Mathematical model of influenza A virus production in large‐scale microcarrier culture

Abstract

A mathematical model that describes the replication of influenza A virus in animal cells in large-scale microcarrier culture is presented. The virus is produced in a two-step process, which begins with the growth of adherent Madin-Darby canine kidney (MDCK) cells. After several washing steps serum-free virus maintenance medium is added, and the cells are infected with equine influenza virus (A/Equi 2 (H3N8), Newmarket 1/93). A time-delayed model is considered that has three state variables: the number of uninfected cells, infected cells, and free virus particles. It is assumed that uninfected cells adsorb the virus added at the time of infection. The infection rate is proportional to the number of uninfected cells and free virions. Depending on multiplicity of infection (MOI), not necessarily all cells are infected by this first step leading to the production of free virions. Newly produced viruses can infect the remaining uninfected cells in a chain reaction. To follow the time course of virus replication, infected cells were stained with fluorescent antibodies. Quantitation of influenza viruses by a hemagglutination assay (HA) enabled the estimation of the total number of new virions produced, which is relevant for the production of inactivated influenza vaccines. It takes about 4-6 h before visibly infected cells can be identified on the microcarriers followed by a strong increase in HA titers after 15-16 h in the medium. Maximum virus yield Vmax was about 1x10(10) virions/mL (2.4 log HA units/100 microL), which corresponds to a burst size ratio of about 18,755 virus particles produced per cell. The model tracks the time course of uninfected and infected cells as well as virus production. It suggests that small variations (<10%) in initial values and specific rates do not have a significant influence on Vmax. The main parameters relevant for the optimization of virus antigen yields are specific virus replication rate and specific cell death rate due to infection. Simulation studies indicate that a mathematical model that neglects the delay between virus infection and the release of new virions gives similar results with respect to overall virus dynamics compared with a time delayed model.

Effects of Aging on Influenza Virus Infection Dynamics

“…Several studies (25,26,33,34,36), including ours, suggest that influenza virus grows rapidly in young hosts. However, we observed (Fig.…”

“…Thus, mathematical modeling has been used to capture the dynamics of influenza virus infection and to understand the interaction of the virus with the immune system (25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38). Much of the work has been focused on the basic relationship between the host and the virus (25,26,32,34,35), whereas other work has strived to quantify the interplay between viral replication and adaptive immunity (27)(28)(29)(30)36). These models have been important to estimate the kinetic parameters describing influenza virus infection (25, 26, 28-30, 35, 36).…”

Quantifying the Early Immune Response and Adaptive Immune Response Kinetics in Mice Infected with Influenza A Virus

“…Mathematical models have long been used to investigate viral dynamics and immune responses to viral infections, including influenza A virus (3,5,7,15,16,31,36,48). We recently described a complex differential equation model to simulate and predict the adaptive immune response to IAV infection (24).…”

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

“…Mathematical analysis of clinical data is an increasingly popular tool for the evaluation of drugs, the elaboration of diagnostic criteria, and the generation of recommendations for effective therapies [9][10][11][12][13][14][15][16][17]. Analyses of animal and cell culture studies have revealed fundamental aspects of viral infections including the specification of the half-life of infected cells and virus, the virus burst size, and the relative contribution of the immune response [18][19][20][21][22][23][24][25][26][27][28][29]. Important results have also been obtained in the analysis of purely in vitro experiments.…”

“…Despite these successes, the available virological data, even for in vitro experiments, have often been limited in that many modeling analyses have been based only on total viral load data (e.g., RNA or DNA copies, hemagglutination assay (HA)) [9][10][11][12][13][15][16][17]20,22,23,26,27] or infectious viral load data (e.g., 50% tissue culture infection dose (TCID 50 ) or plaque forming units (PFU)) [18,19,25]. Thus, while the applied mathematical models typically depend on the interaction of many components of the infection -including the populations of susceptible and infected cells -they are often only confronted by a single biological quantity: the time-course of the viral load.…”