A NEW MODEL FOR CAPILLARY FILTRATION BASED ON RECENT ELECTRON MICROSCOPIC STUDIES OF ENDOTHELIAL JUNCTIONS

Abstract

Existing models to predict the filtration and permeability of hydrophilic solutes in the capillary interendothelial cleft have been based largely on one-dimensional models of channels with constrictions that are represented by long rectangular slits of 6 to 8 nm gap width that run along the length of the junction and do not interact with one another [1,7–10]. It has been commonly assumed based on these simple models that the water and solute fluxes are proportional to the area of the junction that is open. Recent electron microscopic studies [7, 11] using freeze fracture and ultrathin serial sectioning techniques indicate that the pores in the tight junctions might be numerous much narrower disruptions in the protein strands of 10 to 20 nm length. A new model is proposed in which the pores are short periodically distributed equivalent cylindrical holes in the junctional strands that have dimensions comparable to individual missing proteins. Since these pores have spacings which are small compared to the depth of the cleft the interaction between pores, neglected in previous models, becomes a crucial determinant of the transport behavior. A two-dimensional Hele-Shaw theory for filtration is developed to describe this interaction. This new model shows that the flux is not proportional to the length of open junction, and far fewer pores are required to accommodate the experimentally measured filtration fluxes than heretofore realized; e.g. the model predicts that only one junctional protein in eight needs to be absent to account for the measured hydraulic conductivity of frog mesentery capillaries and one in eighty for frog muscle. In contrast, traditional one-dimensional models with slit constrictions predict that the junction is open along nearly its entire length for frog mesentery capillaries and ten percent open for muscle capillaries. This basic Hele-Shaw model is then modified to describe the resistance of bridging molecules or fibers that might span the wide portions of the cleft as proposed in the fiber matrix model of Curry and Michel [16]. The results of this model depart significantly from those of the fiber matrix theory developed in [16] using the Carman-Kozeny equation and suggest that the fiber matrix, if it exists in the wide portion of the cleft, must be much more diffuse than previously predicted. The periodic fiber model shows that the Carman-Kozeny equation grossly underpredicts the filtration resistance since it neglects the influence of the channel walls on the viscous layers surrounding the fibers.