Fig 1.
Tight junction structure and model simplification.
(A) A schematic figure showing how the tight junctions (TJs) encircle the apical end of the paracellular space between the epithelial cells, and thus form the barrier. (B) Close up of the bTJ strands (top) that form a network dividing the space between the cells into compartments and the tTJ central tube at the intersection of three cells (bottom). (C) A 2D depiction of the TJ strands and the compartment ultrastructure, based on the cutting plane shown in b. This structure is further simplified to form the 2D TJ strand network used in the model.
Fig 2.
Schematic description of the molecular permeability and TER models.
Schematic descriptions of the molecular permeability and the TER models as well as the geometrical parameters. An example of the geometrical idea of the models with three strands and the width of three compartments. (A) The molecular permeability model comprises bTJ compartments (numbered 1–7) lined by the TJ strands and the basal and apical compartments below and above the TJs, respectively. Rate constants kij describe the rate of permeation from compartment i to j. We assume low concentration in the apical compartment, and thus omit the backflow into the small compartments. To describe the strand breaks, the rate constant values are varied based on given probabilities that depend on length of strand between the compartments. (B) The TER model consists of a similar geometry, but instead of compartments the basic model units are the current loops (numbered 1–10). The outer current loop (number 11) has a voltage source (Vs) to enable the computation of the total resistance. Resistance Rij is the resistance of the strand shared by current loops i and j, except for those with i = j, when the resistor is not shared by other loops. Again, the resistances vary based on given probabilities that depend on the length of strand between the compartments. (C) Illustration of the geometrical parameters that describe the bTJ strands. nstrand, strand number; hcomp, small compartment height; wcomp, small compartment width; wTJ TJ half-width; hstrand, height of single bTJ strand; lbreak, size of the break in the bTJ strand.
Table 1.
Model parameters.
Table 2.
Values of the model parameters used to fit the molecular permeability and the TER model.
Fig 3.
Relative roles of the tricellular and bicellular pathways.
The relative roles of tTJ (solid) and bTJ (dashed) on both the molecular permeability (red) and TER (blue) for all the simulated epithelia (Caco-2 [33], MDCK C7 [33], MDCK IIa [33], MDCK IIb [34], MDCK IIc [83], MDCK IId [54], MDCK IIb ZO-1 KD [34], and MDCK IIc ZO-1/2 dKD MDCK IId [54]).
Fig 4.
Effect of strand number on permeability and TER.
The effect of strand number (nstrand = [2, 6]) on (A) molecular permeability and (B) TER in average MDCK II (red and blue) and MDCK C7 (orange and cyan), shown relative to the system with 4 strands. The relative roles of tTJ (solid) and bTJ (dashed) pathways are also illustrated relative to the 4-strand total values. (C) Raw simulation data of the 512 simulations of the apical amount of substance (qapical) as a function of time for average MDCK II (top) and MDCK C7 (bottom) for systems with the strand number from 2 to 6. The average values of the 512 for each time point are shown with the black lines. (D) TER as a function of time for average MDCK II (top) and MDCK C7 (bottom) during a 2-hour section of the simulation for systems with the strand number from 2 to 6. The average values for the whole simulation are shown with the black lines.
Fig 5.
Relative equilibrium concentrations in the equilibrium state.
The relative equilibrium concentrations are shown in relation to the concentration in the basal compartment (compartment row 0) for the 2–6 strand TJ systems. The compartment row with relative concentration of 0 refers to the apical compartment for that system, since its concentrations was assumed to remain very low during the simulations.
Table 3.
The lag times in minutes for MDCK II and MDCK C7 with the different strand numbers.
Fig 6.
Comparison between the dynamic and steady-state models.
Comparison between the bTJ results of our dynamic (dyn) model (squares) and a simple steady-state (SS) model (circles) for (A) permeability and (B) resistance. The simulations were run both for MDCK II (red and blue) and C7 (orange and cyan).
Fig 7.
Parameter sensitivity analysis.
Results of the parameter sensitivity analysis. We varied the values of the chosen parameters by ±25% and both the permeability and TER simulation results were compared with the normal system. The analysis was conducted for average MDCK II permeability (A) and TER (C) as well as MDCK C7 permeability (B) and TER (D). pbreak, break forming probability; pseal, break sealing probability; lbreak, break size; lcb, strand length per area; ρtTJ, tricellular TJ pore density; Rstrand, strand resistance.