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after about the peak of the immune response until it reaches a quasi-plateau
several weeks later [4]. This process, termed anity maturation, implies that a
selection process for higher anity Abs takes place during that time. In higher
vertebrates the SMH and selection processes take place at Germinal Centers
(GC) [2]. These are short-lived structures, generated within primary follicles of
secondary lymphoid tissue by migration of Ag-activated lymphocytes, and char-
acterized by intense proliferation and apoptosis of Ag-specific B cells. In contrast,
lower vertebrates do not generate GCs [2] so that SHM during immune responses
to protein Ags takes place more or less diffusely in lymphoid tissue. Correspond-
ingly in them the serum anity during immune responses increases significantly
less than in higher vertebrates. This indicates a less ecient selection process,
currently attributed to their lack of GCs [2].
A higher rate anity maturation process requires a more ecient (stronger)
selection than a poorer anity maturation process. On the other hand, the
higher the eciency the more specific the selected Abs will be, but the lower
the remaining diversity related to the triggering Ag. However, thinking in evo-
lutionary terms, keeping the diversity in the Ab repertoire seems at least as
important as having the ability to selectively expand B cells producing Abs with
higher specificity. For instance, while a 'selection structure' (
i.e.,
GCs) has been
selected for in higher vertebrates, many lower vertebrates have life spans similar
to many higher vertebrates. Also, mutant mice that lack an enzyme essential for
the SHM process get strong intestinal inflammation due to massive infiltration
of normal anaerobic gut flora [5].
Because the more ecient the selection the less the diversity, and because of
the importance of both anity maturation and diversity, a trade-off between
those two goals possibly emerged during the evolution of vertebrates in those
species endowed with the physiologic possibility to generate GC-like structures.
We hypothesize that such trade-off may have determined the size, life span,
organization, etc. of GCs. In order to approach this issue, we have developed
a simple stochastic/CA hybrid model that allows us to compare the degree of
anity maturation and diversity generated in different scenarios, intended to
represent evolutionary stages of species with increasing GC size. In this model
the process of anity maturation within GCs is formally equivalent to a pop-
ulation genetics model of the evolution of clonal populations under mutation
and selection. This allows us to put our findings in context with a number of
analytical results from population genetics.
2
The Model
A model of the immune response incorporating SHM and selection, in which
lymphoid tissue is represented by a 25
25 square grid with periodic bound-
ary conditions, was implemented in language
C
.InitBcellsareassumedtobe
distributed evenly in the small squares of the grid and are modeled as a large
population with many subpopulations of equal size named demes. More specif-
ically, each single square holds a deme of
N
d
B cells (thus the whole system
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