Multi-physics modeling for ion homeostasis in multi-compartment plant cells using an energy function

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 changes of volumes and chemical effects, modeling these exchanges remains a challenge that has only been partially adressed. 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 that allows us to derive the equations satisfied by each variable in a systematical way. This results in a modular, unified approach that can be interpreted analytically. We illustrate these properties 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, resulting in an interpretable model with few parameters. We perform numerical simulations to investigate the role of each hydrogen pump in this process. We show that this energy-based approach allows us to highlight a hierarchy between the forces involved in the system, that can be exploited to interpret the emergent properties of this complex multi-physics system.