# Abstract

Hematopoietic dysfunction has been associated with a reduction in the number of active precursors. However, precursor quantification at homeostasis and under diseased conditions is constrained by the scarcity of available methods. To address this issue, we optimized a method for quantifying a wide range of hematopoietic precursors. Assuming the random induction of a stable label in precursors following a binomial distribution, the estimation depends on the inverse correlation between precursor numbers and the variance of precursor labeling among independent samples. Experimentally validated to cover the full dynamic range of hematopoietic precursors in mice (1 to 10^{5}), we utilized this approach to demonstrate that thousands of precursors, which emerge after modest expansion during fetal-to-adult transition, contribute to native and perturbed hematopoiesis. We further estimated the number of precursors in a mouse model of Fanconi Anemia, showcasing how repopulation deficits can be segregated into autologous (cell proliferation) and non-autologous causes (lack of precursor). Our results support an accessible and reliable approach for precursor quantification, emphasizing the contemporary perspective that native hematopoiesis is highly polyclonal.

# Introduction

The continuous self-renewal and differentiation of hematopoietic stem and progenitor cells (HSPCs) are fundamental to blood production. Even though rare cases exist where a single HSPC clone supports hematopoiesis, the HSPC population contributing to homeostatic hematopoiesis is usually highly polyclonal [1]. For example, the number of HSPCs actively participating in white blood cell production was estimated to range from 20,000 to 200,000 in humans [2,3]. Conversely, a decline in the number of active hematopoietic precursors has been linked to hematopoietic dysfunctions. For example, in humans older than 70 years of age, hematopoietic dysfunction coincides with an abrupt reduction in the HSPCs population actively contributing to blood production [3].

These observations underscore the association between a low number of active hematopoietic precursors and hematological dysfunction. Yet, few methods are suitable for quantifying active hematopoietic precursors in a native environment [2–7]. In mice, methods utilizing *in situ* barcodes often suffer from barcode homoplasy, preventing total precursor number estimation [8,9]. In humans, estimations based on somatic mutations and computational modeling carry high uncertainty [2,3]. The absence of precise precursor quantification methods in their natural environment hampered the study of precursor numbers across different conditions and their potential usage as predictive functional markers.

In mice, the quantification of developmental hematopoietic precursors has been achieved using mice with a Confetti cassette [10]. This cassette can randomly recombine and express one of four fluorescence proteins (FPs, being RFP, CFP, YFP, or GFP) upon Cre induction, resulting in variability in Confetti expression pattern in mice inversely correlating with precursor numbers (Figure 1A) [10]. While suitable for developmental hematopoiesis, this method has limited linear range (50-2500), impeding its potential application to adult hematopoiesis or clonal hematopoiesis. To measure hematopoietic precursors in various conditions, expansion of the detection range is desired.

Interestingly, the random induction of Confetti colors in HSPCs bears similarity with X-chromosome inactivation (XCI). In XCI, one of the X chromosomes is randomly inactivated in precursor cells, a process that adheres to a binomial distribution. Formula derivation from binomial distribution implied that higher XCI variance among individuals correlates with a smaller number of precursors at the time of inactivation (Figure 1B). As XCI is faithfully maintained in the progeny, this correlation has been used to estimate precursor numbers from mature blood cells in human and mouse, leading to the discovery of the first mutation (Tet2) that contributes to clonal hematopoiesis [6,11–13]. Nonetheless, XCI occurs exclusively in females, limiting its applicability in males. Additionally, XCI takes place during early development when few precursors are present, resulting in low sensitivity in adulthood [14].

Building on insights from Confetti mice and XCI studies, we investigated whether random induction of Confetti FPs in precursor cells can be similarly modeled by a binomial distribution, thus the variance of FPs inversely correlates with precursor numbers. Based on this relationship, we asked if we could broaden the measurable range of precursor number, which would allow us to measure the numbers outside the existing correlation range.

Examining the premises of binomial distribution and setting some assumptions, we established that the random induction of FPs among a group of mice or cells could be modeled by a binomial distribution. Experimental validation established a broader linear range, covering the full spectrum of precursor numbers (1∼10^{5}) and overcoming the prior range limit. We leveraged this correlation to probe the number of hematopoietic precursors at homeostasis, post-myeloablation, during developmental expansion, and in a mouse model of inherited bone marrow failure.

# Results

## Binomial distribution underlies the inverse linear correlation between FP% variance and the precursor numbers

To broaden the limited correlation range, we aimed to elucidate the mathematical relationship between variance and precursor numbers [10]. Inspired by XCI, we asked how the stochastic induction of Confetti FPs in precursors may satisfy the premises of binomial distribution [15,16]. We found that when we assume the number of precursors remain the same for the condition tested, then induction of FPs meet the required premises : (1) the number of precursors, denoted as *n*, remains constant within a group of mice or cells; (2) each observation (e.g. each precursor) is independent; (3) each observation yields one of two outcomes (e.g., it signifies the presence or absence of RFP in a precursor); (4) the probability of success, represented as *p* (e.g., the likelihood of a precursor expressing RFP upon Confetti induction), remains consistent across all observations.

Should the induction of a FP adhere to a binomial distribution, precursor numbers can be estimated using the following equation:

where signifies the estimated number of precursors, represents the estimated probability of a precursor being one given FP (e.g., ), and denotes the estimated coefficient of variance (CV) of one given FP (e.g., ). CV is the standard deviation divided by the mean, utilized by the empirical correlation formula.

The equation proposed a direct linear relationship between the precursor number and the CVs of individual FP, supporting the empirical correlation formula [10]. Indeed, by analyzing a published dataset providing precursor numbers and the corresponding distribution of FPs, we found that the correlation between *n* and individual CVs of FP exhibits superior fit (>0.93), higher than the empirical correlation equation based on all three CVs (0.75) (Figure S1A) [10]. Moreover, according to equation 1, the y-intercept of correlation between precursor number and CV was influenced by FP_{mean}%, while the slope was the same (-2) regardless of FP_{mean}%. Given the unequal value of RFP_{mean}%, CFP_{mean}%, and YFP_{mean}% in the published dataset, their correlation equations showed significantly distinct y-intercepts (p<0.0001) (Figure S1B). In contrast, the slopes of these correlation equations were similar (p=0.49, with all 95% confidence intervals encompassing -2, the theoretical value).

In conclusion, the FP induction in precursor cells can be modeled by a binomial distribution with the assumption that precursor numbers are constant among a group of mice. This sets the mathematical basis for the inverse linear correlation between variance of FP% and the number of precursors.

A broad range of precursor numbers correlates with variance of FP%

While the correlation formula derived from binomial distribution does not impose any range limitation, experimental errors may confound the measurement of variance. We next aimed to experimentally confirm this correlation. To streamline the calculation, we used standard deviation instead of CV to compute variance. The correlation between standard deviation and precursor numbers is expressed through the following equation:

where denotes the estimated standard deviation of a given FP% (e.g. ).

Given this equation, exhibits a linear and inverse correlation with . Indeed, , and exhibited linear and inverse correlation with in the published data (Figure S1C) [10].

To simplify the validation, we used a two-color cell model HL-60 bearing one of the two FPs (BFP and GFP, GFP represents non-BFP) (Figure 1C). Although the Confetti cassette recombination can generate one of four colors, our estimation is based on a given FP (e.g. a precursor expresses RFP or not), making this simplification justifiable.

We first proved that neither BFP nor GFP HL-60 cells had a competitive growth advantage over the other, ensuring that HL-60 progenies mirrored the seeding population (Figure S1D). We next sorted one to 10^{5} cells into individual wells and allowed them to proliferate for at least three generations before assessing BFP% at the end of the culture (Figure 1C). We seeded up to 10^{5} cells as 1.4x10^{5} non-HSC LSK and 5.2x10^{3} active HSCs were previously estimated in an adult female mouse, which corresponded to the highest possible precursor numbers in mice [17]. We considered the survival rate of cells in wells receiving a single HL-60 cell (53% to 60%), to ensure the accuracy of the number of cells seeded.

Consistent with the proposed correlation, as seeded number increased, BFP% standard deviation decreased (Figure 1D and E). The variance of BFP% displayed an inverse correlation with the seeding numbers (R^{2} = 0.996) (Figure 1F). After normalizing for cell survival rates, the calculated numbers closely aligned with the expected numbers (Figure 1G). We had anticipated that measurement of small variance in high precursor numbers may be confounded by experimental errors. Yet, at 10^{5} seeded cells, the estimated number of precursors did not plateau, suggesting minimal impact from experimental error even at 10^{5} cells.

## Experimental practices for accurate precursor number measurement

It is crucial to ensure the accuracy of variance measured because variance of FP% is solely used for estimation. Based on the data from the two-color HL-60 model, we concluded that there were at least three experimental practices required for accurate cell estimates: (1) exclusion of outliers; (2) sufficient flow cytometry recorded events; (3) sufficient sample size per group. Both outliers and insufficient recorded events inaccurately inflate sample variance, leading to underestimation of precursor numbers (Figure S1E and F). We found that the minimum recorded events increase in tandem with the seeded number, in contrary to the reported 500-event threshold (Figure S1F) [10].

While having a small sample size per biological replicate is possible, the variability of estimations among replicates would be high (Figure S1G). Practically, achieving a large sample size (>20) is cumbersome in mice. To determine a feasible sample size for relatively accurate estimates, we resampled datapoints to calculate the amount of variability reduction as sample size increased (Figure S1H). Our analyses revealed that five samples per group were sufficient to dramatically reduce error, where additional increase in sample size led to marginal error reduction. We therefore used at least five mice per biological replicates for our precursor estimations.

## Inducible HSC-Scl-CreER^{T}-targeted Confetti labeling in the active blood precursors at the adult stage

To label hematopoietic precursors and quantify their number *in vivo*, we considered the Cre mouse line to be crossed with Confetti. Historically, hematopoietic precursors were thought to be hematopoietic stem cells (HSCs) capable of long-term repopulation. However, recent studies indicate that multipotent progenitors (MPPs) also contribute alongside HSCs in maintaining blood production [18–21]. Hence, both HSCs and MPPs should be labeled.

Among limited Cre mouse lines capable of labeling HSCs and MPPs simultaneously at the adult stage (such as Rosa26^{CreERT2}, Mx1-Cre, and HSC-Scl-CreER^{T}), we chose HSC-Scl-CreER^{T} because of its preference for labeling HSPCs (immunophenotypically defined as Lin^{-}Sca-1^{+}cKit^{+} (LSK)) [22]. To validate the specificity of HSC-Scl-CreER^{T}, we generated mice possessing a single Confetti allele and homozygous HSC-Scl-CreER^{T} alleles. We then examined Confetti expression one day after two-day tamoxifen administration. We observed Confetti expression in the LSK population, consistent with prior reports of HSC-Scl-CreER^{T} activity (Figure 2A, Figure S2A-C). Confetti expression was additionally detected in T cells, NK cells, CD41^{+} cells, non-inflammatory monocytes (SSC-A^{low}Ly6C^{-}Ly6G^{-}CD11b^{+}), common myeloid progenitors (CMP, Lin^{-}Sca-1^{-}cKit^{+}CD16/32^{-/low}CD34^{+}), and granulocyte-monocyte progenitors (GMP, Lin^{-}Sca-1^{-}cKit^{+}CD16/32^{+}CD34^{+}) [20] (Figure S2D-G). Considering the relatively shorter lifespan of these cells compared to HSC/MPP, the labeling in these cells should minimally impact precursor calculations, especially with a chase period post-labeling. While the Confetti induction in the relatively long-lived T cells precludes estimation based on mature T cells, we concluded that HSC-Scl-CreER^{T} remained a practical choice for labeling active hematopoietic precursors.

The stability of Confetti labeling after induction is required for binomial distribution. Therefore, the absence of background Cre activity after Confetti induction is critical. We determined the background Cre activity in HSC-Scl-CreER^{T}/Confetti animals by two approaches: (1) detecting Confetti expression in non-induced animals; (2) identifying cells co-expressing two Confetti FPs months after tamoxifen induction due to cassette “flipping” from background Cre activity. We observed no Confetti-expressing cells without tamoxifen treatment in mice up to 50 weeks old and minimal co-expression of two Confetti FPs in induced HSC-Scl-CreER^{T}/Confetti animals (Figure S3A-B). Conversely, Vav-Cre/Confetti animals constitutively express Cre, resulting in ∼15% cells co-expressing two Confetti colors in peripheral blood (PB) T cells (Figure S3C-D). Both pieces of evidence support minimal Cre background activity in HSC-Scl-CreER^{T} and its feasibility to be used as a Cre driver for precursor number calculation.

## Variance of FP% inversely correlates with precursor numbers *in vivo*

To ascertain the inverse correlation between variance of FP% and the number of hematopoietic precursors *in vivo*, we first investigated the variance of FP% in mice hosting various numbers of hematopoietic precursors. We generated these mice by non-competitively transplanting 0.25x10^{6} or 4x10^{6} induced CD45.2^{+} HSC-Scl-CreER^{T}/Confetti mouse bone marrow (BM) cells into CD45.1^{+} recipient mice (Figure 2B). Given the constant frequency of precursors in the donor BM (1/10^{5}) and the varying doses of donor BM cell received, these mice received approximately 2.5 (“low precursor number”) or 40 (“high precursor number”) precursors [15,23–25]. While similar experiments transplanting defined numbers of precursors have been reported, the estimation for precursor numbers lower than 50 has not been explored.

Due to the scarcity of hematopoietic precursors in the BM, the precursor number seeded in recipients followed Poisson distribution instead of being constant, violating premise (1) of binomial distribution. Nonetheless, our simulations showed that the seeding number variation among recipient mice was relatively small, therefore the variance resulting from precursor number differences still dominated and inversely correlated with precursor numbers. A minor problem was that the estimated numbers were not at one-to-one ratio to expected numbers at low precursor number range (<10, see Methods) (Figure S4A).

As cells were not 100% labeled with Confetti, for clarity, we use “FP_{PB}%” or “FP_{BM}%” to represent the frequency of a given FP in the PB or BM, and use “FP_{Conf}%” to represent the frequency of a given FP in the Confetti^{+} population. For total precursor number calculations, we normalized the number calculated from the Confetti-labeled population to Confetti labeling efficiency.

As expected, we observed higher RFP_{Conf}% variance across all PB cell types in mice belonging to the “low precursor number” groups (Figure 2C and Figure S4B). Since variance of any FP following a binomial distribution inversely correlates with precursor numbers, we also observed higher CFP_{Conf}% and YFP_{Conf}% variance in the “low precursor number” groups (Figure S4D-E). Following the same principle, we observed higher RFP_{PB}%, CFP_{PB}%, YFP_{PB}% and Confetti% variance in “low precursor number” mice (Figure S4F).

Applying equation 2, we found that the precursor numbers of B cells and myeloid cells were noticeably higher in the first two months than at four months post-transplantation, suggesting transient progenitor contribution at early time points (Figure 2D). At four months post-transplantation, the estimated precursor numbers aligned with the expected values (in myeloid cells, 94 for “high precursor number” groups, three for “low precursor number” groups, Figure 2D). Again, for any FP following binomial distribution, variance of FP% inversely correlates with precursor numbers and thus can be leveraged to calculate precursor numbers (Methods). Since different FPs measured the same population of precursors, we expected the estimations from different FPs to be similar. Indeed, precursor numbers derived from RFP_{Conf}% highly correlated with those estimated from YFP_{Conf}% or CFP_{Conf}% (R^{2} = 0.885 for CFP% in Confetti^{+}, R^{2} = 0.769 for YFP% in Confetti^{+}), as well as those from RFP_{PB}%, YFP_{PB}% and CFP_{PB}% (Figure 2E, Figure S4G).

Consistent with PB data, higher variance of RFP_{Conf}% was also observed in the BM HSPCs of “low precursor number” mice (Figure S5A). The precursor numbers estimated from various HSPC subpopulations aligned well with each other and were consistent within the same group (Figure 2F). However, in “high precursor number” groups, estimates from BM HSPCs were lower than those derived from PB myeloid cells (27 for BM HSPC, 94 for PB myeloid cells, Figure 2F). This discrepancy may reflect uneven seeding of precursors to the BM throughout the body after transplantation, and the fact that we only sampled a part of the BM (femur, tibia, and pelvis). In summary, we validated the inverse correlation between variance of FP% and precursor numbers *in vivo*. Moreover, the quantification of precursor numbers was feasible even for precursor numbers outside the empirical correlation range.

## Cell frequency measurements fail to reflect the differences in precursor numbers

Given that transplantation was performed non-competitively and the recipients were lethally irradiated, we expected to see minimal differences in donor chimerism between two groups, despite drastic differences in donor precursor numbers. Indeed, although we observed substantially lower donor chimerism in mice belonging to “low precursor number” groups during the first two months post-transplantation, the chimerism differences were very small by four months post-transplantation (5.5±2.8%, Figure 2G and Figure S4B). The initial differences in donor precursor numbers did not affect PB cell frequencies except for the first month post-transplantation, when higher PB myeloid frequencies was observed in the “low precursor number” groups (Figure 2H). This suggests myelopoiesis is preferred when very few precursors are available after irradiation-mediated injury (Figure 2C).

In BM, nucleated cell counts, donor chimerism and HSPC frequencies were mostly similar regardless of donor precursor numbers, suggesting that even extremely low numbers of hematopoietic precursors can still repopulate effectively a non-competitive environment (Figure S5B-D). Therefore, in cases where hematopoietic precursors expand or attrite without competition, stem cell frequencies are less informative to study precursor activity. Measuring precursor numbers is more meaningful as low number of active precursors may be hindered by compensatory proliferation.

## Thousands of hematopoietic precursors contribute to native hematopoiesis

While the empirical formula, which measures 50-2500 precursors, supports quantification of precursors labeled at fetal stages, it may not be applicable to measure native hematopoiesis as the total precursor number may exceed 2500. Having validated the feasibility for measuring precursor numbers *in vivo* by Confetti animals, we next sought to investigate the number of active precursors contributing to native hematopoiesis. In HSC-Scl-CreER^{T}/Confetti animals, we opted to label a smaller portion of HSPCs with two-day treatment despite the potential to label up to 60% HSPCs with Confetti (CFP+YFP+RFP) by 14-day tamoxifen treatment (Figure 3A, Figure S6A). This precautionary measure aimed to mitigate potential toxicity arising from prolonged tamoxifen treatment.

Unexpectedly, we observed a successive decline of CFP_{Conf}% and CFP_{PB}% in some animals, which distorted the distribution of CFP_{Conf}% (Figure S6B and C). A similar decline was not observed in RFP_{Conf}% or YFP_{Conf}%, nor the RFP_{RPF+YFP}% (calculated by RFP_{PB}%/(RFP_{PB}%+YFP_{PB}%)) (Figure S6D and E). Declining CFP_{Conf}% was also not observed in animals where Confetti was induced during fetal development, suggesting a potential immune response to CFP in adult-induced animals (Figure S6F). Since only ∼2% of myeloid cells were labeled with CFP, we reasoned that the decline of CFP in some animals was unlikely to affect the calculation of total precursor numbers based on other FPs. Therefore, we solely relied on the variance of RFP_{RPF+YFP}% for adult precursor calculations. In transplantation studies, precursor numbers calculated with variance of RFP_{RFP+YFP}% linearly correlated with those calculated with variance of RFP_{Conf}% (Figure S4G).

To ensure accuracy, we focused on PB myeloid cells, as (1) Confetti labeling of T cells resulted from direct induction by HSC-Scl-CreER^{T}, but not differentiation from HSPCs (Figure S2D); (2) Confetti labeling (RFP and YFP) of B cells did not plateau at seven months post-induction (Figure 3B); (3) myeloid cells are of shorter lifespan. In myeloid cells, we focused on precursor numbers after four months post-induction, when their labeling reached a plateau (Figure 3B). We also examined average RFP_{RFP+YFP}% (Figure 3C). Its stability suggested an equal contribution of RFP^{+} and YFP^{+} cells to the PB, a prerequisite for estimating precursor numbers from FP% distributions in the progenies (PB myeloid cells). The average RFP_{RFP+YFP}% in BM HSPC subpopulations mirrored those observed in PB, supporting non-biased differentiation of RFP^{+} and YFP^{+} precursor cells (Figure 3C).

Fitting data to equation 2, we estimated an average of 2667 precursors contributing to native myelopoiesis (Figure 3D, average of numbers at five to seven months post-induction after myeloid cell labeling plateaued). This number closely aligns with the clone number estimated by transposon-based barcodes and statistic method in granulocytes (831/30% = 2770) [1].

The average myeloid precursor number at the time of BM analysis (1958) matched the average precursor number calculated from BM myeloid progenitors (MP, Lin^{-}Sca-1^{-}cKit^{+}) and HSPCs (1773 and 1917), but it was five-fold higher than that of LT-HSC (Figure 3E). Although LT-HSCs were conventionally believed to sustain steady-state hematopoiesis, recent studies suggest that ST-HSC and MPPs persist long-term and are the primary contributors to adult hematopoiesis [1,18,20,26]. The observed discrepancy between the number of precursors contributing to LT-HSC and those contributing to MPPs indicates that at least some MPPs were not replaced by progenitors directly differentiated from LT-HSC at seven months post-induction, affirming the long life of MPPs (Figure 3E). Furthermore, the fact that PB myeloid and BM MP precursor numbers were closer to those of MPPs than LT-HSC confirm active and long-term (at least seven months) contributions from MPPs to steady-state myelopoiesis.

Of note, the quantity of precursor does not necessarily correlate with the frequency of cell type in the BM. For example, the cell frequency of MPP2 (Lineage^{-}cKit^{+}Sca-1^{+}Flk2^{-}CD48^{+}CD150^{+}) in BM was very low, but MPP2 comprised a modest number of precursors, making its frequency-to-precursor-number ratio the lowest among the HSPC subtypes (Figure 3F and S6G). The frequency-to-precursor-number ratio reflects how well precursors of a particular type proliferate to expand their absolute cell count. The low frequency-to-precursor-number ratio of MPP2 suggests that it expands more poorly than other HSPC subtypes.

In summary, we detected thousands of hematopoietic precursors contributing to adult hematopoiesis. At the time of BM analysis, the number of PB myeloid precursors was comparable to those observed in BM MP and HSPCs.

## Precursor numbers determined by FP% variance confirmed reduced clonality of progenitors after myeloablation

Myeloablation through 5-fluorouracil (5-FU) treatment depletes most actively cycling cells, forcing quiescent stem cells to proliferate [27]. Previous studies have indicated a significant reduction in the number of clones detected within the c-Kit^{+} population (consisting of MP and HSPC) of the BM following a single dose of 5-FU treatment [8]. However, questions arise regarding whether this observed reduction is an artifact stemming from potential under-sampling of the highly expanded c-Kit^{+} population after 5-FU treatment by single-cell sequencing. Given the quantitative estimation of a wide range of precursor numbers through equation 2, we aimed to investigate whether precursor numbers within progenitor populations indeed reduce ten days post-5-FU treatment (Figure 4A).

To compare the precursor changes post-5-FU treatment, we used the animals described in Figure 3A as untreated (UT) benchmark, which were collected at the same age. At ten days post 5-FU injection, the efficacy of 5-FU treatment was validated by lower PB myeloid cell frequency post-treatment and higher frequencies of BM progenitors compared to UT animals (Figure S7A and B). The high progenitor frequencies in the BM corresponded to the depletion of cycling cells in the BM and the enhanced proliferation of HSPCs following 5-FU treatment.

Compared to UT animals, the precursor numbers of MP (including CMP, GMP, MEP) and HSPC significantly decreased, confirming a reduction in clonality in the c-Kit^{+} population (Figure 4B) [8]. By contrast, the precursor numbers of LT-HSC did not show a decreasing trend. While transplantation studies supported unchanged clonality of primitive stem cells after a single dose of 5-FU, similar investigation in a native environment has not been assessed [28]. Our findings support the notion that native LT-HSC clonality remains unaltered following one-dose 5-FU treatment. Together, myeloablation treatment reinforces how the dynamics of precursor numbers can be tracked through assessing Confetti pattern variations.

## Active lifelong precursors expand poorly in development ontogeny

HSCs are thought to undergo substantial expansion in the fetal liver during fetal development [29–31]. However, a recent study employing the empirical formula challenged this notion by quantifying endogenous lifelong hematopoietic precursors labeled at various developmental stages [32]. It revealed limited expansion of hematopoietic precursors during the fetal liver stage (from E10 to E15,1.8-to 2.7-fold) as well as a gradual and moderate increase from the fetal liver to the post-natal stage (2.4-to 10-fold) [32]. Although intriguing, most post-natal measurements in this study fell outside the empirical linear range, leaving the genuine degree of post-natal precursor expansion unknown. As our formula quantitatively assesses a wide range of precursor numbers, we set out to directly compare the numbers of precursor labeled at various development stages (E11.5 and E14.5, by one dose of tamoxifen; adult-stage, benchmark shown in in Figure 3A, all analyzed at the same age) (Figure 4C).

For accuracy, we first examined the dynamics of Confetti labeling. In E14.5-induced animals, the Confetti labeling of T cells almost doubled from one month to four months of age (4.7% at one month, 9.3% at four months), suggesting Confetti^{+}-labeled precursors contributed more to post-natal T cell than non-labeled precursors (Figure 4D). Therefore, for T cells in E14.5-induced animals, we focused on precursor numbers generated after three months of age. The Confetti labeling for E11.5-induced animals remained stable for all timepoints examined (Figure S7C).

Similar to adult-induction, the distribution of average FP% was stable for fetal-induction, supporting equal proliferation of RFP^{+} and YFP^{+} cells (Figure S7D). Unlike adult-induction, fetal-labeled precursor numbers can be calculated with various combination of FP%, since the expression of CFP introduced at the fetal stages was stable (Figure S6F). Nonetheless, for consistency, all precursor numbers were calculated with variance of RFP_{RFP+YFP}%, the one employed in adult-induction animals.

The resulting precursor numbers estimated for E11.5 and E14.5-labeled cohorts were similar in all PB cell types except at two and three months of age, echoing the previous study reporting limited lifelong precursor expansion in the fetal liver (Figure 4E) [32]. Precursor numbers calculated from BM subpopulations were also comparable between the two timepoints (Figure 4F). Although E9.5-labeled clones were reported to seed non-uniformly across bones, the precursor numbers calculated from PB myeloid cells did not significantly differ from those calculated from BM MP and HSPC in E14.5-labeled animals (Figure 4F) [8].

For comparison between fetal- and adult-induced animals, we focused on PB myeloid cells, as adult-induced animals had non-saturated labeling in B cells and non-HSPC-rooted Confetti labeling in T cells (Figure 3B). We observed a relatively small increase of precursor numbers in adult-induced animals in PB and BM compared to those labeled at the fetal stage (Figure 4E and F). The increase between E11.5/E14.5- and adult-labeled precursors were less than ten-fold, a level similar to a previous report (Figure 4G) [32].

Together, we detected minimal to no expansion of lifelong precursors in the fetal liver stage and minor expansion of expansion of lifelong precursors from fetal liver to adult stage.

*Fancc ^{-/-}*mice have normal quantity of hematopoietic precursors at steady-state

Our approach provided an opportunity to investigate the number of active HSPC precursor in the native environment of genetic mouse models. To showcase precursor quantification in genetic mouse models, we focused on Fanconi Anemia (FA), the most common inherited bone marrow failure syndrome [33]. Current FA mouse models exhibit mostly normal adult hematopoiesis at steady state but demonstrate reduced repopulation ability upon BM transplantation [34–39]. It remains unclear if their steady-state blood production is sustained by a reduced number of precursors, predisposing them to repopulation defects after transplantation.

To quantify precursor number in a mouse model of FA, we generated *Fancc*^{+/+}, *Fancc*^{+/-} and *Fancc*^{-/-} mice with a single Confetti allele and homozygous HSC-Scl-CreER^{T} alleles (Fancc^{+/+}Confetti^{fl/+}HSC-Scl-CreER^{T/T}, hereafter *Fancc*^{+/+}; Fancc^{+/-}Confetti^{fl/+}HSC-Scl-CreER^{T/T}, hereafter *Fancc*^{+/-}; Fancc^{-/-} Confetti^{fl/+}HSC-Scl-CreER^{T/T}, hereafter *Fancc*^{-/-}) [40]. Consistent with previous literature, we observed similar PB cell frequencies and blood counts between *Fancc*^{+/+} and *Fancc*^{-/-} mice (Figure S8A-C) [39]. BM nucleated cell counts, as well as HSPC and MP frequency, were mostly identical, except for ST-HSC frequencies, which were significantly reduced in *Fancc*^{-/-} mice compared to *Fancc*^{+/-} mice (Figure S8D-E).

To label hematopoietic precursors in FA animals, Confetti expression was induced at two months of age, and FP% was monitored over seven months (Figure 5A). The absence of *Fancc* did not affect Confetti labeling efficiency, Confetti labeling dynamics or average FP% (RFP_{RFP+YFP}%), suggesting precursor numbers in *Fancc ^{-/-}* can be similarly calculated (Figure 5B and Figure S8F). As in adult-induction animals, RFP

_{RFP+YFP}% was used to estimate precursor numbers. The resulting myeloid and BM precursor numbers were comparable regardless of

*Fancc*genotype, albeit

*Fancc*

^{-/-}mice had a slight reduction in HSPC precursor numbers (Figure 5C and D). These observations collectively suggest that a normal number of precursors sustained blood production in

*Fancc*mice.

^{-/-}## The number of precursors remained unchanged in mice transplanted with young donor cells

While *Fancc*^{-/-} mice have similar number of precursors with their wildtype counterparts at homeostasis, it is unknown whether their reduced repopulation ability post-transplantation stems from diminished precursor numbers, reduced cell expansion, or a combination of both [35]. To understand the underlying mechanism, we performed competitive transplantation using BM cells from three-month-old Confetti-induced *Fancc*^{+/+}, *Fancc*^{+/-} or *Fancc*^{-/-} mice along with CD45.1^{+} competitor cells (Figure 5E, Figure S9A). Consistent with previous studies, recipient mice of *Fancc*^{-/-} cells showed significantly lower donor chimerism in the PB and BM compared to those of *Fancc*^{+/+} or *Fancc*^{+/-} cells (Figure 5F, Figure S9B). Despite lower donor chimerism, PB and BM precursor numbers were unaffected in *Fancc*^{-/-} recipient mice (Figure 5G, Figure S9C-E). This suggests that reduced *Fancc*^{-/-} cell proliferation instead of fewer active precursors was likely to be the cause for the reduced repopulation capacity post-transplantation.

Ageing *Fancc*^{-/-} mice have reduced number of lymphoid hematopoietic precursors upon transplantation

Ageing *Fancc*^{-/-} mice have been reported to develop hematologic neoplasms, resulting in decreased survival [41]. To determine if aging *Fancc ^{-/-}* cells also maintain similar precursor numbers post-transplantation, we competitively transplanted BM cells from nine-month-old Confetti-induced

*Fancc*or

^{+/+}*Fancc*mice with CD45.1

^{-/-}^{+}competitor cells, a stage when aging

*Fancc*mice started to show decreased survival [41] (Figure S9F).

^{-/-}The diminished repopulation ability of *Fancc ^{-/-}* cells was reaffirmed by lower PB and BM chimerism (Figure 5H, Figure S9I). While no differences in precursor numbers were noted during the initial post-transplantation period, a slight yet consistent reduction in lymphoid precursors was observed in

*Fancc*recipient mice at three to five months post-transplantation (Figure 5I, Figure S9G and H). Changes in precursor numbers in the BM of KO recipients were less clear as we observed high variance in several HSPC subtypes (Figure S9J). Nonetheless, precursor numbers of MEP, LSK and ST-HSC showed a consistent reduction. In conclusion, aging

^{-/-}*Fancc*mice showed a modest but consistent loss of active PB lymphoid precursors post-transplantation, implying decreased lymphoid precursors additionally contribute to reduced repopulation capacity as

^{-/-}*Fancc*mice age.

^{-/-}# Discussion

The polyclonal nature of endogenous hematopoiesis imposes methodological problems on a robust dynamic measurement. Inspired by the XCI studies, we successfully employed the correlation formula informed by binominal distribution to quantify precursor number in native hematopoiesis. Using HSC-Scl-CreER^{T}/Confetti animals, we estimate thousands of precursors contributing to adult native hematopoiesis, a number comparable to the previous report [1]. This number resulted from a moderate increase during fetal-to-adult transition and responded dynamically to myeloablation by 5-FU. Applying to a mouse model of inherited bone marrow failure (Fancc^{-/-} mice), we detected normal precursor numbers at steady state and decreased lymphoid precursors upon transplantation of aging donors. In sum, the study underscores the flexibility of the approach and the value in analyzing precursor contributions *in situ*.

Although the linear relationship between variance of FP% and precursor numbers has been described, its measurable range was limited [10]. Estimates outside this linear range may erroneously fall within it, making it challenging to distinguish accurate measurements within the range from inaccurate ones beyond it [10]. Based on binomial distribution, we expanded the measurable range to encompass the possible dynamic range of hematopoietic precursors in mice, minimizing the likelihood of inaccuracies. Futhermore, the linear correlation based on binomial distribution can accommodate any labeling system that follows the underlying premises, alleviating the need for the intricate Confetti cassette.

Having established a quantitative measurement, we were initially surprised to confirm the moderate number differences between fetal and adult-precursors seen in other report [32]. The maximum increase observed (seven-fold observed in CMP) was substantially lower than the increase of competitive repopulation units (CRU) from E12 to E16 determined by limited dilution assays (∼38-fold) (Figure 4G), as well as the escalation from immunophenotype-defined HSPC counts (28-to 47-fold, from 3-5x10^{3} at E14.5 to 1.4x10^{5} at two months old) (Figure 4G) [17,30,42,43]. It is possible that we overestimated E11.5 precursors, as the numbers of lifelong E11.5 precursors were substantially higher (on average 753 PB myeloid precursor, 512 HSPC precursors) than the one to two repopulation units estimated with transplantation [44]. Nonetheless, our results were comparable to the ∼870 hematopoietic cluster cells observed at E11.5 [45]. On the other hand, we may have underestimated precursor numbers in adult-labeled animals, as most adult HSCs are quiescent [27]. However, HSC precursor numbers did not increase after induced proliferation by one dose 5-FU treatment (Figure 4B). In sum, our results suggest that the moderate precursor numbers difference between fetal- and adult-stage are likely genuine, emphasizing the analysis of hematopoiesis in a native environment. Future studies using different methods to investigate precursor activity locally is required to validate this result.

Novel methods tracing clones *in situ* offer new opportunities to study native hematopoiesis, yet most are challenging to apply to genetic mouse models [1,8,9,46,47]. Since only two mouse lines are required (sometimes Cre is already used for conditional deletion of alleles), our approach is more convenient to study hematopoiesis in mouse models of genetic disorders. Applying precursor measurements to *Fancc ^{-/-}* mice, we observed a minor decrease in precursor numbers after transplantation of aging donors. Although donor chimerism differences had been linked to difference in precursor numbers, reduced proliferation capacity may also contribute to reduced competitive repopulation capacity [25]. In this case, precursor number analysis is necessary to differentiate these possibilities.

Currently, concerns regarding clonal restriction in the context of FA gene therapy arises, as the engraftment of gene-corrected stem cells has yielded marginal clinical benefits [48]. For the first time, we demonstrated that FA cell maintaining a normal precursor quantity post-transplantation, thereby disproving clonal attrition, including putative homing deficits post-transplantation as a cause [49]. However, it is imperative to acknowledge that the majority of murine models of FA, including the *Fancc ^{-/-}* model utilized herein, do not manifest spontaneous bone marrow failure, raising uncertainty regarding the extent to which FA mouse models recapitulate the pathophysiology observed in FA patients. Future investigations in other FA mice and studies leveraging FA patient-derived materials will be pivotal in corroborating and validating the findings presented here.

While we implemented careful data processing procedure, one pitfall of our analyses was that we inferred precursor numbers from their progenies, assuming uniform and linear expansion from precursor to progenies. A recent study has showed non-uniform precursor clone sizes, although the level of non-uniformity is low [47]. In cases where the non-uniformity is high, according to mathematical modeling, we measured the major contributors to hematopoiesis[50]. Another potential caveat is that the relative contribution of Confetti-labeled precursors to blood production compared to non-labeled precursors remains unknown. Future studies using different Cre drivers will help validate the precursor numbers for steady-state hematopoiesis.

In summary, we established a wide applicable range of the correlation between variance of FP% and the precursor based on binomial distribution. We discovered thousands of precursors contributing to steady-state adult hematopoiesis and validated that fetal-to-adult precursor expansion were limited. This analysis highlights active precursor number as an important metric in both normal and genetic mouse models.

# Methods

## Variance modeling with two-color HL-60

HL-60 cells were cultured with IMDM containing 20% FBS (Gemini) and 5% Penicillin-Streptomycin (Gibco) and maintained at 1 x 10^{5} and 1 x 10^{6} cells/ml. Mycoplasma tests (Lonza) were performed routinely to ensure no mycoplasma contamination. BFP-HL-60 and GFP-HL-60 were generated with lentivirus transduction of pGK-BFP (Genscript) and LeGO-V2 (a gift from Dr. Stefano Rivella lab). For seeding of one to 10,000 cells, sorting of HL-60 mixture was performed using a BD FACS Aria III. For seeding of 100,000 cells, cell counting and dilution was used. After expansion, HL-60 was fixed with BD fixation buffer before proceeding to Aurora (Cytek) or Cytoflex (Beckman Coulter) for analysis.

## Mice

HSC-Scl-CreER^{T} mice **[22]** were crossed with R26R-Confetti mice (B6.129P2-*Gt(ROSA)26Sor ^{tm1(CAG-} ^{Brainbow2.1)Cle}*/J) to generate HSC-Scl-CreER

^{T/T}Confetti

^{fl/+}(HSC-Scl-CreER

^{T}/Confetti) animals. HSC-Scl-CreER

^{T}/Confetti animals were crossed with

*Fancc*

^{+/-}mice

**[40]**to generate HSC-Scl-CreER

^{T/T}Confetti

^{fl/+}

*Fancc*

^{+/+}(

*Fancc*), HSC-Scl-CreER

^{+/+}^{T/T}Confetti

^{fl/+}

*Fancc*

^{+/-}(

*Fancc*), and HSC-Scl-CreER

^{+/-}^{T/T}Confetti

^{fl/+}Fancc

^{-/-}(

*Fancc*) mice. Vav-Cre was generously offered by Dr. Wei Tong (Children’s Hospital of Philadelphia). Vav-Cre/Confetti animals were generated by crossing Vav-Cre with R26R-Confetti mice. All animals are B6 CD45.2 background unless otherwise stated. Six-to twelve-week-old females were used for timed pregnancies. Eight-week-old mice were used for adult Confetti induction. Both female and male mice were used indistinctly

^{-/-}**[10]**. Six-to eight-week-old old female B6 CD45.1 mice (B6.SJL-

*Ptprc*/BoyJ, Jackson laboratories) were used as competitors and recipients for transplantation studies. All mice were maintained in the conventional small animal facility at the Children’s Hospital of Philadelphia (CHOP). All procedures involving animals were approved by the Institutional Animal Care and Use Committee at the Children’s Hospital of Philadelphia.

^{a}Pepc^{b}## Animal identification

Tail snip DNA was extracted using KAPA Express Extract Kit (Roche). Genotyping PCR was performed with HotStarTaq Master Mix (Qiagen) according to manufacturer’s instruction. Genotyping primers used are summarized in Table S3. To determine the zygosity of HSC-Scl-CreER^{T}, qPCR was additionally performed with purified tail snip DNA using SYBR™ Green Universal Master Mix (Applied Biosystems).

## Animal procedures

For fetal inductions, timed matings of HSC-Scl-CreER^{T/T}Confetti^{fl/fl} mice and HSC-Scl-CreER^{T/T} mice were set up. The mice were separated the next morning and the noon of the day of separation was considered E0.5. Tamoxifen was delivered at 100mg/kg to the dam orally at E11.5 or E14.5. Pups were C-sectioned and cross-fostered at E18.5 due to reported delivery difficulties caused by tamoxifen treatment **[51]**. For mice used for defined number of transplantation (Figure 2), tamoxifen was delivered at 70mg/kg orally once per day for 14 days at eight-week-old. For adult induction (Figure 3), tamoxifen was delivered at 70mg/kg orally once per day for two days at eight-week-old. For one dose 5-fluorouracil (5-FU, Sigma) treatment, 5-FU was intraperitoneally injected once ten days before BM harvest (37-week-old) at 150 mg/kg. To obtain peripheral blood for Confetti analysis, mice were anesthetized using isoflurane and retro-orbitally bled or submandibularly bled for *Fancc ^{-/-}* mice with occasional congenital eye defects

**[52]**for 1 capillary of blood (50ul). For peripheral blood counts, blood was collected in EDTA tubes using similar bleeding methods and was analyzed by the Translational Core Lab (Children’s Hospital of Philadelphia).

## Bone marrow sample processing

To collect BM cells, mice were euthanized by CO_{2} inhalation. Tibia, femur and pelvis were dissected, and the bone marrow cells were flushed with 26-gauge needles. The single-cell suspension generated with 18-gauge needles was then filtered through 70µm strainers. Erythrocytes in the bone marrow cells were hemolyzed by RBC lysis buffer before antibody staining or transplantation. For stem cell enrichment, bone marrow cells were further lineage depleted using EasySep™ Mouse Hematopoietic Progenitor Cell Isolation Kit (STEMCELL Technologies).

## Flow cytometry analysis

The peripheral blood and bone marrow cells were analyzed using Aurora (Cytek) or BD FACS Aria III and the flow cytometry data was analyzed using FlowJo (Tree Star). The combinations of the following cell surface markers were used to define the peripheral blood populations: myeloid cells: CD11b^{+} or Gr-1^{+}; T-cell: CD3ε^{+}; B-cell: B220^{+}. The following combinations of cell surface markers were used to define the bone marrow stem and progenitor cells (Lineage/Lin: CD11b, Gr-1, B220, CD3ε, Ter119): LTHSC: Lin^{-}c-Kit^{+}Sca1^{+}Flk2^{-}CD150^{+}CD48^{-}; MPP2: Lin^{-}c-Kit^{+}Sca1^{+}Flk2^{-}CD150^{+}CD48^{+;} MPP3: Lin^{-}c-Kit^{+}Sca1^{+}Flk2^{-}CD150^{-}CD48^{+}; MPP4: Lin^{-}c-Kit^{+}Sca1^{+}Flk2^{+}CD150^{-}CD48^{+}; STHSC: Lin^{-}c-Kit^{+}Sca1^{+}Flk2^{-}CD150^{-}CD48^{-}; MEP: Lin^{-}c-Kit^{+}Sca1^{-}CD34^{-}CD16/32^{-}; CMP: Lin^{-}c-Kit^{+}Sca1^{-}

CD34^{mid}CD16/32^{mid}; GMP: Lin^{-}c-Kit^{+}Sca1^{-}CD34^{+}CD16/32^{+}. For bone marrow stem and progenitor cell analysis, DAPI (Biolegend) was used to distinguish dead cells. Representative examples of flow cytometry gating can be found in Figure S2C. The antibodies were used at optimized dilutions listed in Table S1.

## Bone marrow transplantation

The day before transplantation, female CD45.1 recipient mice were lethally irradiated (5.2Gy x 2, 3h apart) using an X-ray irradiator (Precision). On the day of transplantation, bone marrow cells from donor mice (CD45.2^{+}) were collected under sterile conditions as described, RBC-lysed and counted for cell number. For Figure 2 (transplantation of defined number of precursors), donor mice were induced to express Confetti as described; only donor bone marrow cells were injected into irradiated recipient mice; each matched high- and low-precursor number group received donor bone marrow cells pooled from three to five mice. For transplantation of young Fancc mice, donor mice were induced to express Confetti at E14.5; 1.5 x 10^{6} donor bone marrow cells were mixed with 2.5 x 10^{5} CD45.1 supporting bone marrow cells and injected into irradiated recipient mice via tail vein. For transplantation of aging Fancc mice, donor mice were induced to express Confetti at two-month-old; 2 x 10^{6} donor bone marrow cells were mixed with 5 x 10^{5} CD45.1 supporting bone marrow cells as donor population.

## Derivation of the correlation between variance of confetti fp% and precursor numbers based on binomial distribution

When a random variable adheres to binomial distribution, studies have established that the following equation holds true:

where *n* signifies the number of precursors, *p* represents the probability of an individual being one of the FPs (e.g., RFP), and σ^{2} denotes the variance of specific FP% (e.g. σ_{RFP}%2)[6]. In experiments, *p* will be estimated with the average FP% in the Confetti^{+} cells (e.g. RFP_{mean}%), and σ^{2} will be estimated with the variance of FP% among a group of individual or mice (e.g. ). Consequently, the estimation of precursors number n is calculated using the following equation:

A logarithmic transformation can then be performed, allowing us to establish a linear relationship between the variance of FP% and the number of precursors:

In a previous study[10],

Therefore,

## Resampling to determine sample size per replicate

FP% data generated from HL-60 was used for re-sampling. For each seeded number, FP% was resampled for different sample sizes from all the FP% with replacement. Variance of estimated n was then calculated by the standard deviation of the estimated precursor numbers generated from the same sample size. Relative error was determined by dividing variance of estimated n with the average of the estimated n. Refer to “varying well numbers.rmd” for detailed R code.

## Simulation to determine the effect of varying FP_{mean}% on correlation between variance of FP% and precursor numbers

Simulation of binomial distribution of varying FP_{mean}% (probability of being a FP) was performed in R, generating corresponding FP% values used for variance calculation. The correlation between variance and precursor number n was then determined by linear correlation, and the slopes and intercepts were compared to each other. Refer to “Simulation of varying FPmean_percent.rmd” for detailed R code.

## Simulation to determine the effect of precursor numbers following Poisson post-transplantation

Precursor numbers in individual samples were simulated to follow a Poisson distribution, where the mean of precursor numbers is the expected precursor numbers (expected n). The induction of a FP in each precursor was then simulated by random assignment, where probability of being a FP was set to be FP_{mean}%. For each expected precursor numbers, variance of FP% among samples was then calculated, and equation 2 was used to estimate precursor numbers (estimated n). The correlation between expected n and estimated n was then plotted. Refer to “Double layer binomial simulation.rmd” for detailed R code.

## Data processing and normalization

Peripheral blood cell subset frequencies were normalized to the total % of granulocytes and myeloid cells, T-cell and B-cell, to avoid an underestimate due to incomplete RBC lysis. For transplant animals, peripheral blood CD45.1^{+}% and CD45.2^{+}% are normalized to total CD45.1^{+}% and CD45.2^{+}% to avoid an underestimate due to incomplete RBC lysis. After normalization of cell frequencies, the sum of Confetti% and FP_{Conf}% (diving FP_{PB}% or FP_{BM}% by sum of Confetti%) were then calculated for each cohort. At each step, potential outliers were removed based on Tukey method. The variance of FP_{Conf}% and average FP_{Conf}% are then fitted into equation 2 to calculate precursor numbers if sample size is at least five. The precursor number is then used to compared with the minimum flow cytometry recorded event of samples. If the estimated number is higher than the minimum flow count of samples, the sample with the minimum flow count will be excluded, and the calculation is performed again on the rest of samples. After exclusion, the resulting precursor number will be compared again with minimum flow count of samples, until it is lower than the minimum flow count or sample size is smaller than five.

# Statistical analysis

## Statistical significance for precursor number estimates

As the distribution of precursor numbers is not predetermined, to compare mean precursor number differences between two conditions from a limited number of biological replicates, we employed permutation test. For unpaired permutation test, if there are three to five biological replicates per condition, the smallest p values possible are . For paired permutation test, if there are three to five biological replicates per condition, the smallest p value possible are 0.125 ∼ 0.03125 (1/2^{3} ∼ 1/2^{5}). Thus, for three to five biological replicates per condition, even though some of the p values may not reach the commonly used alpha level (0.05), it still represents substantial number differences. For those p values that were lowest possible but did not reach the alpha level, we specifically labeled with a “#” in the figures and legends.

## Statistical analyses of other data

All other two-sample statistical analyses were performed using Student’s t test, if the sample was normally distributed, or Welch’s t test, when the sample was not normally distributed (F test). For multiple comparison, one-way ANOVA or two-way ANOVA was used.

# Data and code availability

The original Confetti% measured in the peripheral blood and the bone marrow and R code to analyze and reproduce all the results, numeric and figures can be found at https://doi.org/10.5281/zenodo.8222789. The re-analyzed data from a previous study can be found in the online version of papers[10].

# Acknowledgements

Work was supported by R01-HL150882. We thank Florin Tuluc (CHOP Flow Cytometry Core) and Jessica Gucwa (Cytek bioscience) for assistance in flow cytometry; Kaosheng Lv (CHOP) for preparation of reagents; Zilu Zhou (Penn) for help in statistical analysis; Nancy Speck (Penn), Wei Tong (Penn), Julia Warren (Penn), Ding-wen (Roger) Chen (CHOP), Stephanie N Hurwitz (Penn), Hua Qing (Genentech), Hui Chen (Penn) for in-depth discussion. Some figure panels were generated using Biorender.

# Supplementary Figure Legend

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