Plant cells control their volume by regulating the osmotic potential of their cytoplasm and vacuole. Water is attracted into the cell as the result of a cascade of solute exchanges between the cell subcompartments and the cell surroundings, which are governed by chemical, electrostatic and mechanical forces. Due to this multi-physics aspect and to couplings between volume changes and chemical effects, modeling these exchanges remains a challenge that has only been partially addressed. As interest for multi-compartment models grows in the plant cell community, this challenge calls for new modeling strategies. In this paper, we introduce an energy-based approach to couple chemical, electrical and mechanical processes taking place between several subcompartments of a plant cell. The contributions of all physical effects are gathered in an energy function, which allows us to derive the equations satisfied by each variable in a systematic way. We illustrate the properties of this modular, unified approach on the modeling of ion and water transport in a guard cell during stoma opening. We represent the stoma opening process as a quasi-static evolution driven by hydrogen pumps in the plasma and vacuolar membranes, and we show that the new formalism explains why the system varies in a particular direction in response to perturbations. Additional numerical simulations allow us to investigate the role of each hydrogen pump in this process. Altogether, we show that this energy-based approach highlights a hierarchy between the forces involved in the system, and to dissect the role of each physical effect in the complex behavior of the system.
