Basic Principles in Modeling Adaptive Regulation and Immunodominance - Mathematical Methods and Models in Biomedicine - page 48

the third most dominant clone partially compensates (see Fig. 6 c) and so on,
but the ability of less reactive T cell responses to compensate for more reactive
ones decreases rapidly. In the case of the TKO experiment shown in Fig. 6 d,
the immune response from clone 4 is much weaker than the original immune
response generated by clone 1 in the control case shown in Fig. 6 a. Our study
of Scenario 1 shows that T cell reactivities play a strong role in determining
immunodominance hierarchies. Furthermore, less reactive T cell clones have
limited ability to compensate for more reactive ones.
The phenomenon of compensation was observed experimentally by van der
Most et at. who showed that loss of epitope-specific responses was almost
inevitably associated with compensatory responses against subdominant epi-
topes. In addition, their experiments showed that noticeable compensation by
a subdominant response depended on the removal of all or most of the more
dominant epitopes, creating room, as it were, for subdominant epitopes to emerge
[ 29 ]. In the same manner, our simulations show that a response from clone 2 does
not substantially emerge until clone 1 is removed and that a response from clone
3 does not emerge until clones 1 and 2 are removed, and so on. By extension, a
response against a subdominant epitope is likely not to emerge until all or most
T cell clones, specific for the dominant epitope (or epitopes), are removed. The
degrees of shift in hierarchy become more prominent in the following examples.
Scenario 2. (Four clones, different initial concentrations). We consider four T
cell clones with the same reactivities. These clones differ only in their initial
concentrations. In this case, the reactivities are set as p i = 1 / 2, i = 1 ,..., 4.

The initial concentrations are taken as: K 1 ( L, K 2 (

0 )= 0 . 04 k/ μ 0 )= 0 . 01 k/ μ L,

K 3 ( 10 − 3 L, K 4 ( 10 − 4

L. As before, we consider
SKO, DKO, and TKO experiments. Figure 7 shows the results of the numerical
simulations.
Figure 7 a shows that the four T cell clones fall into a hierarchy based on
their initial concentrations. Specifically, the T cell response of clone 1 starts and
remains exactly four times higher than that of clone 2. Likewise, the response
of clone 2 starts and remains exactly four times higher than that of clone 3, and
so on. Since the reactivities p i are identical for all four clones, the equations
determined by Eqs. ( 15 )-( 19 ) for each clone are also identical, meaning that
the four T cell responses fall into a linear relation determined by their initial
conditions.
When the 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. 7 b). Indeed, the T cell response for
clone 2 more than doubles between the control and SKO experiments. Similarly,
when the two most dominant clones are removed the third most frequent clone
also compensates effectively and so on (see Fig. 6 c, d).
Scenario 3. (Two clones, one with a higher reactivity and one with a higher
precursor concentration). In Scenarios 1 and 2, we examined the effects of
varying reactivities and initial concentrations separately. In this case we vary
both parameters and consider two clones. We start by considering a possible

0 )= 2 . 5 × k/ μ 0 )= 6 . 25 × k/ μ