Sequential infection experiments for quantifying innate and adaptive immunity during influenza infection

Abstract

Laboratory models are often used to understand the interaction of related pathogens via host immunity. For example, recent experiments where ferrets were exposed to two influenza strains within a short period of time have shown how the effects of cross-immunity vary with the time between exposures and the specific strains used. On the other hand, studies of the workings of different arms of the immune response, and their relative importance, typically use experiments involving a single infection. However, inferring the relative importance of different immune components from this type of data is challenging. Using simulations and mathematical modelling, here we investigate whether the sequential infection experiment design can be used not only to determine immune components contributing to cross-protection, but also to gain insight into the immune response during a single infection. We show that virological data from sequential infection experiments can be used to accurately extract the timing and extent of cross-protection. Moreover, the broad immune components responsible for such cross-protection can be determined. Such data can also be used to infer the timing and strength of some immune components in controlling a primary infection, even in the absence of serological data. By contrast, single infection data cannot be used to reliably recover this information. Hence, sequential infection data enhances our understanding of the mechanisms underlying the control and resolution of infection, and generates new insight into how previous exposure influences the time course of a subsequent infection.

Fig 1. A subset of the synthetic data.

(a) The line shows the simulated ‘true’ viral load for a single infection, with the arrow showing the time of exposure. The simulated viral load with noise is shown as crosses. The horizontal line indicates the observation threshold (10 RNA copy no./100μL); observations below this threshold are plotted below this line. Values below the observation threshold were treated as censored. (b—c) For sequential infections with the labelled inter-exposure interval, the dashed and dotted lines show the simulated ‘true’ viral load for a primary and challenge infection respectively; the arrows show the times of the primary and challenge exposures. The simulated viral load with noise is shown as crosses.

Fig 2. Verification that the fitting procedure recovered the viral load.

(a) For a single infection, the blue and green areas are the 95% credible intervals for the viral load (in the absence of noise), as predicted by the models fitted to the sequential infection and single infection data respectively. (b—c) For sequential infections with the labelled inter-exposure interval, the grey and blue areas show the 95% credible intervals for the primary and challenge viral load respectively, predicted by the model fitted to sequential infection data. The other elements of the figure are identical to Fig 1: the dashed and dotted lines show the simulated ‘true’ viral load for a primary and challenge infection respectively; the arrows show the times of the primary and challenge exposures; and the horizontal line indicates the observation threshold.

Fig 3. Predicting the viral load for a single infection when various immune components were absent.

The vertical lines indicate, for the ‘true’ parameter values, the times at which the immune components labelled under each panel took effect. These times were determined by when the viral load for the baseline model (red dotted line) deviated from the viral load when the immune components were absent (black dashed line). These times were recovered using sequential infection data in all of the panels (95% prediction intervals for the viral load in blue), while the timing of adaptive immunity in (a) was recovered using single infection data (intervals in green). In addition, the viral load when adaptive immunity was suppressed was accurately predicted using sequential infection data (a). However, the viral load was not accurately predicted using either dataset in the remaining scenarios (b—e). Prediction intervals were constructed without measurement noise.

Fig 4. Predicting the outcomes of further sequential infection experiments.

Sequential infection data, but not single infection data, enabled prediction of further sequential infection experiment outcomes. The lines show the simulated ‘true’ viral loads for inter-exposure intervals of (a) 2 and (b) 20 days. The shaded areas show the 95% prediction intervals for the challenge viral load.

Fig 5. Predictions of the challenge viral load for a one-day inter-exposure interval when the mechanisms mediating cross-protection were restricted.

The black solid lines show the challenge viral load for the ‘true’ parameter values when the mechanisms mediating cross-protection were restricted using (a) model XC, (b) model XIT, (c) model XI, or (d) model XT. The red dotted lines show the viral load for the baseline model. Comparing the two sets of lines revealed that innate immunity mediated cross-protection, whereas cellular adaptive immunity and target cell depletion did little to mediate cross-protection. The model fitted to sequential infection data accurately predicted the challenge outcomes for models XC and XIT, but not model XI or model XT (95% prediction intervals shown). It thus correctly attributed cross-protection to target cell depletion and/or innate immunity, but could not definitively distinguish between the two. For clarity, the viral load for the primary infection is not presented in this figure.

Fig 6. The within-host influenza model for a single strain.

(Top) Viral dynamics and innate immune response; (middle) humoral adaptive immune response; (bottom) cellular adaptive immune response. Solid arrows indicate transitions between compartments or death (shown only for immune-enhanced death processes); dashed arrows indicate production; plus signs indicate an increased transition rate due to the indicated compartment.