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.

Impact of the H275Y and I223V Mutations in the Neuraminidase of the 2009 Pandemic Influenza Virus In Vitro and Evaluating Experimental Reproducibility.

The 2009 pandemic H1N1 (H1N1pdm09) influenza virus is naturally susceptible to neuraminidase (NA) inhibitors, but mutations in the NA protein can cause oseltamivir resistance. The H275Y and I223V amino acid substitutions in the NA of the H1N1pdm09 influenza strain have been separately observed in patients exhibiting oseltamivir-resistance. Here, we apply mathematical modelling techniques to compare the fitness of the wild-type H1N1pdm09 strain relative to each of these two mutants. We find that both the H275Y and I223V mutations in the H1N1pdm09 background significantly lengthen the duration of the eclipse phase (by 2.5 h and 3.6 h, respectively), consistent with these NA mutations delaying the release of viral progeny from newly infected cells. Cells infected by H1N1pdm09 virus carrying the I223V mutation display a disadvantageous, shorter infectious lifespan (17 h shorter) than those infected with the wild-type or MUT-H275Y strains. In terms of compensating traits, the H275Y mutation in the H1N1pdm09 background results in increased virus infectiousness, as we reported previously, whereas the I223V exhibits none, leaving it overall less fit than both its wild-type counterpart and the MUT-H275Y strain. Using computer simulated competition experiments, we determine that in the presence of oseltamivir at doses even below standard therapy, both the MUT-H275Y and MUT-I223V dominate their wild-type counterpart in all aspects, and the MUT-H275Y outcompetes the MUT-I223V. The H275Y mutation should therefore be more commonly observed than the I223V mutation in circulating H1N1pdm09 strains, assuming both mutations have a similar impact or no significant impact on between-host transmission. We also show that mathematical modelling offers a relatively inexpensive and reliable means to quantify inter-experimental variability and assess the reproducibility of results.

The H275Y neuraminidase mutation of the pandemic A/H1N1 influenza virus lengthens the eclipse phase and reduces viral output of infected cells, potentially compromising fitness in ferrets.

The H275Y amino acid substitution of the neuraminidase gene is the most common mutation conferring oseltamivir resistance in the N1 subtype of the influenza virus. Using a mathematical model to analyze a set of in vitro experiments that allow for the full characterization of the viral replication cycle, we show that the primary effects of the H275Y substitution on the pandemic H1N1 (H1N1pdm09) strain are to lengthen the mean eclipse phase of infected cells (from 6.6 to 9.1 h) and decrease (by 7-fold) the viral burst size, i.e., the total number of virions produced per cell. We also find, however, that the infectious-unit-to-particle ratio of the H275Y mutant strain is 12-fold higher than that of the oseltamivir-susceptible strain (0.19 versus 0.016 per RNA copy). A parallel analysis of the H275Y mutation in the prior seasonal A/Brisbane/59/2007 background shows similar changes in the infection kinetic parameters, but in this background, the H275Y mutation also allows the mutant to infect cells five times more rapidly. Competitive mixed-strain infections in vitro, where the susceptible and resistant H1N1pdm09 strains must compete for cells, are characterized by higher viral production by the susceptible strain but suggest equivalent fractions of infected cells in the culture. In ferrets, however, the mutant strain appears to suffer a delay in its infection of the respiratory tract that allows the susceptible strain to dominate mixed-strain infections.

Quantification system for the viral dynamics of a highly pathogenic simian/human immunodeficiency virus based on an in vitro experiment and a mathematical model.

BACKGROUND: Developing a quantitative understanding of viral kinetics is useful for determining the pathogenesis and transmissibility of the virus, predicting the course of disease, and evaluating the effects of antiviral therapy. The availability of data in clinical, animal, and cell culture studies, however, has been quite limited. Many studies of virus infection kinetics have been based solely on measures of total or infectious virus count. Here, we introduce a new mathematical model which tracks both infectious and total viral load, as well as the fraction of infected and uninfected cells within a cell culture, and apply it to analyze time-course data of an SHIV infection in vitro. RESULTS: We infected HSC-F cells with SHIV-KS661 and measured the concentration of Nef-negative (target) and Nef-positive (infected) HSC-F cells, the total viral load, and the infectious viral load daily for nine days. The experiments were repeated at four different MOIs, and the model was fitted to the full dataset simultaneously. Our analysis allowed us to extract an infected cell half-life of 14.1 h, a half-life of SHIV-KS661 infectiousness of 17.9 h, a virus burst size of 22.1 thousand RNA copies or 0.19 TCID50, and a basic reproductive number of 62.8. Furthermore, we calculated that SHIV-KS661 virus-infected cells produce at least 1 infectious virion for every 350 virions produced. CONCLUSIONS: Our method, combining in vitro experiments and a mathematical model, provides detailed quantitative insights into the kinetics of the SHIV infection which could be used to significantly improve the understanding of SHIV and HIV-1 pathogenesis. The method could also be applied to other viral infections and used to improve the in vitro determination of the effect and efficacy of antiviral compounds.

Assessing the in vitro fitness of an oseltamivir-resistant seasonal A/H1N1 influenza strain using a mathematical model.

In 2007, the A/Brisbane/59/2007 (H1N1) seasonal influenza virus strain acquired the oseltamivir-resistance mutation H275Y in its neuraminidase (NA) gene. Although previous studies had demonstrated that this mutation impaired the replication capacity of the influenza virus in vitro and in vivo, the A/Brisbane/59/2007 H275Y oseltamivir-resistant mutant completely out-competed the wild-type (WT) strain and was, in the 2008-2009 influenza season, the primary A/H1N1 circulating strain. Using a combination of plaque and viral yield assays, and a simple mathematical model, approximate values were extracted for two basic viral kinetics parameters of the in vitro infection. In the ST6GalI-MDCK cell line, the latent infection period (i.e., the time for a newly infected cell to start releasing virions) was found to be 1-3 h for the WT strain and more than 7 h for the H275Y mutant. The infecting time (i.e., the time for a single infectious cell to cause the infection of another one) was between 30 and 80 min for the WT, and less than 5 min for the H275Y mutant. Single-cycle viral yield experiments have provided qualitative confirmation of these findings. These results, though preliminary, suggest that the increased fitness success of the A/Brisbane/59/2007 H275Y mutant may be due to increased infectivity compensating for an impaired or delayed viral release, and are consistent with recent evidence for the mechanistic origins of fitness reduction and recovery in NA expression. The method applied here can reconcile seemingly contradictory results from the plaque and yield assays as two complementary views of replication kinetics, with both required to fully capture a strain's fitness.

Exploring the effect of biological delays in kinetic models of influenza within a host or cell culture.

BACKGROUND: For a typical influenza infection in vivo, viral titers over time are characterized by 1-2 days of exponential growth followed by an exponential decay. This simple dynamic can be reproduced by a broad range of mathematical models which makes model selection and the extraction of biologically-relevant infection parameters from experimental data difficult. RESULTS: We analyze in vitro experimental data from the literature, specifically that of single-cycle viral yield experiments, to narrow the range of realistic models of infection. In particular, we demonstrate the viability of using a normal or lognormal distribution for the time a cell spends in a given infection state (e.g., the time spent by a newly infected cell in the latent state before it begins to produce virus), while exposing the shortcomings of ordinary differential equation models which implicitly utilize exponential distributions and delay-differential equation models with fixed-length delays. CONCLUSIONS: By fitting published viral titer data from challenge experiments in human volunteers, we show that alternative models can lead to different estimates of the key infection parameters.

Design considerations in building in silico equivalents of common experimental influenza virus assays.

Experimentation in vitro is a vital part of the process by which the clinical and epidemiological characteristics of a particular influenza virus strain are determined. We detail the considerations which must be made in designing appropriate theoretical/mathematical models of these experiments and show how modeling can increase the information output of such experiments. Starting from a traditional system of ordinary differential equations, common to infectious disease modeling, we broaden the approach by using an agent-based model, applicable to more general experimental geometries and assumptions about the biological properties of viruses, cell and their interaction. Within this framework, we explore the limits of the assumptions made by more traditional models and the conditions under which these assumptions begin to break down, requiring the use of more sophisticated models. We apply the agent-based model to experimental plaque growth of two influenza strains, one resistant to the antiviral oseltamivir, and extract the values of key infection parameters specific to each strain.

The I222V neuraminidase mutation has a compensatory role in replication of an oseltamivir-resistant influenza virus A/H3N2 E119V mutant.

Oseltamivir-resistant A/H3N2 influenza isolates with or without the E119V and I222V neuraminidase (NA) mutations were recovered from an immunocompromised patient. Based on plaque size, yield assays, and NA activity, the impaired viral fitness of the E119V mutant was partially restored by the I222V NA mutation.