Quantification of Ebola virus replication kinetics in vitro.

Mathematical modelling has successfully been used to provide quantitative descriptions of many viral infections, but for the Ebola virus, which requires biosafety level 4 facilities for experimentation, modelling can play a crucial role. Ebola virus modelling efforts have primarily focused on in vivo virus kinetics, e.g., in animal models, to aid the development of antivirals and vaccines. But, thus far, these studies have not yielded a detailed specification of the infection cycle, which could provide a foundational description of the virus kinetics and thus a deeper understanding of their clinical manifestation. Here, we obtain a diverse experimental data set of the Ebola virus infection in vitro, and then make use of Bayesian inference methods to fully identify parameters in a mathematical model of the infection. Our results provide insights into the distribution of time an infected cell spends in the eclipse phase (the period between infection and the start of virus production), as well as the rate at which infectious virions lose infectivity. We suggest how these results can be used in future models to describe co-infection with defective interfering particles, which are an emerging alternative therapeutic.

Preexisting compensatory amino acids compromise fitness costs of a HIV-1 T cell escape mutation.

BACKGROUND: Fitness costs and slower disease progression are associated with a cytolytic T lymphocyte (CTL) escape mutation T242N in Gag in HIV-1-infected individuals carrying HLA-B*57/5801 alleles. However, the impact of different context in diverse HIV-1 strains on the fitness costs due to the T242N mutation has not been well characterized. To better understand the extent of fitness costs of the T242N mutation and the repair of fitness loss through compensatory amino acids, we investigated its fitness impact in different transmitted/founder (T/F) viruses. RESULTS: The T242N mutation resulted in various levels of fitness loss in four different T/F viruses. However, the fitness costs were significantly compromised by preexisting compensatory amino acids in (Isoleucine at position 247) or outside (glutamine at position 219) the CTL epitope. Moreover, the transmitted T242N escape mutant in subject CH131 was as fit as the revertant N242T mutant and the elimination of the compensatory amino acid I247 in the T/F viral genome resulted in significant fitness cost, suggesting the fitness loss caused by the T242N mutation had been fully repaired in the donor at transmission. Analysis of the global circulating HIV-1 sequences in the Los Alamos HIV Sequence Database showed a high prevalence of compensatory amino acids for the T242N mutation and other T cell escape mutations. CONCLUSIONS: Our results show that the preexisting compensatory amino acids in the majority of circulating HIV-1 strains could significantly compromise the fitness loss due to CTL escape mutations and thus increase challenges for T cell based vaccines.

Fitness costs and diversity of the cytotoxic T lymphocyte (CTL) response determine the rate of CTL escape during acute and chronic phases of HIV infection.

HIV-1 often evades cytotoxic T cell (CTL) responses by generating variants that are not recognized by CTLs. We used single-genome amplification and sequencing of complete HIV genomes to identify longitudinal changes in the transmitted/founder virus from the establishment of infection to the viral set point at 1 year after the infection. We found that the rate of viral escape from CTL responses in a given patient decreases dramatically from acute infection to the viral set point. Using a novel mathematical model that tracks the dynamics of viral escape at multiple epitopes, we show that a number of factors could potentially contribute to a slower escape in the chronic phase of infection, such as a decreased magnitude of epitope-specific CTL responses, an increased fitness cost of escape mutations, or an increased diversity of the CTL response. In the model, an increase in the number of epitope-specific CTL responses can reduce the rate of viral escape from a given epitope-specific CTL response, particularly if CD8+ T cells compete for killing of infected cells or control virus replication nonlytically. Our mathematical framework of viral escape from multiple CTL responses can be used to predict the breadth and magnitude of HIV-specific CTL responses that need to be induced by vaccination to reduce (or even prevent) viral escape following HIV infection.

Modeling sequence evolution in acute HIV-1 infection.

We describe a mathematical model and Monte Carlo (MC) simulation of viral evolution during acute infection. We consider both synchronous and asynchronous processes of viral infection of new target cells. The model enables an assessment of the expected sequence diversity in new HIV-1 infections originating from a single transmitted viral strain, estimation of the most recent common ancestor (MRCA) of the transmitted viral lineage, and estimation of the time to coalesce back to the MRCA. We also calculate the probability of the MRCA being the transmitted virus or an evolved variant. Excluding insertions and deletions, we assume HIV-1 evolves by base substitution without selection pressure during the earliest phase of HIV-1 infection prior to the immune response. Unlike phylogenetic methods that follow a lineage backwards to coalescence, we compare the observed data to a model of the diversification of a viral population forward in time. To illustrate the application of these methods, we provide detailed comparisons of the model and simulations results to 306 envelope sequences obtained from eight newly infected subjects at a single time point. The data from 68 patients were in good agreement with model predictions, and hence compatible with a single-strain infection evolving under no selection pressure. The diversity of the samples from the other two patients was too great to be explained by the model, suggesting multiple HIV-1-strains were transmitted. The model can also be applied to longitudinal patient data to estimate within-host viral evolutionary parameters.

Modeling and estimation of kinetic parameters and replicative fitness of HIV-1 from flow-cytometry-based growth competition experiments.

Growth competition assays have been developed to quantify the relative fitness of HIV-1 mutants. In this article, we develop mathematical models to describe viral/cellular dynamic interactions in the assay system from which the competitive fitness indices or parameters are defined. In our previous HIV-viral fitness experiments, the concentration of uninfected target cells was assumed to be constant (Wu et al. 2006). But this may not be true in some experiments. In addition, dual infection may frequently occur in viral fitness experiments and may not be ignorable. Here, we relax these two assumptions and extend our earlier viral fitness model (Wu et al. 2006). The resulting models then become nonlinear ODE systems for which closed-form solutions are not achievable. In the new model, the viral relative fitness is a function of time since it depends on the target cell concentration. First, we studied the structure identifiability of the nonlinear ODE models. The identifiability analysis showed that all parameters in the proposed models are identifiable from the flow-cytometry-based experimental data that we collected. We then employed a global optimization approach (the differential evolution algorithm) to directly estimate the kinetic parameters as well as the relative fitness index in the nonlinear ODE models using nonlinear least square regression based on the experimental data. Practical identifiability was investigated via Monte Carlo simulations.

How antigen quantity and quality determine T-cell decisions in lymphoid tissue.

T lymphocytes (T cells) express T-cell receptor (TCR) molecules on their surface that can recognize peptides (p) derived from antigenic proteins bound to products of the major histocompatibility complex (MHC) genes. The pMHC molecules are expressed on the surface of antigen-presenting cells, such as dendritic cells (DCs). T cells first encounter antigen on DCs in lymph nodes (LN). Intravital microscopy experiments show that upon entering the LN containing antigen, CD8+ T cells first move rapidly. After a few hours, they stop and make extended contacts with DCs. The factors that determine when and how this transition occurs are not well understood. We report results from computer simulations that suggest that the duration of phase one is related to the low probability of productive interactions between T cells and DCs. This is demonstrated by our finding that the antigen dose and type determine when such a transition occurs. These results are in agreement with experimental observations. TCR-pMHC binding characteristics and the antigen dose determine the time required for a productive T-cell-DC encounter (resulting in sustained contact). We find that the ratio of this time scale and the half-life of the pMHC complex itself provide a consolidated measure of antigen quantity and type. Results obtained upon varying different measures of antigen quantity and type fall on one curve when graphed against this ratio of time scales. Thus, we provide a mechanism for how the effects of varying one set of parameters are influenced by other prevailing conditions. This understanding should help guide future experimentation.

Stochastic model of an influenza epidemic with drug resistance.

A continuous-time Markov chain (CTMC) model is formulated for an influenza epidemic with drug resistance. This stochastic model is based on an influenza epidemic model, expressed in terms of a system of ordinary differential equations (ODE), developed by Stilianakis, N.I., Perelson, A.S., Hayden, F.G., [1998. Emergence of drug resistance during an influenza epidemic: insights from a mathematical model. J. Inf. Dis. 177, 863-873]. Three different treatments-chemoprophylaxis, treatment after exposure but before symptoms, and treatment after symptoms appear, are considered. The basic reproduction number, R(0), is calculated for the deterministic-model under different treatment strategies. It is shown that chemoprophylaxis always reduces the basic reproduction number. In addition, numerical simulations illustrate that the basic reproduction number is generally reduced with realistic treatment rates. Comparisons are made among the different models and the different treatment strategies with respect to the number of infected individuals during an outbreak. The final size distribution is computed for the CTMC model and, in some cases, it is shown to have a bimodal distribution corresponding to two situations: when there is no outbreak and when an outbreak occurs. Given an outbreak occurs, the total number of cases for the CTMC model is in good agreement with the ODE model. The greatest number of drug resistant cases occurs if treatment is delayed or if only symptomatic individuals are treated.

A novel antiviral intervention results in more accurate assessment of human immunodeficiency virus type 1 replication dynamics and T-cell decay in vivo.

Mathematical models provide an understanding of in vivo replication kinetics of human immunodeficiency virus type 1 (HIV-1). With a novel intervention designed for increased potency, we have more accurately deduced the half-lives of virus-producing CD4(+) T cells, 0.7 day, and the generation time of HIV-1 in vivo, approximately 2 days, confirming the dynamic nature of HIV-1 replication.