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

在1980年代初，一种新的病毒开始传播，造成免疫系统的严重损害;人类免疫缺陷病毒（HIV）。尽管对这种病毒进行了深入的研究，但尚未发现针对艾滋病毒的成功疫苗。所有现有的疫苗，如麻疹、风疹或流感疫苗，都能刺激免疫系统产生抗体。这些抗体在侵入宿主时中和入侵病毒。除了确定针对HIV的广泛中和抗体的困难之外，定量方面可能会增加谜团，为什么没有候选疫苗可以成功预防HIV感染。候选疫苗可能无法刺激产生足够的抗体来中和所有入侵的病毒体。为了验证这一点，我将在第一个项目中研究中和一个病毒体所需的抗体数量。我将联合收割机结合化学计量的概念，最近引入到病毒学，与结合动力学的化学概念。通过该链接，可以确定滴定曲线中中和所需的抗体数量。这些滴定曲线在病毒学中广泛用于表征抗体的中和潜力。如果疫苗不能刺激免疫系统产生足够的抗体来清除所有入侵的病毒粒子，那么就有可能进化出对抗体中和有抵抗力的病毒变体。在第二个项目中，我将估计对抗体结合有抗性的变异出现的速率。为此，我将使用一个数学模型来描述两种不同病毒株的病毒动力学。利用该模型，可以确定对各种抗体应答的逃逸率。结合这两个项目，可以测试候选疫苗是否刺激足够高的抗体滴度。如果不是这种情况，则可以测试针对刺激的抗体应答产生抗性病毒变体的速度。

In the early 1980s, a new virus began to spread that caused severe damages of the immune system; the human immunodeficiency virus (HIV). Despite intensive studies of this virus, no successful vaccine against HIV has been found yet. All the existing vaccines, e.g. against measles, rubella or influenza stimulate the immune system to produce antibodies. These antibodies neutralize invading viruses when entering the host. Beside the difficulties to determine broadly neutralizing antibodies directed against HIV, quantitative aspects might add to the riddle, why no vaccine candidate could successfully prevent HIV infection. The vaccine candidates might not be able to stimulate the production of enough antibodies to neutralize all invading virions. To test this, I will study the number of antibodies needed to neutralize one virion in a first project. I will combine the concept of stoichiometries that was recently introduced into virology, with the chemical concept of binding kinetics. With this link it will be possible to determine the number of antibodies needed for neutralization out of titration curves. These titration curves are widely used in virology to characterize the neutralization potential of antibodies. If a vaccine cannot stimulate the immune system to produce enough antibodies sufficient to clear all the invading virions, the evolution of viral variants resistant to antibody neutralization is possible. In the second project, I will estimate the rates at which variants arise that are resistant against antibody binding. To this end, I will use a mathematical model describing the viral dynamics of two different viral strains. With this model, it is possible to determine the escape rates to various antibody responses. Combining the two projects, vaccine candidates can be tested whether they stimulate sufficiently high antibody titers. If this is not the case, it can be tested how fast resistant viral variants arise against the stimulated antibody response.