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Limits for Antibody Affinity Maturation and
Repertoire Diversification in
Hypervaccinated Humans
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of June 14, 2017.
Tine Rugh Poulsen, Allan Jensen, John S. Haurum and Peter
S. Andersen
J Immunol published online 19 September 2011
http://www.jimmunol.org/content/early/2011/09/16/jimmun
ol.1000928
http://www.jimmunol.org/content/suppl/2011/09/16/jimmunol.100092
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Supplementary
Material
Published September 19, 2011, doi:10.4049/jimmunol.1000928
The Journal of Immunology
Limits for Antibody Affinity Maturation and Repertoire
Diversification in Hypervaccinated Humans
Tine Rugh Poulsen,1 Allan Jensen,2 John S. Haurum,3 and Peter S. Andersen
W
hen challenged with a foreign substance, the immune
system mounts a genetically diverse polyclonal response of specific Abs, which initially are of predominantly low to intermediate binding affinity (1–3). Binding
strength of subsequent generations of Abs is improved through
further diversification by introducing point mutations in the V
regions, and the resulting variants are selected on the basis of
improved binding to Ag (2–4).
Recent advances in cloning of Ab genes from single human
B cells have provided important new insights into the molecular
composition of Ab responses from single individuals (5–11). What
remain to be determined are the actual limits of the repertoire
diversification processes and their functional outcome in terms
of affinity maturation of Abs. Such knowledge can be gained
by studying the progression of Ab repertoires in individuals repeatedly exposed to an invariant B cell Ag. Determination of such
limits is scientifically important as it reveals some basic features
of the adaptive immune system in the protection against infectious
diseases and hence is clinically important in the design and
implementation of vaccines and development of Ab-based drugs.
Ab V gene repertoires in response to antigenic challenges have
been reported to display extensive genetic diversity, utilize most of
Symphogen A/S, 2800 Lyngby, Denmark
1
Current address: Novo Nordisk A/S, Måløv, Denmark.
2
Current address: Pfizer, Aberdeen, U.K.
3
Current address: ImClone, New York, NY.
Received for publication March 25, 2010. Accepted for publication August 1, 2011.
T.R.P. was supported by a fellowship from the Danish Agency for Science, Technology and Innovation.
Address correspondence and reprint requests to Dr. Peter S. Andersen, Symphogen A/S, Elektrovej Building 375, 2800 Lyngby, Denmark. E-mail address:
[email protected]
The online version of this article contains supplemental material.
Abbreviations used in this article: IMGT, International ImMunoGeneTics; MSD,
multiplicative standard deviation; RU, response unit; TT, tetanus toxoid; TT1, tetanus
toxoid Ab repertoire donor 1; TT2, tetanus toxoid Ab repertoire donor 2.
Copyright Ó 2011 by The American Association of Immunologists, Inc. 0022-1767/11/$16.00
www.jimmunol.org/cgi/doi/10.4049/jimmunol.1000928
the known germline gene fragments, and originate from up to 50
clonally different rearrangements (7, 11) pointing to Ab repertoires
being limited to ∼100 clonally different Abs (7). However, it is
unresolved how the diversity of B cell repertoires develops in
response to repeated exposures to the same Ag as is often the case
in prophylactic vaccination of adults. Do repertoires converge to
be dominated by a few B cell clones? Do they maintain their
clonal composition or are they dynamic and constantly recruiting
new B cells? Also, to what extent can somatic hypermutations be
introduced to increase repertoire diversity? And finally, to what
extent do the diversification processes influence the physical limits
for affinity maturation? Kinetic boundaries for maturation of Ab
affinity have been proposed on theoretical grounds (12, 13). By
considering physiochemical limits for association rates (kon) and
the rate of receptor internalization upon Ag binding as limiting
dissociation-rate (koff) maturation, Foote and Eisen (12) predicted
a maximum natural kon in the range 105 to 106 M21 s21 and
minimal natural koff in the range 1023 to 1024 s21 leading to
a natural affinity ceiling with equilibrium dissociation constants
(KD) of the order 1028 to 10210 M. Supporting this, an average
affinity of 2.3 3 1029 M was reported for Abs isolated from two
human donors after a single vaccination with tetanus toxoid (7).
This was ∼5-fold higher than the average from an influenzavaccinated donor (8) and two orders of magnitude higher than
that of Abs isolated from a donor receiving an HBV booster vaccination (10). Combined, these results clearly point to a progressive (and Ag-dependent) development of Ab responses.
To determine the aforementioned limits for Ab repertoire diversification and affinity maturation, Ab gene repertoires were
prepared and characterized from two individuals after three repeated challenges with a tetanus toxoid (TT). TT was chosen as
model Ag, as it is one of the most immunogenic vaccines used in
man and known to induce a strong, long-lasting, and presumably
unbiased Ab response. Thus, any observed boundaries in the Ab
repertoires are likely to be independent of the Ag but inherent to the
adaptive immune system. A representative panel of Abs specific for
TT was isolated after each boost resulting in a total of 594 unique
Abs estimated to originate from at least 195 different naive B cell
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The immune system is known to generate a diverse panel of high-affinity Abs by adaptively improving the recognition of pathogens
during ongoing immune responses. In this study, we report the biological limits for Ag-driven affinity maturation and repertoire
diversification by analyzing Ab repertoires in two adult volunteers after each of three consecutive booster vaccinations with tetanus
toxoid. Maturation of on-rates and off-rates occurred independently, indicating a kinetically controlled affinity maturation process.
The third vaccination induced no significant changes in the distribution of somatic mutations and binding rate constants implying
that the limits for affinity maturation and repertoire diversification had been reached. These fully matured Ab repertoires remained
similar in size, genetically diverse, and dynamic. Somatic mutations and kinetic rate constants showed normal and log-normal
distribution profiles, respectively. Mean values can therefore be considered as biological constants defining the observed boundaries.
At physiological temperature, affinity maturation peaked at kon = 1.6 3 104 M21 s21 and koff = 1.7 3 1024 s21 leading to a
maximum mean affinity of KD = 1.0 3 1029 M. At ambient temperature, the average affinity increased to KD = 3.4 3 10210 M
mainly due to slower off-rates. This experimentally determined set of constants can be used as a benchmark for analysis of the
maturation level of human Abs and Ab responses. The Journal of Immunology, 2011, 187: 000–000.
2
LIMITS FOR HUMAN Ab RESPONSES
progenitors. We hereby present a comparative genetic and functional analysis of these Abs leading to experimental estimates of
the natural limits for Ab repertoire diversification and affinity
maturation in humans.
Materials and Methods
Donors and vaccination
Donors were vaccinated in parallel with a commercially available TT
vaccine (State Serum Institute, Copenhagen, Denmark). The three vaccinations were done over a 5-y period separated first by 3.5 y and subsequently by 1.5 y. Blood was donated 6 to 7 d after each vaccination. The
project was approved by the regional Ethical Committee in Copenhagen,
Denmark. Informed consent was obtained from each of the donors prior to
each vaccination.
Generation and analysis of Ab repertoires
Affinities (KD), on-rates (kon), and off-rates (koff) were determined by
surface plasmon resonance analysis on a Biacore 2000 (GE Healthcare/
Biacore, Uppsala, Sweden) or a Proteon XPR36 (Bio-Rad). Mass transport
limitation was minimized by measuring at low ligand densities and relatively high flow rates. Briefly, TT was immobilized at low ligand densities
on CM5 chips (Biacore) or GLC chips (Bio-Rad), resulting in maximum
response unit (RU) values of ∼100 RU or less when binding Fab fragments. Fab fragments were diluted to 96 or 48 nM, and rate constants were
measured by injection of at least four serial or parallel (depending on
apparatus setup) 2-fold dilutions at 50 ml/min. Purified Fab fragments were
diluted in running buffer (10 mM HEPES pH 7.4, 0.15 M NaCl, 3 mM
EDTA, 0.005% surfactant P20 on Biacore 2000 and PBS pH 7.2, 0.005%
Tween 20 on Proteon XPR36 as recommended by each manufacturer) and
passed over the chip at 50 ml/min. All data included in this study fitted well
to a single exponential 1:1 interaction model after referencing with a
blank. All measurements were conducted at 25˚C or 37˚C. Association was
measured for 5 min and dissociation for 20–30 min. However, for interactions with very slow off-rates (below 1 3 1024 s21), dissociation was
measured for longer periods of time, up to 16 h, depending on the off-rate.
Global analysis of the serially diluted analyte responses was performed
with either BIAevaluation or Proteon software 2.0.
Statistical analyses
All statistics were performed using SAS JMP version 7.0 or 8.0. Logtransformed experimental data were fitted to the standard equation for
a normal distribution:
!
1
ðx 2 lÞ2
fðxÞ ¼ pffiffiffiffiffiffiffiffiffi exp 2
:
2s2
2ps
Estimates of the geometric mean and the multiplicative SDs describing
the normal distribution were obtained using the following equations:
n
1
x ¼ 10∧
+ ½log10ðxi Þ
n i¼1
1
0
x i2 1=2
1 nh
C
i
+ log10 S ¼ 10 @
A:
x
n 2 1 i¼1
∧B
Results
Ab responses were followed in two human volunteers subjected
to three consecutive boosts with the standard TT vaccine. Vaccinations were separated by at least 1.5 y, and blood was drawn for
analysis 6 d after each challenge, at which time point the circulating
Ab-secreting cells specific for TT are known to peak (16, 17). Using
the Symplex technology (5), Ab repertoires were prepared from
circulating plasma blasts separately after each challenge. Cognate
pairs of VH and VL genes were covalently linked from single
plasma blasts by PCR leading to repertoires representing 400–
2400 different plasma blasts (Table I). Ab genes from 2100 to
3600 bacterial clones from each of the repertoires were expressed
Table I. Results of Symplex repertoire cloning
Donor
TT1
TT1
TT1
TT2
TT2
TT2
Total
Boost
Number
Estimated Number of
Isolated Ab-Producing Cellsa
Number of Bacterial
Clones Screened
Number of TTSpecific Clones
Number of
Clones Sequenced
Number of Unique V Domain
Amino Acid Sequences
Estimated Number
of Clonotypes
V1
V2
V3
V1
V2
V3
400
1,700
2,400
400
1,600
1,400
7,900
3,600
2,100
2,600
3,400
3,500
3,600
18,800
338
427
372
187
95
104
1,523
169
155
176
102
82
83
767
120
108
154
84
69
59
594
30b
50
67
42b
36
29
195
a
Number of single cells where PCR products were obtained were estimated by gel electrophoresis of a representative set of single-cell RT-PCR samples (from 10 to 20% of
the total). Unique V genes were identified based on the deduced amino acid sequences from DNA sequencing. Abs were assigned to the same clonotype if they shared VH, JH,
VK, and JK family segments, H chain CDR3 lengths, and a consensus sequence in CDR3 for both H and L chains.
b
The estimated number of clonotypes from Poulsen et al. (7) (TT1-V1 and TT2-V1) were adjusted from 29 and 40 to 30 and 42, respectively, due to a slightly stricter
clonotype definition.
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Repertoires from the first and the second vaccinations were prepared as
previously described (5, 7). For the third vaccination, the procedure for
sorting single B cells had been optimized to include a marker for CD27.
For all repertoires, single plasma blasts were applied directly into microtiter plates for the Symplex PCR procedure. Briefly, VH and LCk genes
were coamplified in a single PCR reaction. VH and LCk genes were linked
and amplified further in subsequent nested PCR reactions using flanking
primers containing appropriate restriction sites. Cloning and screening of
the first set of repertoires were reported previously (7). Ab V gene pairs
were cloned into an Escherichia coli Fab expression vector, and single
bacterial colonies were grown in 96-well plates where Fab expression was
induced with 0.1 mM isopropyl b-D-1-thiogalactopyranoside (5, 7), after
which supernatants were screened for TT reactivity by ELISA. Repertoires
from the second and third vaccination were cloned into a mammalian Fab
expression vector (14), and single Ab clones were expressed by transient
transfection of HEK293 cells in 384-well plates. Supernatants were harvested and screened for TT reactivity. Screening using the two expression
systems worked equally well and yielded a compatible frequency of hits
with similar genetic diversity indicating no significant screening bias associated with the expression system (data not shown). A compatible
number of TT-positive clones were selected for DNA sequencing of variable genes (Table I; GenBank accession numbers: H chains, JN110463–
JN111216; L chains, JN111217–111975; http://www.ncbi.nlm.nih.gov/
genbank/). The deduced VH-Vk amino acid sequences were aligned and
grouped into clusters according to sequence homology. For each group,
the V-D-J usage and location of somatic mutations were determined by
alignment with germline sequences using the International ImMunoGeneTics (IMGT, http://www.imgt.org) sequence directory (15). Ab clones
were selected for kinetic characterization based mainly on representation
of the genetic differences within the repertoire as well as on homology to
Abs from previous repertoires from the same donor to follow the affinity
maturation progress within a single genetic cluster. Fab fragments of the
first set of repertoires were produced in up to 1-l E. coli cultures including induction of expression with 0.1 mM isopropyl b-D-1-thiogalactopyranoside overnight. Fab fragments from the second and third set of
repertoires were produced in 50–200 ml cultures of HEK293 cells transiently transfected with Ab DNA. Fab fragments were purified using a
mini spin column kit with Protein L beads (Thermo Fischer Scientific).
The concentration of purified Fab fragments was determined by an indirect
immunoassay.
Surface plasmon resonance
The Journal of Immunology
as Fab fragments and screened for TT binding, and a comparable
number of positive clones were picked for DNA sequencing and
functional characterization. As previously described (7), V and J
gene segment usage and somatic mutations were determined by
aligning VH and VL gene sequences to the IMGT database (15).
The amino acid sequences of 594 unique TT-specific Ab clones
were analyzed and estimated to originate from at least 195 different
naive B cell progenitors (termed clonotypes). The entire Ab panel
was highly diverse and contained germline gene segments from
all the major families of VH, JH, VK, and JK except for the rarely
found VK6 (see Supplemental Table 1a and 1b).
Despite repeated Ag challenge and consequently consecutive
rounds of somatic mutations and affinity selection, the overall
number of somatic mutations present in each repertoire remained
constant for each donor (Fig. 1A–C). Thus, the maximum tolerated
level of somatic mutations appeared to have been reached. Statistical analysis of the combined distribution of amino acid so-
matic mutations in all six repertoires indicate a normal distribution
around clearly defined mean values of 13.2, 7.3, and 20.5 for VH,
VL, and the combined repertoire, respectively. Previous reports on
somatic mutations (8, 18–21) fall within the presently observed
limits, which can thus be regarded representative for a fully matured response.
The number of unique clonotypes identified in each repertoire
varied between 29 and 67 (Table I), and the maximum likelihood
estimates of the overall repertoire sizes were determined as previously reported (7, 22) (Fig. 1D). It appears that Ag-induced
human IgH-VK repertoires do not exceed of the order 100 clonotypes (7). As the Ag is not considered to impose any restrictions
to the observed responses, the observed limitation in repertoire
sizes is likely to be intrinsic to the immune system when
responding to large, structurally complex Ags (5, 11, 21, 23).
Approximately two thirds of the clonotypes in the TT Ab donor
2 repertoires (TT2) were found associated with only a single
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FIGURE 1. Statistical analysis of
the frequency of somatic amino acid
mutations in V gene segments and
repertoire size. A–C, The number of
somatic mutations for H chains (A), L
chains (B), and heavy and light pair
combined (C) are plotted for each
repertoire (indicated below). Quantile
box plots show distributions of the full
data set containing all six repertoires.
The box plots show the maximum,
minimum, and median values, the 25th
and 75th interquartile values, and the
90% and 10% percentiles. The diamonds mark the mean with a 95%
confidence interval. To the far right,
distributions are shown as histograms
including a superimposed fitted normal
distribution profile. “n” indicates the
number of unique amino acid sequences in each data set. D, Analysis of
repertoire sizes. The darker shade
(bottom) represents the number of
clonotypes observed in at least two of
the repertoires from each donor. The
lighter shade (top) represents the clonotypes that are uniquely associated
with a single repertoire. Diamonds illustrate statistical maximum likelihood
estimates of repertoire sizes derived
statistically from the total number of
unique sequences and the number of
clonotypes from each repertoire (7,
22).
3
4
LIMITS FOR HUMAN Ab RESPONSES
vaccination event, and this fraction appeared to increase for TT Ab
donor 1 repertoires (TT1) as vaccinations progressed (Fig. 1D).
Furthermore, several clonotypes unique to the TT1 repertoires
carried no somatic mutations, notably after the second booster
vaccination. Together, this suggests a constant influx of new clonotypes from the naive repertoire to an already existing repertoire.
Therefore, despite repeated exposure, Ab responses against complex Ags remain unrestricted and dynamic rather than converge
Table II. Biological constants for affinity maturation at different temperatures
Temperature (˚C)
25
37
Parameters
kon (M21 s21)
x*, geometric mean
68% upper CI (x*·s*)
68% lower CI (x*/s*)
s*, MSDc
x*, geometric mean
68% upper CI (x*·s*)
68% lower CI (x*/s*)
s*, MSDc
2.0 3 10
1.2 3 106
3.1 3 104
6.4
1.6 3 105
7.6 3 105
3.5 3 104
4.6
5
koff (s21)
25
7.0 3 10
2.6 3 1024
1.9 3 1025
3.7
1.7 3 1024
5.5 3 1024
5.0 3 1025
3.3
KD (M)a
210
3.4 3 10
2.9 3 1029
3.9 3 10211
8.6
1.0 3 1029
7.6 3 1029
1.3 3 10210
7.6
t1/2 (min21)b
165
619
44
3.7
70
232
21
3.3
Values were obtained by fitting the standard equation for a normal distribution to log10 transformed experimentally determined data sets. MSD, multiplicative standard deviation.
a
KD was calculated as koff/kon.
b
t1/2 was calculated as ln(2)/(koff/60).
c
MSDs are unit-less.
CI, confidence interval.
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FIGURE 2. Limits for affinity maturation measured at 25˚C. A–C, Experimentally determined kon (A), koff (B), and calculated KD (C) values are plotted
for each repertoire as indicated. Medians are shown as black bars. A two-way ANOVA was conducted for each data set (on-rates, off-rates, and affinities) to
test for differences between repertoires. The arrow indicates that the off-rate of this particular Ab was too slow to measure accurately using surface plasmon
resonance. Hence, this data point only indicates an upper limit for the off-rate and affinity. D–F, Statistical analysis of the distribution of binding constants.
Distributions of log10 transformed kon (D), koff (E), and calculated KD (F) plotted as normal quantile plots (upper panels) and histograms (lower panels).
Data from all six repertoires were combined in the analysis of on-rate, and data from the last two vaccinations were combined for the analysis of the
distribution of off-rates and affinities. The log10 transformed data were fitted by the normal distribution to identify the limit for affinity maturation on
kinetic constants. The horizontal line in the normal quantile plots represents the mean, and the curved dotted lines are 95% confidence intervals.
The Journal of Immunology
toward a few clonotypes with optimal binding properties, as it has
been reported for hapten-driven responses (24–27).
To determine the progression in affinity maturation, kon and koff
were determined at 25˚C for a genetically diverse set of 19–35
Abs from each repertoire (Fig. 2A–C). The differences between
the six repertoires in distributions of kon values were not statistically significant, indicating that the ceiling for maturation of kon
had already been reached prior to the first booster vaccinations of
this study. This is in accordance with the Danish child vaccination
program, which involves at least four tetanus immunizations. To
quantify the limit for affinity maturation of kon, koff, and KD, selected data sets were combined and analyzed statistically (Fig.
2D–F, Table II). The joint distribution of kon appeared log-normal
with a geometric mean of 2.0 3 105 M-1 s21. For both donors,
5
repertoires from the first vaccination had significantly faster average koff (TT1: p = 0.001; TT2: p , 0.001) indicating that the
limit for maturation of koff was first reached after the second
vaccination. Thus, to quantify the limit for affinity maturation of
koff, the four data sets from the last two vaccinations were combined for statistical analysis. They showed a clear log-normal
distribution with a geometric mean at 7.0 3 1025 s21. As a consequence of the relatively dispersed and fully matured kon, differences between repertoires were insignificant for KD. The
combined average KD from the second and third vaccinations was
determined to be 3.4 3 10210 M.
To determine the limits for affinity maturation at physiologically
relevant temperature, the rate constants were determined at 37˚C
for a representative set of 50 Abs from the last two vaccinations
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FIGURE 3. Limits for affinity maturation measured at 37˚C. A–C, Binding constants kon (A), koff (B), and calculated KD (C) were determined from a set
of 50 Abs evenly selected from the four repertoires of the last two booster vaccinations. D–F, Statistical analysis of the distribution of binding constants
measured at physiological temperature as presented in Fig. 2. The superimposed lines indicate the normal distribution determined at 37˚C (solid) and 25˚C
(dotted).
6
from both donors (Fig. 3A–C). As observed for measurements at
ambient temperature, data were log-normally distributed around
clearly defined mean values (Fig. 3D–F). The geometric mean for
kon was not affected by the change in temperature. In contrast, the
koff geometric mean value increased 2.4-fold to 1.7 3 1024 s21,
which corresponds with a drop in average interaction t1/2 from 165
min to 70 min when binding at physiological temperature. Combined, this gave a 3.0-fold change in the mean KD leading to an
average affinity of 1.0 3 1029 M (Table II).
Discussion
after the second booster vaccination. The observed separate maturation of kinetic rate constants supports that maturation of Ab
responses is kinetically rather than thermodynamically controlled
(2, 3, 29) implying, as proposed by Foote and Eisen (12), that
clonal selection by on-rates and off-rates occurs through independent mechanisms. Furthermore, the identified kinetic mean
constants at physiological temperature are in accordance with the
proposed theoretical ranges (12) although the relatively long mean
half-life at physiological temperature of 70 min suggests that apart
from Ag internalization, with a t1/2 of 8 min, additional factors
such as competition for Ag in germinal centers (30, 31) could influence the affinity maturation process.
We hereby report the experimental determination of the limits
for Ab affinity maturation and repertoire diversification in single
individuals in response to repeated vaccinations. The reported
biological constants can be used to evaluate the maturation level
of Ab repertoires, polyclonal sera, and mAbs in particular and
are hence of value in basic immunological science as well as in
Ab drug discovery and vaccine development.
Acknowledgments
We thank Lars S. Nielsen, Per-Johan Meijer, Klaus Koefoed, Mette Thorn,
and Johan Lantto for advice and critical discussions.
Disclosures
All authors are employees (with equity interests) or former employees of
Symphogen.
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To determine the natural boundaries for maturation of human Abs
in response to Ag, individual Ab repertoires were made from two
human donors after each of three booster vaccinations with TT.
Repertoires were characterized at the clonal level to make a
comprehensive genetic and functional analysis of evolving Ab
responses against a well-defined Ag.
As previously reported for the repertoires from the first vaccinations (7), Abs were generally extensively mutated, and within
each repertoire it was not possible to observe any correlation
between binding strength and level of somatic mutations indicative of highly matured responses. Furthermore, the average
level of somatic mutations did not change in the course of this
study demonstrating that the maximum tolerated level of somatic
mutations had already been reached during the preceding routine
vaccination program. The L chain VK genes accumulated on average 7.7 and 6.8 aa transitions and H chain VH genes accumulated on average 14.9 and 11.5 aa transitions for donor TT1 and
TT2, respectively. The difference in mutational level of VH repertoires between donors is significant (p , 0.01) and can be
explained by allelic variations in VH gene segments relative to the
IMGT reference database (15). Nevertheless, as the accumulation
of somatic mutations occurs irrespective of the particular Ag in
use, the peak average of 20 aa transitions per variable domain
appears to represent an average measure for the maximal level
of degeneracy tolerated by an evolving Ab repertoire.
Ab repertoires remained genetically dynamic and diverse in
response to the repeated exposures to the TT vaccine. Approximately two thirds of the B cell clonotypes were uniquely associated
with a single vaccination event. This parallels previous observations in hapten responses (24) and supports a compartmentalization of the B cell response in oligoclonal germinal centers (25,
27). The most likely immunological significance of this dynamic
behavior is that it provides an efficient countermeasure to the
constant genetic evolution of pathogenic microorganisms. Compartmentalization would also explain the apparent restrictions in
repertoire size of the order 100 clonotypes with the limiting factor
being the actual number of germinal centers formed during an
immune response.
For all repertoires, the distribution of binding constants fitted well
to log-normal distribution profiles with clearly defined medians and
unit-less multiplicative standard deviations (MSDs) ranging from 3.7
to 8.6. Compared with log-normal distributions in other biological
systems, where MSDs usually range from 1.1 to 3.2 (28), Ab repertoires can be considered strongly skewed toward log-normal behavior. Therefore, given the good fit of the statistical analyses, it
appears meaningful to use mean values as biological constants
describing the observed boundaries for affinity maturation.
The distribution of on-rates did not vary significantly between
vaccinations indicating that maximal maturation of this binding
parameter had already been reached prior to this study. In contrast,
the distribution of off-rates improved significantly as a result of the
second vaccination but remained unchanged thereafter. Thus, for
both donors, the Ab repertoires could be considered fully matured
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