Mathematical models: a key to understanding HIV envelope interactions?

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

Heterogeneous Host Susceptibility Enhances Prevalence of Mixed-Genotype Micro-Parasite Infections

Dose response in micro-parasite infections is usually shallower than predicted by the independent action model, which assumes that each infectious unit has a probability of infection that is independent of the presence of other infectious units. Moreover, the prevalence of mixed-genotype infections was greater than predicted by this model. No probabilistic infection model has been proposed to account for the higher prevalence of mixed-genotype infections. We use model selection within a set of four alternative models to explain high prevalence of mixed-genotype infections in combination with a shallow dose response. These models contrast dependent versus independent action of micro-parasite infectious units, and homogeneous versus heterogeneous host susceptibility. We specifically consider a situation in which genome differences between genotypes are minimal, and highly unlikely to result in genotype-genotype interactions. Data on dose response and mixed-genotype infection prevalence were collected by challenging fifth instar Spodoptera exigua larvae with two genotypes of Autographa californica multicapsid nucleopolyhedrovirus (AcMNPV), differing only in a 100 bp PCR marker sequence. We show that an independent action model that includes heterogeneity in host susceptibility can explain both the shallow dose response and the high prevalence of mixed-genotype infections. Theoretical results indicate that variation in host susceptibility is inextricably linked to increased prevalence of mixed-genotype infections. We have shown, to our knowledge for the first time, how heterogeneity in host susceptibility affects mixed-genotype infection prevalence. No evidence was found that virions operate dependently. While it has been recognized that heterogeneity in host susceptibility must be included in models of micro-parasite transmission and epidemiology to account for dose response, here we show that heterogeneity in susceptibility is also a fundamental principle explaining patterns of pathogen genetic diversity among hosts in a population. This principle has potentially wide implications for the monitoring, modeling and management of infectious diseases

The effect of interference on the CD8+ T cell escape rates in HIV

In early HIV infection, the virus population escapes from multiple CD8+ cell responses. The later an escape mutation emerges, the slower it outgrows its competition, i. e. the escape rate is lower. This pattern could indicate that the strength of the CD8+ cell responses is waning, or that later viral escape mutants carry a larger fitness cost. In this paper, we investigate whether the pattern of decreasing escape rate could also be caused by genetic interference among different escape strains. To this end, we developed a mathematical multi-epitope model of HIV dynamics, which incorporates stochastic effects, recombination and mutation. We used cumulative linkage disequilibrium measures to quantify the amount of interference. We found that nearly synchronous, similarly strong immune responses in two-locus systems enhance the generation of genetic interference. This effect, combined with densely spaced sampling times at the beginning of infection and sparse sampling times later, leads to decreasing successive escape rate estimates, even when there were no selection differences among alleles. These predictions are supported by experimental data from one HIV-infected patient. Thus, interference could explain why later escapes are slower. Considering escape mutations in isolation, neglecting their genetic linkage, conceals the underlying haplotype dynamics and can affect the estimation of the selective pressure exerted by CD8+ cells. In systems in which multiple escape mutations appear, the occurrence of interference dynamics should be assessed by measuring the linkage between different escape mutations