Basic Principles in Modeling Adaptive Regulation and Immunodominance - Mathematical Methods and Models in Biomedicine - page 33

immunodominance [ 21 ]. De Boer et al. formulate a mathematical model to analyze
experimental measurements of the CD8+ T cell response to lymphocytic chori-
omeningitis virus [ 10 ]. The response consists of one immunodominant response
and one subdominant response against different epitopes. De Boer et al. propose
that differences in growth rate and recruitment times of different T cell populations
can account for immunodominance. Antia et al. also formulate a model in which
multiple epitope-specific T cell populations undergo a brief period of expansion in
response to antigen, followed by a period of antigen-independent proliferation and
contraction [ 1 ]. Handel and Antia develop a mathematical model to explain the shift
in the immunodominance hierarchy between the primary and secondary responses
to influenza A [ 12 ]. Scherer et al. present an alternative mathematical model in
which the down-modulation of antigen-presentation leads to long-term coexistence
of T cell responses [ 25 ]. A related work by Scherer et al. is an agent-based model
to understand whether T cells compete for nonspecific stimuli, such as access to the
surface of APCs, or for specific stimuli, such as MHC:epitope complexes [ 27 ].
Our main goal in developing mathematical models for the primary immune
response and immunodominance is to identify at least some of the main mechanisms
by which the primary immune response is regulated and by which immun-
odominance emerges. After carefully studying other approaches, we developed
mathematical models that are based on the following basic principles:

1. The primary immune response should be adaptively controlled. This adaptive
process can work in combination with any proliferation preprograms.
2. The adaptive control is conducted by regulatory cells. The number of regulatory
cells cannot be directly proportional to the total number of effector cells as the
body has no way of keeping track of this number. Instead, the process should
depend only on the dynamics of individual cells.
3. Immunodominance is a by-product of adaptive regulation. Adaptive regulatory
cells, which are created in an epitope-specific way, can then regulate the system
in a nonspecific fashion.

When it comes to adaptive regulation, our main observation in [ 17 ] was that the
preprogram paradigm as is, is inconsistent with the experimental data of Badovinac
et al. [ 2 ], which showed that a 10,000-fold difference in antigen-specific naıve T
cell concentrations only led to a 13-fold higher peak in the effector response. Any
mechanism that relies only on a preprogrammed cell division must scale linearly
with the precursor frequencies. This led us to derive a mathematical model that is
based on adaptive regulatory T cells (iTregs). Our hypothesis is that T cell responses
are adaptively regulated in a process that results from the dynamics of immune cells
that interact based on relatively simple rules. Following the same line of thought, our
model of immunodominance from [ 16 ] is based on considering immunodominance
as a by-product of the regulated T cell contraction. It is sufficient to add a single rule
to the model of adaptive regulation to explain immunodominance.
The model in [ 16 ] represents an “extended” model that divides T cells into helper
(CD4)

) subpopulations and considers interactions among helper
T cells, killer T cells, and iTregs. This model has the advantage of presenting a more

+ and killer (CD8 +