Detection and analysis of recognition and selection in the immune response

Dynamics on tumor immunotherapy model with periodic impulsive infusion

A periodic pulse differential equation model of tumor immunotherapy is established by considering the periodic and transient behavior of infusing immune cells. Using comparison theorem and Floquet multiplier theory of the impulsive differential equation, the boundedness of the model solution, the existence and stability of the free-tumor periodic solution are given. Furthermore, the persistence of the system is analyzed. Numerical simulations are carried to confirm the main theorems.

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. In this paper we address the question of why such apparently complicated modes of response should have been adapted by evolution. We construct mathematical models of the immune response to growing antigens which incorporate complement dependent cell lysis. By comparing the times required to eliminate antigen we show that under certain conditions it is advantageous for an animal to switch some of its lymphocytes from IgM to IgG production during a primary response, but yet to secrete only IgG during a secondary response. The sensitivity of such a conclusion to parameter variations is studied and the biological basis and implications of our models are fully discussed.

Time and antigen dose-dependent variations of IgM antibody affinity

Affinity of IgM antibodies elicited in mice by a single injection of dinitrophenylated dextran was measured by equilibrium dialysis. Maturation of affinity was found to occur with time, the rate of increase being higher after larger antigen doses. Maturation was followed by a decrease of affinity with time, the fall being more pronounced after lower antigen doses. These findings are more in line with the theory of antigen-induced diversity rather than with the maturation theory.