A mathematical model of B lymphocyte differentiation: Control by antigen

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Abstract
A mathematical model of B lymphocyte differentiation, based on experimental results, has been developed. The model focuses on the role of antigen in initiating and regulating B cell differentiation while other mechanisms, acting in concert with antigen but the functioning of which can be circumvented under appropriate conditions, are not considered. The importance of presence of antigen at individual stages of B cell differentiation was studied in experiments with an easily metabolizable antigen. Immunocompetent cells (ICC), arising by antigen-independent differentiation of stem cells, are activated by antigen (they become immunologically activated cells — IAC). Excess of antigen drives IAC into the terminal stage (antibody-forming cells — AFC) thereby restricting proliferation. Exhaustive terminal differentiation results in tolerance. A low primary dose permits IAC to escape antigen; IAC proliferate and later give rise to resting memory cells (MC) which are amenable to reactivation. MC have higher avidity for antigen (due to higher affinity, number and density of receptors) and the effect of different doses of antigen on MC is diverse. A very low secondary dose induces tolerance, a medium dose secondary response, and the administration of a high dose of antigen also brings about tolerance. The model suggests that the fate of memory cells is controlled by the ratio R∶Ag, of the number of immunoglobulin receptors on B cells (R) to the number of available antigenic molecules (Ag), low values of R∶Ag favouring stimulation to differentiation while high values of R∶Ag favouring inactivation. A nonlinear system of ordinary differential equations, describing the development of the populations involved in antigen driven B cell differentiation, was used to simulate experiments and good qualitative agreement was achieved.