A spatial model of the efficiency of T cell search in the influenza-infected lung

Abstract

Emerging strains of influenza, such as avian H5N1 and 2009 pandemic H1N1, are more virulent than seasonal H1N1 influenza, yet the underlying mechanisms for these differences are not well understood. Subtle differences in how a given strain interacts with the immune system are likely a key factor in determining virulence. One aspect of the interaction is the ability of T cells to locate the foci of the infection in time to prevent uncontrolled expansion. Here, we develop an agent based spatial model to focus on T cell migration from lymph nodes through the vascular system to sites of infection. We use our model to investigate whether different strains of influenza modulate this process. We calibrate the model using viral and chemokine secretion rates we measure in vitro together with values taken from literature. The spatial nature of the model reveals unique challenges for T cell recruitment that are not apparent in standard differential equation models. In this model comparing three influenza viruses, plaque expansion is governed primarily by the replication rate of the virus strain, and the efficiency of the T cell search-and-kill is limited by the density of infected epithelial cells in each plaque. Thus for each virus there is a different threshold of T cell search time above which recruited T cells are unable to control further expansion. Future models could use this relationship to more accurately predict control of the infection.

Keywords: Agent-based model; Computational biology; Immunology; Systems biology; Virology.

Fig. 1

Model of T cell search. Activated T cells originate in the lymph node and enter the bloodstream after which they randomly navigate through 14 vascular bifurcations of the bronchial network. Upon reaching a capillary, T cells exit into tissue if cytokine signal is present. In the absence of signal, the T cell recirculates either through the lymph network or through the pulmonary vein back to the top of the network.

Fig. 2

Visual representation of the model. Healthy epithelial cells infected by virus begin secreting virus after the incubation delay. Activated T cells traverse the bronchial vascular network and may be recruited by inflammatory cytokine. Chemotaxing T cells climb the chemokine gradient and induce apoptosis in infected cells. Solid arrows represent a cell state transition from one behavior to another. Dashed arrows display the mechanism used to induce a transition. Dotted arrows indicate the production of new virus.

Fig. 3

Empirical viral and cytokine titers for three strains of influenza: Avian H5N1, Seasonal sH1N1, and Pandemic pH1N1. Viral titer (blue circles) is in PFU/mL, and IP-10 (red triangle) and RANTES (yellow square) are shown in pg/mL. sH1N1 IP-10 secretion exceeded measurement accuracy above 8500 pg/mL and these three values (empty red triangles) were not included in the model fitting. An extended differential equation model from Mitchell et al. (2011) was fit to IP-10 and RANTES data (Eq. (1)). These fits were used to obtain chemokine production values for use in the spatial CyCells model. Human bronchial epithelial cells were infected at an MOI of 0.01 (10,000 virions) with one of the three strains of influenza. Apical fluid for viral secretion and basal media for chemokine secretion were collected at the given time intervals post-infection. Viral culture was performed by a standard plaque assay and chemokine levels were measured using 30 μl aliots for a panel of 17 chemokines and cytokines (not shown). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

Fig. 4

Model results: Time series plots of 100 runs of aH5N1 (A), sH1N1 (B), and pH1N1 (C) infections (gray). Each run took the calculated viral production and chemokine production rates for the three different strains of influenza as input (Table 1) and reported the total number of infected cells, including incubating, virus secreting and apoptotic, but not including dead cells. Therefore the figures approximate the rate of plaque growth over time. IP-10 and RANTES were simulated in each run, except for aH5N1, which produced only RANTES. Each run was initialized identically for each strain save for the random seed. The middle line shows the mean while the red dashed lines show the 96% credible confidence interval. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

Fig. 5

Simulated sH1N1 infection. Screenshots from day 4, day 5.5, and day 7. The top row shows the spreading focus of infection through the color coding of individual cells: healthy cells in uninfected tissue (gray), virus-incubating cells (yellow), virus-secreting cells (orange), apoptotic cells (red), dead cells (brown), and T cells arriving at day 5 (green). Free virus and chemokine particles are represented by compartmentalized concentrations of mols/mL and ng/mL. Chemokine shown is an aggregate of total IP-10 and RANTES concentrations. See Videos S1–S3 for an animated visualization of each row. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

Fig. 6

Simulated infections of aH5N1, sH1N1, and pH1N1. Plotted values: total plaque size (blue), number of virus incubating cells (yellow), number of virus secreting cells (green), total number of T cells (black), and T cells at the focus of infection (FOI) (red). T cells clear secreting and incubating cells in aH5N1, fail to clear incubating cells in sH1N1, and fail to clear either type of infected cell in pH1N1. The number of incubating cells (yellow) after day 5 differs markedly among the three strains indicating that the T cells have differing success at controlling the infection. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

Fig. 7

Simulated infections of aH5N1, sH1N1, and pH1N1 with instant cell death. The model results show that the combined delay of the T cell kill time and apoptosis time form a barrier to infection clearance. Removing both delays results in infection clearance for all strains.