An approach based on linear programming to build experimentally driven pump-leak models

Pump-Leak (P-L) models are powerful tools in membrane and cellular physiology, providing a quantitative framework to understand how cells regulate intracellular ion concentrations, cell volume, and membrane potential thorugh ion transport mechanisms. However, constructing a P-L model for a specific cell type is challenging, because it requires numerous cell-specific parameters, many of which are experimentally inaccessible. Here, we present a linear programming-based method to estimate such parameters, using only a subset of experimentally determined values. This inverse approach exploits the system of differential equations underlying the P-L model and enforces steady-state conditions by setting all time derivatives to zero. Experimentally measured steady-state intracellular ion concentrations, membrane potential, and cell volume are used as constraints, while model parameters are treated as variables. Linear programming is then employed to systematically explore feasible parameter ranges, allowing experimentally determined values to be assigned to selected parameters by progressively restricting the ranges of the remaining ones until convergence to unique solutions is achieved. We applied this strategy to construct a P-L model for the U87-MG glioblastoma cell line. The resulting model accurately predicts several dynamical behaviors, including volume changes induced by reductions in extracellular Na⁺ and by suppression of resting ion conductance. A simple computer application implementing this method is provided, offering a general strategy for parametrizing P-L models in different cell types.