Mathematical model of a virus-neutralizing immunglobulin response.

We present a mathematical model to simulate the kinetics of B-cell activation and the virus-neutralizing immunoglobulin response in the spleen of mice after infection with vesicular stomatitis virus (VSV). Our model combines data from in vitro experiments and in vivo kinetic observations. A system of eight nonlinear differential equations was used in the computer experiments and numerically solved. The isotype switch from IgM to IgG in the presence of T-cell help was modelled by a time variable function, used as a parameter. The model solutions indicate fast kinetics of the generation of VSV-neutralizing IgM antibodies within 2-3 days post immunization peaking on day 5 at a serum concentration of approximately 80 microgram ml-1 IgM, which is the equivalent to about 10% of the total IgM serum concentration. The frequency of virus-specific B cells increases about 1000-fold within the first 4 days after immunization. Protective levels of VSV-neutralizing IgG antibodies (>/=10 microgram ml-1) are reached within 5 to 6 days post immunization. Fitting the model solution to the experimentally observed neutralizing serum titers suggests an increase in the neutralizing activity of IgGs occurring between days 5 and 8 post-infection. The model indicates that less than 10 VSV-specific B cells have to be triggered daily to maintain protective IgG serum titers during the memory phase. Copyright 1998 Academic Press.