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HEMATOPOIESIS
From the Department of Haematology, Medicine and
Therapeutics, University of Aberdeen, Foresterhill, Aberdeen, UK; the
Twin Research and Genetic Epidemiology Unit, St Thomas's Hospital,
London, UK; and the Department of Mathematical Sciences, Meston
Building, University of Aberdeen, Old Aberdeen, UK.
Skewed X-chromosome inactivation in peripheral blood granulocytes
becomes more frequent with increasing age, affecting up to half of
those over 75 years old. To investigate the mechanisms underlying this
phenomenon, X-inactivation profiles in 33 monozygotic and 22 dizygotic
elderly twin pairs were studied. Differential methylation-sensitive
restriction enzyme cutting at a hypervariable locus in the human
androgen receptor gene (HUMARA) was studied on purified
granulocytes using T cells as controls. A large genetic effect on
skewed granulocytic X inactivation was shown (P < .05); heritability was estimated to be 0.68. A minor part (SD .0151 relative
allele frequency [ie, larger/smaller] units) of the observed variance
is due to experimental error. A further contributor to acquired skewing
is stochastic asymmetric stem cell division, which was modeled and
shown as unlikely to account for a substantial part of variance. Two
monozygotic twin pairs had X-inactivation ratios skewed markedly in
opposite directions, evidence for a further stochastic mechanism,
suggestive of a single overrepresented clone. In conclusion, all 3 suggested mechanisms contribute to acquired X inactivation but the
dominant mechanism is genetic selection. The observed proportion of
putatively clonal hematopoiesis is similar to the lifetime incidence of
hematopoietic stem cell malignancy consistent with the concept that
clonal hematopoiesis precedes stem cell malignancy.
(Blood. 2001;97:1274-1281) One of 2 X chromosomes is randomly inactivated
early in female embryonic development,1 so that it becomes
transcriptionally inactive and thereby equalizes the dosage of X-linked
genes between males and females. After this period, techniques able to
distinguish between the 2 X chromosomes can be used to track the fate
of the 2 different cellular populations. Initially distinction was
achieved using polymorphic enzyme variants,2 but, more
recently, the fact that placental mammals methylate the inactive X
chromosome and certain restriction enzymes selectively cut the
unmethylated allele has allowed more widespread
application.3,4 In particular, the human androgen receptor
locus has been found to be useful due to its high proportion (about
90%) of polymorphism.5 In this way, many
tumors,6 including leukemias,7,8
myelodysplasia,9 and myeloproliferative
disorders,10-12 have been shown to express only one X
chromosome, implying derivation from a single cell.
The process of X inactivation is thought to be initiated by a
cis-acting element at the X-inactivation center,
Xist,13-16 first expressed at the 4-cell stage. A
genome-wide demethylation occurs between the 8-cell stage and the
blastocyst stage, so that Xist expression is expressed randomly with
respect to the paternal and maternal X chromosomes. The X inactivation
that ensues, before the gastrula stage, is then believed to be random.
X inactivation, or lyonization, ratios in tissues then follow a
binomial distribution. This theory has allowed estimation of the number
of hemopoietic precursor cells at the time of lyonization to be
calculated in bone marrow,17-20 with other organs tending
to inactivate at different times.21 However, as more
experience has been gained it was suspected,22 then
demonstrated, that it is a common event occurring in up to half of
elderly women.20,23-25 Furthermore, this acquired skewing
seems to be most marked in the granulocytic fraction, the distribution
for elderly T cells being similar to that for younger subjects.
Three mechanisms underlying acquired skewed X inactivation have been
proposed. First, a "selective advantage" of one X chromosome over
the other, the only nonstochastic mechanism.26 This is a
well-described phenomenon in the extreme case where one X chromosome is
known to carry a disease gene and appears to be selected
against.27 That this mechanism can operate in the absence
of an obviously deleterious phenotype has been shown in cats, where the
X chromosome of the Geoffroy cat has a selective advantage over that of
the domestic cat.28 Furthermore, a genetic influence on
X-chromosome representation in the blood of elderly monozygotic human
twins has been reported.29 Second, because it is believed
that stem cell division may stochastically result in zero, 1, or 2 daughter stem cells,25,30 certain stem cells may become
overrepresented or correspondingly underrepresented by chance. This
effect may be accentuated by stem cell depletion.30 Third
is the expansion of a clone derived from a single stem cell or stem
cell precursor with a "proliferative advantage."
In this paper, the importance of the first proposed mechanism is
assessed by reporting the skewing of X inactivation in monozygotic and
dizygotic twins. If genetic selection were an important mechanism, then
the direction and magnitude of acquired skewing in granulocytes compared to T cells should be more similar in monozygotic twins than
expected by chance alone. We assess stochastic mechanisms by both
measuring the variance of the difference within twin pairs beyond
experimental error and also by modeling stem cell division mathematically. Finally, by deducting the contributions of the first 2 mechanisms, we assess the relative importance of the third.
Subjects
Cellular fractionation
X-chromosome inactivation analysis DNA was extracted from granulocytes and T cells using the Nucleon kit (Scotlab, Coatbridge, United Kingdom).Analysis of the X-inactivation status at the HUMARA locus was performed according to Allen and coworkers5 with slight modifications. DNA (2 µg) was incubated with 20 U HpaII (MBI Fermentas, Vilnius, Lithuania) in a 30-µL reaction; then 3 to 6 µL of the restricted product was subject to polymerase chain reaction (PCR) in 10 mM Tris HCl, pH 8.8, 50 mM KCl, .08% Nonidet-40 using 1.5 Us Taq DNA polymerase (MBI Fermentas) on a Techne Progene (Cambridge, United Kingdom) thermal cycler. Primer sequences were 5'-GCT GTG AAG GTT GCT GTT CCT CAT-3' and 5'-TCC AGA ATC TGT TCC AGA GCG TGC-3'. Cycling conditions were 120 seconds at 40°C, 300 seconds at 95°C: 28 × 45 seconds at 95°C, 30 seconds at 60°C, 30 seconds at 72°C. The former primer was labeled with 5' FAM (Oswel, Southampton, United Kingdom). PCR products were analyzed on 4% denaturing acrylamide gels using an Applied Biosystems Prism 377 (PerkinElmer, Foster City, CA). Band quantitation was performed using the peak values defined by ABI software. Data were taken as a ratio of peak heights of the longer to shorter alleles. No correction was performed for efficiency of PCR of the 2 alleles using undigested samples because we found that the degree of methylation of each allele was inversely correlated with efficiency of amplification. This effect will be analyzed in a subsequent paper (in preparation). Statistical analysis Ideally, a summary measure of the direction and magnitude of acquired skewing in granulocytes away from T cells would be used to analyze concordance between twin pairs. However, due to the underlying distribution of T-cell values, no such unbiased measure exists. To illustrate this point, consider whether G = 0.7 versus T = 0.5 exhibits a greater or lesser degree of skewing than G = 0.2 versus T = 0.1. Instead, we analyze the concordance of allele ratios for each cell type.The statistical analyses presented here are of 3 forms: nonparametric randomization tests, Pearson or Spearman correlations on both untransformed and transformed data, and Bayesian inference Using Gibb's Sampling using the BUGS program.31 For randomization tests, a statistic is calculated from the data and is then compared to a large number of such statistics calculated from randomly matched pairs of individuals. These were generated through permutation, by selecting one member of each twin pair, and matching unselected twins at random. The P value of the test is the proportion of permuted values more extreme than our observed value. We can measure the direction of drift of granulocytes from T cells by
subtracting the observed proportion of the upper allele of the
granulocytes from the proportion in the T cells. The degree of drift
can then be compared in the twin pair by subtracting this measurement
of drift in one of the pairs from the other. In this case, if the
degree of acquired skewing were the same in each of the twin pairs then
the difference would be 0. If they were different, and we ignore the
sign by taking the modulus, that is
|x|, then the value would be
greater. In summary,
d = |(t1 To make the data amenable to analysis using normal
distributions, the natural logarithm of the ratio of the height of the longer, hl, and shorter, hs, allele The BUGS package is designed for complex problems with the potential to make inferences about many unknown parameters. The program does not output point estimates; rather it generates the entire joint distribution of the parameters of interest. This is in the form of large (typically 10 000 here) numbers of samples from which we can recreate the distribution or calculate statistics such as the median or mean as point estimates. The structure of these models can be described as Directed Acyclic Graphs. We used 2 models here: one for the joint estimation of experimental errors and the variance covariance matrix, described in this section, and one to estimate stem cell numbers, described in a later section. Further details of the models and code are available from our Web site, http://www.maths.abdn.ac.uk/~ijw/BUGS. For many of the twin pairs we have results from 2 PCR reactions and 3 gel runs, for others 2 gel runs and either one or 2 PCR reactions. This
gave us the opportunity to investigate the relative errors in different
parts of the genetic analysis: digestion, PCR, gel electrophoresis, and
quantification. The errors arising from the quantification of the gel
peaks were very small (data not shown). To model these inferences we
used a 2-stage process. If the logit of the allele frequency for a cell
type in an individual is r, then the logit frequency after
extraction and the PCR reaction is
rpcr = r + epcr,
where epcr is a normally distributed error term
with mean 0 and SD The running of the gel and quantification of bands was also
assumed to produce an error, erun, which is
also normally distributed with mean 0 and SD
BUGS allowed us to take account of these errors and estimate their SDs, assuming independence between errors. BUGS treats the true values of r and rpcr as unobserved random variables, and samples from the joint distribution with the error SDs conditional on the observed set of robs. The logit T-cell relative allele frequencies and logit granulocytic relative allele frequencies, r, were then assumed to come from a multivariate normal distribution with mean 0, with an unknown variance-covariance matrix that could be different for both monozygotic twin pairs and dizygyotic twin pairs. BUGS sampled from the posterior distribution of covariance matrices given the data. The correlation could then be calculated from these matrices. We minimized dependence on the estimates of prior parameters by using very weakly informative (flat) priors. The error terms for PCR and gel runs had independent gamma priors for the precision (1/variance) with mean 1 and variance 1000. The prior precision matrix had a Wishart prior with diagonal elements 1 and off-diagonal elements 0 giving prior correlations between twin pairs with mean 0, and variances with a large range and order of magnitude 1. Mathematical modeling of stem cell division to explain acquired skewing Assuming a constant number of stem cells, when a stem cell divides, the 2 daughter cells may both become stem cells. Alternatively, one or neither may become stem cells, instead differentiating or dying. Therefore, the progeny of any single stem cell may become overrepresented or underrepresented in later generations by chance and it has been suggested that this mechanism of asymmetric stochastic stem cell division might explain all or some of acquired X inactivation.19,23 We propose that this mechanism is equivalent to random genetic drift, which has been analyzed extensively by population geneticists.32 If a steady-state population of organisms is considered, where 2 alleles are represented with no selective pressure associated with either, the proportion of the population with either allele can similarly fluctuate with time by chance alone. If 2 organisms/stem cells are taken at random, they may both have arisen from a single organism/stem cell that has just divided or alternatively 2 different organisms/stem cells. With N organisms/stem cells and no selection, the probability that they have not come from a single cell is 1/N. The probability that after g generations they still do not share a common ancestor is
 F, where F is the probability of identity,
the probability that genes (here cells) share a common ancestral allele
more recently than at some reference in the past. The geometric
distribution for nonidentity is well approximated by an exponential
distribution, giving F = 1 exp( g/N),
where g is the average number of cell divisions and
N is the effective population size (which is the actual
population size divided by the variance in the number of offspring,
which in a purely random model is one). It can be shown that the beta
distribution is an exact model for the island model of genetic
drift,33 and is a good approximation when the initial allele frequency is 0.5 and there is no significant fixation, that is,
allele proportions of 0 or 1. Our and others' data appear to fit these
assumptions. The distribution of allele frequencies follows
approximately a beta distribution with parameters
 = (1/F 1)p and
 = (1/F 1)(1 p),
where p is the initial allele frequency.32
We measure the drift of the allele frequency of T cells away from 0.5, and the drift of granulocytes away from T-cell frequencies using g, N, and the beta distribution. The model assumes that the amount of drift is different for each twin pair and estimates the mean and variance of the individual Fs. Priors for PCR- and gel-run errors were the same as for the multivariate-normal model, described in the last section. Details of this model are available from our Web site, http://www.maths.abdn.ac.uk/~ijw/BUGS.
A total of 120 individuals comprising 33 monozygotic and 27 dizygotic pairs were analyzed. Five dizygotic pairs gave technically unsatisfactory results, mainly because of substandard cellular fractionation in one of the 4 fractions required for each pair, and
were excluded from subsequent analyses. Four monozygotic and 3 dizygotic pairs were both monoallelic or had alleles that were so close
in size that it was felt that they could not be reliably distinguished.
In one of the dizygotic pairs, only one of the pairs was monoallelic.
These rates are in accordance with previous experience at this locus.
All such findings were checked by PCR of undigested samples. These
exclusions left 29 monozygotic and 18 dizygotic pairs suitable for
statistical analysis. The data are illustrated in Figures
1, 2, and
3. As referred to above, we were unable
to develop a completely satisfactory measure of acquired skewing but
illustrate a simple measure (allele ratio in granulocytes-allele ratio
in T cells) in Figure 4.
Randomization statistics The randomization and simple correlation tests were performed on the mean of the results from each individual; no account was taken of experimental error. The statistic d was calculated, using the first equation, to be 2.67 for monozygotic pairs and 1.4 for dizygotic pairs (P < .003 ± .0005 and < .3 ± .0045, respectively).Simple correlation The major effect is that the allele ratio of granulocytes is highly correlated with that from T cells within any individual (Pearson correlation coefficient 0.87). The Pearson correlation coefficients (95% confidence intervals) between the untransformed allele ratios within each twin pair are 0.24(0.10-0.59) and 0.52(0.26-0.79) for the
T-cell and granulocytic fractions, respectively, with those for
dizygotic twins 0.38(0.02-0.77) and 0.25(0.19-0.68), respectively.
Corresponding Spearman (nonparametric) coefficients are 0.28, 0.46, 0.24, and 0.20, respectively.
For subsequent analyses the mean of the logit (hl/hs) was
considered; modeling experimental error as assessed by duplicate measurements is considered in a later section. The Pearson correlations (95% confidence intervals) between the T-cell and granulocytic values
of monozygotic twins are 0.21( The only statistically significant result is that for granulocytes within the monozygotic twin pairs. These results give an indication of the association between the twin pairs but take no account of any experimental error. Measuring experimental error In units of relative allele frequency (ie, longer/shorter), the estimated SDs are given in Table 1, based on runs of length 10 000 from BUGS. These indicate that levels of experimental error are low compared to other sources of variation in the models. The errors of the 2 stages of measurement appear to have approximately the same magnitude and have considerable overlap. This hierarchical model for relative allele frequencies is used in subsequent analyses unless otherwise stated.
Association between allele frequencies in different twins The means of all the correlations, illustrated in Figure 5, are more than 0, indicating a positive correlation. Only the granulocytic allele frequencies for monozygotic twins have a negligible proportion of the distribution less than 0. For the monozygotic T cells, dizygotic T cells, and granulocytes, about 10% of the distribution is below 0, which suggests some congenital effect also.
The genetic component can be expressed as the ratio of additive genetic
variance to total phenotypic variance (h2). In the case of twins, this can be expressed as
h2 = 2(rMZ
Mathematical modeling of stem cell division to explain acquired skewing We use prior distributions for N and G, which are shown in Figure 6 as dotted lines: a distribution for N, which is centered around 106 but with values from 105 to 107,36-38 and a distribution for g, which had a mean of 50 but allowed values from 0 to 400.39 The inferred distributions are well away from the prior values, indicating that the random drift model is insufficient to explain the amount of drift seen in these allele frequencies. In other words, only an unrealistically low number of stem cells and/or an unrealistically high number of divisions could wholly account for the amount of acquired skewing observed. Indeed, Abkowitz and coworkers had to decrease the number of stem cells to about 30 before stochastically acquired skewing was evident.30
The main finding of this study is a large genetic component in the determination of asymmetric methylation of X-chromosome alleles in the granulocytes of elderly twins. This is in accordance with a recent paper by Christensen and colleagues.29 Our data extend these observations. Not only do we present data comparing X inactivation in granulocytes versus T cells, rather than just peripheral blood, but we also have analyzed the effect in dizygotic as well as monozygotic twins, which permits an estimate of heritability. Furthermore, our estimates of correlation and therefore heritability take into account experimental error. Finally, we have provided a quantitative analysis of acquired stochastic skewing. Our estimate of the heritability of acquired skewing is 68% of the observed variance in granulocytic allele frequencies. Although the conclusion that genetic factors are important is statistically significant, it should be emphasized that the confidence intervals of the estimate of heritability are wide (0%-100%), due to the relatively low number of dizygotic twins analyzed. We believe the most plausible mechanism underlying this phenomenon is genetically determined selection of hematopoietic stem cells (HSCs) with one active X chromosome over those with the other, although other possible mechanisms are discussed later. Stem cells are believed to divide throughout life. After each division, the 2 daughter cells may remain as stem cells or either differentiate or die. The first of these possibilities is believed to occur with a probability of 0.5, so that each stem cell has a probability of 1.0 of continuing as a stem cell after division. Furthermore, good evidence indicates that this choice is stochastically determined, both with respect to fate and time.30,40 If the replacement ratio were higher in the stem cells with one X chromosome active than those with the other, then one X chromosome would predominate over the other with passing years. Because this effect would likely be exponential, the absolute difference in ratio from 1.0 need only be relatively small. To estimate the magnitude of this effect, it is necessary to know the mean rate of stem cell division, which has not been measured directly in humans. However, extrapolating from the rate of telomere loss with age,41 as well as an independent approach analyzing the randomization of mutant cells with age,39 indicates that human HSCs divide about once per year. It seems unlikely that division occurs much less often. In this case, a difference of 0.02 in the replacement ratio (1.01 for one X chromosome, 0.99 for the other) would lead to a ratio of 3.32 in the ratio of the 2 alleles over 60 years or divisions. Likewise, a difference of 0.002 in the replacement ratio (1.001 for one X chromosome, 0.999 for the other) would lead to a ratio of 1.13. These figures span most of the reported range of acquired skewing. Furthermore, this mechanism, being exponential, is consistent with the degree of acquired skewing being inapparent throughout most of the life span, then apparently increasing markedly over the age of 60. However, longitudinal data from Safari cats imply that the process of genetic selection may be more complex than the simple exponential model considered here.28 The degree of skewing seen in our study was less than that reported by others. We believe the most likely explanation for this discrepancy is that our subjects were slightly younger than the subjects of other studies. Another possible explanation is that both the number of stem cells and their cycling rate increase in old age. Although the number of stem cells is believed to remain approximately constant with respect to age, some evidence indicates that the number may increase in elderly mice.42,43 Although the degree of acquired skewing in our study is relatively weak, it appears to be common. Perusal of Figures 1 through 4, and the supporting randomization statistic from the first equation, indicate that the deviation of granulocytic from T-cell allele ratios tends to be in the same direction even when the degree of deviation is small. Thus, it appears that most X-chromosome pairs have some degree of differential selective pressure that becomes apparent after many cell divisions. However, the degree of selection varies between different pairs of X chromosomes and so the time of life at which the difference becomes apparent also varies. We would predict that if sufficiently old individuals were studied most would exhibit acquired skewing, even by the rigorous criteria of other authors.20,23-25,29 The second main finding of this study is that there is probably a congenital component in the determination of asymmetric methylation of X-chromosome alleles in the T cells of elderly twins. This may arise from some form of genetic determination or a shared placental circulation. On one hand, evidence from a study of X-inactivation ratios of monozygotic twins during childhood revealed that the two thirds of monozygotic twins who were monochorionic had more similar allele ratios than those of dichorionic monozygotic twins.44 Although the form in which those data were reported precludes exact comparison with our data, when our data for T cells are presented in a similar way the 2 distributions are not easy to distinguish (analysis not shown). This observation suggests that the main reason for the correlation of T-cell ratios in our study is that many twins shared a circulation in utero. On the other hand, the degree of similarity in T cells in our study was similar in both dizygotic and monozygotic twins. In dizygotic twins, many of the alleles could be clearly distinguished from one another and we saw no evidence of a contribution from any "third" alleles. These observations suggest a degree of genetic determination of T-cell allele ratios. T cells are relatively long lived and so, in studies on X inactivation in adults, they have been considered to reflect X-inactivation status at the time of birth. Furthermore, the status at the time of birth is assumed to be determined randomly, in fact by a binomial process where the number of cells at inactivation is about 7 to 15.17-20 If T-cell inactivation ratios are partly genetically determined, then one or both of these assumptions are wrong. A priori considerations concerning T-cell physiology would suggest the former assumption is inaccurate in at least 2 ways. First, although most T-cell production from HSCs occurs early in life, some production continues throughout life45,46 and so skewed HSCs will result in skewed T cells, although the degree of skewing will lag behind that in the granulocytic fraction. Second, T cells comprise a pool of constant size within which clones dynamically expand and contract depending on antigenic exposure.47 These processes should also contribute to stochastically determined variance. It is also possible that the latter processes are partly determined by polymorphic X-linked determinants, but this would be expected to be subject to too many uncertainties to make quantitative modeling worthwhile. Furthermore, the assumption that the distribution of inactivation ratios is determined by a small number of cells at the time of inactivation may also be wrong. Several other explanations are also possible. First, it is possible that some alleles are preferentially amplified in the PCR reaction over others. Although this can be controlled for by comparing prerestriction and postrestriction ratios, our unpublished data (manuscript in preparation) suggest that methylation status may affect the predigestion ratio, making it difficult to quantitate such an effect. Second, the process of X inactivation itself might be subject to polymorphic X-linked determinants.48 In particular, it is possible that a residual degree of imprinting at the Xist locus before gastrulation may render the process nonrandom. Our data cannot cast light on these possibilities; longitudinal studies on twinned neonatal blood and other family members would have to be studied. Whatever the mechanism underlying the correlation of T-cell ratios, our data indicate that caution should be exercised in regarding T cells as controls for the original state of X-inactivation. Although our data indicate that genetic factors are important determinants of acquired skewing, this effect does not account for all of the observed variance. Experimental error accounts for some of the remaining variance, but it seems plausible that asymmetric stochastic cell division accounts for much of the remaining variance. However, in addition to our experimental data, we have provided a quantitative analysis of the likely effects of this mechanism on acquired skewing and have shown that, on current estimates of stem cell number and turnover, the mechanism is unlikely to account fully for the data. Although it would be possible in principle to use the observed residual variance to estimate stem cell number and turnover, we feel the uncertainties in such a process would make the values of the parameters obtained of little use. It is also possible that environmental effects contribute but these would be difficult to analyze. Finally, 2 monozygotic individuals exhibited markedly skewed
granulocytic X inactivation compared to their respective T cells and
compared to their cognate twin (Figures 4 and 7). The degree of discrepancy is beyond that which can be easily explained by any
stochastic asymmetric division mechanism superimposed on genetic selection. We suggest that these cases represent overrepresentation of
a single clone of cells. It is of interest that this frequency is about
the same as the proportion who will go on to develop a hematopoietic
stem cell malignancy (myeloproliferative disorders, chronic myeloid
leukemia, most acute myeloid leukemia and myelodyplasia in the elderly)
over the next 30 years.49 However, the peripheral blood
count of one of these 2 individuals was not significantly different
from that of either their twin or the other individuals in the study.
Data on the other individual were not available.
In summary, the mechanisms controlling X-inactivation ratios in normal subjects are complex. Our data show that there is a large genetic component in the determination of this ratio in granulocytes and indicate a smaller genetic component in the ratio of T cells. It seems likely that stochastic asymmetric stem cell division contributes to acquired skewing, but is unlikely to be the major contributor. Two of the 94 informative subjects studied had X-inactivation ratios skewed markedly in the opposite direction to their twin, which may be explained by clones with a proliferative advantage.
We thank Rona Morrison for many of the DNA extractions, Gabriella Surdelescu for blood collection, and Kourosh Ahmadi for assistance with the twin analysis.
Submitted April 4, 2000; accepted October 6, 2000.
Supported by the Aberdeen Royal Infirmary Leukaemia Research Fund. The Twin Research Unit receives grants from the Arthritis and Rheumatism campaign, the Wellcome Trust and Gemini Genomics Ltd.
The publication costs of this article were defrayed in part by page charge payment. Therefore, and solely to indicate this fact, this article is hereby marked "advertisement" in accordance with 18 U.S.C. section 1734.
Reprints: Mark A. Vickers, Department of Haematology, Medicine and Therapeutics, University of Aberdeen, Foresterhill, Aberdeen, AB25 2ZD, UK; e-mail: m.a.vickers{at}abdn.ac.uk.
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© 2001 by The American Society of Hematology.
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A. Mankad, T. Taniguchi, B. Cox, Y. Akkari, R. K. Rathbun, L. Lucas, G. Bagby, S. Olson, A. D'Andrea, and M. Grompe Natural gene therapy in monozygotic twins with Fanconi anemia Blood, April 15, 2006; 107(8): 3084 - 3090. [Abstract] [Full Text] [PDF]
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E. Henckaerts, H. Geiger, J. C. Langer, P. Rebollo, G. Van Zant, and H.-W. Snoeck Genetically determined variation in the number of phenotypically defined hematopoietic progenitor and stem cells and in their response to early-acting cytokines Blood, May 13, 2002; 99(11): 3947 - 3954. [Abstract] [Full Text] [PDF]
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Abstract
Introduction
often
called the logit transformation
pcr.
