Development and analysis of mathematical models for the quantification of the number of antibodies needed for virus neutralization, and for estimating the rates at which viral escape variants arise under selection pressure induced by the antibody response
Final Report Abstract
During the last two years, I developed and analysed mathematical models of virus neutralisation and viral escape from antibody responses. Studying antibody neutralisation is in general very important for vaccine development, because most of the available vaccines stimulate the immune system to produce protective antibodies. However, vaccines could not have been developed for many diseases, including the Human Immunodeficiency Virus. Reasons for this failure could be that these vaccines cannot stimulate the immune system to produce a sufficiently high number of antibodies or that the virus can escape neutralisation by the produced antibodies too quickly. In one project I studied a mathematical model that describes antibody neutralisation of HIV virions combining binding kinetics with stoichiometries. This study was a proof of concept study and I extended it in a second project to study the impact of parameters of the conceptual model on the neutralisation capacity of these viruses. Viruses have a short generation time and a high mutation rate. Therefore, variants that can evade selective pressure induced e.g. by antibodies can arise shortly after the selective pressure kicked in. This means that upon the generation of neutralising antibodies, a variant that is more fit in the presence of this antibody, an escape variant, is very likely to invade and dominate the HIV population. The fitness of such a variant is dependent on the environment and with increasing antibody concentration its fitness will decrease. In a third project I study these concentration ranges, also called mutant selection windows, with a huge data set in which thousand of antibody/virus combinations were tested. In addition I coauthored a review on mathematical models that describe the infection with HIV in one host from the time point of infection to the onset of AIDS. This review gives a concise overview of these models and their explanations of the onset of AIDS. These models aid in understanding which factors drive the infection and in a second step how to suppress these factors in HIV therapy. In a fourth part I studied models of mixed HIV trimer formation and experimental systems to analyse data obtained in these systems. In these projects I show how mathematical modeling and experimental design go hand in hand and can benefit from each other to solve questions related to the function of HIV trimers.
Publications
- (2012). Modelling the Course of an HIV Infection: Insights from Ecology and Evolution. Viruses 2012, 4, 1984-2013
Alizon S and Magnus C
- (2013). Virus Neutralisation: New Insights from Kinetic Neutralisation Curves. PLOS Computational Biology 9(2):e1002900
Magnus C
