Stability and Robustness of a Generalized Pump-Leak Model for Epithelial Vesicles

Area of Science:

• Physiology
• Biophysics
• Mathematical Modeling

Background:

• Epithelial cells maintain homeostasis via pumps, channels, and paracellular pathways, typically modeled by single-compartment pump-leak equations (PLEs).
• Classical PLEs do not capture the complex geometry of cell-luminal space interactions crucial for many epithelial functions.
• Understanding ion and volume regulation in these complex geometries is vital for physiological and pathological states.

Purpose of the Study:

• To develop a novel two-compartment pump-leak equation (PLE) model for epithelial systems.
• To analyze the impact of geometry and Na+/K+-ATPase (NKA) localization on epithelial ion and volume homeostasis.
• To provide a tractable framework for studying epithelial transport and predicting pathological conditions.

Main Methods:

• Formulation of a ten-dimensional PLE system for a two-compartment (intracellular and luminal) epithelial model.
• Derivation of analytical equilibria and steady-state formulas for passive and active (NKA-driven) systems.
• Application of stability analysis, global sensitivity, and robustness methods to identify key determinants of homeostasis.

Main Results:

• The model predicts distinct behaviors based on NKA placement (apical vs. basolateral).
• Basolateral membrane potential shows wide variation, while apical potential remains small.
• Insufficient apical potassium recycling can lead to pathological luminal volume expansion.

Conclusions:

• The two-compartment PLE model offers a mathematically tractable and physiologically grounded approach to epithelial transport.
• Pump localization significantly influences epithelial function, with implications for conditions like lumen expansion.
• This framework aids in predicting how changes in pump localization and conductance affect epithelial stability.