A distributed two-pore model: theoretical implications and practical application to the glomerular sieving of Ficoll

Abstract

In the present study, an extended two-pore theory is presented where the porous pathways are continuously distributed according to small- and large-pore mean radii and SDs. Experimental glomerular sieving data for Ficoll were analyzed using the model. In addition, several theoretical findings are presented along with analytic solutions to many of the equations used in distributed pore modeling. The results of the data analysis revealed a small-pore population in the glomerular capillary wall with a mean radius of 36.6 Å having a wide arithmetic SD of ∼5 Å and a large-pore radius of 98.6 Å with an even wider SD of ∼44 Å. The small-pore radius obtained in the analysis was close to that of human serum albumin (35.5 Å). By reanalyzing the data and setting the distribution spread of the model constant, we discovered that a narrow distribution is compensated by an increased mean pore radius and a decreased pore area-to-diffusion length ratio. The wide distribution of pore sizes obtained in the present analysis, even when considering electrostatic hindrance due to the negatively charged barrier, is inconsistent with the high selectivity to proteins typically characterizing the glomerular filtration barrier. We therefore hypothesize that a large portion of the variance in the distribution of pore sizes obtained is due to the molecular "flexibility" of Ficoll, implying that the true variance of the pore system is lower than that obtained using flexible probes. This would also, in part, explain the commonly noted discrepancy between the pore area-to-diffusion length ratio and the filtration coefficient.

Reduced glomerular size selectivity in late streptozotocin-induced diabetes in rats: application of a distributed two-pore model

“…2004; Rippe et al. 2006; Öberg and Rippe 2014). Here we used a distributed two-pore model (Öberg and Rippe 2014) for the theoretical analysis of the data.…”

“…Podocytes embrace the capillaries and stabilize the GFB as a whole. The sieving characteristics of the GFB are selective not only for molecular size but also for shape, deformability, and charge (Venturoli and Rippe 2005; Öberg and Rippe 2013, 2014). The changes in size selectivity that occur when the glomeruli are injured by disease are usually characterized by an increase in the number of low-selective pathways (large-pores) in the filtration barrier.…”

“…The charge selectivity of the GFB is probably related to the presence of sulfated glycosaminoglycan (GAG) side chains of heparan sulfate (HS) proteoglycans in the anionic glycocalyx of podocytes and endothelial cells (van den Born et al. 2006; Öberg and Rippe 2013, 2014). Although the concept of charge selectivity of the GFB has been recently debated, a surface charge density of −5–20 mC/m 2 is thought to be sufficient to prevent albuminuria (across high selectivity pathways) in normal conditions (Axelsson et al.…”

Letter to the Editor: “Can early plasma elimination rate be used to quantify renal clearance of macromolecules?”

“…In addition, the permeability for Ficoll both in the GFB and synthetic membranes apparently lies somewhere between that of globular proteins and dextran (1,3,13,20,28). For example, if the plasma clearance of a bolus dose of albumin was only due to renal excretion, this would imply a plasma half-life of ϳ2,000 h, corresponding to a TER alb of Ͻ0.04% (i.e., Ͼ50 times less than that measured by Vuchkova et al) (29).…”

Continuum of historical controversies regarding the structural-functional relationship of the glomerular ultrafiltration unit

“…similar hydrodynamic radii permeate through relatively small pores (45-50 Å) of the GUU, according to the "two-pore model" proposed by Deen et al (11). Extensive discussions on this complex theoretical issue have been the subject matter of many past and recent reviews (21).…”