A singular perturbation approach to diffusion reaction equations containing a point source, with application to the hemolytic plaque assay

Journal of Mathematical Biology
A S Perelson, L A Segel

Abstract

Many cells secrete factors which diffuse and bind to receptors on neighboring cells. These processes can be described by a nonlinear diffusion equation with a point source and spatially distributed binding reaction. We show via perturbation analysis how approximate solutions can be obtained for such equations when the binding reaction is fast compared to diffusive transport. We base our analysis on an example which is of great practical importance in immunology, the hemolytic plaque technique.

References

Jun 1, 1975·Journal of Theoretical Biology·C DeLisi
Aug 1, 1975·Journal of Theoretical Biology·C DeLisi
Jun 1, 1977·Biophysical Chemistry·B Goldstein, A S Perelson
Jul 1, 1976·Biophysical Chemistry·B Goldstein, A S Perelson
Jan 1, 1974·Proceedings of the National Academy of Sciences of the United States of America·C P De Lisi, G I Bell
Jan 1, 1974·Transplantation Reviews·N K JerneI Lefkovits
Nov 1, 1973·Scientific American·M M Mayer
Jan 1, 1962·Annual Review of Microbiology·G J NOSSAL, O MAKELA
Dec 1, 1962·The Biochemical Journal·N C HUGHES-JONESR TELFORD
May 8, 1963·Annals of the New York Academy of Sciences·L A DAYS J SINGER
Sep 1, 1963·The Biochemical Journal·N C HUGHES-JONESR TELFORD
Mar 1, 1964·Vox Sanguinis·N C HUGHES-JONESR TELFORD
Apr 1, 1964·The Journal of Experimental Medicine·J S INGRAHAM, A BUSSARD
Apr 22, 1938·Science·E A Kabat, K O Pedersen
Apr 26, 1963·Science·N K Jerne, A A Nordin

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Citations

Aug 29, 2006·Journal of Mathematical Biology·N B Grover
Feb 21, 1987·Journal of Theoretical Biology·A CheerG Oster
Feb 1, 1983·Clinical Pediatrics·A Yates

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