Modelling activated T cell homing and recirculation

The adaptive immune response must conduct two “searches” to neutralize pathogens. First, recirculating antigen-specific T and B cell precursors must interact with antigen-loaded dendritic cells, and the architecture of the lymph node facilitates this interaction as shown in the previous section (Modular RADAR and Scale Invariance of Immune Response Rates and Times). The second search is T cells activated in the lymph node efficiently finding and neutralizing infected cells in tissue with the help of inflammatory signals. We analyzed these two searches in response to influenza infection in the lung (paper).

T cells are activated within the infected site LN and are released into the bloodstream where they travel through a branching network of arteries until they reach a capillary in the lung. Capillaries in infected regions of the lung are permeated by an inflammatory signal that causes T cells to exit the capillary and enter the lung tissue, where a chemokine gradient guides the T cell to infected cells. When T cells recognize the antigen displayed on the surface of infected cells, they neutralize those cells. The information represented by the inflammatory signals is local, and occurs in an initially small region of the lung surface, possibly as small as a few mm² in a 100 m² surface area in a human lung.

Without an inflammation signal indicating which capillaries are near infected tissue, T cells would have to exit capillaries in random locations and begin a slow random walk (at speeds measured in microns per minute) through the large area of lung tissue to search for the site of infection. With the inflammatory signal, T cells can exit the relatively fast flow of the circulatory network only when they are in close proximity to infected cells (described in figure below).

Figure. A region (A of radius r) of infected tissue, chemokines and inflammatory signals, surrounded by region B which does not have any infected cells, inflammation or chemokines. T cells (green hexagons) leave the LN at rate s and travel through the branching arteries to capillaries. If capillaries are inflamed (in region A) T cells exit capillaries and search for infected cells (small red circles) in lung tissue. If the capillaries are not inflamed (in region B) the T cells recirculate.

In this work we described two sets of models (paper). The first (null) model predicts how long it would take for T cells to find infected cells by searching via a random walk through the entire lung tissue. The second set of models are simplified representations of how inflammatory signals guide CTL search in real immune systems. This second set of models is parameterized from experimental data. By comparing predictions of the null model to the more realistic model with inflammation, we estimated how much the inflammatory signal reduces the time for T cells to find and eradicate influenza.

We use ordinary differential equation (ODE) and agent-based models (ABM) to quantify the value of the inflammatory signal, measured as the decrease in the time it takes for T cells to both find and eradicate virus from the lung. The ABM incorporates the spatial aspect of virus spread and T cell mediated killing of infected cells, and the ODE model can scale up to realistic cell population sizes.

We quantified how much inflammation of infected tissue improves the adaptive immune response. The speed up for the first T cell to arrive in the infected region in a mouse is tens of times faster in both the ODE and ABM models. The number of T cells that reach the infected region by day five post activation in the LN is thousands of times faster in both models. The ABM which also includes T cell mediated killing of infected cells predicts that with an inflammatory signal, the number of infected cells at day five is 87 times lower.

We scaled up the ODE model to make the same predictions for the human lung which is 10,000 times larger than the mouse lung. The ODE models predict that with an inflammatory signal the speed up in arrival of the first T cell humans is 270 times faster and 3800 times more T cell arrive at the site of infection at day five. Thus, the inflammatory signal improves the T cell search much more in the human than in the mouse.

The ABM used in the model (CyCells) is shown below

Figure. A snapshot of the CyCells ABM in action. The epithelial cell layer is made up of healthy cells (dark red), infected incubating cells (green), virus expressing cells (blue), and dead cells (yellow). The area of lighter red surrounding the infection shows that free virus particles (semi-transparent white) are present. T cells (pink) are seen swarming over locations with high virus concentration.