The cycle of EBV infection explains persistence, the sizes of the infected cell populations and which come under CTL regulation

Abstract

Previous analysis of Epstein-Barr virus (EBV) persistent infection has involved biological and immunological studies to identify and quantify infected cell populations and the immune response to them. This led to a biological model whereby EBV infects and activates naive B-cells, which then transit through the germinal center to become resting memory B-cells where the virus resides quiescently. Occasionally the virus reactivates from these memory cells to produce infectious virions. Some of this virus infects new naive B-cells, completing a cycle of infection. What has been lacking is an understanding of the dynamic interactions between these components and how their regulation by the immune response produces the observed pattern of viral persistence. We have recently provided a mathematical analysis of a pathogen which, like EBV, has a cycle of infected stages. In this paper we have developed biologically credible values for all of the parameters governing this model and show that with these values, it successfully recapitulates persistent EBV infection with remarkable accuracy. This includes correctly predicting the observed patterns of cytotoxic T-cell regulation (which and by how much each infected population is regulated by the immune response) and the size of the infected germinal center and memory populations. Furthermore, we find that viral quiescence in the memory compartment dictates the pattern of regulation but is not required for persistence; it is the cycle of infection that explains persistence and provides the stability that allows EBV to persist at extremely low levels. This shifts the focus away from a single infected stage, the memory B-cell, to the whole cycle of infection. We conclude that the mathematical description of the biological model of EBV persistence provides a sound basis for quantitative analysis of viral persistence and provides testable predictions about the nature of EBV-associated diseases and how to curb or prevent them.

Figure 1. EBV biological model.

A) Newly infected B-cell Blasts move into the follicle and enter the GC, where they continue to divide as EBV-infected GC B-cells before exiting into the periphery as latently infected memory B-cells. A small subset of these are induced to undergo lytic reactivation, progressing through the lytic stages Immediate early, Early and Late before finally bursting and releasing infectious virus that may be amplified through infection of the epithelium (not detailed in the model) but ultimately culminate in the infection of new naive B-cells which become Blasts, thus completing the cycle. Theoretically each stage has the capacity to generate a CTL response. The Blast, Immediate early and Early stages are always regulated, while the GC and Late stages may not always be regulated , , . Memory is never regulated under normal biological conditions , , . This model of EBV biology is used to generate the CPM framework presented in this paper. B) Infected populations as displayed as circles whose area is proportional to their frequency within all tonsils (1∶5∶1.5×10²∶10⁴∶10⁴∶0.5×10⁴, Late∶Early∶ImmEarly∶Memory∶GC∶Blast). This graphic highlights the very large range in the sizes of these populations.

Figure 2. Diagrammatic representation of our test procedure for CPM.

A) Here we describe the methodology for just 2 parameters, X and Y. a and b represent the range of biologically tenable values for these two parameters. From this we can project a 2-dimensional parameter space that consists only of all the biologically tenable combinations of the two parameters. We can then sample random points in this space (in this case 10). B) Each point is a parameter set which consists of a single value for each of the two parameters (parameter values). These can then be used to interrogate the model and predict outcomes. In our model there are actually 25 parameters generating a 25 dimensional parameter space (the parameter cube) from which we randomly sampled 10,000 sets of parameters.

Figure 3. Biologically plausible immune patterns of regulation.

Out of 10,000 randomly chosen parameter sets from the physiologically tenable parameter space, for this particular run, 93.1% produced biologically plausible patterns (described in the insert). A. Columns represent the total fraction of patterns for which each stage was regulated. B. The patterns of regulation ordered by frequency of occurrence. Note the four highest are the biologically plausible patterns and the highest is the most likely to occur biologically.

Figure 4. Testing the consequences of an immunologically invisible memory stage.

A) The same analysis was performed as in Figure 3, with the exception that the memory compartment was allowed to be antigenic. The most frequent patterns of regulation seen are shown in the insert. B) The same analysis as A, but showing only the fraction where the four biologically plausible patterns of regulation were seen.

Figure 5. Analysis of the memory compartment.

A) The size of the infected memory compartment and flow rates through this stage is shown graphically as a pie chart. The left half shows gains by the population and the right half shows the losses. Since the system is at equilibrium, the population size is constant and the gains must equal the losses, i.e., the size of the two halves of the pie chart must be the same. B) To test how well the range of values predicted for the memory compartment by CPM compared to what is seen biologically, we calculated the predicted steady state size of the memory compartment for 10,000 randomly chosen parameter sets (green bars) and compared this to the actual number of EBV infected memory B-cells in Waldeyer's ring for 42 independent tonsils from persistently infected individuals (purple bars). The predicted values have a similar mean and median value as compared to the experimental data (log mean: biological 4.48; CPM 4.36; log median: biological 4.65; CPM 4.31; p-value = 0.079 using a two-sided, unpaired, two-sample Mann-Whitney test).

Figure 6. Analysis of the GC compartment.

A). The size of the infected-GC compartment and flow rates through this stage in an example where the infected-GC population is regulated by CTLs is shown graphically as a pie chart. The left half shows gains by the population and the right half shows the losses. Since the system is at equilibrium, the population size for each stage is constant and the gains must equal the losses, i.e., the size of the two halves of the pie chart must be the same. Gain can occur either from input from the previous stage or as the end product of cell division, i.e., proliferation. Losses can occur via death, killing by CTLs, differentiation to the next stage or as input into cell division (it is simplest to consider cell division to be the consequence of loss of one cell and the appearance of two new cells). B) The same analysis as A, however for an example where the infected-GC population is not regulated by CTLs. C) The predicted size of the infected-GC population is shown for the cases in which it is not regulated by the immune response (3,193 out of 10,000 random trials; green bars). In purple, we have plotted the experimentally measured size of the infected-GC population from 42 independent tonsils from persistently infected individuals.

Figure 7. Analysis of the Blast compartment.

A and B) Flow rates for the Blast stage are shown using the amplification factors of 20 (A) and 10,000 (B). C) The predicted mean time between killing for CTLs specific for Blasts in Waldeyer's ring is plotted against a wide range of amplification factors. The green line represents our high estimate for this CTL population, while the blue line is the low estimate.

Figure 8. Validation of CPM.

A) A permutation test was performed 1000 times where the values for the parameters were randomly scrambled. For details see text. The histogram shows the number of examples where different fractions of biologically plausible patterns of regulation were seen. Note that only 13 scrambled parameter sets had an equal or higher level of biologically plausible patterns of regulation as compared to the biologically plausible parameter set (p-value of 0.013). B) A permutation test was performed 1000 times in which all parameters are permuted (as in A), with the exception of the values for c_i. Note that only 33 scrambled parameter sets (holding c_i constant) had an equal or higher level of biologically plausible patterns of regulation as compared to the unscrambled sets (p-value of 0.033), allowing us to reject the hypothesis that the observed patterns of regulation were determined by the values for net antigenicity. C) The range of values for each parameter was increased by up to 100-fold above what was biologically plausible and the fraction of biologically plausible patterns measured. The fraction of the parameter space which produces plausible patterns quickly falls off, demonstrating that the default set of parameters was very close to optimal.