Analysis of Biochemical Equilibria Relevant to the Immune Response: Finding the Dissociation Constants

L. J. Cummings, R. Perez-Castillejos, E. T. Mack

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This paper analyzes the biochemical equilibria between bivalent receptors, homo-bifunctional ligands, monovalent inhibitors, and their complexes. Such reaction schemes arise in the immune response, where immunoglobulins (bivalent receptors) bind to pathogens or allergens. The equilibria may be described by an infinite system of algebraic equations, which accounts for complexes of arbitrary size n (n being the number of receptors present in the complex). The system can be reduced to just 3 algebraic equations for the concentrations of free (unbound) receptor, free ligand and free inhibitor. Concentrations of all other complexes can be written explicitly in terms of these variables. We analyze how concentrations of key (experimentally-measurable) quantities vary with system parameters. Such measured quantities can furnish important information about dissociation constants in the system, which are difficult to obtain by other means. We provide analytical expressions and suggest specific experiments that could be used to determine the dissociation constants.

Original languageEnglish (US)
Pages (from-to)1171-1206
Number of pages36
JournalBulletin of Mathematical Biology
Issue number5
StatePublished - May 2012

All Science Journal Classification (ASJC) codes

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


  • Aggregation
  • Antibody
  • Bivalent ligand
  • Immune system


Dive into the research topics of 'Analysis of Biochemical Equilibria Relevant to the Immune Response: Finding the Dissociation Constants'. Together they form a unique fingerprint.

Cite this