Physiological Gels

Polyelectrolyte gels play critical roles in physiology. In particular, the mucus gel which lines our airways, gastrointestinal tract, reproductive systems, and other surfaces of our body topologically external to it is a polyelectrolyte gel. Such a gel consists of a polymer network immersed in a water bath containing dissolved ions. Typically, both the polymer network and the ions carry charge. The dynamics of the mixture of network, solvent, and ions are driven by chemical forces (electrical, entropic, short range interactive) and mechanical forces (pressure, viscous, drag) and by chemical reaction among the ions and between the ions and the network.

We developed models that account for all of these interactions as described in

Sarthok Sircar, James P. Keener, Aaron L. Fogelson, The Effect of Divalent vs. Monovalent Ions on the Swelling of Mucin-like Polyelectrolyte Gels: Governing Equations and Equilibrium Analysis, J Chem Phys, 2013, 138, 014901.

James P. Keener, Sarthok Sircar, and Aaron L. Fogelson, The Influence of the Standard Free Energy on Swelling Kinetics of Gels, Physical Review E, 2011, 83, 041802.

James P. Keener, Sarthok Sircar, Aaron L. Fogelson, Kinetics of Swelling Gels, SIAM J Appl Math, 2011, 71, 854-875.

This work was supported by NSF Grant DMS-1160432.

We have applied those models and extensions of them to understand the behavior of the mucus gel that lines the inside of the stomach, the gastric mucus lining. In two papers, we look at the explosive swelling of mucus as occurs when highly condensed mucus in epithelial cell storage granules is exocytosed, largely driven by a replacement of divalent calcium ions that cross-link mucus strands within the granules by monovalent sodium ions in the extracellular environment.

Jian Du, Owen Lewis, James P. Keener, Aaron L. Fogelson, Modeling and Simulation of the Ion-Binding-Mediated Swelling Dynamics of Mucin-like Polyelectrolyte Gels’, Gels, 2021, accepted.

Owen Lewis, James P. Keener, Aaron L. Fogelson, Electro-diffusion-mediated swelling of a two-phase gel model of gastric mucus, Gels, 2018, 4, 76.

We have also looked at how the mucus layer and secretions from the epithelial cells that line the stomach work together to maintain the very steep hydrogen ion gradient between the stomach lumen (pH = 2) and the epithelial cell surfaces (pH = 6.5).

Owen Lewis, James P. Keener, Aaron L. Fogelson, A Physics-based Model for Maintenance of the pH Gradient in the Gastric Mucus Layer, Am J Physiol Gastrointest Liver Physiol, 2017, 313, G599-G612.

We are currently adapting the model described in the 2021 Gels paper to construct a two-dimensional model of the gastric mucus layer with secretion from both the gastric pits and the epithelial cells. We will use this model to try to understand the maintenance of the gastric mucus layer and the pH gradient in the face of degradation of mucus at the luminal side of the layer by the enzyme pepsin and the resupply of mucus, hydrogen ions, and the pepsin precursor, pepsinogen, by secretion by stomach-lining cells and transport toward the lumen.

The extended model’s equations will be solved using novel computational methods that are described on the ‘Numerical Solution of PDEs’ page.

Our work on gastric mucin is done in collaboration with Henry Fu (Utah), Rama Bansil (Boston U), Jim Wilking and Diane Bimczok (both of Montana State U) and is supported by NIGMS Grant 1R01GM131408.