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.
Funk
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GA
Mathematical Institute, University of Zurich, Winterthurerstrasse 190, Zurich, 8057, Switzerland.
Barbour
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Hengartner
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H
Kalinke
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U
D000818:Animals; D000914:Antibodies, Viral / Q000097:blood; D001402:B-Lymphocytes / Q000276:immunology; D007074:Immunoglobulin G / Q000276:immunology; D007075:Immunoglobulin M / Q000276:immunology; D007136:Immunoglobulins / Q000276:immunology*; D008213:Lymphocyte Activation; D051379:Mice; D018448:Models, Immunological; D018353:Rhabdoviridae Infections / Q000276:immunology*; D013154:Spleen / Q000276:immunology*; D013601:T-Lymphocytes / Q000276:immunology; D013997:Time Factors; D014721:Vesicular stomatitis Indiana virus
D000914:Antibodies, Viral; D007074:Immunoglobulin G; D007075:Immunoglobulin M; D007136:Immunoglobulins