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PopulationsSudden Collapses of Germinal Center B CellNonsynchronized Growth and Suggest Broad Volume Distributions Indicate

Schuchhardt and Michal Or-GuilWeiser, Werner Zuschratter, Michael Sibila, Johannes Nicole Wittenbrink, Tom S. Weber, Anke Klein, Armin A.

http://www.jimmunol.org/content/184/3/1339doi: 10.4049/jimmunol.0901040January 2010;

2010; 184:1339-1347; Prepublished online 6J Immunol 

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0.DC1http://www.jimmunol.org/content/suppl/2010/01/06/jimmunol.090104

Referenceshttp://www.jimmunol.org/content/184/3/1339.full#ref-list-1

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Print ISSN: 0022-1767 Online ISSN: 1550-6606. Immunologists, Inc. All rights reserved.Copyright © 2010 by The American Association of1451 Rockville Pike, Suite 650, Rockville, MD 20852The American Association of Immunologists, Inc.,

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The Journal of Immunology

Broad Volume Distributions Indicate NonsynchronizedGrowth and Suggest Sudden Collapses of Germinal CenterB Cell Populations

Nicole Wittenbrink,*,† Tom S. Weber,*,† Anke Klein,*,† Armin A. Weiser,*,†

Werner Zuschratter,‡ Michael Sibila,*,x Johannes Schuchhardt,|| and Michal Or-Guil*,†

Immunization with a T cell-dependent Ag leads to the formation of several hundred germinal centers (GCs) within secondary lym-

phoid organs, a key process in the maturation of the immune response. Although prevailing perceptions about affinity maturation

intuitively assume simultaneous seeding, growth, and decay ofGCs, our previousmathematical simulations led us to hypothesize that

their growth might be nonsynchronized. To investigate this, we performed computer-aided three-dimensional reconstructions of

splenic GCs to measure size distributions at consecutive time points following immunization of BALB/c mice with a conjugate of

2-phenyl-oxazolone and chicken serum albumin. Our analysis reveals a broad volume distribution of GCs, indicating that individual

GCs certainly do not obey the average time course of the GC volumes and that their growth is nonsynchronized. To address the cause

and implications of this behavior,we comparedour empirical datawith simulations of a stochasticmathematicalmodel that allows for

frequent and sudden collapses ofGCs. Strikingly, thismodel succeeds in reproducing the empirical average kinetics ofGCvolumes as

well as the underlying broad size distributions. Possible causes of GC B cell population collapses are discussed in the context of the

affinity-maturation process. The Journal of Immunology, 2010, 184: 1339–1347.

The humoral arm of the adaptive immune response iscrucially important for fighting invading pathogens be-cause it leads to the generation of high-affinity Abs. These

Abs arise as a consequence of Ag-driven B cell differentiationwithin the unique environment of germinal centers (GCs), where Bcells undergo clonal expansion, somatic hypermutation (SHM),antigenic selection, class switch recombination, and affinity mat-uration (1–5). In addition, plasma cell commitment and memory Bcell formation are linked to GCs (6–8).During T cell-dependent immune responses, following a first

exposure to Ag, GCs form de novo in secondary lymphoid organs,grow, and eventually regress. The overall GC response involves anensemble of coexisting GCs, several hundreds in the case of themurine spleen (9). Flow cytometric and histological observationsof formation and decay of GCs in rodents revealed a commonlyaccepted temporal evolution of the primary GC response; theprimary GC response spans ∼3 wk, first becoming detectable by

day 4 postimmunization, peaking at around days 10 to 12, andthen gradually decaying (9–14). However, the data generated sofar [e.g., number of GCs (9, 11, 14), relative volume occupied byGCs (10, 14), mean area and diameter of GCs (15), and frequencyof lymphocytes with a GC B cell phenotype (12)], can only de-termine the average kinetics of the GC ensemble (eGC) withcertainty, but not necessarily the growth kinetics of individual GCs(iGCs). The growth kinetics of iGCs can only be inferred from theaverage eGC kinetics if iGC growth is synchronized (i.e., if alliGCs show a kinetic behavior following average eGC kinetics).Therefore, the so-far unaddressed issue of synchronization of GCgrowth is of major importance. If GCs grow in a synchronizedmanner, their volume distribution should be quite narrow at eachtime point of the immune response. By contrast, broad GC volumedistributions would indicate nonsynchronized growth, therebyunequivocally ruling out the possibility of inferring iGC growthkinetics from average eGC kinetics.In this study, we analyzed GC size distributions and the occu-

pation of follicular niches within the microenvironment of themurine spleen following primary immunization of BALB/c micewith the hapten 2-phenyl-oxazolone (phOx) coupled to the carrierprotein chicken serum albumin (CSA). Time-dependent changes inthe frequency of follicular niches occupied by GCs indicated thatnewly formed GCs emerge over an extended period of time.Moreover, three-dimensional (3D) reconstruction of splenic GCsrevealed that the volume distributions of iGCs are strikingly broadand are further characterized by high frequencies of rather smallGCs.Taken together, our results demonstrate that thegrowthof iGCsis nonsynchronized; thus, all attempts to deduce iGCgrowthkineticsfrom average eGC kinetics are prone to failure. In addition, com-paring our empirical data on GC volume distributions with simu-lation data from a stochastic mathematical GC growth modelrevealed that sudden, fast, and frequent collapses of GCs explain theempirical GC volume distribution and might play an important rolein the affinity-maturation process.

*Systems Immunology Group, Institute for Theoretical Biology, Humboldt Univer-sity Berlin; †Research Center ImmunoSciences, Charite–Universitatsmedizin Berlin;xBernstein Center for Computational Neuroscience; ||MicroDiscovery GmbH, Berlin;and ‡Leibniz Institute for Neurobiology, Magdeburg, Germany

Received for publication March 31, 2009. Accepted for publication December 1,2009.

This work was supported by the Volkswagen Foundation and the Bundesministeriumfur Bildung und Forschung (Germany) Grant 0315005B.

Address correspondence and reprint requests to Dr. Michal Or-Guil, Institute for The-oretical Biology, Systems Immunology Group, Humboldt University Berlin, Invalid-enstr. 43, D-10115 Berlin, Germany. E-mail address: m.orguil@biologie.hu-berlin.de

The online version of this article contains supplemental material.

Abbreviations used in this paper: 3D, three-dimensional; CSA, chicken serum albu-min; eGC, ensemble of germinal centers; FDC, follicular dendritic cell; GC, germinalcenter; iGC, individual germinal center; phOx, 2-phenyl-oxazolone; ROI, region ofinterest; SHM, somatic hypermutation.

Copyright� 2010 by The American Association of Immunologists, Inc. 0022-1767/10/$16.00

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Materials and MethodsMice and immunization

Six to eight-week-old BALB/c mice were immunized with a single i.p. in-jection of 100mg phOx coupled toCSA at a ratio of 10:1 and precipitated ontoalum, as described previously (16). To ensure that the examined GCs are theresult of the immunizationprotocol,wedrewsamples and examined spleens ofunimmunized mice that were housed in the same cage with immunized mice.In unimmunized controls, we were not able to record GC size distributions,because environmental Ag-induced GCs were observed only occasionally, invery low numbers, and were of very small size. BALB/c mice were bred andmaintained under specific pathogen-free conditions at the facilities of theBundesinstitut fur Risikobewertung, Berlin. All animal experiments wereperformed in accordance with institutional, state, and federal guidelines.

Immunofluorescence

For two-dimensional cross-sectional evaluation of GC growth kinetics,cohorts of immunizedmice (n=2–4)were killed at days 4, 6, 8, 10, 12, 14, 16,18, and 21 postimmunization. Spleens were removed, bisected, frozen inTissue-Tek OCT compound (Sakura Finetek, Zoeterwoude, The Nether-lands), and stored at270˚C. Longitudinal sections of 10-mm thickness werecut on a cryostat microtome and mounted onto Superfrost Plus glass slides(Roth,Karslruhe, Germany). The sectionswere air-dried for 1 h, fixed in coldacetone for 10 min, air-dried again for$2 h, and stored at220˚C until fur-ther analysis. To establish the 3D volumetric growth kinetics of splenic GCs,cohorts of immunized mice (n = 3) were killed at days 6, 10, and 14 post-immunization. Spleens were removed and processed identically, except thatwhole spleen sections were cut as longitudinal sections of 25-mm thickness.

Prior to staining, spleen sections were pretreated by fixation in ice-cold 1%paraformaldehyde for 30 min and permeabilization in ice-cold 1% sodiumcitrate containing 1% Triton X-100 (Promega, Mannheim, Germany) for 2min. Spleen sectionswere blocked in PBScontaining 3%BSA for 30min. Fortwo-dimensional cross-sectional evaluation of GC growth kinetics, spleensections were triple stained with unconjugated rat anti-mouse Ki-67 (cloneTEC-3, Dako, Glostrup, Denmark), biotinylated anti-mouse follicular den-dritic cells (FDCs) (clone FDC-M2, ImmunoK, Abingdon, U.K.), and AlexaFluor 488-labeled anti-mouse CD3 (clone KT3, AbD Serotec, Dusseldorf,Germany). Bound Ki-67 and biotinylated FDC-M2 Abs were detected usingAlexa Fluor 647-labeled anti-rat IgG and Alexa Fluor 546-conjugatedstreptavidin (both from Invitrogen, Karslruhe, Germany), respectively.

For 3D reconstruction of GCs, whole spleen sections were quadruplestained for proliferating cells, FDC networks, T cells, and macrophages bychronologically incubating them with mixtures of Abs as follows: 1) un-conjugated rat anti-mouse Ki-67 (clone TEC-3, Dako), 2) Alexa Fluor 647-labeled anti-rat IgG (Invitrogen), 3) Alexa Fluor 488-labeled anti-mouseCD3 (clone KT3, AbD Serotec), 4) unconjugated rabbit IgG anti-AlexaFluor 488 (Invitrogen) and biotinylated anti-mouse FDCs (clone FDC-M2,ImmunoK), and 5) Alexa Fluor 594-labeled anti-rabbit IgG (Invitrogen),Alexa Fluor 555-conjugated streptavidin (Invitrogen), and Alexa Fluor488-labeled anti-mouse CD68 (clone FA-11, AbD Serotec). Stained sec-tions were mounted in FluoromountG (Southern Biotechnology Asso-ciates, Birmingham, AL).

Two-dimensional analysis of cross-sectional GC size

For each spleen specimen, two independent tissue sections (S1 and S2,distance$ 400 mm) were triple stained for Ki-67+ proliferating cells, FDCnetworks, and T cells, as described above. Digital images of GCs, as iden-tified by Ki-67 reactivity and anatomical location, were acquired on a LeicaDM Ire2 confocal laser-scanning microscope using a340 objective and theLeica LCS software (Leica, Wetzlar, Germany). GC boundaries were man-ually assigned to each GC and saved as regions of interest (ROIs). The cross-sectional size of GCs was obtained by measuring the area of ROIs. In ad-dition, the number of Ki-67+ cells within assigned ROIs was determined byapplying an adapted version of the Nucleus Counter Plugin of the ImageJsoftware (National Institutes of Health, Bethesda, MD) (17).

3D reconstruction of splenic volumes

For each spleen specimen, seven serial sections (s01–s07), spaced at intervalsof 50 mm and spanning a total thickness of 300 mm, were quadruple stainedfor Ki-67+ proliferating cells, FDC networks, T cells, and macrophages, asdescribed above. Digital images of whole spleen sections were capturedwith a310 objective by performing meander scans using a Leica TCS SP2confocal microscope equipped with a motorized x/y stage (Merzhauser,Wetzlar, Germany) that was automatically actuated by the Arivis browsersoftware (Arivis, Rostock, Germany). Images of serial spleen sections wereintegrated as separated layers into a Photoshop file (Adobe Systems, SanJose, CA). Follicular niches were marked by consecutive numbering and

traced throughout serial spleen sections where their status (i.e., empty [FDCnetwork only] or occupied [FDC network + GC]), was recorded. Computer-aided 3D reconstruction was performed for all GCs that were wholly con-tained within or spanned the overall image series. Following manual seg-mentation of GCs, as defined by Ki-67 staining using the ImageJ software(17) and a binarization of the segmented outline, they were aligned slice-wise, according to their center of mass, using the 3D reconstruction softwareAmira (Mercury Computer Systems, Chelmsford, MA). After alignment,a principal component analysis was performed on the filled outlines inMatlab (MathWorks, Ismaning, Germany), resulting in three orthogonal ei-genvectors. The length and angles of the eigenvectors were visualized asellipsoids (Amira), and the volume of the manual segmented data served asa constraint. Volumes of fitted ellipsoids (VE) were calculated according tothe formula VE ¼ 4

3×p×R1×R2×R3, in which R1, R2, and R3 refer to the half-axes of ellipsoids as given by the lengthof the three eigenvectors. Thenumberof B cells per GC was estimated using the density of B cells per cross-sec-tional GC area (0.0116 cells/mm2, Supplemental Fig. 1) recorded duringcross-sectional evaluation. Histograms of the distribution of GC volumeswere calculatedwith restriction toGCs that intersect the central section (s04).

Stochastic simulation of GC seeding and growth kinetics

Tomodel the B cell population kinetics of iGCs, we used an extended Rickerdiscrete population model that involves two phases of iGC growth: freegrowth and competitive growth.

Free growth phase:

Ptþ1 ¼ Pt exp

�lnð2Þ×Dttfree

�with 

P0;free ¼ M   for  Pt � Pcritical:

ð1Þ

Competitive growth phase:

Ptþ1 ¼ Pt exp

�lnð2Þ×Dttcomp

�12

Pt

Ki

��x: ð2Þ

During the freegrowthphase, iGCs thatwere foundedby adefinednumberM of B cells grow exponentially and B cells proliferate with a constant di-vision time tfree (Equation 1) until iGCs exceed the critical size Pcritical andsubsequently enter the competitive growth phase. The critical sizePcritical ¼ M2j is defined by the number of generations j, where j is drawnfrom a normal distribution Nðm;s2Þ. After iGCs have entered the competi-tive growth phase, they grow according to a Ricker discrete time populationmodel (18) extended by a multiplicative noise term (x) to account forfrequently large and unpredictable impacts on the B cell population size dueto SHM and (e)migration of B cells. In Equations 1 and 2, Pt is the B cellpopulation size of an iGC at time t, Ki is the carrying capacity of the fol-licular niche, and tcomp is themaximal division time. The carrying capacitiesKi were linearly interpolated between days i ¼ 6;  10;  14. The noise termxt is drawn from a uniform distribution U N (0, 1)t that represents a randomvalue between ½0; 1�.

The ensemble kinetics of GCs was attained assuming a constant seedingprobability ε of follicular niches and by carrying out consecutive MonteCarlo simulations of 100,000 iGCs according to the two-phased modelspecified above, in which the time resolutionDtwas 1.2 h for the free growthand 24 h for the competitive growth phase. Simulated B cell population sizesof iGCs were retrieved and recorded in the form of rank plots at days 6, 10,and 14 after immunization. These rank plots were subsequently comparedwith rank plots of the experimentally obtained data at the correspondingtime points. To enable comparison of simulated and experimental data, rankplots were adapted so that the index of the smallest-sized GC from theexperimental data set and the simulated GC with the most similar size andthe maximal index values of both sets had the same values. The first measureaccounts for the smallest safely empirically detectable GCs. The fittedmodel parameters, as summarized in Table I, resulted in an excellent matchover two orders of magnitude.

ResultsTwo-dimensional cross-sectional evaluation reveals robustaverage growth kinetics of eGCs based upon a notable sizedistribution of iGCs

The kinetics of GC growth was initially assessed by quantitativeanalysis of cross-sectional GC size in spleens of phOx-CSA–challengedBALB/cmice at different timepoints after immunization.

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GCs were identified as clusters of Ki-67+ proliferating cells in closeproximity to FDC networks and adjacent to T cell zones (Fig. 1A).After manual assignment of GC boundaries (Fig. 1A), enclosedcross-sectional areas andnumbers ofKi-67+ cellswere automaticallymeasured as described inMaterials andMethods. The number of Ki-67+ cells correlated with the cross-sectional area of GCs at all timepoints analyzed (Supplemental Fig. 1). As a result, the density of Bcells per cross-sectional GC area was estimated as 0.01166 0.0008cells/mm2. In total, we evaluated 1093 GCs in 44 sections derivedfrom 23 mice (Table II).Well-established GCs, typically of very small size (3786 6 271

mm2), were first detected on day 4 after immunization (Fig. 1B).The mean size of GCs subsequently increased steeply, reachinga maximum at day 10 (18,551 6 2,134 mm2) and then graduallydeclining until day 21 (10,397 6 1,274 mm2) (Fig. 1B). Thevariance among mice at the same time point or spleen sectionsobtained from the same animal was small (Fig. 1B and data notshown). However, a wide range of GC sizes was observed withinindividual spleen sections (e.g., 1,300–70,000 mm2 at day 8;Fig.1C). Notably, the cross-sectional area distribution of splenicGCs was very robust for the cohorts of mice analyzed at each timepoint (example for day 8 after immunization shown in Fig. 1C).Additionally, the area distribution of cross-sectional GCs wasshown to be subject to time-dependent changes. We observeda marked shift toward higher frequencies of large GCs from days4–8 after immunization (Fig. 1D); the area distribution remainedin an almost steady-state between days 8 and 14. After day 14, thearea distribution gradually shifted back toward smaller GCs. Inaccordance with other studies, the background level of GCswithout immunization was minimal, indicating that the examinedGCs were induced by immunization (19).

3D approach to evaluating GC growth kinetics

Our previous computer simulations showed that the experimentallyrecorded cross-sectional profile of GC growth is consistent withdifferent hypothetical ensemble kinetics, including marked non-synchronization of GC formation and growth (20). Therefore,cross-sectional profiling alone is inconclusive and, in general, isinsufficient to assess the growth behavior of GCs. Because wewere particularly interested in assessing the synchronization ofGC formation and growth, we turned to 3D evaluation of murinespleens. For this purpose, series of serial longitudinal spleensections were quadruple stained for proliferating cells, FDC net-works, T cells, and macrophages. Subsequently, composite mi-

crophotographs of whole spleen sections were obtained byconfocal microscopy in conjunction with meander scan technol-ogy (Fig. 2A). Three spleens were examined each at days 6, 10,and 14 after primary immunization with phOx-CSA, with sampledsplenic volumes ranging between 9.2 and 14.9 mm3 (Table III).The quadruple staining resulted in high morphological resolutionof the spleen, including demarcation of red and white pulp regionsand authentic identification of follicular niches (empty FDC net-works or FDC networks occupied by GCs) (Fig. 2). The totalnumber of follicular niches identified per spleen sample rangedbetween 206 and 322, with no obvious differences related to thetime after immunization (Table III). The high morphologicalresolution of quadruple-stained spleen sections also contributedpositively to tracing follicular niches throughout the sampledsplenic volumes (Fig. 2B), with its overall efficiency rated as.95% (Table III).

Newly formed GCs emerge over an extended period of time

The induction of GC formation after antigenic challenge is stillpoorly defined, in that the time frame when new GCs arise isunknown. To address this, we examined the density and occupationof follicular niches within murine spleens at days 6, 10, and 14 afterprimary immunization with phOx-CSA, using the 3D approachillustrated in Fig. 2 and outlined above. The time courses of thedensities of total, occupied, and empty follicular niches (or thosein which occupation remained below the detection level) are il-lustrated in Fig. 3. Densities are given as the numbers of follicularniches per 12 mm3, corresponding to the average volume ana-lyzed per spleen specimen (Table III). The overall density offollicular niches proved to be remarkably fixed, not even changingduring progression of the immune response (231 6 13, 234 6 35,and 225 6 24 at days 6, 10, and 14, respectively; Fig. 3). How-ever, the density of follicular niches occupied by GCs increasedsignificantly from 128 6 25 at day 6 to 189 6 27 at day 10 (p =0.024; Student t test); thereafter, the density decreased slightly to177 6 29 at day 14. Accordingly, the frequency of follicularniches occupied by GCs continued to increase from day 6 (56%)to day 10 (81%) and was rather stable by day 14 (79%). In-terestingly, the frequency of empty follicular niches was high,even at days 10 and 14 after immunization (19% and 21%, re-spectively; Fig. 3). Thus, the formation of new GCs was not re-stricted to the very early phase of the immune response; itcontinued for an extended period of time, even between days 6and 10 postimmunization.

Table I. Parameters for the two-phased model of GC seeding and growth kinetics

Parameter Symbol Value

Number of founder B cells M 3Seeding probability of empty follicular niches per 1.2 h ε 0.013Free growthDivision time (h) tfree 9.65Mean number of generations m 6.35Variance of the mean number of generations s2 1.8

Competitive growthDivision time (h) tcomp 13.20Carrying capacity of follicular niches at day 6 K6 21,445Carrying capacity of follicular niches at day 10 K10 35,420Carrying capacity of follicular niches at day 14 K14 11,914

The parameter value M was chosen according to the literature (10, 42). Assuming reasonable initial values, all otherparameters were fitted by minimizing the sum of the mean distances between simulated and experimental rank plots

(D ¼ Sday

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

indexmaxSindexðsimulated2measuredÞ2

q;  day ¼ 4;  6;  10;  14). Day 4 GCs were assumed to be spherical,

and their volume (V ) was calculated according to their cross-sectional area (A) as V ¼ 43p

ffiffiffiffiffiffiffiffiffiðApÞ3

q. Notably, the values of the

fitted model parameters for the division times of GC B cells (tfree and tcomp) fully agree with published experimental values(34–36).

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3D volumetric evaluation reveals a considerable volumedistribution of GCs

We performed 3D reconstructions of GCs on serial sections fromthree spleen specimens at days 6, 10, and 14 postimmunization. Forreasons of feasibility and to facilitate inspection, 3D reconstructionswere confined to thoseGCscompletely containedwithinor spanningthe overall series of serial sections. Lateral views of 3D recon-structions and detail enlargements from representative spleenspecimens at days 6, 10, and 14 postimmunization are shown in Fig.4A. The actual numbers of three-dimensionally reconstructed GCs,as well as their mean, range, and total volume, are summarized inTable III. Although the numbers of reconstructed GCs fluctuatedwith respect to the three spleen specimens analyzed per time point(e.g., 23, 27, and 42 at day 10), no striking differences were detectedfor the different time points analyzed. Naturally, fluctuations in GCnumbers were also reflected by the total volume of the GCs them-

selves (e.g., 55.0, 80.8, and 112.93 106 mm3 at day 10). However,the total volume of reconstructed GCs was significantly lower onday 6 (21.2, 23.1, and 41.13 106 mm3) than on day 10 (55.0, 80.8,and 112.93 106mm3) or day 14 postimmunization (107.4, 40.8, and80.9 3 106 mm3). Likewise, the estimated mean GC volume wassmall for day 6 (0.5 6 0.6, 0.6 6 0.8, and 1.4 6 1.8 3 106 mm3)compared with day 10 (2.4 6 3.5, 3.0 6 4.4, and 2.7 6 3.7 3 106

mm3) and day 14 (2.66 2.8, 2.06 2.1, and 1.66 1.93 106 mm3).The particularly high SDs were due to a nonnormal, right-skeweddistribution of GC volumes (Fig. 5). A striking characteristiccommon to all analyzed spleens is the concomitance of very dif-ferently sized GCs (Fig. 4A). The smallest and largest GCs differedby amaximal factor of 220 on day 6, 2070 on day 10, and 555 on day14 (Fig. 4, Table III). Although the smallest GC volume remainedrather constant during progression of the immune response (0.01,0.01, and 0.02 3 106 mm3 at days 6, 10, and 14, respectively (i.e.,equivalent to GCs comprising ∼25 Ki-67+ cells); the largest valueincreased from day 6 to days 10 and 14 (4.0, 20.7, and 11.1 3 106

mm3). Hence, GCs of rather small volume are not restricted to theearly phase butwere also frequently found at the peak of the immuneresponse. By contrast, larger-volume GCs only occurred at the peakof the immune response.Collectively, the 3D reconstructions of GCs showed that a broad

volume distribution of splenic GCs exists at any time point analyzed(Fig. 5). Although the volume distribution of GCs proved veryrobust for the three mice analyzed at each time point (data notshown), it is subject to fundamental changes over the duration of theimmune response (Fig. 5). The volume distribution of day 6 GCs isnarrow, with 91% of GCs within the smallest size class (between0.01 and 3.53 106 mm3 or between 15 and 4400 GC B cells) (Fig.5). Toward day 10, the GC volume distribution broadens and shiftsin favor of larger-sized GCs. However, the frequency of GCs as-signed to the smallest size class is still high, although decreased(59%). The volume distribution of splenic GCs at day 14 is similarto day 10, but there has been a minor shift back toward smaller-sized GCs (i.e., 71% of GCs fall into the smallest size class).The distributions of GC volumes were not normal; they were

strongly right-skewed as the result of a small frequency of verylarge GCs (Fig. 5). In contrast, GCs comprising ,1254 B cellsaccount for as much as 55%, 40%, and 29% of all GCs at days 6,10, and 14, respectively. The volume distribution of small GCs isbest resolved in logarithmic histograms (Supplemental Fig. 2).

Simulation of GC population kinetics indicates that frequentand large collapses of iGCs might account for the empiricallyobserved broad volume distributions of GCs

To further address the origin of broad volume distributions of GCs,we compared our empirical data with simulation results from a two-phased stochastic Ricker population growth model. In the freegrowth phase of the model, iGCs are first seeded and subsequentlygrow until they finally reach a critical size and enter the competitivegrowth phase. During this second phase, the B cell population ki-netics of iGCs suffer from frequent collapses in population size.Although the classical Ricker map is widely used for modelingpopulation growthunder strong competition for resources (21, 22), itturned out to be unsuitable for reproducing experimental data onGC size distributions because it underestimated the frequency ofsmall-sized GCs (data not shown). Therefore, we extended theclassical Ricker map during the competitive growth phase bya stochastic component accounting for effects other than compe-tition for resources, such as unpredictable events possibly due toSHM and migration. A defining characteristic of the extendedRicker map is that iGCs grow constantly but can suffer multiple,and sometimes, large collapses at any stage during the competitive

FIGURE 1. Two-dimensional cross-sectional evaluation reveals a robust

primary GC response based upon a broad size distribution of GCs. A, GCs

were identified as Ki-67+ cell clusters and by anatomical location in triple

immunofluorescence stainings of proliferating cells (blue, mAb Ki-67),

T cells (green, mAb CD3), and FDC networks (red, mAb FDC-M2). The

cross-sectional size of GCs was measured after manual assignment of GC

boundaries (white selection) using ImageJ software (17). The image shown is

representative of a GC at day 8 after immunization (original magnification

340). Scale bar, 50mm. B, BALB/cmicewere immunized with phOx-CSA,

and spleens were removed at the indicated time points. Two independent

sectionswere stained for each spleen, and the cross-sectional size ofGCswas

recorded as illustrated in A (for details, see Table II). Open circles represent

mean cross-sectional GC sizes of individual mice; the solid line indicates the

average course over time. C, Size distributions of day 8 GCs plotted as cu-

mulative frequencies of cross-sectional GC areas. Each curve refers to one

individual mouse at day 8 postimmunization.D, Time-dependent transitions

of the size distribution illustrated by plotting the cumulative frequencies of

cross-sectional GC areas at different time points after immunization. Each

curve is representative of the entire recorded GCs at the indicated time point

after immunization.

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growth phase (for details see Materials and Methods). Comparedwith other simple deterministic growth models, the extendedRicker map proved to be the mathematical model that best repro-duced the experimental data on GC growth (Supplemental Fig. 3).Monte Carlo simulations of the extended two-phased population

growth model reproduce the empirical data on GC volume dis-tributions at days 4, 6, 10, and 14 after immunization (Fig. 6A–D)for a suitable parameter set as specified in Table I. Our simulationsfurther emphasize that growth kinetics of iGCs can differ sub-stantially from each other, deviating strongly from the averagekinetics (Fig. 6E), which explains the empirically observed broadvolume distributions of GCs. The model’s response to represen-tative variations of the chosen parameter values is shown inSupplemental Table I.

DiscussionWe addressed the issue of synchronization of de novo formation andgrowth of murine splenic GCs by examining the occupation offollicular niches and size distributions of GCs over the duration ofthe primary phOx-CSA response. We showed that the overall GCresponse is characterized by amarked size distribution ofGCs that isrobustbetween individuals but subject to substantial time-dependentchanges. Moreover, the occupation of follicular niches by newlyformingGCswasnot restricted to thevery early stageof the responsebut occurred over an extended period of time, even between days 6and 10 postimmunization.The reported average growth kinetics of the phOx-CSA–induced

GC response (Fig. 1B) is in line with previous studies of the GCresponse in rodents using different Ags (9–11, 15, 23, 24). GCs are

FIGURE 2. 3D approach to evaluation of GC growth kinetics. A, Serial longitudinal spleen sections (s01–s07) spaced at intervals of 50 mm and spanning

a total thickness of 300 mm, were quadruple stained for proliferating cells (blue, mAb Ki-67), FDC networks (white, mAb FDC-M2), T cells (red, mAb

CD3), and macrophages (green, mAb CD68). Entire areas of spleen sections were imaged by meander scans using a 310 objective. Follicular niches, as

identified by FDC-M2 reactivity and anatomical location, were numbered consecutively, and each niche was traced throughout the series of imaged spleen

sections. During tracing, follicular niches were marked as occupied or empty by virtue of the concomitant existence or absence of GCs. B, Follicular niche

tracing for the boxed region in A. Illustrated are image details of the image series s01–s07 shown in A; three occupied niches (GC105, GC108, and GC112)

and one empty niche (N129) are highlighted. Occupied and empty niches were consistently found to span different numbers of spleen sections. The image

series is representative of a spleen obtained 10 d after primary immunization with phOx-CSA. Scale bar, 1 mm (A, B).

Table II. Survey of cross-sectional GC size evaluation

Daya

No. of Evaluated GCs

M1b M2b M3b M4b

+cS1 S2 S1 S2 S1 S2 S1 S2

4 10 17 4 11 426 11 16 19 15 16 35 15 11 1388 18 31 35 45 27 37 19310 27 10 19 31 41 12812 22 16 37 52 12714 27 25 44 12 10816 34 26 50 26 25 16118 21 20 30 39 11021 17 22 19 28 86

1093

aMice were killed at the indicated time points after immunization and spleens were collected.bNumber of GCs evaluated per bisected spleen section. Two to four mice (M1–M4) were analyzed per time point. Two

independent spleen sections (S1 and S2, distance $ 400 mm) were evaluated per individual.cTotal number of GCs evaluated per time point.

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first observed by day 4 after immunization, peak at around day 10

to 12, and then gradually decline. Despite agreeing with previous

reports, our data support the notion that GCs might not be present

for only ∼3 wk, as initially proposed by earlier studies (8, 10), but

might be present for several weeks after immunization (25, 26).

The mean cross-sectional size of GCs at day 21 postimmunization

(10,397 mm2) still accounts for as much as 56% of the peak size of

GCs (18,551 mm2) (Fig. 1B). However, this decline in mean size

does not necessarily imply a reduction in the total number of GCs;

it may also reflect the decreasing frequency of large-sized GCs

(Fig. 1D). Indeed, we still detected a considerable number of

splenic GCs at day 21 postimmunization, a finding that also ap-

plies to studies performed with SRBCs (11, 23). Likewise, al-

though flow cytometric data usually show a decrease in the

frequency of GC B cells from the peak to day 21 (12, 13, 26),

frequencies ∼10 times above the background level have been re-

ported at 2–3 mo postimmunization (25, 26). Hence, we believe

that the previously described phenomenon of ongoing late affinity

maturation of serum Ab and post-GC selection (8) might be at-

tributed to the prolonged presence of a population of rare and

small, and thus, easily overlooked, GCs.As we showed previously, two-dimensional cross-sectional pro-

filing of GCs is insufficient to infer the real size distribution of GCs

(20). To copewith this shortcoming,we directly assessed the kinetics

of GC growth by monitoring the real size of iGCs, estimating their

volumes as revealed by 3D reconstruction of consecutive image

series. Volumetric analyses revealed a broad size distribution of GCs

that ismarkedly right-skewed (mean.median) because of very high

frequencies of small GCs (Figs. 1, 5, Supplemental Fig. 2). This

distribution is by no means a Gaussian distribution. The importance

of this finding is substantial, becausemathematicalmodels of affinity

maturation often rate a selectionmechanism successful only if every

single iGC simulation run reproduces the average eGC kinetics as

closely as possible (27–31). This is equivalent to narrowGC volume

distributions. However, as we showed in this study, this strategy is

flawed because GC volume distributions are not narrow, but, to the

contrary, are strikingly broad. Hence, conclusions drawn from

mathematical models that infer selection mechanisms from GC size

kinetics [e.g., the prediction that competition for T cell help exists

(29)], have to be carefully reconsidered.

At first glance, broad GC volume distributions leave us withvarious potential explanations regarding the underlying kinetics ofiGC growth. The abundance of small GCs might be readily at-tributed to the extended emergence period of new GCs (Fig. 3).However, because this scenario fails to reproduce the high frequen-cies of small GCs, it has to be ruled out. If all GCs existed for ∼3 wkand all reached the maximal size, then around the peak of theresponse, the majority of GCs would be large, as we illustratedpreviously by computer simulations (20). Instead, we provide twoalternative explanations: 1) all iGCs follow the same averagegrowth kinetics, but they differ considerably in their attainedmaximal size and most of them stay small or 2) the growth anddecay of iGCs is nonsynchronized and substantially “faster” thanthe average. With the latter, every iGC may achieve maximal size,

FIGURE 3. Newly formed GCs emerge over an extended period of time.

Changes in the mean densities of total, occupied (GC), and empty follicular

niches are shown over the duration of the primary immune response against

phOx-CSA. Values of individual mice (n = 3 for each time point) are in-

dicated by different symbols. Follicular niches were identified and traced as

outlined in Fig. 2. To improve interpretation, densities are reported as the

numbers of niches per 12mm3, corresponding to the estimatedmean volume

analyzed per spleen (for details see Table III). Significant differences as

calculated by the Student t test are indicated. pp, 0.05.

Table III. 3D evaluation of GC growth kinetics

Daya Volumeb (mm3)

3D Tracing Volume of GC (106 mm3)c

FDCd Efficiency (%)e GCf Mean 6 SD Range +

6 10.8 234 97.0 43 (44) 0.5 6 0.6 0.01–2.2 21.26 13.3 260 95.4 37 (28) 0.6 6 0.8 0.03–3.7 23.16 14.9 322 90.7 29 (15) 1.4 6 1.8 0.06–4.0 41.110 9.2 226 95.6 23 (14) 2.4 6 3.5 0.02–11.7 55.010 14.1 260 99.2 27 (14) 3.0 6 4.4 0.01–20.7 80.810 13.5 247 97.6 42 (22) 2.7 6 3.7 0.01–11.8 112.914 11.3 240 98.7 41 (21) 2.6 6 2.8 0.02–11.1 107.414 10.4 206 87.4 20 (14) 2.0 6 2.1 0.04–9.4 40.814 13.8 264 97.0 50 (28) 1.6 6 1.9 0.02–8.1 80.9

aMice were killed at the indicated time points after immunization, and spleens were collected. For each spleen, a seriesof seven serial sections, spaced at intervals of 50 mm and spanning a total thickness of 300 mm, were stained and analyzedas described in Materials and Methods and illustrated in Fig. 2.

bThe volume of each series of serial sections was estimated by multiplying their mean area by their total thickness (300mm).

cMean, range and total volume (+) of GCs wholly contained within or spanning the overall series of serial sections. Thevolumes of GCs were estimated as described in Materials and Methods.

dTotal number of follicular niches (FDC networks) identified within splenic volumes.eEfficiency of 3D tracing of follicular niches. Indicated are the percentages of follicular niches that could be unambig-

uously traced throughout the analyzed splenic volume.fNumber of three-dimensionally reconstructed GCs that were wholly contained within or spanned the overall series of

serial sections. Values in parentheses indicate the percentage in terms of the total number of identified GCs.

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but it remains large for only a short period of time. In support ofthe first explanation, Kleinstein and Singh (32) introduced a sto-chastic version of the Oprea-Perelson GC growth model (33) in2001. In this study, we propose a new stochastic populationgrowth model in favor of the second explanation.According to the model of Kleinstein and Singh (32), many GCs

remain small if the survival of GC B cells depends on the affinity oftheir BCRs, if the probability of generating high-affinity mutants islow, and when selection is driven by escape from apoptosis.However, a strong, but experimentally unvalidated, prediction oftheir model is that iGC size is positively correlated with the level ofaffinity maturation (32).In our proposed stochastic population growth model, new GCs

emerge over a prolonged period of time and subsequently grow byB cell proliferation. With increasing size, B cell proliferationbecomes more and more restrained by competition for a commonresource, whereas sudden and fast collapses of iGCs may occurstochastically. In this scenario, GCs may achieve maximal size, but

remain large for only a short period of time. In contrast to the modelof Kleinstein and Singh (32), our model neither includes an ex-plicit selection mechanism nor does it assess the fraction of high-affinity B cells in GCs. Although being deliberately simple, thepresented model succeeds in reproducing our empirical data. Its mostcharacteristic feature, the extended Ricker map, best reproduced theexperimental data compared with other deterministic growth models(Supplemental Fig. 3). Notably, the values of the fitted model pa-rameters for GC B cell division times (tfree and tcomp) (Table I)completely agree with experimental values from the literature(34–36). Volume distributions of splenic GCs at days 6, 10, and 14after primary immunization are well reproduced by our modelover two orders of magnitude (Fig. 6B–D).The simulations of our model further emphasize that growth and

decaykinetics of iGCsize aremuchmoredynamic thanaverage eGCsize kinetics (Fig. 6E). The abundance of small GCs at the peak ofthe GC reaction is due to iGCs attaining maximal size for onlya short time because they frequently collapse. In fact, for the chosenparameter set, ∼11% of all GCs shrank to one third of their sizewithin 1 d. However, the same model without the stochastic featureof sudden collapses does not fit the experimental data for any pa-rameter value. If GC B cell populations grew continuously, all GCswould be large at the peak of the immune response.According to ourmodel, iGCs of small size serve as indicators for

newly formed GCs or recent collapses. Several mechanisms mightlead to collapses after a dramatic selection, emigration period, orboth. Such collective B cell behavior can result from intercalatedphases of proliferation and selection or from intercalated phases ofSHM and mutation-free expansion, as suggested by Kepler andPerelson (37). Alternatively, the unpredictable appearance of cellsbearing very high-affinity BCRs, due to SHM or immigration,combined with winner-takes-all selection mechanisms, as sug-gested by Kesmir and de Boer (38), can lead to the substantial andquick loss of iGC B cells.

FIGURE 5. Volume distributions of GCs indicate nonsynchronized

growth of splenic GCs during the primary immune response. Illustrated are

histograms of the volume distributions of three-dimensionally reconstructed

splenic GCs at days 6, 10, and 14 postimmunization (for details, see Figs. 2,

4). The reported frequencies of GC volumes refer to merged data sets of

three mice at each time point and include all GCs that crossed the central

section (s04) and were wholly contained within or spanned the analyzed

splenic volumes. GC sizes are presented as volumes and estimated numbers

of B cells contained in these volumes. The total numbers of three-di-

mensionally reconstructed GCs are indicated (S), with the values for in-

dividual mice given in parentheses.

FIGURE 4. 3D reconstructions of splenic GCs during the primary im-

mune response. 3D reconstructions of GCs were performed using meander

scans of immunofluorescence-stained serial longitudinal spleen sections

(Fig. 2). Briefly, GC outlines were segmented, and GCs were aligned slice-

wise according to their center of mass. After alignment, ellipsoid fitting

was performed on GCs (turquoise). A, Images are representative of spleens

obtained at days 6, 10, and 14 after immunization. 3D reconstructions were

restricted to the fractions of GCs that were wholly contained within or

spanned the overall analyzed splenic volumes. B, Detail enlargement of the

3D reconstruction of the day 10 splenic volume relating to the series of

meander scans shown in Fig. 2. The positions of the occupied niches

GC105, GC108, and GC112 are indicated by arrows, with their volumes

and estimated numbers of B cells shown. For orientation purposes, staining

of the respective region (proliferating cells [blue, mAb Ki-67], FDC net-

works [white, mAb FDC-M2], T cells [red, mAb CD3], and macrophages

[green, mAb CD68]; scale bar, 1 mm) is superimposed for serial section

s03, and s03 is highlighted in the 3D reconstruction.

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Although the currently available data donot permit speculation ondetailed selection mechanisms, one can discuss the functionalcontext of sudden collapses of GCs. As pointed out by Or-Guil et al.(20), sudden massive B cell death followed by vigorous pro-liferation provides for the fast and effective takeover of GCs andexplains why GCs are often found to be oligoclonal (10, 39, 40).Rapid takeover of GCs was first described by Radmacher et al. (41),who observed that within a GC, usually all or none of the BCRscarry the key mutation. This all-or-none behavior of GCs is as-sumed to rely on a winner-takes-all selection mechanism, where,once found, B cells bearing high-affinity key mutations rapidly takeover the entire population of a GC (32). Notably, sudden collapses,as predicted by our model, have the intrinsic property of generatinga rapid takeover and oligoclonality.As implemented in the extended Ricker model, the actual pro-

liferation rate of GC B cells decreases with an increasing populationsize because resources within a GC run low (resource-limited com-petition) (Equation 2). Consequently, GCs enter a state of “stagna-tion” when their population size reaches their maximal carryingcapacity. In this scenario, high-affinity GC B cells cannot prevailbecause their expansion is detained. Sudden collapses of GCscounteract this stagnation, leading to a quick release of resources,

thereby allowing unrestricted proliferation of the few remaining ornewly entering GC B cells. If one assumes that sudden collapses ofGCs are affinity dependent, this scenario provides a basis for un-restricted expansion and diversification of high-affinity GC B cells,a hallmark of an effective selection mechanism.Although the actual growth behavior of iGCs cannot be directly

monitored in vivo and remains enigmatic, our results challenge thecurrent perception about affinity maturation. The experimental datapresented herein showed that iGCs grow nonsynchronously and thattheir growth behavior strongly deviates from the average eGCgrowth kinetics. Ourmathematicalmodel further suggests that thesedeviations are due to frequent collapses of GC B cell populations,after which the populations resume growth by B cell proliferation.The results presented in this study underscore the need for

extending the perception of the GC response to a more systemicdescription level, from individual GCs toward ensembles of GCsand from deterministic toward stochastic processes. By implication,this also advises caution in interpreting averaged GC developmentand growth data, because very different GC responsesmight seem tobe similar based on averaged data.

AcknowledgmentsN. Wittenbrink, A. Klein, and M. Or-Guil especially thank the German

Rheumatism Research Center, Berlin, for providing laboratory space,

equipment, generous support, and advice during the project. T.S. Weber

thanks Dr. Jorge Carneiro, Gulbenkian Institute of Science, Portugal, for

hospitality. The authors are further indebted to the Electron and Laser Scan-

ning Microscopy Facility, Leibniz Institute for Neurobiology, for excellent

technical help and Johannes Eckstein for valuable comments.

DisclosuresThe authors have no financial conflicts of interest.

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