Theory of equilibrium binding of symmetric bivalent haptens to cell surface antibody: application to histamine release from basophils. [Mathematical model]

Journal Article · Sat Jul 01 04:00:00 EDT 1978 · J. Immunol.; (United States)

OSTI ID:6880621

Dembo, M; Goldstein, B

We present a theory of equilibrium binding of symmetric bivalent haptens to cell surface antibody in the presence or absence of monovalent hapten. Bivalent haptens can link together antibodies to form linear chains or rings on cell surfaces. We show how to calculate the amount of any complex of bound bivalent hapten, monovalent hapten, and antibody. We are particularly interested in the mole fraction of antibody involved in complexes made up of two or more antibodies, i.e., the fraction of antibody that is cross-linked (x/sub poly/). We treat the case when the antibody on the cell surface, which is specific for the hapten, is homogeneous. For this case we prove a number of general properties about x/sub poly/: (1) x/sub poly/ approaches zero at both high and low bivalent hapten concentration, (2) x/sub poly/ becomes a maximum when the bivalent hapten concentration equals A/sub max/, where A/sub max/ = 1/H + B/2. H is twice the equilibrium constant for the binding of a single hapten site to a single antibody side and B is the monovalent hapten concentration, (3) a plot of x/sub poly/ vs the log of the bivalent hapten cencentration is symmetric about the maximum value of x/sub poly/. We use these and other properties of x/sub poly/ in this paper to clarify the relationship between cross-link formation and histamine release.

• Research Organization: Los Alamos Scientific Lab., NM
• OSTI ID: 6880621
• Journal Information: J. Immunol.; (United States), Journal Name: J. Immunol.; (United States) Vol. 121:1; ISSN JOIMA
• Country of Publication: United States
• Language: English

Related Subjects

550200 -- Biochemistry
551000* -- Physiological Systems
59 BASIC BIOLOGICAL SCIENCES
AMINES
ANIMAL CELLS
ANTIBODIES
ANTIGEN-ANTIBODY REACTIONS
ANTIGENS
AZOLES
BASOPHILS
BINDING ENERGY
BIOLOGICAL MATERIALS
BLOOD
BLOOD CELLS
BODY FLUIDS
CARBOHYDRATES
CHEMICAL REACTIONS
CONNECTIVE TISSUE CELLS
CORRELATIONS
CROSS-LINKING
ENERGY
HETEROCYCLIC COMPOUNDS
HISTAMINE
IMIDAZOLES
LEUKOCYTES
MAST CELLS
MATHEMATICAL MODELS
ORGANIC COMPOUNDS
ORGANIC NITROGEN COMPOUNDS
POLYMERIZATION
POLYSACCHARIDES
RECEPTORS
SACCHARIDES
SECRETION
SOMATIC CELLS