Antigen binding to receptors on immunocompetent cells. II. Thermodynamic and biological implications of the receptor cross-linking requirement for B-cell activation

Representing and defining patterns by graphs: applications to sol-gel patterns and to cytoskeleton

The problems of interdisciplinary interests--applying methods of graph theory to sol-gel patterns and to cytoskeleton--are discussed. The importance of sol-gel transition phenomena in living cells and the possibility of periodic sol-gel transition phenomena are briefly reviewed. Representing patterns by graphs and using graph probabilistic representation for calculating structure-property relationships are discussed and applied to sol-gel transition patterns.

Fc-dependent effector functions of idiotype-anti-idiotype immune complexes

Some effector functions of antigen-antibody and antibody-antibody (idiotype-anti-idiotype) complexes were analyzed. As a model system a monoclonal IgM antibody specific for the hapten NP (antibody B1-8) was reacted either with hapten and hapten-carrier conjugates or with monoclonal anti-idiotope antibodies with specificity for B1-8 idiotopes. The precipitating, C1q-binding, complement-activating and Fc receptor binding properties of these complexes were compared. Binding of both hapten-carrier conjugates and anti-idiotope antibodies to B1-8 results in formation of complexes which depending on the B1-8:ligand ratio precipitate, activate complement, bind C1q and exhibit increased avidity for Fc mu and Fc gamma receptors of mouse spleen cells. In both types of complexes cross-linking of IgM molecules is essential for triggering these Fc-dependent functions, and a functional heterogeneity if idiotype-anti-idiotope complexes based on different idiotype-anti-idiotope ratios could also be observed. The functional similarity of B1-8-hapten-carrier and B1-8-anti-idiotope complexes suggests that regulatory functions so far assigned to antigen-antibody complexes could be carried out also by idiotype-anti-idiotope complexes.

Theory of equilibrium binding of a bivalent ligand to cell surface antibody: the effect of antibody heterogeneity on cross-linking

We investigate the equilibrium binding of symmetric bivalent ligands to a heterogeneous population of symmetric bivalent cell surface receptors. The receptors are heterogeneous in their binding affinities (equilibrium binding constants) for the ligand. For any distribution of receptor binding affinities we show how to calculate the total concentration of receptors that are cross-linked by the ligand, i.e., the concentration of cell surface aggregates composed of two or more receptors, as well as the concentration of any given aggregate. We show that certain qualitative properties of cross-linking which hold for homogeneous antibody populations fail to hold in the heterogeneous case. We use our results to interpret certain in vitro experiments in which synthetic bivalent haptens are used to trigger histamine release from basophils which have on their surface antibody specific for the hapten.

Mathematical models of antibody response

An antigen triggers the clonal expansion of B lymphocytes accompanied by antibody production. This paper presents and compares the basic ideas of three mathematical models of B cell differentiation and proliferation.

Quantitative aspects of a unified model of diffusion mediated receptor--cyclase coupling

A quantitative model is presented of diffusion mediated coupling of adenylate cyclase to multivalent plasma membrane receptors which accounts for a wide range of phenomena including non linear occupation-activation plots with either positive or negative second derivatives, spare receptors, silent receptors, and negative and positive binding cooperativity. A non linear least square fit of the predicted equation for cyclase activation to available data predicts translational diffusion coefficients in the range of (10(-10) - 10(-11))cm2/s.