Basic Principles in Modeling Adaptive Regulation and Immunodominance - Mathematical Methods and Models in Biomedicine - page 32

[ 20 ]. In another study of CD8+ T cell expansion, Kaech et al. showed that upon
antigenic stimulation, naıve CD8+ T cells divide at least 7-10 times and differentiate
into functional effector and memory cells even if antigen is removed [ 13 ]. An
alternative experimental approach by van Stipdonk et al. also focused on CD8+ T
cell stimulation [ 31 ]. They showed that naıve CD8+ T cells become activated after
only 2 h of exposure to mature antigen-presenting cells (APCs). After activation,
these T cells divided and differentiated into effector and eventually memory cells
without a need for further antigenic stimulation. In a subsequent paper, they
observed that naıve CD8+ T cells that have been stimulated for 20 h were able
to carry out extensive proliferation and cytotoxic activity, characteristic of a fully
developed immune response [ 30 ]. They proposed that the fate of a T cell response
is governed by a “cell-instrinsic developmental program” that is set even before the
first cell division takes place.
A couple of mathematical models of the T cell proliferation program have been
developed in parallel to these experiments. Antia et al. devised a mathematical
model to investigate whether the program is completely specified by the initial
encounter with antigen or whether it can be subsequently modified by the amount
of antigen present [ 1 ]. Their results favor the second paradigm in which the
T cell population briefly expands in response to the amount of antigen present
before committing to a fixed program. Wodarz and Thomsen [ 32 ] developed a
mathematical model to find the optimal fixed program that could respond effectively
to a wide variety of infections. They concluded that the 7-10 divisions observed
experimentally represented such an optimum.
All together the experimental and mathematical modeling papers propose a
general paradigm for T cell expansion, which can be stated as follows: upon
stimulation, T cells enter a minimal developmental program of about 7-10 divisions
that is followed by a period of antigen-dependent proliferation that terminates after
a certain time or after a certain number of cell divisions.
While the precise mechanisms of immunodominance are not well understood,
the majority of experimental and theoretical works agree on some form of T cell
competition [ 4 , 11 , 14 , 15 , 22 , 23 ]. The two most prevailing theories on the matter
are that either T cells passively compete for a limited resource, most likely access
to APCs, or that T cells actively suppress the development of other T cells.
Our approach to deriving a mathematical model of immunodominance is based
on extending the adaptive regulation model to consider the case of multiple,
simultaneous T cell responses. This point of view implies that immunodominance
may occur as a natural result of the iTreg-mediated contraction of the T cell response
proposed in [ 17 ].
Several mathematical models for immunodominance have been developed in the
literature. Here we mention several key works and refer to [ 16 ] for a more complete
overview of these works and their results. De Boer and Perelson show that for
each target epitope only the T cell clone with the highest affinity will survive long-
term T cell competition [ 7 , 8 ]. Nowak develops a mathematical model and predicts
that for an antigenically homogeneous virus population, the immune response will
ultimately be directed against only one epitope, a situation known as complete