Carsten’s research is driven by the questions of how antibodies neutralise viral infections such as HIV or Influenza, and how viruses shape the evolution of the immune system and vice versa. We borrow mathematics from various fields such as stochastic processes, statistics, differential equations, phylodynamics, and antigenic mapping to unravel these mysteries. Mathematical models are crucial in modern biology, because they can be used to analyse big data, to make predictions leading to testable hypotheses, to guide optimal experiment design, and to be able to transfer one concept from one area to another. Thus, our research is most often performed in close collaboration with experimentalists. We are specifically interested in the following topics:

Which antibody concentrations are needed to neutralise HIV?

Antibodies have the ability to protect against new infection if (i) the antibody has the potential to efficiently neutralise HIV virions and (ii) the antibodies are present in sufficiently high concentrations at the port of entry. We derived a complete theory of antibody based neutralisation building upon numerical values of viral entry (how many viral spikes are required such that the the virion can infect its host cell) and neutralisation (how many antibodies have to bind to one spike such that it looses its functionality). The picture shows the main result, namely a prediction of penile to vaginal transmission probability as a function of antibody concentration. This framework is nicely described in our latest paper on antibody based neutralisation, which you can find here. In the future, we will extend this framework to study the effect of passively transferred antibodies.

Which antibody concentrations facilitate escape mutations?

When antibodies are present in concentrations that are not sufficient for complete neutralisation, the virus population can evolve resistant viral strains. These concentrations are referred to as mutant selection windows. These ranges can be calculated by comparing the fitness of the antibody sensitive strain and a resistance mutation as displayed in the picture to the left. Determining these concentrations are important when antibodies are used as therapeutic interventions, as resistance evolution needs to be prevented. We describe this framework here. In the future, we will use this concept to predict failure of antibody-based neutralisation.

How does the virus protect itself from antibody binding?

The HIV spike is extremely variable and a difficult target for antibodies. Several regions on the HIV spike are variable, the so called variable loops. In particular, the variable loop V1V2 has been proven to extend in length during disease progression. This loop has the ability to protect epitopes. We developed methods to unravel whether this loop can protect epitopes located on neighbouring protomers or on the same protomer. Our mathematical models predict different outcomes for particular setups of binding experiments. In Magnus et al. 2013 we summarise these methods and give an overview about their applicability.

How does within-host evolution influence between-host reconstruction?

During HIV infection the initially very few transmitted viral strains evolve to an extremely diverse population of viral strains, often referred to as quasispecies. Only very few of these strains are transmitted. Phylogenetic methods are used to reconstruct transmission chains of HIV infection based on sequences sampled from HIV infected individuals. We study under which conditions the within-host diversity still allows correct transmission chain reconstruction.

How can we use mathematical models to personalise vaccination schemes?

A protective anti-HIV vaccine is the ultimate goal of HIV research, because such a vaccine could lead to eradication of HIV. However, no HIV vaccine tested until now has been successful in mounting a protective immune response (e.g. summarised in Klein et al. 2013). The vaccine research community uses so called broadly neutralising antibodies as blueprints for vaccine design (Burton et al. 2012). These antibodies arise in a small percentage of HIV-infected individuals after a long period of virus-antibody coevolution. We develop methods to study virus-antibody coevolution with the goal to help rationally design sequential vaccines. Please contact us if you want to learn how we envision tackling this problem or if you want to fund us for this promising line of research.

Further interests

I am also interested in the spread of diseases and specifically in how viral sequence data can be used to learn about outbreak dynamics. We recently studied the Zika virus epidemics in the Americas and found that a certain level of information must be included in sequence data to reliably estimate parameters. More information can be found here.