A method for determining whether the descending limb of a biphasic histamine release curve reflects insufficient cross-linking.

We introduce a kinetic method for determining whether the descending limb of a biphasic histamine release dose-response curve is the result of insufficient cross-linking, and delineate conditions under which it is applicable. The method involves examining kinetic curves showing for various fixed antigen concentrations the cumulative amount of histamine release as a function of time. From the slope of the kinetic curves measured at some fixed time one determines how the rate of release depends on concentration.

Theoretical considerations of the role of antigen structure in B cell activation.

Thymus-independent antigens generally are polymeric molecules with repeating arrays of antigenic determinants. Immunological studies of the activity of haptenated thymus-independent antigens have shown that small changes in hapten density can transform a polymeric antigen from nonimmunogenic to immunogenic, and from immunogenic to tolerogenic. In this paper we compute the equilibrium configuration of a linear flexible, haptenated polymer absorbed to a B cell surface, and correlate configurational features of the molecule with its immunological functioning.

Optimal strategies in immunology III. The IgM-IgG switch.

During a primary immune response generally two classes of antibody are produced, immunoglobulin M (IgM) and immunoglobulin G (IgG). It is currently thought that some lymphocytes which initially produce IgM switch to the production of IgG with the same specificity for antigen. During a secondary immune response IgG is the predominant antibody made throughout the response.

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

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.

Optimal strategies in immunology. II. B memory cell production.

After a first encounter with most antigens, the immune system responds to susequent encounters with a faster, more efficient and more strenuous antibody response. The memory of previous antigen contacts is carried by lymphocytes. Expanding on the model developed in Part 1 of this paper, we examine the optimal strategy available to the immune system for B memory cell production.

Antigen modulation of antibody forming cells: the relationship between direct plaque size, antibody secretion rate and antibody affinity.

Using the mathematical theory of direct plaque growth, we have analyzed the expected variation of plaque size with IgM affinity and secretion rate. We use the theory to comment on recent effector cell blockage experiments and show how the theory can be used to determine the change in the secretion rate of a single antibody-forming cell subjected to blockage by a multivalent antigen. We also argue, using the mathematical theory, that under the usual experimental conditions employed in the plaque assay, cells that produce low affinity IgM antibodies will give rise to smaller plaques than cells that produce high affinity IgM antibodies.

Mathematical models for the evolution of multigene families by unequal crossing over.

Mathematical models of homologous but unequal crossing over between sister chromatids are presented. For mispairing by one repeat, the evolution of a multigene family by unequal crossing over can be represented by a linear birth-death process. The fixation rate of one repeat in a multigene family is estimated.

Optimal strategies in immunology. I. B-cell differentiation and proliferation.

The optimal strategy available to the immune system for responding to a non-replicating thymus-independent antigen is examined. By applying Pontryagin's maximum principle to a set of mathematical models of lymphocyte populations and their antibody production, it is found that the optimal strategy of bang-bang control appears robust. In a variety of structurely related biological models, similar behaviour is observed.

The electrophoretic hemolytic plaque assay -- theory.

We use the mathematical theory of plaque qrowth to determine if there is merit in performing a hemolytic plaque assay in the presence of an external electric field. In particular, we study the effects of an electric field on the transport of antibodies secreted by a single lymphocyte and on the size and shape of the plaques they produce. Our results indicate that in the presence of an applied electric field: (1) The mobility of the antibodies produced by the antibody forming cell can be determined from the plaque shape.