Mathematical Model Reveals the Role of Memory CD8 T Cell Populations in Recall Responses to Influenza

Abstract

The current influenza vaccine provides narrow protection against the strains included in the vaccine, and needs to be reformulated every few years in response to the constantly evolving new strains. Novel approaches are directed toward developing vaccines that provide broader protection by targeting B and T cell epitopes that are conserved between different strains of the virus. In this paper, we focus on developing mathematical models to explore the CD8 T cell responses to influenza, how they can be boosted, and the conditions under which they contribute to protection. Our models suggest that the interplay between spatial heterogeneity (with the virus infecting the respiratory tract and the immune response being generated in the secondary lymphoid organs) and T cell differentiation (with proliferation occurring in the lymphoid organs giving rise to a subpopulation of resident T cells in the respiratory tract) is the key to understand the dynamics of protection afforded by the CD8 T cell response to influenza. Our results suggest that the time lag for the generation of resident T cells in the respiratory tract and their rate of decay following infection are the key factors that limit the efficacy of CD8 T cell responses. The models predict that an increase in the level of central memory T cells leads to a gradual decrease in the viral load, and, in contrast, there is a sharper protection threshold for the relationship between the size of the population of resident T cells and protection. The models also suggest that repeated natural influenza infections cause the number of central memory CD8 T cells and the peak number of resident memory CD8 T cells to reach their plateaus, and while the former is maintained, the latter decays with time since the most recent infection.

Keywords: T cell; central memory; influenza; recall response; resident memory.

Figure 1

Schematic of a within-host model of influenza infection. The model variables are target (uninfected) epithelial cells (T), infected epithelial cells (I), virus titer (V), innate immunity (cytokines) (M), antigen presented by dendritic cells (A), and four populations of CD8 T cells such as virus-specific precursor cells (T_P), proliferating cells (T_E), central memory cells (T_M), and cells which are resident at the respiratory tract (T_R). We do not separately model dendritic cells, instead we consider them together with antigen as one variable. An immune response to the influenza virus mainly occurs in the two compartments – lining of the respiratory tract, which is the actual site of infection and secondary lymphoid tissue (lymph nodes) where expansion of virus-specific T cells occurs.

Figure 2

Dynamics of primary immune response to influenza infection. Model parameters and initial values for model variables are shown in Tables 1 and 2.

Figure 3

(A) shows the dynamics of loss of resident CD8 T cells after primary infection and estimation of the value of parameter d_R (the rate of decay of resident T cells) from the data on mice intranasally infected with primary influenza A virus strain A/HKx31 (H3N2) at 30,000 50% egg infectious dose (EID₅₀). Numbers of lung resident CD8 T cells specific for influenza epitopes FluNP and FluPA were measured at indicated time points. Each data point is the average from 5 to 20 mice. All experiments were completed in accordance with the Institutional Animal Care and Use Committee guidelines of Emory University. (B) shows the dynamics of virus during primary versus recall infections when recall infection happens 30 days or 1 year after the first infection. For secondary infections the initial values for T_P and T_R were taken from the corresponding values of variables T_P + T_M and T_R, respectively, in simulation of primary infection with other parameters and initial values as in Tables 1 and 2.

Figure 4

Dependance of integral viral load achieved during secondary influenza infection on the time between primary and recall infections. Different symbols show three different indicated values for the model parameter d_R describing the decay of resident T cells at the site of infection. (A) shows the case when resident memory T cells are able to kill the virus infected cells immediately after the onset of secondary infection. (B) considers the case when resident T cells require activation to be able to kill virus-infected cells. Corresponding parameters are k_act = 0.2 TCID₅₀⁻¹ ml day⁻¹, k_RM = 0.2, ϕ_R = 1.

Figure 5

Integral viral load dependence on the number of central memory and resident memory T cells at the onset of recall infection. All parameters are as in Figure 2 and Table 1.

Figure 6

Recall responses to sequential influenza infections. (A) shows how integral viral load and number of central memory T cells (T_M) depends on the number of influenza infections. The initial amount of T_M for each infection is taken from the established equilibrium level values after preceding infection. (B) shows the dependance of integral viral load in tertiary (3°) influenza infection on the time between 2° and 3° infections. The model prediction is shown for three indicated values of the rate of loss of resident memory T cells (d_R).