Leukocyte telomere dynamics and human hematopoietic stem cell kinetics during somatic growth

Experimental Hematology 2009;37:514–524

Leukocyte telomere dynamics and humanhematopoietic stem cell kinetics during somatic growth

Igor Sidorova, Masayuki Kimurab, Anatoli Yashinc, and Abraham Avivb

aDepartment of Medical Microbiology, Leiden University Medical Center, Leiden, Netherlands;bThe Center of Human Development and Aging, University of Medicine and Dentistry of New Jersey,

New Jersey Medical School, Newark, NJ, USA; cThe Center for Population Health and Aging, Duke University, Durham, NC, USA

(Received 5 September 2008; revised 15 October 2008; accepted 25 November 2008)

Offprint requests

Development and A

Orange Avenue, Roo

[email protected]

0301-472X/09 $–see

doi: 10.1016/j.exph

Objective. A central question in stem cell research is knowing the frequency of human hema-topoietic stem cells (HSC) replication in vivo.

Materials and Methods. We have constructed a model that characterizes HSC kinetics and therelative sizes of the hematopoietic progenitor cell (HPC) and HSC pools from birth onward.The model capitalizes on leukocyte telomere length (LTL) data and body weight-gain chartsfrom birth to the age of 20 years. The core premise of the model is that during human growth,LTL dynamics (birth LTL and age-dependent LTL shortening afterward) chronicle theexpansions of the HSC and HPC pools.

Results. The model estimates that by the end of the first year of life, HSC have replicated w17times and they replicate w2.5 times/year between the ages of 3 and 13 years. Subsequently,HSC replication slows considerably. In adults HSC replicate at a rate of w0.6 times/year.In addition, the model predicts that newborns with small birth weight would have shorterLTL as adults and that women would have longer LTL than men.

Conclusion. Our findings will be useful in bone marrow transplantations and might explaina body of clinical observations related to LTL distribution in the general population. � 2009ISEH - Society for Hematology and Stem Cells. Published by Elsevier Inc.

One of the cardinal questions in stem cell research is sizes of the HSC and hematopoietic progenitor cell
learning how frequently human hematopoietic stem cells(HSC) replicate in vivo as they balance self-renewal withdifferentiation. As telomere repeats are clipped off witheach division of somatic cells [1], telomere shorteningover time might be a useful measure of the replicativehistory of somatic cells in vivo. Assuming that telomereshortening in circulating granulocytes mirrors the sameprocess in HSC [2], a previous model used stochastic simu-lation of granulocyte telomere shortening to estimate thereplication rate of human HSC [3]. To gain insight intoHSC kinetics, we have focused on somatic growth andleukocyte telomere length (LTL) at birth and age-dependentLTL shortening during the first 20 years of human life.Using weight-gain trajectories from the US Centers ofDisease Control and Prevention Web site [4] and data onLTL in newborns [5,6] and adults [7�16], our model offersa comprehensive picture of HSC kinetics and the relative
to: Abraham Aviv, M.D., The Center of Human

ging, New Jersey Medical School, 185 South

m F–464 MSB, Newark, NJ 07103, USA; E-mail:

front matter. Copyright � 2009 ISEH - Society for Hemat

em.2008.11.009

(HPC) pools.The basis of our model is that the rapid shortening of

LTL during early life [17�19] corresponds to the expansionof the HSC and HPC pools, which is driven by symmetricreplications, i.e., an HSC generating two daughter HSC andan HSC generating two daughter HPC; and asymmetricreplications, i.e., a HSC generating one daughter HSCand one daughter HPC (Fig. 1) [20,21]. We note that inour model we consider only the first generation of HPCderived from HSC, i.e., those HPC atop the hierarchy ofdifferentiating blood cells. We also note that the relativelyslow LTL shortening in the adult is largely driven by‘‘housekeeping’’ functions of the HSC pool, i.e., self-renewal to offset the loss of replicating HSC and HPCdue to quiescence, senescence, and apoptosis.

Methods

Principles of the modelDuring the first 20 years of life, the body and the peripheral leuko-cyte (PL) pool experience dramatic increases in weight and total

ology and Stem Cells. Published by Elsevier Inc.

mailto:[email protected]

gHH

gPP

dH

gHP

dP

HSC HPC

HPC

HPC

HSC

HSC HSC ×q

×q

×q

Figure 1. Model of symmetric and asymmetric hematopoietic stem cells (HSC) division. The different scenarios include: (i) HSC cells undergo divisions

with the total rate g 5 gHH þ gHP þ gPP, where gHH and gPP correspond to the rates of symmetric divisions in which HSC(H) may give rise to two daughter

HSC (H/HþH) or to two daughter HPCs (P) (H/PþP), respectively; (ii) HSC may undergo asymmetric divisions (H/HþP) with rate gHP; (iii) HSC and

HPC can also exit their pools by undergoing apoptosis or attaining a state of senescence or quiescence with rates dH and dP, respectively (dashed gray circles).

Although hypothetical symmetric replication of HSC into two daughter HPC is also considered in the model, for simulation, we assumed that gPP 5 0 and,

therefore, the corresponding arrows are shown by dashed lines. HPC undergoes a finite number of replications q downstream to the hierarchy of differen-

tiating blood cells and this number of replications is constant at any age (dashed orange circles). For further details, see Appendix.

515I. Sidorov et al./ Experimental Hematology 2009;37:514–524

cell number, respectively. After the age of 20 years, these param-eters display minor changes compared with previous years. Theelderly tend to lose weight because of wasting of muscle andbone, while in the United States and many other countries, youngand middle-aged people are prone to gain weight in the form offat. These changes may indeed affect LTL [7,10,14,16], but theiroverall influence on LTL dynamics is probably minor comparedto that exerted by the drastic somatic growth during the first 20years of life. For this reason, our model regards body weight(BW), HSC, HPC, and PL pools as relatively unchanged afterthe age of 20 years. As such, LTL shortening during this periodreflects only housekeeping replicative activity of the HSC pool.

Accordingly, for a given individual, the relations of the HSCand HPC pools to BW, i.e., HSC/BW, HPC/BW, and, therefore,HPC/HSC, are constant during most of the human lifespan. Thesame holds for the relations of the HSC and HPC pools to thePL pool, i.e., HSC/PL, and HPC/PL are constant. Given that ourmodel assumes that the HSC and HPC pools are proportional toBW, LTL shortening that arises from housekeeping activity wouldbe constant throughout life. That is to say, the same portion of theHSC pool is engaged in housekeeping regardless of BW.

The model is delineated by the following key suppositions:

1. The sizes of HSC and HPC pools are defined only bythose HSC that partake in symmetric and asymmetricreplications. The relative sizes of these pools are thesame (although with anticipated biological variation)in magnitude in all human newborns;

2. LTL shortening during the first 20 years of human life,which is very rapid during infancy and early child-

hood, arises primarily from the expansions of theHSC and HPC pools to accommodate age-relatedsomatic growth (BW gain) and the concomitantincrease in the PL pool;

3. The ratios of the HSC and HPC pools to BW and PLpool are constant during most of the human lifespan;

4. The relatively slow LTL shortening during adult life(age older than 20 years) results mainly from house-keeping proliferative activity of the HSC pool thatsustains its own self-renewal and replaces the lossfrom the HPC pool;

5. Telomere shortening due to replication downstreamfrom HPC to PL remains constant throughout life.

General proceduresThe two panels in Figure 2 display age–dependent BW gain, frombirth to 20 years, of males and females (ranked at the 50th percen-tile for BW and BW gain trajectories), based on data derived fromthe Web site of the Centers of Disease Control and Prevention,National Center for Health Statistics (A) [4] and the rates ofBW gain as a function of age, which we computed from thesedata (B). In terms of the rate of BW gain, the fastest somaticgrowth occurs immediately after birth and then it decreases upto the age of w2.8 years for both males and females. Thereafter,the rate of BW gain increases to the age of 14 years for males and12 years for females, when it declines in both sexes.

As shown in the Appendix (equations A19 and A20), LTLshortening during the first 20 years is a function of four variablesdescribing the numbers of HSC replication related to:

Figure 2. Age-dependency of body weight (BW) and the rate of BW gain. (A) BW gain data for a male and a female ranked at the 50th percentiles for

birth BW and BW gain between birth and 20 years (Wt) derived from the Centers for Disease Control and Prevention Website (B) Computed rate of BW gain

(dWt/dt) vs age.

516 I. Sidorov et al./ Experimental Hematology 2009;37:514–524

housekeeping for HSC and HPC pools, and the expansion of theHSC and HPC pools for a t-year old individual:

dHt=ln2; housekeeping for HSC; ð1Þ

gdPt=ln2; housekeeping for HPC; ð2Þ

lnWt

W0

=ln2; for expanding the HSC; ð3Þ

glnWt

W0

=ln2; for expanding the HPC; ð4Þ

where: t, time; ln 2, natural logarithm of 2; dH, dp, rates ofexit from the HSC and HPC pools, respectively, due toapoptosis, quiescence or senescence; W0, Wt, BW at birthand at age t, respectively; g constant ratio between HPCand HSC. The contributions of these variables to LTL short-ening (Lt) can be calculated as:

Lt5L0�l

ln2

�ðgþ 1ÞlnWt

W0

þ dHtþ gdPt

�; ð5Þ

where: L0, LTL at birth and l, LTL shortening rate perreplication.

Equations 1 through 5 were used for the initial simulationsshown in Figure 3 for replication related to housekeeping activity(A), growth of the HSC (B), and HPC (C) pools, total number ofreplication (D), the rate of the total number of replication (E), andLTL shortening between birth and the age of 20 years. The modelconsiders neither the numbers of HPC replication to furtherexpand the size of the HPC pool, nor those to generate morecommitted cells, which give rise to peripheral leukocytes. Itassumes that the number of these replications is constant (5 lnq/ln 2, where q is the magnitude of expansion), as proposed ina previous model attempting to estimate the frequency of HSCreplication based on telomere dynamics in granulocytes [3].Although LTL depends on q and for any age Lt � l ln q/ln 2, is

observed, the number of replications for certain period of lifedoes not depend on q:

nt5ðL0el ln q=ln 2eLt þ l ln q=ln 2Þ=l5ðL0eLtÞ=l

Initial estimationsBased on published data of LTL in newborns [5,6] and adults[7�16], we assume that for the average individual (a male ora female), LTL shortens from L0 5 11 kb at birth to L20 5 8.2kb at the age of 20 years. Thus, LTL shortening for that individualin this time period amounts to 2.8 kb. Based on the rate of LTLshortening in adults [7,8,10�16], we assume as a starting pointthat HSC replication to maintain housekeeping of both the HSCand HPC pools accounts for LTL shortening at a rate h w0.03kb/year. If telomere length shortens by l w0.05 kb for each divi-sion of somatic cells [22], the HSC pool in the adult undergoesw0.6 (5 h/l 5 0.03/0.05) replications per year due to house-keeping. Our model posits that the same rate holds throughoutlife. It follows that for housekeeping activity, the HSC pool (forboth males and females) would undergo w12 replications duringthe first 20 years of life. This amounts to LTL shortening by w0.6kb (12 replications � 0.05 kb/replication) (Fig. 3A). Thus, the re-maining 2.2 kb (2.8�0.6 kb) of LTL shortening between birth and20 years is due to the expansion of the HSC pool and the HPCpools.

The HSC and the HPC pools are proportional to BW withconstant ratios b 5 HPC/BW, a 5 HSC/BW, and HPC/HSC 5

b/a 5 g. For the average male (birth BW 5 3.53 kg andBW 5 70.60 kg at the age of 20 years), the HSC pool undergoes:

lnW20

W0

=ln2wln70:6

3:53=ln254:32

replications to reach its adult size (Fig. 3B). It follows thatthe expansion of the HSC pool from birth to 20 yearsresults in the shortening of LTL by 4.32 replications �0.05 kb/replication 5 0.216 kb. The remaining LTL short-ening, i.e., 2.200 � 0.216 kb 5 1.984 kb would result fromreplications of the HSC pool to expand the HPC pool. Thus,

Figure 3. Simulations with parameters shown in Table 1. Hematopoietic stem cells (HSC) doubling kinetics for the average male and female ranked within

the 50th percentiles for birth body weight (BW) and BW gain between birth and 20 years: (A) population doublings for housekeeping (same dynamics for

male and female); (B) population doublings for the expansion of the HSC pool; (C) population doublings for the expansion of the hematopoietic progenitor

cell (HPC) pool. (D) Total number of HSC population doublings [sum of dynamics represented in (A), (B), and (C)]. (E) Rate of changes of total number of

HSC population doublings with time. (F) The downward trajectories for birth leukocyte telomere length (LTL) (L0) toward LTL at 20 years (L20), based on

the BW gain data displayed in panels (A) and (B) of Figure 2.


the total number of replications of the HSC pool to expandthe HPC pool by the age of 20 years in the average malewould be 1.984 kb/0.05 5 39.68 (Fig. 3C). Figure 3Ddisplays the overall HSC replication between birth to 20

years due to housekeeping, and the expansion of the HSCand HPC combined. Figure 3E shows the rate of HSC repli-cation throughout this time period, while Figure 3F depictsLTL shortening between birth LTL, L0 (5 11 kb) and LTL


at the age of 20 years, L20 (5 8.2 kb), based on the assump-tion that LTL shortening is a proxy for telomere shorteningof the HSC pool. LTL dynamics mirror total HSC popula-tion doublings (Fig. 3E), being fastest immediately afterbirth and slowest when approaching the age of 20 years.

It is noteworthy that while LTL is the same in newborn boysand girls [5,6], age-adjusted LTL is longer in women than men[8–11,13,16], though it is not clear at what age this gender-relateddifference becomes evident [16]. At this stage of constructing themodel, we have assigned the same magnitude of LTL to 20 year–old males and females, though considerations below suggestotherwise.

From the relationship between the HPC pool to BW gainbetween birth and 20 years glnWt

W0=ln2539:68 divisions, we can

compute the ratio g 5 39.68 replications/4.32 divisions 5 9.18.Based on this value of g and assuming that dH 5 0, we can

estimate dp using the equation gdpt/ln 2 5 12 divisions for 20years. Thus, dp 5 12 divisions � ln2/20 years/9.18 5 0.045/year, which corresponds to 15 years of half–life for HPC.

Although HSC do not live indefinitely and their lifespan mightbe influenced by factors such as oxidative stress [23], in our calcu-lation we used dH 5 0 year�1, assuming that for HSC cells the rateof apoptosis or attaining a senescence or quiescence state are rela-tively low. The impact of this rate on total number of replication isabout 10 times smaller (g 5 9.18) that for dp and a small nonzerovalue for dH would not considerably influence the outcome.

Modeling. Using these estimations, we performed simulations invirtual persons, focusing on parameters that relate to HSCkinetics, birth BW, and BW gain thereafter, as expressed in LTLdynamics between birth and 20 years. These parameters are shownin Table 1.

For calculating the rate of BW gain Ai for a given age ti andBW Wi, we used the following equation: Ai 5 (Wi � Wi�1)/(ti �ti�1). To simulate increase in BW gain, values of BW, Wi, wascalculated for each time point, starting from the value W0 ofa given birth BW using the equation Wi 5 Wi�1 þ lAi (ti �ti�1), which is equal to the following transformation of knownBW values: Wi /W0 þ l(Wi - W0). Thus, if the birth BW is3.53 kg and BW at age 20 year is 70.60 kg for male, the increasein BW gain of 30% above the average (l 5 1.3) would result ina value of 90.72 kg 5 3.53 þ 1.3 � (70.60 � 3.53) kg.

Equation 5 was used for all simulations displayed in Figure 4,where one parameter was changed at a time, i.e., telomere

Table 1. Parameters used for simulations

Value for

Parameter Males Females Reference

dH (kb/year) 0 0 Assumption

dP (kb/year) 0.05 0.04 Calculated

g 9.18 9.74 Calculated

L0(kb) 11.0 11.0 Published5,6

L20 (kb) 8.2 8.2 Published7–16

W0 (kg) 3.53 3.40 Published4

W20 (kg) 70.60 58.22 Published4

l (kb/replication) 0.05 0.05 Assumption

h (kb/year) 0.03 0.03 Published7,8,10–16

shortening per replication, l (A); LTL at birth, L0 (B); g ratio,(C); and dp, rate of exit from the HPC pool (D). Equation 5 wasalso used for simulations shown in Figure 5 using transformationWi /W0 þ l(Wi � W0).

Simulation model I. Holding constant parameters of somaticgrowth (weight at birth 5 3.53 kg and at 20 years 5 70.60 kg),while changing parameters of HSC telomere dynamics: Figure 4shows the effect of variations in the following parameters onLTL dynamics during the first 20 years of life: Variation in l(range, 0.02�0.08 kb) profoundly affects LTL at the age of 20years (L20 5 6.52�9.88 kb) (Fig. 4A). With everything else beingequal, a relatively shorter (or longer) LTL at birth (range,9.5�12.5 kb) would be expressed in a relatively shorter (or longer)LTL afterwards (Fig. 4B). Of particular interest with respect toLTL dynamics is the variation in the l (range, 4�16), whichaccounts for HSC replication devoted to build up the HPC poolcompared with those devoted to build up the HSC pool. Clearly,there is a considerable effect of this ratio on LTL dynamics(Fig. 4C). Variation in dp (0.001–0.089 year-1) also affects LTLshortening, the cumulative amount of which increases with age(Fig. 4D).

Simulation model II. Holding constant parameters of HSC telo-mere dynamics and changing parameters of somatic growth(BW gain after birth and birth BW). Figure 5 depicts the effectof variation in the rate of BW gain on LTL shortening betweenbirth and the age of 20 years. Dynamics of BW gain from theaverage birth BW of 3.53 kg and L0 5 11 kb for different valuesof l (range, 0.7�1.3) are presented in Figure 5A and 5B. Thisrange corresponds to BW of 50.48 to 90.72 kg and the respectivevalues for L20 5 8.02�8.45 kb at the age of 20 years.

As shown in Figure 5C, when l is fixed at 1, variation in birthBW (1�4 kg), exerts a minimal effect on BW at the age of20 years. However, as shown in Figure 5D, birth BW variationexerts a considerable influence on LTL dynamics within thistime period. For instance, with birth LTL, L0, of 11 kb, L20 ofan individual with birth BW of 1 kg would be 7.30 kb, comparedwith that of 8.19 kb for an individual with birth BW of 3.53 kg.This is because the ratio of the increase in BW is relatively higherfor an individual with relatively lower birth BW.

Finally, Figure 6 depicts the combined effect of birth BW(1�4 kg) and the rate of BW gain (l 5 0.7�1.3), when birthLTL, L0 5 11 kb, on BW (A) and L20 (B) at the age of 20 years.For a given birth BW, individuals with a higher rate of BW gainwould of course be heavier at the age of 20 years (Fig. 6A). Bythe age of 20 years, the joint effects of small birth BW anda high rate of BW gain shorten LTL considerably more than theindependent effect of each of these variables.

DiscussionIn this work, we resorted to published LTL data innewborns and adults and Centers of Disease Control andPrevention growth trajectories between birth and 20 yearsto characterize HSC kinetics in humans. Our model treatsnot only the HSC and HPC pools, but also the PL pool,as expanding up to the age of 20 years and being relatively

Figure 4. Simulations of leukocyte telomere length (LTL) dynamics for virtual persons with body weight (BW) of 3.53 kg at birth and BW of 70.60 kg at age

20 years. (A) Telomere loss per hematopoietic stem cells (HSC) division, l 5 0.02 to 0.08 kb/division; (B) Birth LTL, L0 5 9.5 to 12.5 kb; (C) ratio of HPC/

HSC, g 5 4 to 16; (D) Housekeeping activity, dP 5 0.001 to 0.089 year�1.


stable afterward. In reality, the size of the PL poolconstantly fluctuates to accommodate the state-of-the-moment needs of the individual. Expansion of the HSCand HPC pools in tandem with the growing soma makesintuitive sense; without this expansion, the rate of LTLshortening would be positivelydrather than negativelydassociated with age between birth and 20 years.

Several attempts were made to model the kinetics of humanHSC [24], the most recent one by Shepherd et al. [3], who haveexploited telomere dynamics in circulating granulocytesbecause these cells are homogeneous, have a short biologicallife, and do not replicate. Indeed, subsets of leukocytes mighthave different telomere lengths [17] and varying survivaltimes in the circulation (e.g., hours or days for granulocytesand many years for memory T lymphocytes). Other subsetsdown the hierarchy of differentiating blood cells may experi-ence different amounts of telomere shortening per replication[25], and some even experience telomere elongation [26].Furthermore, the absolute number of cells belonging tothese subsets and their relative proportions [27�29] are

reconfigured with age. However, for whatever duration oftime and at any age, the turnover of these cells and theirdifferent degrees of telomere shortening would ultimatelyimpact telomere dynamics in HSCs and, therefore, telomerelength in all leukocytes. Thus, variations in telomere lengthwithin leukocyte subsets due to different proliferative activi-ties, telomere loss per replication, and survival time in thecirculation are relatively small compared with the overallchanges that take place due to the expansion of the HSC andHPC pools, as well as housekeeping between birth and 20years. These factors largely determine LTL within this timeframe.

In computing the kinetics of HCS, we have exploiteda vast body of weight-gain data and known LTL values innewborns and adults. As shown in Table 1, by excludingdH as a major player in LTL kinetics, in testing our modelwe are left with only one unknown, l, the amount of telo-mere shortening with each HSC division in vivo. Thisparameter was deduced from findings in cultured somaticcells [22]. However, l of HSC in the bone marrow might

Figure 5. Simulations of leukocyte telomere length (LTL) dynamics in relation to body weight (BW) dynamics for virtual persons: (A) Variation in rate of

BW gain with parameter l ranging from 0.7 to 1.3 of magnitude of the average gain, resulting in BW 5 50.48 to 90.42 kg at the age of 20 years; (B) LTL

dynamics corresponding to the different rates of BW gain displayed in (A). (C) Variation in birth BW 5 1 to 4 kg, which result in BW 5 68.07 to 71.07 kg

range at the age of 20 years; (D) LTL dynamics corresponding to the different birth BW displayed in (C).


not be the same as that of cells grown in artificial growthmedia under oxygen tension that does not replicate the invivo state [30]. In addition, developmental changes mightalso affect the replicative behavior of HSC [31]. Thatsaid, simulations displayed in Figure 4A suggest that, onaverage, l is between 0.04 and 0.06 kb, as LTL shorteningafter birth based on these values yields L20 within the rangeobserved in young adults.

Although highly variable, the rate of LTL shortening inadults is w0.03 kb/year. Accordingly, in the adult human,for a presumptive l 5 0.05 [22], HSC replicate at a rate ofabout 0.6 times/year or once every 86 weeks. However,there might be considerable interindividual variation inthis parameter, given the wide range of LTL-shorteningrates in adults [7,8,10�16]. With that said, this value isclose to the upper range of the replication rate estimatedby Shepherd et al., based on telomere analyses in granulo-cytes, for humans (once every 23�67/week) [3] andbaboons (once every 11�75/week) [32]. We note that

our approach provides an estimate of the frequency ofHSC division not only for adults but also for childrenfrom birth.

As shown in Figure 3, the rate of HSC replicationdecreases from w42/year immediately after birth to w2.5/year at the age of 3 years (parameters for simulations areshown in Table 1). During this period alone, the HSC poolundergoes a total of w23 replications, causing telomereshortening of w1.2 kb (Fig. 3E). Between the ages of 3and 13 years, the rate of HSC replication is relatively stableat w2.5/year, leading to an additional telomere shortening ofw1.1 kb. After age of 13 years, HSC replicate at w0.7/yearwith further telomere shortening that amounts to w0.5 kb.

Simulations displayed in Figure 4C might provide a poten-tial explanation for enigmatic observations we made aboutracial difference in LTL. While birth LTL is equivalent inAfrican Americans and in Caucasians [5], by the 3rd decadeof life LTL is longer in African Americans by w0.6 kb [16].African Americans and other individuals of African ancestry

Figure 6. The joint effects of birth and the rate of body weight (BW) gain on BW and leukocyte telomere length (LTL) at the age of 20 years: (A) effect of

birth BW and BW gain on BW at 20 years. (B) Effect of birth BW and BW gain on LTL at 20 years with birth LTL, L0 5 11 kb. For both (A) and (B), birth

BW 5 1 to 4 kg and change in the rate of BW gain, l 5 0.7 to 1.3.


have lower circulating leukocyte and neutrophil counts thanCaucasians [16,33�37], and because this racial difference isnot due to increased margination of neutrophils in venules, itprobably reflects the kinetics of HSC within the bone marrow.Figure 4C shows that a small variation in the ratio of HSCreplication devoted to the build up the HPC pool comparedwith that devoted to build up the HSC pool, g, has a consider-able influence on L20. For instance, for g values of 8 and 10,the corresponding values of L20 are 8.53 kb and 7.97 kb.These values are compatible for the observed racial differ-ence in LTL [16]. Thus, the racial difference in leukocytecount might be due to a smaller HPC pool in relation to theHSC pool in African Americans than Caucasians.

The relationship between LTL and BW gain betweenbirth and the age of 20 years, displayed in Figures 5 and6, might also be of medical importance. While newborngirls and boys have the same LTL [5,6], adult womenhave longer LTL than men [8�11,13,16]. Females attainan adult BW that is considerably less than that of males,primarily because of gender-related differences in BWgain trajectories (Fig. 2A). Figure 5 shows that fora 3.53-kg newborn, different growth rates that lead toBWs of 50.48 to 90.42 kg at the age of 20 years exertonly modest effect on L20. Therefore, based on somaticgrowth alone, our model predicts that women would havelonger LTL than men. However, other factors might alsocontribute to the gender gap in LTL during adulthood [38].

While BW gain trajectories have only a modest effect onL20, a small birth BW has a pronounced effect on this param-eter, and this effect occurs primarily during the first 2 years oflife (Fig. 5C and D). The birth BWeffect is further magnifiedwhen an individual with a small birth BW assumes a trajec-tory that leads to an above average BW during adulthood(Fig. 6). Such findings are of interest because in their hypoth-esis about the fetal origins of adult diseases, Barker and

colleagues have postulated that small-for-gestational-agebabies are prone to increased BW and a host of aging-relateddiseases as adults [39,40]. Indeed, shortened LTL has beenobserved in a host of aging-related diseases [41]. Moreover,a recent study reported that at the age of 5 years, children bornwith low birth weight had a shorter LTL than their peers bornwith normal birth weight [42], as predicted by our model.

Leukocyte telomere dynamics reflect the input of manyfactors in addition to BW gain during early life. Theseinclude both genetic and environmental factors that osten-sibly increase the cumulative burden of oxidative stressand inflammation, which might accelerate telomere short-ening in HSC or even lead to the demise of these cells[23]. Although a controversy had existed about whetherLTL is linked to human longevity [43�47], more recentstudies in same–sex elderly twins [48,49] have conclusivelyshown that a relatively short LTL in one of the co-twinsforecasts early mortality in that co-twin compared withthe other one. Because LTL shortening with age mirrorstelomere shortening in HSC, in principle, a faster LTLshortening during adulthood suggests a faster telomereshortening in HSCda process that might affect longevity.One cannot ignore, however, the possibility that telomereshortening in HSC during growth and development mightexert a lasting impact on human longevity.

Finally, our model’s predictions and most of its parame-ters can be empirically tested in clinical/epidemiologicalsettings that examine LTL in relation to growth trajectories,leukocyte counts and indices of aging and longevity indifferent ethnic groups.

AcknowledgmentsSupported by National Institutes of Health grants AG16592,AG020132 and AG008761. We would like to thank Peter Lansdorpfor his insightful suggestions. There are no conflicts of interest.


Appendix

Model of symmetric and asymmetric HSC division

Figure 1 depicts symmetric replication of HSC intoeither two daughter HSC (H) or two HPC (P) and asym-metric replication producing one H and one P. In thisscheme, H replicates at an overall rate g 5 gHH þ gHP þgPP, where, where gHH and gPP are the rates for symmetricreplications, i.e., H / H þ H and H / P þ P. H cells alsoundergo asymmetric replication, i.e., H / H þ P at the rategHP. Both H and P exit the pool at rates dH and dP. Onceexiting the pool, cells are not considered in the model.All these rates may depend on time and this is shown byadding subscript t for each rate: gHH 5 gHHt, gPP 5 gPPt,gHP 5 gHPt, and dH 5 dHt,

Thus, the equation for HSC kinetics can be written as:

dHt

dt5� ðgHHt þ gHPt þ gPPtÞHt þ 2gHHtHt þ gHPtHt � dHtHt

ðA1Þ

In this equation: gt 5 gHHt þ gHPt þ gPPt, rate of leavingquiescent state; 2gHHt, rate of generation of two HSC cellsby symmetric replication (H / H þ H); gHPt, rate ofgeneration of one HSC cell and one HPC by asymmetricreplication (H / H þ P); dHt, rate of HSC exiting thereplicative pool.

HPC kinetics is:

dPt

dt52gPPtHt þ gHPtHt � dPtPt ðA2Þ

where: 2gPPt, rate of generation of two HPC aftersymmetric division (H / P þ P); gHPt, rate of increasedue to generation of one HPC and one HSC after asym-metric replication (H / H þ P), dPt, rate of exit fromthe pool of HPC.

Equations (A1) and (A2) can be rewritten in a shorterform:

dHt

dt5ðgHHt � gPPtÞHt � dHtHt; ðA3Þ

dPt

dt5ð2gPPt þ gHPtÞHt � dPtPt: ðA4Þ

Accordingly, the kinetics of Ht depend only on the rates oftwo types of symmetric replications: gHHt and gPPt, whereH / H þ H replications are responsible for the exponen-tial growth of the HSC pool and H / P þ P replicationsaccount for the exponential decay of HSC pool. The inter-play between these modes of replication can provide expo-nential growth, decay and constant kinetics of the HSCpool. If the rates of these replications are equal, Ht

dynamics depends only on the rate of the exit of HSCfrom the replicative pool, dHt. For HPC cells two different

types of replications would cause an exponential growthwith rate 2gPPt þ gHPt, which can be attenuated by exitfrom the pool, dPt.

The following is the solution of this system for any t O0 with the initial values of the cell numbers H0 and P0 for t5 0 and if all the parameters do not depend on time:

Ht5H0eðgHH�gPP�dHÞt ðA5Þ

Pt5P0e�dPt þH0

2gPP þ gHP

gHH � gPP � dH þ dP

�eðgHH�gPP�dHÞt

� e�dPt�

ðA6Þ

Parameters of growth

When model parameters depend on time, Ht kinetics canbe written as:

Ht5H0exp

0@Z t

0

ðgHHx� gPPx � dHxÞdx

1A: ðA7Þ

BW gain (Wt) can be calculated as:

Wt5W0exp

0@Z t

0

axdx

1A; ðA8Þ

assuming that at is the exponential rate of BW gain at time tand W(0) 5 W0, initial value of BW (BW at birth).

If a is the constant representing the proportionalitybetween Ht and Wt for all time points t $ 0 (i.e., volumeof HSC pool is proportional to BW), then from Equations(A7) and (A8):

a5Ht

Wt

5H0

W0

exp

0@Z t

0

ðgHHx� gPPx � dHx � axÞdx

1A for t$0;

ðA9Þ

meaning that gHHt � gPPt � dHt 5 at, or

gHHt5at þ gPPt þ dHt ðA10Þ

Let us assume that for all time points t $ 0 there isa constant ratio b between BW and the size of the HPCpool:

Pt

Wt

5b ðA11Þ

Accordingly,

Pt5Wtb5Ht

ab5gHt; where g5

b

a5

Pt

Ht

; ðA12Þ

using (A3) and (A4), we get

ð2gPPt þ gHPtÞHt � dPtPt5gðgHHt � gPPt � dHtÞHt: ðA13Þ


This equation leads to

gHPt5gðgHHt � gPPt � dHt þ dPtÞ � 2gPPt5gðat þ dPtÞ� 2gPPt:

ðA14Þ

Relation between BW gain andnumber of replications of the HSC cells

The number of doublings for HSC pool size can becalculated as

mt5lnHt

H0

=ln25

0@Z t

0

ðgHHx � gPPx � dHxÞdx

1A=ln2: ðA15Þ

However, it would be incorrect to use this number forcalculating aging–related decline in telomere length. Thechanges in telomere length are related to the number oftimes the HSC cells enter the cell cycle. Equation (A1)shows that the rate of this process is gHHt þ gHPt þ gPPt,so the total number of replications of HSC that accountsfor the expansions of both HSC and HPC cells and whichis the main cause of LTL shortening is the following:

nt5

0@Z t

0

ðgHHxþ gPPx þ gHPxÞdx

1A=ln2 ðA16Þ

Taking into account formulas A10 and A14 one cancalculate:

gHHt þ gPPt þ gHPt5at þ gPPt þ dHt þ gPPt þ gðat þ dPtÞ� 2gPPt5at þ dHt þ gðat þ dPtÞ

ðA17Þ

and rewrite A16 taking in account A8 as:

nt5

0@Z t

0

ðaxðgþ 1Þ þ dHx þ gdPxÞdx

1A=ln2

5

0@ðgþ 1ÞlnWt

W0

þZ t

0

ðdHxþ gdPxÞdx

1A=ln2 ðA18Þ

or in simple case, when the rates of exiting of HSC andHPC pools do not depend on time (dHt 5 dH and dPt 5

dP and for any t O 0):

nt5

�ðgþ 1ÞlnWt

W0

þ dHtþ gdPt

�=ln2: ðA19Þ

Knowing number of replication of HSC nt one can calculatetelomere length L for HSC at time t:

Lt5L0� ntl ðA20Þ

where: L0 is LTL at birth (t 5 0) and l is LTL shorteningrate per replication.

References1. Harley CB, Vaziri H, Counter CM, Allsopp RC. The telomere hypoth-

esis of cellular aging. Exp Gerontol. 1992;27:375–382.

2. Notaro R, Cimmino A, Tabarini D, Totoli B, Luzzatto L. In vivo telo-

mere dynamics of human hematopoietic stem cells. Proc Natl Acad

Sci U S A. 1997;94:13782–13785.

3. Shepherd BE, Guttorp P, Lansdorp PM, Abkowitz JL. Estimating

human hematopoietic stem cell kinetics using granulocyte telomere

lengths. Exp Hematol. 2004;32:1040–1050.

4. National Center for Health Statistics in Collaboration with the

National Center for Chronic Disease Prevention and Health Promo-

tion. Available at: http//www.cdc.gov/growthcharts; 2000; Accessed

December 2007.

5. Okuda K, Bardeguez A, Gardner JP, et al. Telomere length in the

newborn. Pediatr Res. 2002;52:377–381.

6. Akkad A, Hastings R, Konje JC, Bell SC, Thurston H, Williams B.

Telomere length in small–for–gestational–age babies. Int J Obstet

Gynecol. 2006;113:318–323.

7. Gardner JP, Li S, Srinivasan SR, et al. Rise in insulin resistance is

associated with escalated telomere attrition. Circulation. 2005;111:

2171–2177.

8. Benetos A, Okuda K, Lajemi M, et al. Telomere length as an indicator

of biological aging: the gender effect and relation with pulse pressure

and pulse wave velocity. Hypertension. 2001;37(Pt 2):381–385.

9. Jeanclos E, Schork NJ, Kyvik KO, Kimura M, Skurnick JH, Aviv A.

Telomere length inversely correlates with pulse pressure and is highly

familial. Hypertension. 2000;36:195–200.

10. Fitzpatrick AL, Kronmal RA, Gardner JP, et al. Leukocyte telomere

length and cardiovascular disease in the Cardiovascular Health Study.

Am J Epidemiol. 2007;165:14–21.

11. Nawrot TS, Staessen JA, Gardner JP, Aviv A. Telomere length and

possible link to X chromosome. Lancet. 2004;363:507–510.

12. Slagboom PE, Droog S, Boosmsma DI. Genetic determination of telo-

mere size in humans: a twin study of three age groups. Am J Hum

Genet. 1994;55:876–882.

13. Bekaert S, De Meyer T, Rietzschel ER, et al. Telomere length and

cardiovascular risk factors in middle–aged population free of overt

cardiovascular disease. Aging Cell. 2007;6:639–647.

14. Valdes AM, Andrew T, Gardner JP, et al. Obesity, cigarette smoking,

and telomere length in women. Lancet. 2005;366:662–664.

15. Njajou OT, Cawthon RM, Damcott CM, et al. Telomere length is

paternally inherited and is associated with paternal lifespan. Proc

Natl Acad Sci U S A. 2007;104:12135–12139.

16. Hunt SC, Chen W, Gardner JP, et al. Leukocyte telomeres are longer in

African Americans than in Whites: the NHLBI Family Heart Study

and the Bogalusa Heart Study. Aging Cell. 2008;4:451–458.

17. Rufer N, Brummendorf TH, Kolvraa S, et al. Telomere fluorescence

measurements in granulocytes and T lymphocyte subsets point to

a high turnover of hematopoietic stem cells and memory T cells in

early childhood. J Exp Med. 1999;190:157–167.

18. Zeichner SL, Palumbo P, Feng Y, et al. Rapid telomere shortening in

children. Blood. 1999;93:2824–2830.

19. Frenck RW Jr, Blackburn EH, Shannon KM. The rate of telomere

sequence loss in human leukocytes varies with age. Proc Natl Acad

Sci U S A. 1998;95:5607–5610.

20. Morrison SJ, Kimble J. Asymmetric and symmetric stem–cell

divisions in development and cancer. Nature. 2006;441:1068–1074.

21. Attar EC, Scadden DT. Regulation of hematopoietic cell growth.

Leukemia. 2004;18:1760–1768.

22. Lansdorp PM. Telomere length and proliferation potential of hemato-

poietic stem cells. J Cell Sci. 1995;108:1–6.

http://www.cdc.gov/growthcharts


23. Ito K, Hirao A, Arai F. Reactive oxygen species act through p38

MAPK to limit the lifespan of hematopoietic stem cells. Nat Med.

2006;12:446–451.

24. Edelstein–Keshet L, Israel A, Lansdorp P. Modelling perspectives on

aging: can mathematics help us stay young. J Theor Biol. 2001;213:

509–525.

25. Hodes RJ. Telomere length, aging, and somatic cell turnover. J Exp

Med. 1999;190:153–156.

26. Weng N-P, Granger L, Hodes RJ. Telomere lengthening and telome-

rase activation during human B cell differentiation. Proc Natl Acad

Sci U S A. 1997;94:10827–10832.

27. Hulstaert F, Hannet I, Deneys V, et al. Age-related changes in human

blood lymphocyte subpopulations. II. Varying kinetics of percentage

and absolute count measurements. Clin Immunol Immunopathol.

1994;70:152–158.

28. Lazuardi L, Jenewein B, Wolf AM, Pfister G, Tzankov A, Grubeck-

Loebenstein B. Age–related loss of naive T cells and dysregulation

of T-cell/B-cell interactions in human lymph nodes. Immunology.

2005;114:37–43.

29. Globerson A, Effros RB. Ageing of lymphocytes and lymphocytes in

the aged. Immunol Today. 2000;21:515–521.

30. Parmar K, Mauch P, Vergilio J–A, Sackstein R, Down JD. Distribution

of hematopoietic stem cells in the bone marrow according to regional

hypoxia. Proc Natl Acad Sci U S A. 2007;104:5431–5436.

31. Lansdorp P. Telomeres, stem cells, and hematology. Blood. 2008;111:

1759–1766.

32. Shepherd BE, Kiem HP, Lansdorp PM, et al. Hematopoietic stem-cell

behavior in nonhuman primates. Blood. 2007;110:1806–1813.

33. Mayr FB, Spiel AO, Leitner JM, Firbas C, Kliegel T, Jilma B. Ethnic

differences in plasma levels of interleukin–8 (IL-8) and granulocyte

colony stimulating factor (G-CSF). Trans Res. 2007;149:10–14.

34. Phillips D, Rezvani K, Bain BJ. Exercise induced mobilization of

marginated granulocyte pool in the investigation of ethnic neutropenia.

J Clin Pathol. 2000;53. 481–448.

35. Hseih MM, Everhart JE, Byrd-Holt DD, Tisdale JF, Rodgers GP. Prev-

alence of neutropenia in the U.S. population: age, sex, smoking status,

and ethnic differences. Annals Int Med. 2007;146:486–492.

36. Athens JW, Raab SO, Haab OP, et al. Leukokinetic studies III. The

distribution of granulocytes in the blood of normal subjects. J Clin

Invest. 1961;40:159–164.

37. Rezvani K, Flanagan AM, Sarma U, Constantinovici N, Bain

BJ. Investigation of ethnic neutropenia by assessment of

bone marrow colony–forming cells. Acta Haematol. 2001;105:

32–37.

38. Aviv A, Shay J, Christensen K, Wright W. The longevity gender gap:

Are telomeres the explanation? Sci Aging Knowledge Environ. 2005;

23:pe16.

39. Barker DJ, Eriksson JG, Forsen T, Osmond C. Fetal origins of adult

disease: strength of effect and biological basis. Int J Epidemiol.

2002;31:1235–1239.

40. McMillen C, Robinson JS. Developmental origins of the metabolic

syndrome: predictions, plasticity, and programming. Physiol Rev.

2005;65:571–633.

41. Aviv A. The epidemiology of human telomeres: faults and promises.

J Gerontol A Biol Sci Med Sci. 2008;63:979–983.

42. Raqib R, Alam DS, Sarker P, et al. Low birth weight is associated with

altered immune function in rural Bangladeshi children: a birth cohort

study. Am J Clin Nutr. 2006;85:845–852.

43. Cawthon RM, Smith KR, O’Brien E, Sivatchenko A, Kerber RA.

Association between telomere length in blood and mortality in people

aged 60 years or older. Lancet. 2003;361:393–395.

44. Bischoff C, Petersen HC, Graakjaer J, et al. No association between

telomere length and survival among the elderly and oldest old. Epide-

miology. 2006;17:190–194.

45. Martin-Ruiz CM, Gussekloo J, van Heemst D, von Zglinicki T, West-

endorp RG. Telomere length in white blood cells is not associated with

morbidity or mortality in the oldest old: a population-based study.

Aging Cell. 2005;4:287–290.

46. Honig LS, Schupf N, Lee JH, Tang MX, Mayeux R. Shorter telomeres

are associated with mortality in those with APOE e4 and dementia.

Ann Neurol. 2006;60:181–187.

47. Harris SE, Deary IJ, MacIntyre A, et al. The association between

telomere length, physical health, cognitive ageing, and mortality in

non–demented older people. Neurosci Lett. 2006;406:260–264.

48. Kimura M, Hjelmborg JV, Gardner JP, et al. Short leukocyte telomeres

forecast mortality: a study in elderly Danish twins. Am J Epidemiol.

2008;167:799–806.

49. Bakaysa SL, Mucci LA, Slagboom PE, et al. Telomere length predicts

survival independent of genetic influences. Aging Cell. 2007;6:

769–774.

Documents

Leukocyte telomere dynamics and human hematopoietic stem cell kinetics during somatic growth