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as large as 20 L , where L is D-region peptide length and
L max ¼
near-saturation [4] . These VH sequences can be captured in
a single sequence read and contain the majority of antibody
diversity. Analysis of each fish's repertoire strengthened
early observations [49] that VDJ recombination is biased
and does not occur with equal probability for each
combination. Rather, the antibody repertoire was found to
be unevenly distributed, with a high number of combina-
tions expressed at a low abundance and a small number of
combinations appearing at very high abundance to make up
a rough total of 9% of combinations in any single fish,
with significant overlap between fish. A specific VDJ
combination may account for more than one antibody due
to the aforementioned processes of somatic hyper-mutation
and junctional changes. By shifting sequence alignment
parameters the researchers were able to estimate which
distinct antibodies were produced. The lower and upper
bounds on the estimated total number of antibodies per fish
were 1200 and 6000, respectively, whereas the antibody
abundance frequency followed a power-law distribution
which has also been observed in many other complex
systems (see Chapter 9). Analysis of V b diversity from
the TCR of human CD8 þ na ¨ ve and memory T cells
yielded similar results: an uneven repertoire distribution,
a large number of distinct combinations expressed in
a single individual at a single point in time [50] (
8), and assessed the measure of diversity in
sequence space, or entropy). Next they analyzed to what
extent the entropy was reduced by observed amino acid
correlations in the data. Whereas simply taking the
observed biases in the use of single amino acids into
account did not reduce the entropy significantly,
accounting for next-most-simple correlations between
'nearest neighbor' and the 'next nearest neighbors' amino
acid captured between two-thirds and 90% of all corre-
lated structure in the distribution of sequences [52] .
Although the model used is somewhat na¨ve, in that it
gives equal probability to all protein sequences irre-
spective of the original genomic sequence of the antibody,
the correlations between amino acid distributions suggests
constraints in somatic hyper-mutation and junctional
diversity mechanisms.
Additional basic insights into repertoire dynamics are
emerging from studying how the antibody repertoire
changes as a function of development and disease. Jian
et al. [3] compared the repertoire of antibody diversity
between young and older fish and found restricted segment
usage in young fish compared to older animals. Diversity
increases with age, but primarily through less biased
somatic hyper-mutation and random clonal expansion
effects, whereas a common deterministic program, with as-
yet unknown mechanisms, biases VDJ use [3] . Boyd et al.
quantified B-cell IgH antibody repertoire in 150 healthy
humans and in blood cancer patients. From healthy indi-
viduals they were able to estimate the normal B-cell
repertoire complexity, whereas disease-specific signatures
were observed in cancer patients, which allowed quantifi-
cation of
10 6 ,
though still negligible compared with the upper theoretical
limit of 10 11 ), and a significant overlap of sequence
repertoires between any two individuals, particularly in
na¨ve cells [51] .
The expressed repertoire is thought to be dependent on
VDJ recombination and mutation, phylogenetic history
and the pathogen environments. It is possible that the
source of the observed structure in the repertoire is simply
the result of convergence. That is, that the environment
individuals experience yields correlated VDJ usage.
Alternatively, the uneven distribution of VDJ choice may
reflect a bias in the VDJ recombination mechanisms,
either due to long-term (over generations) selection factors
or to previously unappreciated inherent limitations in the
recombination and mutation mechanisms that yield anti-
body and TCR diversity. This would have important
implications, as it is thought that the diversity of repertoire
defines the range of pathogens to which the organism can
respond effectively. Using the above-described zebrafish
dataset [4] , Mora et al. borrowed from statistical physics to
measure the D-region diversity using entropy and test the
degree to which the diversity could be explained by
structural constraints [52] . The genomic origins of the D
region is 11
>
the number and identity of
the dominant
cancerous B-cell clonal receptors [53] .
Apparent lessons on repertoire dynamics can be learned
not only from organism development, but also from cellular
differentiation itself. By separating CD8 þ na¨ve and
memory cell types prior to sequencing TCR repertoire,
Robins et al. showed that repertoire sequences with high
relative frequency in na¨ve cells are more likely to be
observed in the memory compartment [50] . No correlation
was observed with respect to repertoire size between the two
cells subsets, suggesting that the mechanism to determine
the clone size in the two cell subsets is different. Wang et al.
sequenced the TCRV b and V a repertoires from one human
individual but separately for each of eight different cell
subsets. When examining the TCRs whose sequence was
most abundant (dominant clones), they detected significant
overlap in TCR repertoire between the different CD8 þ cell
subsets. There has been a long-standing debate on the role of
individual TCRs in determining cell fate. Two theories
prevail: that a cell's fate is determined in a 'stochastic'
fashion with survival dependent on a later selective TCR
signal, or in an 'instructive' manner by the affinity of the
14 nucleotides long, whereas in the zebrafish
antibody data it was the most variable sequenced region,
with sequences ranging from 3 to 18 nucleotides in length,
which is often difficult to align to the original genomic
copy. Modeling repertoire sequences in protein space, they
assumed that every possible sequence is possible (a space
e
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