Increasingly biologically accurate models of influenza A virus infection spread in vivo & in vitro

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Christian Quirouette


Mathematical modelling is essential to investigate and elucidate the mechanisms behind the rich tapestry of virus infection behaviours observed experimentally and clinically. It also provides a frame- work to develop and optimize antiviral therapy. This mini-symposium brings together researchers from various groups with a range of expertise, all working to improve a slightly different aspect of influenza A virus infection modelling. All work is solidly anchored in experimental data, and tackles different clinically important questions.

Christian Quirouette

Ryerson University
"A mathematical model describing the localization and spread of influenza A virus infection within the human respiratory tract"
Within the human respiratory tract (HRT), virus diffuses through the periciliary fluid (PCF) bathing the epithelium. But it also undergoes advection: as the mucus layer sitting atop the PCF is pushed along by the ciliated cell’s beating cilia, the PCF and its virus contents are also pushed along, upwards towards the nose and mouth. Many mathematical models (MMs) describe the course of influenza virus infections in vivo, but none consider the impact of both diffusion and advection on the infection’s kinetics and localization. Our MM represents the HRT as a one-dimensional track extending from the nose down to the lower HRT, wherein stationary cells interact with virus which moves within (diffusion) and along with (advection) the PCF. Diffusion was found to be negligible in the presence of advection which effectively sweeps away virus, preventing infection from disseminating below the depth of deposition. Higher virus production rates (10-fold) are required at higher advection speeds (40 micron/s) to maintain equivalent infection severity and timing. Because virus is entrained upwards, upper parts of the HRT located downstream of the advection flow see more virus than lower parts, and so infection grows, peaks, and resolves later in the lower HRT. Clinically, the infection would appear to progress from the upper towards the lower HRT, as reported in mice, even when the lower HRT infection precedes, and indeed causes, that in the upper HRT. When the spatial MM is expanded to include cellular regeneration and an immune response, it reproduces tissue damage levels reported in patients. It can also captures the kinetics of both seasonal and avian strain infections via parameter changes consistent with reported differences between these strains. This new MM offers a convenient and unique platform from which to study the localization and spread of respiratory viruses (flu, RSV, COVID-19) within the HRT during an infection.

Amber Smith

University of Tennessee Health Science Center
"Modeling Influenza–Mediated Acute Lung Injury"
Influenza viruses infect millions of individuals each year and cause a significant amount of morbidity and mortality. Understanding how the virus spreads within the lung, how efficacious host immune control is, and how each influences acute lung injury and disease severity is critical to combat the infection. Thus, we used an integrative model-experiment exchange to establish the dynamical connections between infection, lung injury, and disease kinetics. Examining these connections during neuraminidase inhibitor (NAI) therapy further validated the model and analysis, and suggested that profound effects on lung injury are possible with minimal changes to host-pathogen kinetics. This work provides important biological and mathematical insight and enhances our ability to effectively forecast the disease and antiviral efficacy.

Daniel Rüdiger

Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
"Multiscale model of DIP replication and its effects on influenza A virus infection in animal cell culture"
Defective interfering particles (DIPs) that lack part of the viral genome are considered for use as antivirals against flu, because they can strongly impede wild type influenza A virus (IAV) replication. Multiple mathematical modeling approaches have been applied to examine the mechanisms of DIP inter- ference. However, these models focused on either the intra- or the extracellular level of virus replication. In this work, we extend a recently published multiscale model to describe DIP propagation in animal cell cultures infected by IAV. This new model covers fundamental steps during the intracellular replica- tion and the spread of DIPs on the population level. Particularly, the model incorporates the infection conditions, i.e. the multiplicity of infection (MOI), which may change drastically during an infection and represent a crucial factor for IAV replication and DIP interference. To elucidate DIP infection dynamics we conducted a set of cultivations observing the effects of DIPs on wild type virus replication using various IAV and DIP seed virus concentrations. Based on these experimental data, we calibrated our multiscale model to enable the prediction of DIP-induced infection dynamics for a wide range of MOI conditions. Furthermore, we used the model to elucidate options for antiviral therapy, i.e. the DIP to IAV ratio required to inhibit the progression of an influenza infection in animals or humans. In summary, we established a mathematical model that provides a comprehensive description of DIP replication on the intra- and extracellular level to facilitate the development of antiviral therapies, and to describe DIP production in animal cell culture for therapeutic use.

João Rodrigues Correia Ramos

Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
"A dynamic model for cell growth, metabolism and virus production of MDCK suspension cells"
Cell culture-based influenza virus production is well established and different virus replication stages have been studied experimentally in detail. In addition, quantitative mathematical models have been derived that describe dynamics of viral replication at the intracellular and the cell population level. However, to better understand the complex interplay between the virus and its host cell, metabolism during virus replication should be considered in more detail. In this context, MDCK suspension cells were cultivated in shaker flasks and concentrations of external and internal metabolites monitored during cell growth and influenza A virus infection. To characterize the impact of virus infection on host cell metabolism, we have formulated a dynamic mathematical model combining a segregated cell growth model with a structured model of intracellular metabolism in a similar manner as models established for other cell lines. Overall, it considers the dynamics of cell growth, virus production, substrates, metabolic by-products and concentration of key intracellular metabolites from glycolysis, citric acid cycle (TCA), glutaminolysis and pentose phosphate pathway. Model parameters were fitted using mock-infections, and simulations describe well the time courses of the viable cell concentration, mean cell diameter, external substrates, metabolic by-products, and key intracellular metabolites. After virus infection, using the same set of parameters, the model also describes well the dynamics of the viable cell concentration, mean cell diameter changes, substrates, and the virus titer. Only minor differences were found for infected versus mock cultures in the glycolytic pathway. Nev- ertheless, differences between experimental data and model simulations regarding metabolites of TCA and metabolic by-products suggest changes in metabolism, which might be virus-induced. As virus in- fection also affects apoptosis and cell lysis, the interpretation of such differences is not straightforward and experimental findings as well as parameters fitted need to be evaluated in more detail to confirm a virus-related impact on the TCA. Overall, this work will contribute to a better understanding of the complex interplay between cell growth, changes in cell size, virus production and metabolism and support the identification of parameters rele- vant for increasing specific viral productivity of MDCK suspension cells.

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