel implementation extends beyond previous bond graph models by explicitly representing volumetric flow as a distinct variable within capacitive modules. Indoing so, our model enables the consideration of mechanotransduction effects, where changes in fluid volume can influence membrane transporter activity, a crucial aspect of PCT function. Our bond graph model of the PCT (BG-PCT) comprises four fluid compartments bounded by five distinct membranes. The BG-PCT considers five chemical species ( Na+, K+, Cl−, HCO3−, and glucose) and six key membrane transporters distributed across the different membranes. Each structural subsystem comprises elementary thermodynamic processes, including dissipation, free-energy change, and power flow. This study demonstrates the advantages of bond graph modeling, particularly in its capacity to couple electrical, chemical, and hydraulic energy domains and its intrinsic modularity, which enables future extensibility. The BG-PCT offers a robust platform for in silico research of epithelial transport dynamics and is available on GitHub under an open-source license to ensure accessibility, reproducibility, and reusability for future research.