Mathematical modeling the radiation effects on humoral immunity

A mathematical model of humoral immune response in nonirradiated and irradiated mammals is developed. It is based on conventional theories and experimental facts in this field. The model is a system of nonlinear differential equations which describe the dynamics of concentrations of antibody and antigen molecules, immunocompetent B lymphocytes, and the rest blood lymphocytes, as well as the bone-marrow lymphocyte precursors. The interaction of antigen molecules with antibodies and with antibody-like receptors on immunocompetent cells is also incorporated. The model quantitatively reproduces the dynamics of the humoral immune response to the T-independent antigen (capsular antigen of plague microbe) in nonirradiated mammals (CBA mice). It describes the peculiarities of the humoral immune response in CBA mice exposed to acute radiation before or after introducing antigen. The model predicts an adaptation of humoral immune system to low dose rate chronic irradiation in the result of which the intensity of immune response relaxes to a new, lower than normal, stable level. The mechanisms of this phenomenon are revealed. The results obtained show that the developed model, after the appropriate identification, can be used to predict the effects of acute and low-level long-term irradiation on the system of humoral immunity in humans. Employment of the mathematical model identified in the proper way should be important in estimating the radiation risk for cosmonauts and astronauts on long space missions such as a voyage to Mars or a lunar colony.