Amsler Lab Research

Leak Pathway Pore Size

One major area of controversy in the field is the question of how big are the openings in the tight junction structure that constitute the Leak Pathway. Several previous studies used a mathematical model, the Renkin sieving equation, to estimate the Leak Pathway pore size (Buschmann et al., Mol Biol Cell. 2013 Oct;24(19):3056-68. doi: 10.1091/mbc.E12-09-0688; Cavanaugh et al. Am J Physiol Cell Physiol. 2006 Apr;290(4):C1179-88. Epub 2005 Nov 9. doi:10.1152/ajpcell.00355.2004; Kim and Crandall. J Appl Physiol Respir Environ Exerc Physiol. 1983 Jan;54(1):140-6. doi:10.1152/jappl.1983.54.1.140; Kawedia et al. J Pharmacol Exp Ther. 2008 Sep;326(3):829-37. doi:10.1124/jpet.107.135798). The estimated Leak Pathway pore radius from these studies was ~50 Angstroms. Some of these studies demonstrated the paracellular movement of solutes with radii of 45 Angstroms or greater, however, which is difficult to reconcile with a pathway with only a 50 Angstrom pore radius.

There are several mathematical models describing the movement of solutes through the tight junction. While it is currently unclear which of these models most accurately describes the Leak Pathway, they all possess a similar format based on the Stokes-Einstein equation for free diffusion. This equation is modified by one group of factors that includes the density of Leak Pathway openings and the length of the openings. These factors are not dependent on the size of the Leak Pathway openings. A second group of factors includes the interaction of the solute with the opening surface (Hindrance Factor) and the interaction of the solute with the walls of the opening (Frictional Factor). These factors are dependent on the size of the Leak Pathway opening. We reasoned that, while we could not determine a radius for the Leak Pathway openings, we could determine how manipulations affect the opening size versus the opening density and/or length by comparing the effect of changing solute Stokes radius on solute apparent permeability (P(app)).

We first confirmed this using a computational approach in which we calculated the P(app) of solutes of different sizes when the Leak Pathway opening radius was held constant and the opening density was varied versus with the Leak Pathway opening radius was held constant and the opening density was varied (Figure 1). We used a frequently used mathematical model, the Renkin sieving equation (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2147404/). Varying Leak Pathway opening density while holding opening radius constant created a series of "parallel" curves when plotted on a semilog graph.

When Leak Pathway opening radius was varied while holding opening density constant created a series of curves which diverged when plotted on a semilog graph (Figure 2). This computational analysis indicates it should be possible to distinguish manipulations that affect Leak Pathway opening density from those that affect opening radius using this approach.

We have used this approach to examine the effect of knocking down the cellular content of two tight junction-associated cytoplasmic proteins, ZO-1 versus ZO-2, on these Leak Pathway parameters in MDCK II cell monolayers. Our results (Physiological Reports, manuscript in press) indicate that knockdown of ZO-1 protein content both decreases Leak Pathway opening radius and increases opening density leading to a net increase in total Leak Pathway P(app) that diminishes with increasing solute size. Knockdown of ZO-2 protein content, in comparison, has either no or only a minimal effect of either of these parameters.

Interestingly, when we compared MDCK II cell monolayers, a relatively leaky epithelium, with monolayers of MDCK I cells, a relatively tight epithelium, the Leak Pathway opening radius was not significantly altered but the MDCK I cell monolayers exhibited a substantially lower opening density leading to a decrease in P(app) for all tested solutes.

The article by Tervonen et al. (PLoS One. 2019 Apr 9;14(4):e0214876. doi:10.1371/journal.pone.0214876) provides a useful starting point for developing a new mathematical model that more accurately describes the Leak Pathway properties and behavior. We are actively pursuing this avenue to learn more about the Leak Pathway properties and how these properties are affected by different experimental manipulations, such as changing the content of one or more tight junction proteins, and in different disease states.