Basic Principles in Modeling Adaptive Regulation and Immunodominance - Mathematical Methods and Models in Biomedicine - page 52

dominant clone is removed, the second most frequent clone compensates effectively,
even though it starts with an initial concentration that is four times less than that of
clone 1 (see Fig. 9 b). In addition, when the two most dominant clones are removed
the third most frequent clone also compensates effectively, and so on (see Fig. 9 c, d).
From Figs. 9 and 7 , we see that the qualitative behavior of immunodominance
seen in the basic model is preserved in the extended model, which explicitly
incorporates separate CD4+ and CD8+ T cell dynamics. The basic model allows
us to focus on the role of negative feedback between effector and regulatory T cells
in producing immunodominance. The extended model captures more biologically
accurate dynamics. However, it requires more comprehensive parameter estimates
and more extensive analysis. The overall characteristics of both models are similar.

5 Conclusion and Discussion

In this chapter we provided an overview of our mathematical models for the
regulation of the primary T cell response and of immunodominance. Our mathe-
matical models were constructed based on a set of basic principles. A robust T cell
contraction was shown to emerge as a result of an adaptive regulatory mechanism.
We also showed that immunodominance may occur as a natural consequence of
iTreg-mediated T cell contraction. For both problems, we provided a basic model
that does not include helper T cells and an extended model that includes the helper
T cells. Our numerical simulations focused on the immunodominance models. The
simulations showed that the qualitative behavior of the simple and of the extended
models is identical.
The main point that we emphasized throughout the chapter is that the modeling
of these biological phenomena should focus on the basic principles that control the
emerging dynamics. While it is desirable that the mathematical models accurately
capture the main biological ingredients, certain simplifications allow us to focus on
the basic principles. A basic model that captures the desirable qualitative features
can be always extended later on to reflect more accurate biology. This was the
methodology we followed when developing these models.
Our models do not take into account the suppression of APCs by iTregs, although
it is a known function of regulatory T cells [ 6 ]. Incorporating suppression of APCs
is a direction for a future work and may partly explain why competition is only
observed for epitopes presented on the same APC. In this light, considering spatial
elements is another relevant extension, since regulatory T cells locally suppress cells
in a contact-dependent manner, but no longer inhibit cells that have moved out of
the vicinity [ 28 ]. In the context of immunodominance, regulatory (or suppressor) T
cells give rise to highly localized inhibition that operates only in the context of one
or a few common APCs [ 26 ]. In their mathematical models, Leon et al. assume that
regulatory and effector cells need to be activated by APCs that are close in space
and time in order to interact [ 18 , 19 ]. Indeed, such localization may be necessary to
prevent a regulatory response from shutting down the whole immune system.