On the time-dependent diffusion of macromolecules through transient open junctions and their subendothelial spread. I. Short-time model for cleft exit region.
In this two-part study we shall quantitatively study, using time-dependent models, the hypothesis that transient open junctions associated with widely scattered endothelial cells undergoing mitosis are the structural equivalent for the large pore pathway via which macromolecules the size of albumin or larger cross the vascular endothelium. In an earlier steady-state model [Am. J. Physiol. 248, H945-960 (1985)], the authors demonstrated that such an open-junction pathway could quantitatively account for the regional differences in macromolecular permeability observed in various mammalian arteries in regions of enhanced cell turnover as indicated by 3H-thymidine although these cells were less than 1% of the population and the open junctions occupied less than 10(-5) of the endothelial surface. The time-dependent models described herein have been used to identify a time window and size of probe molecule wherein this hypothesis could be tested experimentally in the larger blood vessels. The first stages of these experiments have now been completed and provide convincing evidence that the junctions of virtually all endothelial cells in the M phase of the cell cycle are leaky to macromolecules (Lin et al., 1988). The statistical frequency of such leakage sites has also been determined. The time-dependent models developed herein contain two important refinements that were not contained in the earlier steady state model. First the finite resistance of the open cleft as a function of molecular size is accounted for by introducing a diffusion coefficient ratio Dj/Dz describing the relative resistance of the open cleft compared to the subendothelial tissue in the direction normal to the endothelial surface. Second the non-isotropy of the vessel wall due to the elastic lamina is considered by introducing a second diffusion coefficient ratio Dx/Dz describing the relative resistance in the lateral as compared to the normal direction. This second ratio can be as large as 100 for the arterial intima, but is of order unity for capillaries. In Part I a short time model is presented to describe the initial labeling of the open cleft and the subendothelial space in the vicinity of the cleft exit following the introduction of a tracer macromolecule. This model is valid for both larger vessels and capillaries since wall thickness and curvature and the interaction between leakage sites does not enter into the model description. In Part II (Wen et al., 1988) a long-time model is developed for larger vessels only which is valid for greater times including steady-state labeling.