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. A polymeric molecule bound to a cell generally will not lie entirely on the surface; rather there will be sections that form loops extending into solution, separated by tightly bound sections, or trains. Trains link antibody receptors on the B cell surface in a fashion that restricts their mobility. Thus trains cause restrictive cross-linking. Our computations show that there is a critical hapten density below which the polymer does not bind to the surface. At hapten densities slightly above the critical density, the polymer binds weakly to the surface with a configuration dominated by a few, rather long loops. These loops cross-link receptors, but do so without bringing the cross-linked receptors into close proximity and without substantially restricting their motion. Long loops thus cause unrestrictive cross-linking. As the hapten density increases, the average loop length decreases and the average train length increases. Thus cross-linking becomes restrictive. In this density range, immune stimulation is observed. At high hapten densities long trains form, separated by few, very short loops and almost all receptors are cross-linked. Consequently cross-linking may be overly restrictive, freezing receptors into place and generating an abundance of cross-linking or other signals that induce a state of immunological tolerance.