Abstract
Dextran has been the most commonly employed test molecule for probing the selectivity of glomerular filtration to macromolecules of varying size. The usual theories for hindered transport of solid spheres through pores have limited utility in interpreting clearance data for dextran or other linear polymers because such polymers in solution more closely resemble random, solvent-filled coils than solid spheres. To provide a model for glomerular filtration of random-coil macromolecules, the equilibrium partitioning of random coils between cylindrical pores and bulk solution was simulated using Monte Carlo calculations, and those results were combined with a hydrodynamic theory for restricted motion of solvent-filled polymer coils in pores. The rates of transport predicted for either neutral random coils or for solid spheres of the same Stokes-Einstein radius were significantly lower than observed transport rates of dextran through the glomerular capillary wall or across synthetic porous membranes. This facilitation of dextran transport was modeled by postulating weak, attractive interactions between dextran monomers and the pore wall. The random-coil model with attractive interactions, modeled using a short-range, square-well potential, was found to adequately represent dextran sieving data in normal rats. Various limitations of this approach are discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Akima, H. 1972. Interpolation and smooth curve fitting based on local procedures.Comm. ACM 15, 914–918.
Bohrer, M. P., G. D. Patterson and P. J. Carroll. 1984. Hindered diffusion of dextran and Ficoll in microporous membranes.Macromolecules 17, 1170–1173.
Callaghan, P. T. and D. N. Pinder. 1983. A pulsed field gradient NMR study of self-diffusion in a polydisperse system: dextran in water.Macromolecules.16, 968–973.
Cannell, D. S. and F. Rondelez. 1980. Diffusion of polystyrenes through microporous membranes.Macromolecules 13, 1599–1602.
Casassa, E. F. 1967. Equilibrium distribution of flexible polymer chains between a macroscopic solution phase and small voids.J. Polym. Sci. Polym. Lett. 5, 773–777.
Davidson, M. G., U. W. Suter and W. M. Deen. 1987. Equilibrium partitioning of flexible macromolecules between bulk solution and cylindrical pores.Macromolecules 20, 1141–1146.
Davidson, M. G. and W. M. Deen. 1988a. Hindered diffusion of water-soluble macromolecules in membranes.Macromolecules 21, 3474–3481.
Davidson, M. G. and W. M. Deen. 1988b. Hydrodynamic theory for the hindered transport of flexible macromolecules in porous membranes.J. Membrane Sci. 35, 167–192.
Deen, W. M. 1987. Hindered transport of large molecules in liquid-filled pores.AIChE J. 33, 1409–1425.
Deen, W. M., C. R. Bridges, B. M. Brenner and B. D. Myers. 1985. Heteroporous model of glomerular size selectivity: application to normal and nephrotic humans.Am. J. Physiol. 249, F374-F389.
Flory, P. J. 1953.Principles of Polymer Chemistry, pp. 399–413. Ithaca, NY: Cornell University Press.
Garg, S. K. and S. S. Stivala. 1978. Assessment of branching in polymers from small-angle x-ray scattering (SAXS).J. Polym. Sci. Polym. Phys. 16, 1419–1434.
Gekko, K. 1971. Physicochemical studies of oligodextran. II. Intrinsic viscosity-molecular weight relationship.Makromol. Chem. 148, 229–238.
Gekko, K. 1981. Solution properties of dextran and its ionic derivatives.ACS Symp. Ser. 150, 415–438.
Guillot, G., L. Leger and F. Rondelez. 1985. Diffusion of large flexible polymer chains through model porous membranes.Macromolecules 18, 2531–2537.
Kathawalla, I. A. and J. L. Anderson. 1988. Pore size effects on diffusion of polystyrene in dilute solution.Ind. Engng Chem. Res. 27, 866–871.
Kramers, H. A. 1946. The behavior of macromolecules in inhomogeneous flow.J. chem. Phys. 14, 415–424.
Kuge, T., K. Kobayashi, S. Kitamura and H. Tanahashi. 1987. Degrees of long-chain branching in dextran.Carbohydrate Res. 160, 205–214.
Lin, N. P. and W. M. Deen. 1990. Effects of long-range polymer-pore interactions on the partitioning of linear polymers.Macromolecules 23, 2947–2955.
Maddox, D. A., W. M. Deen and B. M. Brenner. 1992. Glomerular filtration. InHandbook of Physiology. Section 8:Renal Physiology. E. E. Windhager (Ed.), pp. 545–638. New York: Oxford University Press.
Marsaglia, G. 1972. Choosing a point from the surface of a sphere.Ann. Math. Stat. 43, 645–646.
Oliver, J. D., III. 1992. Analysis of glomerular permselectivity in the rat using theoretical models of hindered transport. Ph. D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Oliver, J. D., III, S. Anderson, J. L. Troy, B. M. Brenner and W. M. Deen. 1992. Determination of glomerular size-selectivity in the normal rat with Ficoll.J. Am. Soc. Nephr. 3, 214–228.
Press, W. H., B. P. Flannery, S. A. Teukolsky and W. T. Vetterling. 1986.Numerical Recipes: The Art of Scientific Computing. New York. Cambridge University Press.
Remuzzi, A., C. Battaglia, L. Rossi, C. Zoja and G. Remuzzi. 1987. Glomerular size selectivity in nephrotic rats exposed to diets with different protein content.Am. J. Physiol. 253, F318-F327.
Senti, F. R., N. N. Hellman, N. H. Ludwig, G. E. Babcock, R. Tobin, C. A. Glass and B. L. Lamberts. 1955. Viscosity, sedimentation, and light-scattering properties of fractions of an acid-hydrolyzed dextran.J. Polym. Sci. 17, 527–546.
Wishart, J. 1949. Cumulants of multivariate multinomial distributions.Biometrika 36, 47–58.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Oliver, J.D., Deen, W.M. Random-coil model for glomerular sieving of dextran. Bltn Mathcal Biology 56, 369–389 (1994). https://doi.org/10.1007/BF02460463
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02460463