Cross-linking of Identical Particles by Multiple Ligand-Types

  • John L. Spouge
Conference paper
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 57)

Abstract

This paper uses branching processes to model the cross-linking of identical particles by multiple ligand-types. We derive gel points and mole- and weight-average cluster sizes for Binomial and Poisson bonding.

In Immunology, this model might apply to cross-linking by antibodies specific to different antigenic sites. It represents a refinement of the Goldberg-Watson theory of immune complex formation and makes predictions readily tested by experiment.

The model makes the undesirable assumption that no intramolecular bonding occurs. Relaxation of this assumption is mathematically challenging and is of interest to polymer chemists.

Keywords

Corn Macromolecule 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Biblography

  1. Athreya, K.B. and Ney, P.E. 1972 Branching Processes (Springer-Verlag, Berlin)MATHGoogle Scholar
  2. Bell, G.I., Perelson, A.S. and Plimbley, G. 1978 Theoretical Immunology (Marcel Dekker, New York)MATHGoogle Scholar
  3. Dostał, H. and Raff, R. 1936 Z. Phys. Chem. B32: 117Google Scholar
  4. Drake, R.L. 1972 in Topics in Current Aerosol Research, Hidy and Brock, eds. (Pergamon Press, New York) Vol. 3, Part 2Google Scholar
  5. Flory, P.J. 1941 J. Am. Chem. Soc. 63: 3083, 3091, 3096CrossRefGoogle Scholar
  6. Goldberg, R.J. 1952 J. Am. Chem. Soc. 74: 5715CrossRefGoogle Scholar
  7. Goldberg, R.J. 1953 J. Am. Chem. Soc. 75: 3127CrossRefGoogle Scholar
  8. Good, I.J. 1963 Proc. Roy. Soc. London A272: 54Google Scholar
  9. Gordon, M. 1962 Proc. Roy. Soc. London A268: 240Google Scholar
  10. Gordon, M. and Scantlebury, G.R. 1964 Trans. Faraday Soc. 60: 604CrossRefGoogle Scholar
  11. Gordon, M. and Scantlebury, G.R. 1966 Proc. Roy. Soc. London A292: 380Google Scholar
  12. Macken, C.A. and Perelson, A.S. 1983 in Lecture Notes in Biomathematics (Springer-Verlag, Berlin) in pressGoogle Scholar
  13. Schulthess, G.K. von, Benedek, G.B., 1980 Macromolecules 13: 393Google Scholar
  14. Sctmlthess, O.K. von, Benedek, G.B. and De Blois, R.W. 1983 Macromolecules in press Google Scholar
  15. Smoluchowski, M. von 1916 Physik Z. 17: 585Google Scholar
  16. Smolchowski, M. von 1917 Z. Phys. Chem. 92: 129Google Scholar
  17. Spouge, J.L. 1983a Macromolecules 16: 121CrossRefGoogle Scholar
  18. Spouge, J.L. 1983b J. Phys. A.: Math. Gen. 16: 767CrossRefMATHMathSciNetGoogle Scholar
  19. Spouge, J.L. 1983c Macromolecules 16: in presssGoogle Scholar
  20. Spouge, J.L. 1983d J. Phys. A.: Math. Gen. 16: in pressGoogle Scholar
  21. Spouge, J.L. 1983e Adv. Appl. Prob, submittedGoogle Scholar
  22. Spouge, J.L. 1983f Proc. Roy. Soc. London A: in pressGoogle Scholar
  23. Stockmayer, W.H. 1943 J. Chem. Phys. 11: 45CrossRefGoogle Scholar
  24. Stockmayer, W.H. 1944 J. Chem. Phys. 12: 125CrossRefGoogle Scholar
  25. Stockmayer, W.H. 1983 Personal CommunicationGoogle Scholar
  26. Watson, G.S. 1958 J. Immunol. 80: 182Google Scholar
  27. Whittle, P. 1965a Proc. Camb. Phil. Soc. 61: 475CrossRefMathSciNetGoogle Scholar
  28. Whittle, P. 1965b Proc. Roy. Soc. London A285: 501Google Scholar
  29. Whittle, P. 1980a Adv. Appl. Prob. 12: 94, 116, 135CrossRefMATHMathSciNetGoogle Scholar
  30. Whittle, P. 1980b Theory Prob. Appl. 26: 350MathSciNetGoogle Scholar
  31. Ziff, R.M. 1980 J. Stat. Phys. 23: 241CrossRefMathSciNetGoogle Scholar
  32. Ziff, R.M., Ernst, M.H. and Hendriks, E.M. 1983 J. Phys. A.: Math. Gen.: submitted.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • John L. Spouge
    • 1
  1. 1.Theoretical BiologyLos Alamos National LaboratoryLos AlamosUSA

Personalised recommendations