Population dynamics of rapid fixation in cytotoxic T lymphocyte escape mutants of influenza A

Abstract

The dynamics of cellular immunity against pathogens, and its interaction with the human MHC system, is a key area for empirical research, both within individual hosts and in population genetic surveys. However, in contrast with humoral immunity, the dynamics of cellular immunity have not been modeled at the population level. Here, we address this lacuna with a model of recently observed dramatic invasions of cytotoxic T lymphocyte escape mutants in human influenza A. In particular, we offer an explanation for the rapid fixation of a HLA-B27 restricted cytotoxic T lymphocyte escape mutant on the nucleoprotein that emerged in the 1993-1994 season. We find that the dynamics within a single season of influenza do not provide a realistic description, but a model of the full annual dynamics can offer a possible explanation. Our model is deterministic for the winter epidemic, and stochastic for the summer period. An escape mutant that leads to a slightly longer infection in a small proportion of hosts has a substantial advantage through summer persistence. Furthermore, if a small number of founding cases are responsible for initiating each epidemic, then this effect of rapid mutant fixation is amplified.

Fig. 2.

Multiseason dynamics. These are some realizations of the stochastic system. The solid curves are the number of infected expressed as a fraction of 1%. The mixed dashed and solid line is the proportion of infections that are caused by the mutant, with the dashed segment representing the change over the summer, including random founder choice with five founders. The mutant is introduced at autumn of year 1 at 1% relative prevalence. About 44% of runs are like the top example: the mutant does not survive until the second year. If the mutant does survive the first summer, then it tends to go to fixation rapidly.

Fig. 1.

Epidemic dynamics. (a and b) HLA-B27-positive hosts are twice as infectious when infected with the mutant. (c and d) HLA-B27-positive hosts have an infection of twice the normal duration when infected by the mutant (Table 2 with k = 2). The solid curves of a and c give the fraction of 1% of hosts infected (starting from 0.01%). The dashed curves give the proportion of these that are infected by the mutant. Initially, the mutant accounted for 10% of all infections. The solid curves of b and d represent the overall effect on the proportion of infected that are CTL escape mutants of the epidemic season. The dotted line is the identity (diagonal), for comparison.

Fig. 3.

Effect of different numbers of founders. A comparison of the probability distribution of the number of mutants at the end of each year for a small and large number of founders. The left column of graphs is for five founders, and the right column is for 50 founders. The mutant is introduced at the start of the first year, accounting for 1% of all infection. The rows correspond to the end of successive years. The x axis gives the number of the founders cases that are caused by the mutant, and the y axis gives the probability of this number. For five founders, the mutant reaches fixation with probability ≈56%. Typically, it has reached either near fixation or extinction after 2 years. For 50 founders, the mutant nearly always will eventually reach fixation, though may take longer than for five founders. In the extreme of a single founder, any mutant is always forced to fixation or goes extinct after the first summer.