Conductivity of a square-lattice bond-mixed resistor network

Percolation analysis in electrical conductivity of Madin-Darby canine kidney and Caco-2 cells by permeation-enhancing agents

The control of permeability through the paracellular route has been paid great attention to for enhanced bioavailability of macromolecular and hydrophilic drugs. The paracellular permeability is controlled by tight junctions (TJ), and claudins are the major constituents of TJ. Despite numerous studies on TJ modulation, the dynamics is not well understood, although it could be crucial for clinical applications. Here, we studied the time (t) course of electrical conductivity (Σ) in a monolayer of Madin-Darby canine kidney (MDCK) and Caco-2 cells upon treatment with modulators, the C-terminus fragments of Clostridium perfringens enterotoxin (C-CPE) and sodium caprate (C10). For C-CPE treatment, Σ remains approximately constant, then starts increasing at t=tc (percolation threshold). For C10, on the other hand, Σ increases to 1.6-2.0 fold of the initial value, stays constant, and then starts increasing again for both MDCK and Caco-2 cells at t=tc. We find that this behavior can be explained within a framework of percolation, where Σ shows a logarithmic dependence on t-tc with the power of μ; μ denotes the critical exponent. We obtain μ=1.1-1.2 regardless of cell type or modulator. Notably, μ depends only on the dimensionality (d) of the system, and these values correspond to those for d=2. Percolation is thus the operative mechanism for the increase in Σ through TJ modulation. The findings provide fundamental knowledge, not only on controlled drug delivery, but also on bio-nanotechnologies including the fabrication of biological devices.