Mathematical model of clonal selection and antibody production

摘要: Abstract A mathematical model is developed for predicting the cellular proliferation and production of circulating antibodies that takes place when an adult animal injected with antigen. clonal selection theory used, in which it assumed certain target cells are capable being stimulated by antigen into a proliferating antibody producing state. The increase number until free concentration reaches low level, whereupon they divide asymmetrically to become plasma memory cells. terminal while identical It carry antibody-like surface receptors combining reversibly average bound determines mitotic activity cell. binding receptor site taken be characterized intrinsic association constant state calculated, at any time, univalent interacting bivalent multivalent Heterogeneous allowed having many groups differ their affinity produce correspondingly differing antibodies. rates change various cell populations, concentrations, governed differential equations embody biological assumptions model. In model, level selects cells, according antigen, proliferation; resulting population reflects this together rapid elimination antigen-antibody complexes. mechanism inducing high dose tolerance included suggested, based on depletion repeated small clones. system solved numerically digital computer program results have been compared experiments 2,4 dinitrophenyl-bovine γ-globulin was used as rabbits. Effective constants concentrations encouraging degree agreement found. indicated some experiments, probably overloaded. Some possible applications planning analysis discussed . By studying time dependence affinity, following injection one can deduce characteristics origin. Moreover, if enough known about targent may tailor exposure so achieve special effects, such tolerance, or homogeneous Experiments studied quantitatively interaction sites would great help confirming denying