Equilibrium theory for the binding of bivalent antibodies to regularly spaced sites on a DNA molecule

In the autoimmune disease, Systemic Lupus Erythematosus, an individual produces antibodies that bind to his or her own DNA. In this paper we consider a single, long DNA-like molecule in a solution containing bivalent antibodies that can bind to the DNA molecule at regularly spaced sites. The antibody can be attached to DNA by either one or two binding sites. We assume that, when an antibody molecule binds through both its sites, it spans a fixed number of free sites that remain accessible to antibody binding. In this model, antibody molecules can interdigitate along the DNA molecule. We allow steric hindrance within such interdigitating clusters of bound antibodies. We derive analytical expressions for the average number of free, monovalently bound and bivalently bound antibodies, and see how this distribution is influenced by steric hindrance and by the relative binding strengths of the singly and doubly bound antibody.