Mucous are glycoproteins of gigantic dimensions, with thousands of amino acid residues per monomer and molecular weight in millions. Their primary structure consists of a linear peptide backbone, to which are attached short polysaccharide side branches. Mucus plays a critical role as a protective, exchange and transport medium in the digestive, respiratory and reproductive systems of humans and other vertebrates. Hence its swelling mechanism are of special interest, e.g. in describing the locomotion of single cell in-vertibrates and in understanding the pathophysiology of respiratory diseases like cystic fibrosis (CF).

Major experimental findings explain mucus swelling as a balance between the osmotic forces created due to the difference in the solvent concentration across the mucus mesh, and Donnan driving forces. It is argued that the 'ensemble of entangled polymer mesh' prevents the residual charges on the mucin chains from migrating out of its matrix and hence the polymer entangles virtually functions as its own semipermeable membrane. However, the osmotic pressure difference could not explain the recent experimental findings of the massive and the explosive post-exocytotic swelling observations. Furthermore, while it is certain to have some Donnanlike effect if there are rapid spatial changes in the polymer concentration, overall, one expects electro-neutrality to be enforced. Hence we suggest that the mucus swelling is due to a combination of steric repulsive interaction within its poly-ionic chains, caused due to a change in its cross-shielding structure during the hydration process, as well as the donnan potential developed across the gel-sol interface.

A mucus gel has negatively charged polyionic chains and in a neutral medium all charges must be balanced cations. There are several possible cations, including sodium, calcium, potassium and hydrogen. The important difference between these is that calcium is divalent and so it must shield two negative charges rather than one. Hence, the divalent Ca++ ions act as a cross-shielding agent between two polymer strands, allowing much tighter condensation than when the negative charges of these network are shielded by monovalent ions, e.g. Na+. An exchange of the divalent ions with the monovalent ions, unshields the polyionic charges of the mucins, driving the mutual repulsion of the polymer chains and triggering a quick expansion of the mucin network. If this is the swelling mechanism, then it follows that a change in the ionic affinity of the mucins or changes in the ionic concentrations in the medium, drastically alters the condensation/hydration process. It has been confirmed experimentally that an incomplete mucus hydration is a result of either a faulty electrolytic composition of water on the mucosal surface or an increased mucin sulfation leading to a higher affinity for cations. Fig 1(a) shows an image of mucus secretion out of the intracellular granule (source: Kuver et. el.) Fig 1(b) is the schematics showing ion-displacement leading to changes in the cross link structure of the mucus matrix and its eventual expansion

To understand this mechanism, my research efforts has been divided into three stages. In the first step I have developed a general theory to understand the swelling kinetics of neutral polymer gels. Gel mechanics are modeled using a two phase mixture which accounts for the polymer volume fraction and the polymer and solvent velocities. The model is proposed as a free boundary problem and can be used to understand both the contraction and swelling, including a complete dissolution or dehydration of these gels. Fluid motion is determined by force balances involving viscous, drag, and chemical forces, in such a way that they satisfy a minimum energy dissipation rate principle similar to the Helmholz minimum dissipation rate principle which holds for a Stokes flow. The free energy is constructed to correctly describe the swelling kinetics. Fig. 2 shows a sample phase-diagram in the material parameter space, with the corresponding swelling variables, Fig 2(b,c).

In the next stage, I have developed a comprehensive model of a polyelectrolyte gel swelling / deswelling mechanism including forces generated through Donnan field as well as the changes in the cross-link structure due to the divalent/ monovalent ions exchange. The chemical forces in the force balance equations are derived from a free energy which includes entropic contributions as well as the chemical interactions among the cross-linked polymer, uncross-linked polymer and the solvent. Fig. 3 shows a sample phase diagram (and the corresponding swelled configurations) in the reaction rate phase diagram. Efforts are currently underway to calibrate this model with the experimental data from my collaborators in the medical school, University of Washington.

The final stage is to identify the relevant material parameter space corresponding to the mucin swelling regime involving Ca2+-Na+ ion exchange. Work is currently underway in this regard. Below are some prelimnary animations for the mucin-swelling/deswelling for different drag and viscosity ocefficients. (Quicktime player required)