# Mathematical models: a key to understanding HIV envelope interactions?

Magnus, Carsten; Brandenberg, Oliver F; Rusert, Peter; Trkola, Alexandra; Regoes, Roland Robert (2013). Mathematical models: a key to understanding HIV envelope interactions? Journal of Immunological Methods, 398-399:1-18.

## Abstract

The spikes of the human immunodeficiency virus (HIV) mediate viral entry and are the most important targets for neutralizing antibodies. Each spike consists of three identical subunits. The role of the spike's subunits in antibody binding is not fully understood. One experimental approach to analyze trimer function uses assays with mixed envelope trimer expressing cells or viruses. As these experiments do not allow direct observation of subunit functions, mathematical models are required to interpret them. Here we describe a modeling framework to study (i) the interaction of the V1V2 loop with epitopes on the V3 loop and (ii) the composition of quaternary epitopes. In a first step we identify which trimers can form in these assays and how they function under antibody binding. We then derive the behavior of an average trimer. We contrast two experimental reporting systems and list their advantages and disadvantages. In these experiments trimer formation might not be perfectly random and we show how these effects can be tested. As we still lack a potent vaccine against HIV, and this vaccine surely has to stimulate the production of neutralizing antibodies, mixed trimer approaches in combination with mathematical models will help to identify vulnerable sites of the HIV spike.

## Abstract

The spikes of the human immunodeficiency virus (HIV) mediate viral entry and are the most important targets for neutralizing antibodies. Each spike consists of three identical subunits. The role of the spike's subunits in antibody binding is not fully understood. One experimental approach to analyze trimer function uses assays with mixed envelope trimer expressing cells or viruses. As these experiments do not allow direct observation of subunit functions, mathematical models are required to interpret them. Here we describe a modeling framework to study (i) the interaction of the V1V2 loop with epitopes on the V3 loop and (ii) the composition of quaternary epitopes. In a first step we identify which trimers can form in these assays and how they function under antibody binding. We then derive the behavior of an average trimer. We contrast two experimental reporting systems and list their advantages and disadvantages. In these experiments trimer formation might not be perfectly random and we show how these effects can be tested. As we still lack a potent vaccine against HIV, and this vaccine surely has to stimulate the production of neutralizing antibodies, mixed trimer approaches in combination with mathematical models will help to identify vulnerable sites of the HIV spike.

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