Figure 1.
Diagrammatic Representation of the Simulation and the Biological Model on which It Is Based
For a detailed description of the biological model, see Introduction and [9–11]. The simulation reflects the biological model with some simplifications (for details see Methods). * denotes that amplification in the simulation is achieved by arbitrarily adding more Vir to the epithelial cell layer at each time step.
Figure 2.
Representative Fields from the Simulation's Virtual Environment (IRVE)
For more details on (A–C), see Video S1, and for more on (D and E) see Video S2.
(A) The basic unit, used to construct the tonsil grid, consists of a solid hexagonal structure representing surface epithelium, lymphoid tissue, and a single germinal center/follicle. The virtual grid along which the agents move is shown as white lines, and the nodes where agents reside and interact are depicted as red boxes. Each hexagonal unit has one HEV entry point from the peripheral blood and one exit point into the lymphatic system.
(B) A view from the side of a single tonsil showing how the hexagonal base units are packed to create the entire grid of the tonsil lymphoepithelium.
(C) An overview of a single complete tubal tonsil showing part of its surface and part of its internal structure.
(D) Skull level view of the simulation showing the on screen control panel (bottom of figure) and an example of one form of graphic representation of the global status of the infection (line graphs, left).
(E) A view at the level of the entire Waldeyer ring demonstrating different methods of quantitation. Graphics in the form of numbers (top left) or bar graphs for a given time step and time line graphs (top right) are shown for various compartments of the simulation. The color signature for the ring is red, which denotes free Vir. The color of the ring denotes the type and level of agent being shown. In this case, the intense red color indicates a high level of free Vir throughout the ring (for an example of infection spreading throughout a single lymph node or the entire ring visualized by changing color intensity, see Figure 3 and Video S2). Note also the draining lymphatics (white vessels) and peripheral circulation (red and blue vessels). These images are screen shots taken on 7/30/2006.
Figure 3.
Progression of the Infection in a Typical Simulation as Visualized by the IRVE
This Figure is similar to Figure 2E except that different time points in the infection process are shown. Vir were seeded evenly over the lingual tonsil and then allowed to spread to the rest of the ring. Note that in this case as time progresses (A–D) the infection spreads evenly to all of the other tonsils and adenoids as indicated by a gradual uniform increase of color intensity. These images are screen shots taken on 3/7/2007.
Table 1.
A Summary of the Agents and Their Governing Rules Used in This Simulation
Figure 4.
Output of the Simulation Employing the Default Parameter Set Matched to Biological Data
(A) Simulation output of the total number of latently infected virtual B cells (BLat) over time in a series of superimposed simulation runs (colored lines) versus the number of actual latently infected memory B cells in the peripheral blood of 15 acutely infected individuals over time (colored circles). The first patient time point is assumed to be at 50 d +/− 10 d (see text for explanation). The simulation runs all use the default parameter set. Stochasticity (i.e., random variations) in the runs are a consequence of the fact that every interaction and motion of agents is governed by a probability and a variability function. So, for example, the initial infectious dose will vary from node to node in the epithelium and will have a certain average. This average we refer to as the initial infectious dose. For a detailed discussion of all the rules governing interactions and motion, see M. Shapiro, K. Duca, E. Delgado-Eckert, V. Hadinoto, A. Jarrah, et al. (2007) A virtual look at Epstein-Barr virus infection: simulation mechanism (unpublished data).
(B) Simulation output of the total number of latently infected virtual B cells (BLat) and virtual B cells replicating virtual virus (BLyt) over time for a single simulation run.
(C) Simulation output of the level of latently infected virtual B cells (BLat) and free virtual virus (Vir) over time for a single simulation run. The insert shows a time course for a typical acutely infected patient for the first 25 d after entering the clinic showing the level of latently infected memory B cells in the peripheral blood and free virions shed into the saliva.
(D) The level of virtual free virus (Vir) over 1 y in the simulation (blue line). The level was assessed every 25 d, once the simulation had entered into the persistent phase defined as a stable level of latently infected virtual B cells (BLat) For comparison, the level of shed virus (Virions) in the saliva of a persistently infected individual, sampled on average approximately every 30 d, is shown (red line). The x-axis denotes the number of days over which sampling was performed and does not relate to the time from initial infection
N.B. Note this figure only allows analysis of overall dynamics, not absolute numbers, since all comparisons between simulation and in vivo data are relative.
Table 2.
Validation of Simulation Output
Figure 5.
Access to the Peripheral Circulation Is Required for Viral Persistence in the Simulation
(A) The virtual virus does not persist when latently infected virtual B cells (BLat) are denied access to the peripheral circulation. The graph shows the level of BLats over time for a simulation run with the default parameter set allowing (red line) or denying (brown line) access of the BLats to the peripheral circulation Note that only the first 60 d of virtual infection are shown. A characteristic series of spikes in BLats is observed that was lost after approximately 30–40 d. These spikes arise because normally BLats spend time in the circulation, and the time they spend there does not advance them towards the lytic state. By denying them access to the blood, both the mean time to burst and the standard deviation of this statistic decrease. This causes the virtual viral bursts and infection of new virtual B cells to arrive synchronously as narrow spikes, one spike per generation of infected virtual cells.
(B) Increasing the initial infectious dose does not allow persistence in the absence of a peripheral blood compartment. The simulation was run without a peripheral blood compartment as described in (A), except the initial infectious dose was increased in increments as shown. The initial infectious dose is the average number of Vir deposited at each mesh point (node) on the surface of the virtual lymphoepithelium. To obtain the total infectious dose, this value is multiplied by the number of surface nodes (16,205). The figure shows runs with infectious dose of 7/mesh point (pink line) and 70/mesh point (green line). The default value for initial infectious dose is 0.7/mesh point.
(C) Increasing the Vir burst size does not allow persistence in the absence of a peripheral blood compartment. The simulation was run without a peripheral blood compartment as described in (A), except the number of Virs released when a BLyt bursts was doubled (default average burst size = 800 Virs).
(D) Decreasing the efficiency of the immune response does not allow persistence in the absence of a peripheral blood compartment. The simulation was run without a peripheral blood compartment as described in (A), except the efficiency with which CTLs are activated and kill their targets was reduced incrementally. With this approach it was possible to find a level of virtual immunosuppression (50% brown line) that produced an infection that lasted for the length of the simulation (880 virtual days). However, this looks nothing like EBV persistence in a real infection. Rather, the virtual infection involves wild oscillations in the number of latently infected virtual B cells (BLat) and it appears that the average level is trending upwards to overwhelm the B cell compartment, a condition we refer to as virtual death. Small incremental increases above 50% immunosuppression (e.g., 75% blue line) resulted in the B cell compartment being rapidly overwhelmed with latently infected virtual B cells (BLat). Small incremental decreases below 50% immunosuppression resulted in clearance of Vir similar to that seen in Figure 5A.
Figure 6.
Comparing Simulation Output, Employing the Default Parameter Set, to What Is Known or Expected from a Real Infection
(A) Varying the initial infectious dose of Vir has no effect on persistent levels of latently infected virtual B cells (BLat). The initial infectious dose is the average number of Vir deposited at each mesh point (node) on the surface of the virtual lymphoepithelium. The simulation was run as described in Figure 4A, except the initial infectious dose of Vir was varied from 0.1 to 10 as shown (the default level is 0.7). Since there are 16,205 surface mesh points, this translates into a total infectious dose ranging from 1.6 × 103 to 1.6 × 105.
(B) Epithelial cell amplification has no effect on persistent levels of latently infected virtual B cells (BLat). Epithelial cell amplification of Vir was simulated by adding an additional amount of Vir at each time step. The virtual amplification achieved varied from none to 2 × 104.
(C) Persistence is highly sensitive to the rate of Vir reactivation. The simulation was run as described in Figure 4A, except the percentage of latently infected virtual B cells (BLat) that initiate Vir replication upon return to the Waldeyer ring was varied as shown (the default percentage is 0.05% based on data from [16]).