Mathematical models: a key to understanding HIV envelope interactions?

Competitive assembly resolves the stoichiometry of essential proteins in infectious HIV-1 virions

During assembly on the plasma membrane, HIV-1 virions incorporate Gag-Pol as well as gp120/gp41 trimers. The Pol region consists of protease, reverse transcriptase and integrase precursors which are essential enzymes required for maturation, reverse transcription, and integration of the viral genome in the next host. gp120/gp41 trimers catalyze the fusion of the virion with its next host. Only a fraction of released virions are infectious. The stoichiometry of gp120/gp41 and Gag-Pol proteins in HIV virions was previously measured using cryotomography and ratiometric protein analysis, but what is the stoichiometry of these proteins in infectious virions remained to be determined. Here we developed a method based on competition between infectious HIV backbones with noninfectious mutants and measured 100 ± 10 Gag-Pol and 15 ± 3 gp120/gp41 proteins incorporated in infectious virions assembled in HEK293 cells from NL4.3 HIV-1 backbone. Our measurements are in broad agreement with cryotomography and ratiometric protein analysis and therefore stoichiometry of gp120/gp41 and Gag-Pol in infectious virions is the same as all released virions. With the development of appropriate mutants and infectivity assays, our method is applicable to other infectious viruses.

Statement of significance

There are 30 million people who have succumbed to the AIDS pandemic with 600,000 additional deaths per year. HIV has an accelerated rate of mutational accumulation with the virus mutating out of neutralizing antibodies within the same patient making development of vaccines challenging. Like most enveloped viruses, only a fraction of released virions are infectious and the question of what selects these virions has remained a mystery. The method developed in this article will allow stoichiometric measurements on infectious virions and therefore allows further studies of causes of infectivity.

Estimating treatment prolongation for persistent infections

Treatment of infectious diseases is often long and requires patients to take drugs even after they have seemingly recovered. This is because of a phenomenon called persistence, which allows small fractions of the bacterial population to survive treatment despite being genetically susceptible. The surviving subpopulation is often below detection limit and therefore is empirically inaccessible but can cause treatment failure when treatment is terminated prematurely. Mathematical models could aid in predicting bacterial survival and thereby determine sufficient treatment length. However, the mechanisms of persistence are hotly debated, necessitating the development of multiple mechanistic models. Here we develop a generalized mathematical framework that can accommodate various persistence mechanisms from measurable heterogeneities in pathogen populations. It allows the estimation of the relative increase in treatment length necessary to eradicate persisters compared to the majority population. To simplify and generalize, we separate the model into two parts: the distribution of the molecular mechanism of persistence in the bacterial population (e.g. number of efflux pumps or target molecules, growth rates) and the elimination rate of single bacteria as a function of that phenotype. Thereby, we obtain an estimate of the required treatment length for each phenotypic subpopulation depending on its size and susceptibility.

Predicting HIV-1 transmission and antibody neutralization efficacy in vivo from stoichiometric parameters

The potential of broadly neutralizing antibodies targeting the HIV-1 envelope trimer to prevent HIV-1 transmission has opened new avenues for therapies and vaccines. However, their implementation remains challenging and would profit from a deepened mechanistic understanding of HIV-antibody interactions and the mucosal transmission process. In this study we experimentally determined stoichiometric parameters of the HIV-1 trimer-antibody interaction, confirming that binding of one antibody is sufficient for trimer neutralization. This defines numerical requirements for HIV-1 virion neutralization and thereby enables mathematical modelling of in vitro and in vivo antibody neutralization efficacy. The model we developed accurately predicts antibody efficacy in animal passive immunization studies and provides estimates for protective mucosal antibody concentrations. Furthermore, we derive estimates of the probability for a single virion to start host infection and the risks of male-to-female HIV-1 transmission per sexual intercourse. Our work thereby delivers comprehensive quantitative insights into both the molecular principles governing HIV-antibody interactions and the initial steps of mucosal HIV-1 transmission. These insights, alongside the underlying, adaptable modelling framework presented here, will be valuable for supporting in silico pre-trial planning and post-hoc evaluation of HIV-1 vaccination or antibody treatment trials.

Different infectivity of HIV-1 strains is linked to number of envelope trimers required for entry

HIV-1 enters target cells by virtue of envelope glycoprotein trimers that are incorporated at low density in the viral membrane. How many trimers are required to interact with target cell receptors to mediate virus entry, the HIV entry stoichiometry, still awaits clarification. Here, we provide estimates of the HIV entry stoichiometry utilizing a combined approach of experimental analyses and mathematical modeling. We demonstrate that divergent HIV strains differ in their stoichiometry of entry and require between 1 to 7 trimers, with most strains depending on 2 to 3 trimers to complete infection. Envelope modifications that perturb trimer structure lead to an increase in the entry stoichiometry, as did naturally occurring antibody or entry inhibitor escape mutations. Highlighting the physiological relevance of our findings, a high entry stoichiometry correlated with low virus infectivity and slow virus entry kinetics. The entry stoichiometry therefore directly influences HIV transmission, as trimer number requirements will dictate the infectivity of virus populations and efficacy of neutralizing antibodies. Thereby our results render consideration of stoichiometric concepts relevant for developing antibody-based vaccines and therapeutics against HIV.

Our estimates of the HIV-1 entry stoichiometry, that is the number of envelope glycoprotein trimers needed to mediate fusion of viral and target cell membrane, close an important gap in our understanding of the HIV entry process. As we show, stoichiometric requirements for envelope trimers differ between HIV strains and steer virus entry efficacy and virus entry kinetics. Thus, the entry stoichiometry has important implications for HIV transmission, as demands on trimer numbers will dictate the infectivity of virus populations, target cell preferences and virus inactivation by trimer-targeting inhibitors and neutralizing antibodies. Beyond this, our data contribute to the general understanding of mechanisms and energetic requirements of protein-mediated membrane fusion, as HIV entry proved to follow similar stoichiometries as described for Influenza virus HA and SNARE protein mediated membrane fusion. In summary, our findings provide a relevant contribution towards a refined understanding of HIV-1 entry and pathogenesis with particular importance for ongoing efforts to generate neutralizing antibody based therapeutics and vaccines targeting the HIV-1 envelope trimer.

Molecular determinants of the ratio of inert to infectious virus particles

The ratio of virus particles to infectious units is a classic measurement in virology and ranges widely from several million to below 10 for different viruses. Much evidence suggests a distinction be made between infectious and infecting particles or virions: out of many potentially infectious virions, few infect under regular experimental conditions, largely because of diffusion barriers. Still, some virions are inert from the start; others become defective through decay. And with increasing cell- and molecular-biological knowledge of each step in the replicative cycle for different viruses, it emerges that many processes entail considerable losses of potential viral infectivity. Furthermore, all-or-nothing assumptions about virion infectivity are flawed and should be replaced by descriptions that allow for spectra of infectious propensities. A more realistic understanding of the infectivity of individual virions has both practical and theoretical implications for virus neutralization, vaccine research, antiviral therapy, and the use of viral vectors.

Neutralization of Virus Infectivity by Antibodies: Old Problems in New Perspectives

Neutralizing antibodies (NAbs) can be both sufficient and necessary for protection against viral infections, although they sometimes act in concert with cellular immunity. Successful vaccines against viruses induce NAbs but vaccine candidates against some major viral pathogens, including HIV-1, have failed to induce potent and effective such responses. Theories of how antibodies neutralize virus infectivity have been formulated and experimentally tested since the 1930s; and controversies about the mechanistic and quantitative bases for neutralization have continually arisen. Soluble versions of native oligomeric viral proteins that mimic the functional targets of neutralizing antibodies now allow the measurement of the relevant affinities of NAbs. Thereby the neutralizing occupancies on virions can be estimated and related to the potency of the NAbs. Furthermore, the kinetics and stoichiometry of NAb binding can be compared with neutralizing efficacy. Recently, the fundamental discovery that the intracellular factor TRIM21 determines the degree of neutralization of adenovirus has provided new mechanistic and quantitative insights. Since TRIM21 resides in the cytoplasm, it would not affect the neutralization of enveloped viruses, but its range of activity against naked viruses will be important to uncover. These developments bring together the old problems of virus neutralization-mechanism, stoichiometry, kinetics, and efficacy-from surprising new angles.

Mathematical model of multivalent virus-antibody complex formation in humans following acute and chronic HIV infections

Antibodies that bind viral surface proteins can limit the spread of the infection through neutralizing and non-neutralizing functions. During both acute and chronic Human Immunodeficiency Virus infection, antibody-virion immune complexes are formed, but fail to ensure protection. In this study, we develop a mathematical model of multivalent antibody binding and use it to determine the dynamical interactions that lead to immune complexes formation and the role of complexes with increased numbers of bound antibodies in the pathogenesis of the disease. We compare our predictions with published temporal virus and immune complex data from acute infected patients. Finally, we derive quantitative and qualitative conditions needed for antibody-induced protection.

Estimated secondary structure propensities within V1/V2 region of HIV gp120 are an important global antibody neutralization sensitivity determinant

Background

Neutralization sensitivity of HIV-1 virus to antibodies and anti-sera varies greatly between the isolates. Significant role of V1/V2 domain as a global neutralization sensitivity regulator has been suggested. Recent X-ray structures revealed presence of well-defined tertiary structure within this domain but also demonstrated partial disorder and conformational heterogeneity.

Methods

Correlations of neutralization sensitivity with the conformational propensities for beta-strand and alpha-helix formation over the entire folded V1/V2 domain as well as within sliding 5-residue window were investigated. Analysis was based on a set of neutralization data for 106 HIV isolates for which consistent neutralization sensitivity measurements against multiple pools of human immune sera have been previously reported.

Results

Significant correlation between beta-sheet formation propensity of the folded segments of V1/V2 domain and neutralization sensitivity was observed. Strongest correlation peaks localized to the beta-strands B and C. Correlation persisted when subsets of HIV isolates belonging to clades B, C and circulating recombinant form BC where analyzed individually or in combinations.

Conclusions

Observed correlations suggest that stability of the beta-sheet structure and/or degree of structural disorder in the V1/V2 domain is an important determinant of the global neutralization sensitivity of HIV-1 virus. While specific mechanism is to yet to be investigated, plausible hypothesis is that less ordered V1/V2s may have stronger masking effect on various neutralizing epitopes, perhaps effectively occupying larger volume and thereby occluding antibody access.