Physiological relevance of epithelial geometry: New insights into the standing gradient model and the role of LI cadherin

We introduce a mathematical model of an absorbing leaky epithelium to reconsider the problem formulated by Diamond and Bossert in 1967: whether “… some distinctive physiological properties of epithelia might arise as geometrical consequences of epithelial ultrastructure”. A standing gradient model of the intercellular cleft (IC) is presented that includes tight junctions (TJ) and ion channels uniformly distributed along the whole cleft. This nonlinear system has an intrinsic homogeneous concentration and the spatial scale necessary to establish it along the cleft. These parameters have not been elucidated so far. We further provide non-perturbative analytical approximations for a broad range of parameters. We found that narrowing of the IC increases ion concentration dramatically and can therefore prevent outflow through tight junctions (TJs) and the lateral membrane, as long as extremely high luminal osmolarities are not reached. Our model predicts that the system is to some extent self-regulating and thereby prevents fluxes into the lumen. Recent experimental evidence has shown that liver-intestine (LI) cadherin can control the up/down flux in intestines via regulation of the cleft width. This finding is in full agreement with predictions of our model. We suggest that LI-cadherin may increase water transport through epithelia via sequential narrowing of the cleft, starting from the highest concentration area at the beginning of the cleft and triggering a propagating squeezing motion.