Kinetics of Coinfection with Influenza A Virus and <em>Streptococcus pneumoniae</em>

<div><p>Secondary bacterial infections are a leading cause of illness and death during epidemic and pandemic influenza. Experimental studies suggest a lethal synergism between influenza and certain bacteria, particularly <i>Streptococcus pneumoniae</i>, but the precise processes involved are unclear. To address the mechanisms and determine the influences of pathogen dose and strain on disease, we infected groups of mice with either the H1N1 subtype influenza A virus A/Puerto Rico/8/34 (PR8) or a version expressing the 1918 PB1-F2 protein (PR8-PB1-F2(1918)), followed seven days later with one of two <i>S. pneumoniae</i> strains, type 2 D39 or type 3 A66.1. We determined that, following bacterial infection, viral titers initially rebound and then decline slowly. Bacterial titers rapidly rise to high levels and remain elevated. We used a kinetic model to explore the coupled interactions and study the dominant controlling mechanisms. We hypothesize that viral titers rebound in the presence of bacteria due to enhanced viral release from infected cells, and that bacterial titers increase due to alveolar macrophage impairment. Dynamics are affected by initial bacterial dose but not by the expression of the influenza 1918 PB1-F2 protein. Our model provides a framework to investigate pathogen interaction during coinfections and to uncover dynamical differences based on inoculum size and strain.</p> </div

Maximum likelihood estimates of parameter values for influenza infection with PR8 and PR8-PB1-F2(1918).

<p>For each virus strain, PR8 and PR8-PB1-F2(1918), the MLE initial viral titer (), infection rate constant (), death rate of productively infected cells (), viral release rate per infected cell (), and viral clearance rate (). Initial number of target cells () is fixed at , and the transition rate for infected cells to produce virus () is fixed at .</p

Parameter ensembles from bootstrap fits of the viral kinetic model.

<p>Plots of the parameters, in the form of two parameter projections of each fit, and the constraints (bottom left) from bootstrap fits of the viral kinetic model (Equations (4)–(7)) to lung titers from mice infected with PR8 (red) or PR8-PB1-F2(1918) (blue).</p

Coinfection model fit to lung titers of mice coinfected with PR8-PB1-F2(1918) and 1000 CFU D39.

<p>Fit of the coinfection model (<a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003238#ppat.1003238.e183" target="_blank">Equations (6)</a>–<a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003238#ppat.1003238.e187" target="_blank">(10)</a>) to viral (panel A) and bacterial (panel B) lung titers from individual mice infected with PR8-PB1-F2(1918) virus followed 7 days later by 1000 CFU <i>S. pneumoniae</i> strain D39. Parameters for the model curves are in <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003238#ppat-1003238-t001" target="_blank">Tables 1</a>–<a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003238#ppat-1003238-t002" target="_blank">2</a>.</p

Summary of the coinfection model hypotheses, results and possible experiments to confirm each hypothesis.

<p>Summary of the coinfection model hypotheses, results and possible experiments to confirm each hypothesis.</p

Log-linear fits to lung viral titers in Phases I and II of an influenza infection with PR8 (solid line, squares) or PR8-PB1-F2(1918) (dashed line, triangles).

<p>The number of data points included in each phase was determined by finding the two lines that produced the maximum likelihood fit. No data point was allowed to be included in both phases. Distributions of peak times (days) and titers (), PR8 - black and PR8-PB1-F2(1918) - gray, from bootstrap replicates of the log-linear fits.</p

Coinfection model fit to lung titers of mice coinfected with PR8 and 1000 CFU D39.

<p>Fit of the coinfection model (<a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003238#ppat.1003238.e183" target="_blank">Equations (6)</a>–<a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003238#ppat.1003238.e187" target="_blank">(10)</a>) to viral (panel A) and bacterial (panel B) lung titers from individual mice infected with PR8 virus followed 7 days later by 1000 CFU <i>S. pneumoniae</i> strain D39. Parameters for the model curves are in <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003238#ppat-1003238-t001" target="_blank">Tables 1</a>–<a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003238#ppat-1003238-t002" target="_blank">2</a>.</p

Link between linear regression analysis and viral kinetic model estimates of the slope and length of viral growth (Phase I) and the slope of virus decay (Phase II).

<p>The MLE parameters in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1001081#pcbi-1001081-t002" target="_blank">Table 2</a> were used in the approximate solution <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1001081#pcbi.1001081-Smith3" target="_blank">[39]</a> of Equations (4)–(7) to find estimates of , , and . The infected cell death rate () was found to be the slope of exponential virus decay. The intercept value (0 days p.i.) (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1001081#pcbi-1001081-t001" target="_blank">Table 1</a>) is the effective initial titer and is an estimate of the constant in Equation (2). Values of the slopes found via linear regression (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1001081#pcbi-1001081-t001" target="_blank">Table 1</a>) were converted from to for an accurate comparison.</p

Distributions of the parameter values from bootstrap fits of the viral kinetic model (<b>Equations (4)</b>–<b>(7)</b>) to lung titers from mice infected with PR8 (black) or PR8-PB1-F2(1918) (gray).

<p>Significant differences were detected in the viral production rate (, ), the infected cell death rate (, ) and the initial viral titer (, ).</p

Infection characteristics for influenza infection with PR8 and PR8-PB1-F2(1918).

<p>For each virus strain, PR8 and PR8-PB1-F2(1918), the virus half-life (), infected cell lifetime (), basic reproductive number (), average number of virions produced per infected cell (), and the average number of cells infected per infectious virion () are given (parameter values used are in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1001081#pcbi-1001081-t002" target="_blank">Table 2</a>). The 95% confidence interval (CI) is given below parameter estimates.</p