ENHANCED ELECTRODIFFUSIVE TRANSPORT ACROSS A MUCUS LAYER

Abstract

Diffusive transport of small ionic species through mucus layers is a ubiquitous phenomenon in physiology. However, some debate remains regarding how the various characteristics of mucus (charge of the polymers themselves, binding affinity of ions with mucus) impact the rate at which small ions may diffuse through a hydrated mucus gel. Indeed it is not even clear if small ionic species diffuse through mucus gel at an appreciably different rate than they do in aqueous solution. Here, we present a mathematical description of the transport of two ionic species (hydrogen and chloride) through a mucus layer based on the Nernst-Planck equations of electrodiffusion. The model explicitly accounts for the binding affinity of hydrogen to the mucus material, as well as the Donnan potential that occurs at the interface between regions with and without mucus. Steady state fluxes of ionic species are quantified, as are their dependencies on the chemical properties of the mucus gel and the composition of the bath solution. We outline a mechanism for generating enhanced diffusive flux of hydrogen across the gel region, and hypothesize how this mechanism may be relevant to the apparently contradictory experimental data in the literature.

Fig. 1.

Level curves of $\mathcal{F}$ and $\mathcal{G}$. The solid black curve indicates $\mathcal{F}\left(j_h,j_c\right)=1$. Colored lines indicate various level sets of $\mathcal{G}\left(j_h,j_c\right)$. The solid gold region indicates fluxes which result in an ill-posed or unphysical problem. The blue circle indicates the numerical solution of $\mathcal{F}=1$, $\mathcal{G}=0$. The purple diamond indicates numerical solution of $\mathcal{F}=1$, $\mathcal{G}=0.5$.

Fig. 2.

Hydrogen and chloride concentrations and electric potential profile as functions of space. The dashed cyan (ionic concentrations) and blue (electric potential) lines indicate values within the “baths”, which in this case are equal to the boundary values for each species. In the case that c_T = 0, electroneutrality guarantees that hydrogen and chloride concentrations are equal. Left panel shows model solution with no applied potential drop (${\Psi }_1^{in}=0$), while the right panel shows solution with an applied potential drop of ${\Psi }_1^{in}=0.5$.

Fig. 3.

Level curves of $\mathcal{F}$ and $\mathcal{G}$. The solid black curve indicates $\mathcal{F}\left(j_h,j_c\right)=1$. Colored lines indicate various level sets of $\mathcal{G}\left(j_h,j_c\right)$. The solid gold region indicates fluxes which result in an ill-posed or unphysical problem. The blue circle indicates the numerical solution of $\mathcal{F}=1$, $\mathcal{G}\approx -0.1247$.

Fig. 4.

Hydrogen and chloride concentrations and electric potential as functions of space. The dashed cyan (ionic concentrations) and blue (electric potential) lines indicate values within the baths.

Fig. 5.

The calculated flux of hydrogen through the interior (j_h) as a function of mucus charge density c_T. The black line indicates calculated values of j_h, while the dashed red line indicates “expected” flux of hydrogen due to Fickian diffusion alone. All data generated with K = 0, $h_0^{out}=1$, and $h_1^{out}=2$.

Fig. 6.

The calculated flux of hydrogen through the interior j_h as a function of mucus charge density c_T and binding hydrogen binding affinity K. All data generated with $h_0^{\text{out }}=1$ and $h_1^{\text{out }}=2$.

Fig. 7.

The ratio of external-to-internal hydrogen concentrations ($h_j^{out}/h_j^{in}$), as well as the Donnan equilibrium potential, shown as a function of external concentration. The left axis indicate concentration ratios, while the right axis shows the Potential drop (${\Psi }_j^{in}-{\Psi }_j^{out}$).