Summary
A simple, universal and fundamental definition of adult stem cell communities is proposed. Key principles of cell lineage methods for defining adult stem cell numbers, locations and behaviors are critically evaluated, emphasizing the imperatives of capturing the full spectrum of individual stem cell behaviors, examining a variety of experimental time periods and avoiding unwarranted assumptions. The focus is first on defining fundamentals and then addresses stem cell heterogeneity, potential hierarchies and how individual cells serve the function of a stem cell community.
Keywords: Adult stem cell, lineage analysis, population asymmetry, dynamic heterogeneity, division-independent differentiation, Drosophila ovarian Follicle Stem Cells, mouse gut stem cells, mouse epidermal stem cells
Graphical Abstract

Introduction
A simple and universal definition of adult stem cells
There is great interest in understanding the mechanisms that regulate the behavior of adult stem cells in order to develop regenerative therapies or prevent development of some cancers, but it is essential first to identify stem cells correctly and thoroughly investigate their normal physiological behavior (Akbari, Arslan, Senturk, & Erdal, 2019; Drost & Clevers, 2017; Gurusamy, Alsayari, Rajasingh, & Rajasingh, 2018; Sanchez-Danes et al., 2016; Vermeulen & Snippert, 2014; White & Lowry, 2015). This begins with defining stem cells appropriately and the consequent tailoring of investigative approaches.
Many cells are lost during the life of a multicellular adult organism and must be replaced to sustain normal physiology. The replacement cells may occasionally arise from division of exactly equivalent cells (S. Wang et al., 2015) but more often they derive from a distinguishable cell. The upstream source cells must collectively fulfill this replacement function throughout adult life, with the most durable cells commonly referred to as stem cells. Each type of adult stem cell can therefore be defined by this fundamental physiological function as the group of cells that maintain production of at least one different cell type throughout adult life (Clevers & Watt, 2018; Post & Clevers, 2019). The condition of life-long function distinguishes stem cells from other upstream cells, which are sometimes referred to as progenitors, precursors or transit-amplifying cells.
Adult stem cells, as a group, can generally only continually supply derivative cells if they are replenished by cell division. A balanced combination of stem cell division and differentiation, often resulting in a roughly constant number of stem cells, is termed self-renewal. Importantly, and often ignored or mis-understood, both the fundamental replenishment function of adult stem cells and the attendant “selfrenewal” characteristics of differentiation, division and lifelong persistence apply to the stem cell community as a group. They do not necessarily apply to each individual stem cell.
It has nevertheless often been stated that a stem cell (singular) is defined by self-renewal (both dividing and differentiating) (Blanpain, Horsley, & Fuchs, 2007; L. Wang, McLeod, & Jones, 2011; Yamashita, 2009). The assertion originates from the earliest paradigms studied (HSCs and Drosophila germline stem cells), where each stem cell is long-lived. However, it is now realized, for several paradigms characterized as exhibiting “population asymmetry”, that individual stem cells exhibit a wide variety of lifetimes and that cell division and differentiation are often balanced only over the whole stem cell population, not at the level of individual stem cells (Fig. 1D, E). In such systems, an individual stem cell exhibits stochastic and unpredictable behavior, and from any instant (or cell marking event) onward it may differentiate without ever dividing (Jones, 2010; Reilein, Melamed, Tavare, & Kalderon, 2018; Ritsma et al., 2014). Thus, not all members of a stem cell community exhibit self-renewal. Similarly, extended longevity cannot be used to define an individual stem cell because each individual stem cell does not have a fixed lifespan (Clevers, 2015; Goodell, Nguyen, & Shroyer, 2015; Keyes & Fuchs, 2018). Although population asymmetry has been widely recognized for several years, there remains a common tacit or explicit residual expectation of longevity and self-renewal of individual stem cells, which can lead to ignoring many members of a stem cell community and making inappropriate assumptions regarding stem cell behavior.
Figure 1. Adult stem cell paradigms and the challenges of population asymmetry.
(A) Drosophila germarium showing three AP layers of Follicle Stem Cells (FSCs) ringing the circumference around a (white) germline cyst. FSCs produce Escort Cells (ECs) to the anterior (left) and Follicle Cells (FCs) to the right. Germline stem cells are adjacent to Cap cells (CC) at the extreme anterior. (B) Mouse small intestine crypt showing crypt base columnar cells that strongly express Lgr5 (dark green) interspersed with quiescent Paneth cells (red) up to the +4 position where Lgr5 expression starts to decline (light green), other characteristic markers (Bmi1, Lrig1, Hopx, Tert) are present and some cells do not divide frequently. The first derivative cells, pictured at +5, are proliferative precursors (light blue) of enterocytes (dark blue) or quiescent progenitors (orange) of various secretory cells (purple) and Paneth cells (Paneth cell precursors are also seen at lower positions). The exact number of stem cells, especially around position +4, and their heterogeneity is not certain. (C) Proliferative cells are present only in the basal layer (BL) of skin epidermis. Overt differentiation involves upward movement towards the thin cornified layers (top) but some basal cells may be committed to differentiate or have limited division potential (progenitors) and there may be different stem cell populations around hair follicles or other locales. (D, E) Diagrammatic representation of stem cell compartments (rectangles housing nine cells) and derivative cells (rectangles with 28 cells), showing the potential progress over time (left to right) of four colored marked stem cells. (D) If maintained by single-cell asymmetry, each stem cell will generally survive without duplication and contribute similar numbers of derivatives over any fixed period of time after marking. (E) If maintained by population asymmetry, each stem cell may be lost early (green) or later (yellow), or amplify (red). Consequently, the number of marked stem cell lineages observed declines over time, while the average representation of surviving lineages increases, maintaining a constant number of marked stem cells on average (here, four of varying color composition). Derivative production for each stem cell lineage is highly variable and changes over time because of stochastic stem cell loss and amplification.
It is possible to define an individual stem cell as a cell that “can,” or has the “potential” to, divide and differentiate (Post & Clevers, 2019). However, this phrasing invites speculation about the relevant circumstances for realizing the stated potential. Moreover, what an individual cell can do is not directly measurable; it is in fact deduced only by ascertaining what all members of a stem cell community do. The severe difficulties of developing a working, inclusive definition of an individual stem cell are resolved by defining stem cells as a community. The community definition also has the virtue of capturing the fundamental physiological role of stem cells in a very simple manner.
A few clarifications may be helpful concerning universal application of the proposed definition of adult stem cells. First, the definition is applied by default to normal physiology; additional cells may take on stem cell function under altered genetic or environmental conditions. Second, the definition implies that stem cells are not replenished over a lifetime by another cell population; in other words, they are the most upstream cells required to maintain production of specific cell derivatives. However, most experimental approaches first identify self-renewing upstream cells over periods less than a lifetime. Such cells are appropriately named stem cells until subsequent investigations indicate otherwise by revealing a definitive hierarchy among them or identifying a new type of cell further upstream. Third, hematopoietic stem cells (HSCs) were originally defined under non-physiological conditions of transplantation into a stressed environment. They were not named according to the proposed general definition of adult stem cells and this historical convention will likely persist even as the cells maintaining production of specific blood cell types are increasingly studied under conditions of normal physiology (Dorshkind, Hofer, Montecino-Rodriguez, Pioli, & Rodewald, 2019; Nazaraliyev, Richard, & Sawai, 2020).
The benefits of widespread, explicit adoption of the proposed community definition of stem cells include the inherent imperative to describe the entire stem cell community, the ability to describe different stem cell paradigms with common language, and common adoption of key principles, discussed below, for investigation of stem cell behavior.
Challenges for adult stem cell investigation by lineage analysis: time and heterogeneity.
The definition of adult stem cells offered above presents two major experimental challenges. First, it is functional and requires cell behavior to be deduced over time. The ideal solution is to observe live cells over the lifetime of an adult organism without disturbing them. In practice it is often necessary to infer behavior by heritable labeling of a cell genetically, commonly through temporally restricted activation of a recombinase, and then looking at all of its descendants at a later time (“genetic lineage analysis”) (Blanpain & Simons, 2013; Fox, Morris, Nystul, & Spradling, 2008; Kretzschmar & Watt, 2012). Employing appropriate time intervals is critical, while inferences are significantly restricted by the opportunity to examine a sample at only one time. Second, the definition applies to the collective role of a group of cells, but experimentally it is usually necessary to follow derivatives of individual cells. This challenge must be met, as in all types of single-cell analyses, by looking at large numbers of examples without bias in order to appreciate the average behavior and diversity of behaviors within a stem cell community. The comprehensive analysis of all stem cell lineages and the use of a variety of carefully chosen time periods are central themes for the effective use of lineage analyses to define adult stem cell locations, numbers and behaviors.
Each stem cell paradigm presents specific experimental advantages and challenges. Consequently, key general principles of lineage analysis can be applied more readily in some cases than others. The application of principles always depends on a thorough understanding of the composition, morphology and dynamics of the relevant tissue (Fox et al., 2008). Three paradigms are considered here; two highly-studied mammalian systems (mouse intestinal stem cells, mouse epidermal stem cells) and Drosophila ovarian Follicle Stem Cells (FSCs), which have numerous similarities to mammalian intestinal stem cells (Fig. 1).
Main Text
Temporal definition of Stem Cells by lineage analysis
Starting with the prospective identification of transplantable HSCs by a combination of surface antigens, there has been a relentless expectation that each type of stem cell will be identified primarily by specific markers or a pattern of gene expression. Consequently, transcriptional signatures are often used to target genetic recombination to mark a specific group of cells for lineage analysis. However, there are significant caveats to the general expectations that gene expression dictates cell function and provides an indispensable means to identify specific cells. First, the range of gene expression patterns compatible with a specific cell function cannot be predicted. Specifically, the inevitable similarity between a stem cell and its immediate product, together with heterogeneity among stem cells, may frequently lead to imperfect overlaps between cell identity and gene expression patterns. Stem cell identity can only be established by functional assays. Second, in solid tissues, cells can alternatively be described and identified by their precise locations. Moreover, the location, number and behavior of stem cells can all be deduced from analyzing lineages initiated in cells without any transcriptional targeting.
The idea that any cell type can be thoroughly investigated independent of gene expression analysis may leave some students and researchers incredulous. It derives from the concept that stem cells can be defined as being upstream of derivative cells by temporal criteria alone. It is illustrated here by studies with Drosophila FSCs. The required careful focus on temporal issues, together with addressing the entire potential stem cell population without restriction, could also benefit paradigms where transcriptionally targeted lineage studies have led to gene expression patterns as primary stem cell descriptors.
Drosophila females can produce an egg from each of roughly thirty ovarioles every 12h throughout adult life. Continued generation of the requisite somatic and germline cells is supported by stem cells, necessarily located in the only stable structure, known as the germarium. From there, egg chambers bud and progress posteriorly on a conveyor belt of development towards mature eggs (Fig. 1 and 2) (Duhart, Parsons, & Raftery, 2017). Germline Stem Cells at the anterior of the germarium yield derivatives, known as Cystoblasts, which divide with incomplete cytokinesis and mature into 16-cell germline cysts as they move posteriorly (Fig. 2B). Near the middle of the germarium, somatic cells surround a lens-shaped “stage 2b” 16-cell cyst and transition towards an epithelial phenotype as they divide and the cyst matures into a rounded “stage 3” cyst, which then buds from the germarium fully encased by a monolayer epithelium. Cells in this expanding monolayer, together with a few specialized somatic “stalk cells” separating egg chambers, and the somatic cells surrounding stage 2b and stage 3 cysts in the germarium (sometimes termed pre-follicle cells) are collectively called Follicle Cells (FCs) here (Fig. 1A, 2B).
Figure 2. Temporal definition of a lineage initiated in a stem cell, illustrated for FSCs.
(A) The cartoons illustrate the germarium (left), housing a lens-shaped stage 2b germline cyst (yellow), followed by a more spherical stage 3 germline cyst (magenta) and five egg chambers of increasing size. Shortly after heat-shock (START) a random, small fraction of proliferating FSCs and Follicle Cells (FCs) have undergone recombination and are genetically marked (six illustrative examples are shown in different colors; in reality, many fewer FSCs than FCs would be marked because there are many more dividing FCs). By two days (four 12h cycles of egg chamber budding), all FCs (yellow, orange and black squares, lower-case labels), defined by stable association with a germline cyst, have amplified into a contiguous patch and have moved posteriorly (to the right) together with their associated germline cysts (shown with matching colors). Those cysts and FC derivatives pass through the entire ovariole within 5d. Any labeled FCs present anywhere in the ovariole after 5d must therefore originate from an initially labeled cell upstream of an FC, defined as an FSC (colored circles, upper-case text for FSC lineages). At 9d the green (G) FSC lineage includes more FSCs than originally labeled, the blue (B) FSC lineage contains only FCs and the magenta (BR) FSC lineage has been lost without trace. The frequency of cell labeling is typically adjusted so that most ovarioles contain only a single marked FSC lineage of a specific color (and many ovarioles lack any FSC lineages of that color) for single-color or multicolor experiments.
(B) The enlarged germarium immediately after cell marking (left) and the ovariole 3d later (right) illustrate how FSC lineages can be discerned at short time intervals (less than 5d). The germarium cartoon shows Germline stem cells (GSCs) and the posterior developmental progression of their derivatives (gray) through 16-cell cysts of varying shape (stage 2a, 2b and 3), Terminal Filament (TF), Cap Cells (CC) and Escort Cells (EC). Most FCs contribute to a growing epithelium but a few become quiescent Stalk Cells (SC) or Polar Cells (PC); all derive from upstream FSCs. The anterior border of strong surface Fas3 protein (red) provides a key landmark. Twin-spot daughters from recombination (left) in a FC (B and GR; arrow) necessarily produce lineages confined to the same egg chamber, while those from a FSC (BR and G; arrowhead) may behave independently, revealing the border between FSC derivatives and FC derivatives 3d later (right). Here the BR daughter became an FC immediately and is present as an unpaired color, showing that the associated egg chamber, and all more anterior FCs, was populated by derivatives of a marked FSC. The G daughter became an FC two budding cycles (about 24h) after division of the parent FSC.
The key defining property of FCs for the purposes of lineage analysis is stable association with a germline cyst. That characteristic guarantees posterior progression of FCs and all of their derivatives along the ovariole until they die no more than 5d after first associating with a stage 2b cyst. Any marked cell that yields a marked FC derivative detected 5d (or more) later, anywhere in an ovariole, was necessarily upstream of an FC and has been named a Follicle Stem Cell, or FSC (Fig. 2A). The marked cells that derive from an FSC constitute an FSC lineage. In a crypt of the mouse small intestine the logic for defining stem cells is similar; all derivative cells destined to turn over (other than Paneth cells) exit the crypt within 2 days, so any marked cell (generated at random or by targeted recombination) that labels such derivative cells in the crypt more than 2d later should be considered a stem cell.
Population Asymmetry
The major potential stumbling block for appropriate design and interpretation of lineage studies is a failure to acknowledge that the stem cells under investigation may (regardless of prior conceptions) be maintained by population asymmetry. If each member of a stem cell population were long-lived and divided with asymmetric outcomes (“single-cell asymmetry”), so that individual stem cells also do not amplify, the design and interpretation of lineage analyses would be very simple. The behavior of all stem cell lineages would be relatively uniform and similar over different time periods, making the identification of all stem cells and their behavior relatively facile (Fig. 1D). However, if individual stem cells within a community do not always undergo divisions with asymmetric outcomes, are lost or duplicate with significant frequency, as in population asymmetry, investigation is considerably more complicated. Now, very diverse behaviors of individual stem cell lineages are expected, requiring that a fully representative spectrum of stem cell lineages is captured (Fig. 1E). This, in turn, requires carefully chosen time periods for experiments, sufficient to define a stem cell lineage but not so long that many stem cell lineages are lost. A lineage study that does not take these issues into consideration because it has been assumed that the stem cells being studied are all long-lived and maintained by invariant single-cell asymmetry will result in false conclusions if those assumptions are not correct. If no such assumptions are made, then correct conclusions will be drawn, regardless of how the stem cell community is maintained.
FSC organization: comprehensive analyses and discarding assumptions
Drosophila FSC studies illustrate the impact of putting aside historical assumptions and fully implementing key principles of lineage analysis, leading to specific suggestions for how analogous approaches could complement current understanding of various mouse stem cell paradigms studied primarily by targeted marking.
FSCs were amongst the first to be defined solely by applying a temporal criterion of (Margolis & Spradling, 1995). The first, seminal study defined a stem cell lineage as including marked FCs beyond the 5d lifetime of an FC. The study also, however, included an implicit assumption that the stem cells are maintained by invariant single-cell asymmetry (Margolis & Spradling, 1995). Specifically, the authors noted that some ovarioles, 9–11 days after lineage marking (well beyond the lifetime of all FCs), included labeled FCs in the germarium and in each subsequent egg chamber (as in Fig. 3G). These were designated archetypal FSC clones or lineages, fitting the contemporary expectation that all stem cells would be long-lived and supply derivative cells through asymmetric division outcomes. The authors did not provide a comprehensive description of the variety of all lineage patterns observed at that time or earlier (from 5–9d). The highlighted FSC lineages were analyzed to measure the proportion of all FCs in an ovariole contributed by a single lineage to deduce that there were two FSCs per germarium. The decay of marked FSC lineage frequency was also measured over time, starting at 9–11d after cell marking to deduce that each lineage has a half-life of about 2 weeks.
Figure 3. Single stem cell output; label only one stem cell and score all lineages.
Lineage tracing is initiated by low frequency recombination so that most physiological units (A-E) have only a single stem cell (green) labeled; many others (not shown) have none. By the time of analysis, any derivative cells initially labeled (magenta) will leave no trace; only (green) stem cell lineages will remain. Each labeled stem cell may amplify either (A) transiently or (B) permanently, or it may be lost (D) early or (C) later. Average derivative production will be over-estimated if only samples with persistent stem cells (A, B) are examined, but can be deduced correctly if all samples with an initially labeled stem cell are scored because the total number of labeled stem cells over all samples should remain constant. Ideally, analysis is at a time just sufficient to be sure that all marked derivatives result from a marked stem cell. At longer times, samples like (D) will accumulate and cannot be scored because the original presence of a marked stem cell can no longer be recognized. In (E) there are no labeled derivatives at the time of analysis, so there is no evidence that an active stem cell was labeled and the sample should not be scored (it is possible, however, that earlier derivative cell production was missed). (F-H) Cartoons illustrating some typical FSC lineages (marked cells in green) found 9d after labeling (Kalderon et al., 2020). (F, G) Lineages with surviving FSCs show variable contributions of labeled FC derivatives to each egg chamber and include variable numbers of FSCs (green circles), as in (A, B), even if originally derived from a single labeled FSC. (H) Some FSC lineages have only labeled FCs and others (not shown) cannot be recognized because all labeled cells have been lost (as in D). The percentage of each egg chamber epithelium populated by labeled FCs is indicated. For the samples shown, the proportion of all FCs that are marked among all five illustrated egg chambers is highly variable at (F) 8%, (G) 47% and (H) 3%, respectively (average 19%).
Those deductions and the appearance of “a prototypical FSC lineage” were largely repeated for two decades without appreciating the hidden assumption of invariant single-cell asymmetry. Later studies, described below, found that the majority of FSC lineages did not resemble the featured “prototypical” lineages and that FSCs are maintained by population asymmetry. The original deduction of two FSCs per germarium, each with a relatively long half-life, could now be seen as based on ignoring the more short-lived FSC lineages, which contribute relatively few FCs, and examining only long-lasting lineages that contribute FCs to each cyst. The latter lineages have generally accumulated multiple FSCs by 9–11d, so that the measured half-life of a lineage and the FC production from a lineage, incorrectly taken as the properties of a single FSC, were far greater than those of an individual FSC.
A comprehensive sampling of lineages originating in FSCs revealed a variety of patterns, indicating markedly diverse behavior of individual FSCs. The patterns of FC contributions also shifted over time, with sparser patterns (as in Fig. 3F, H) more evident at earlier times, consistent with the accumulation of multiple FSCs over time in surviving lineages (Reilein et al., 2017). Those characteristics make plain the need to look at all FSC lineages and at a variety of times to capture the full spectrum of behavioral heterogeneity. These two assertions, and the appropriate lineage methods described below, apply to all stem cell paradigms.
Foundational stem cell characteristics; numbers, location and turnover
Lineage studies in the mouse intestine established long ago that at least some crypt cells with high expression of the Wnt-responsive gene Lgr5 function as stem cells (Barker et al., 2007; Beumer & Clevers, 2020). But how can the experimental cell lineage approach be extended to deduce whether all crypt cells with strong Lgr5 expression behave as stem cells, whether those cells exhibit functional heterogeneity or if additional cells act as stem cells? Three basic approaches to establishing foundational stem cell properties are described below. One only addresses the number of stem cells present, by measuring the fraction of all derivative cells produced by a single stem cell on average. Another strategy counts the number of differently labeled stem cell lineages present at a variety of times after marking (using multicolor labeling) to determine stem cell numbers and turnover. The third strategy examines many lineages with only a single candidate stem cell to determine all stem cell locations. Each strategy has limitations and requires careful tailoring to the specific stem cell paradigm.
1. Single stem cell output: score ALL lineages
The average proportion of all derivatives contributed by a single marked stem cell within a physiological unit (such as an intestinal crypt or an ovariole) can reveal the number of active stem cells. However, there are three important practical hurdles for this “single stem cell output” approach. First, only a single stem cell should initially be marked in each unit that is scored. The most common experimental solution is to induce genetic marking events at a low frequency overall (Blanpain & Simons, 2013; Fox et al., 2008). Second, many stem cell lineages must be examined without bias to account for heterogeneous stem cell behavior. Third, and not always appreciated, a marked stem cell lineage will not necessarily maintain exactly one stem cell throughout the experiment (Fig. 3).
Individual marked stem cells will frequently amplify or be lost in paradigms governed by population asymmetry. However, the average number of marked stem cells over all samples should not change over time if the total stem cell population remains constant and if marking does not influence function. Thus, the average contribution of a single stem cell will still be measured if every sample that originally contained a marked stem cell is examined.
The experimental challenge is to identify all relevant samples. Crucially, there will be no trace of initial labeling of a stem cell if the stem cell and all of its derivatives have been lost prior to analyzing samples (Fig. 3D). The optimal experimental time period is therefore prior to losing all trace of a labeled stem cell but must be greater than the maximum lifetime of a derivative cell (5d for FCs if examining the entire ovariole) to determine that a stem cell was initially labeled. In practice, there will be some biological variability among individual animals and physiological units, so the chosen time must be slightly longer than the theoretical optimum, in order to be certain that every lineage derives from a stem cell. The associated failure to capture and count products from the shortest-lived stem cells, which will inevitably have produced relatively few derivatives (Fig. 2A and Fig. 3C, D), will lead systematically to over-estimating the average derivative contribution of a single stem cell and therefore under-estimating the total number of stem cells. This error will be greater for longer time periods. It would be further compounded if some observable stem cell lineages were discounted because of pre-conceived ideas about stem cell behavior.
When this strategy was first used to assert that there are exactly two FSCs per germarium, clones were examined several days beyond the 5d minimum and only if they conformed to an expectation of contributing FCs to each cyst (Margolis & Spradling, 1995). A recent reprisal of the strategy (Fadiga & Nystul, 2019) showed that many other types of FC-containing lineages were present, as reported by others (Reilein et al., 2017), but still imposed the selective criteria of the original study by counting only lineages with marked FCs in the germarium and both of the first two egg chambers, leading to a large under-estimation of stem cell numbers (as in Fig. 3B, G). The underlying reason for selecting only a subset of FSC lineages was the enduring pre-conception that each FSC should be long-lived and continuously produce FCs (Kalderon, Melamed, & Reilein, 2020).
Reilein et al (2017) considered all FSC lineages with persisting FSCs (as in Fig. 3A, B, F, G) scored 9d after clone induction. Lineages containing FCs but no surviving cells in FSC territory (Fig. 3C, H) should have been included to derive a more accurate measurement; they were not counted in order to consider only FSCs that had demonstrated self-renewal. The measured average lineage contribution of about 15% of all FCs in an ovariole was artificially high also because FSC lineages without any surviving FC derivatives (those lost between 5d and 9d; Fig. 3D) could not be identified and were therefore not included. The result allowed the conclusion that there are at least 6–7 (1/0.15) active FC-producing FSCs per germarium, but omission of lineages that had lost FSCs makes this a severe under-estimate. A better assessment (1/0.092=11 FSCs) was made by examining a shorter period and including FC-containing FSC lineages where the FSC had been lost (Reilein et al., 2017).
2. Count differently colored stem cell lineages: label ALL lineages and test different times
The total number of different stem cell lineages present in a physiological unit can be counted directly if each lineage is labeled distinctively (for example, with a different color or combination of colors). An ideal system allows highly efficient marking by a large variety of colors (Fig. 4A, top), so that all stem cells are labeled and no two stem cells share the same label. In practice, the number of stem cells may exceed the number of colors available. Here, the distribution of the number of lineage colors present over many samples at any one time point can be used to estimate (based on frequencies of different colors and expected binomial combination frequencies) how often lineages share the same color, and hence the average number of lineages present (Fig. 4A, middle) (Reilein et al., 2017). Importantly, this method can only give a correct estimate if all, or almost all, stem cell lineages are labeled (Fig. 4A, bottom).
Figure 4. Multicolor labeling to count stem cell lineages and measure turnover.
(A) The boxed circles in the left column represent initially-labeled stem cells, with the next two columns portraying changes over time. If every stem cell can initially be marked with a different color (top row) the number of stem cell lineages that survive at later times can be counted directly (here 12 declines to 8 and then 6). The loss of lineages will be fastest at early times because each lineage initially has only one stem cell. When the number of stem cells exceeds the number of colors (middle row; only 6 colors available), the distribution of the number of different colors present among many samples can be used to estimate the number of labeled stem cell lineages present by using statistical methods (“nCr”) that account for the probability of shared colors. The counting approach is not effective if a significant fraction of stem cells is not labeled initially (bottom row); here, only 5/12 of all stem cells are marked, so the inferred number of stem cells would be too low by the same factor. (B) One of 50 scored ovarioles for one time-point from Reilein et al., 2017, showing the presence of all five possible differently colored recombinant FSC lineages (B, G, BG, BR, GR).
A major virtue of this approach is that it allows explicit counting of surviving stem cell lineages over a variety of experimental time periods, providing direct information on the loss of stem cell lineages over time (Fig. 4A). That stem cell turnover information provides key evidence for maintenance by population asymmetry or invariant single-cell asymmetry. It also allows extrapolation to zero elapsed time to determine the total number of stem cells that are marked before any are lost.
This approach was applied to FSCs by Reilein et al (2017), who developed a genetic system in which recombination events could lead to the loss of different combinations of three markers (lacZ, later visualized as “Blue” (B), GFP (G) and RFP (R)) to generate recombinant lineages of five different colors (B, G, BG, BR, GR) in addition to the parental color (BGR). At 9d after labeling, ovarioles had a variable number of differently colored FSC lineages (average of 4.5 colors), including some with all six available colors (Fig. 4B), collectively indicating the statistically estimated presence of 9–10 FSC lineages. Since the portion of ovarioles examined included FCs produced from FSCs over a period of roughly 4d, the authors deduced that 9–10 of the originally marked FSCs were still present 5d after marking. The number of distinct FSC lineage colors declined substantially over a time-course of 30d, with many ovarioles eventually retaining only a single color. The number of lineages declined especially fast at early times. The exponential and quite rapid loss of individual stem cell lineages is characteristic of stem cells maintained by population asymmetry.
Those results were very similar to observations in the mouse gut using multicolor labeling (Snippert et al., 2010). In both paradigms, the loss of individual stem cell lineages over time can also be observed using a single color. However, using multiple colors directly showed that the decline in the number of colors in derivative cells is always accompanied by expanding contributions from surviving lineages in the same sample, indicative of an increased number of stem cells of matching color, and presenting a direct visual image of competition among differently colored lineages within a stem cell pool of potentially constant number. Moreover, the amplification of one specific color in one crypt or ovariole and loss of the same color in another, with no apparent color bias, showed that none of the marked lineages was inadvertently endowed with altered stem cell function.
In both paradigms, stem cells were originally thought, or assumed, to be uniformly long-lived. In fact, the first published study of lineages from Lgr5-high cells (Barker et al., 2007) reported no decline in the frequency of labeled crypts sampled at 1, 5, 35 and 60 days. Those results were directly contradicted by later data from the same laboratory showing dramatic loss of lineages, especially over the first 14d (Snippert et al., 2010). The contradiction was not explicitly addressed (the quoted results from 2007 are presumably incorrect) but the more recent results were immediately and widely accepted as demonstrating population asymmetry. The greater reluctance to acknowledge the analogous revision for FSCs (Fadiga & Nystul, 2019; Kalderon et al., 2020) is perhaps due to the additional two decades the original dogma lasted.
Extrapolation of the time-course of surviving multicolor FSC lineages to 0d suggested the presence of about 16 FSC lineages prior to any losses (Reilein et al., 2017). The number is not precise because the estimate of 9–10 surviving FSC lineages at 5d is significantly compromised by the use of only six distinguishable colors and because shorter time intervals cannot easily be used without infringing on the temporal definition of a stem cell lineage. In contrast to most stem cell lineage strategies, where labeling of single cells (“clonal labeling”) is critical, high-density labeling is essential in this application (with multiple colors still allowing deduction of origins in different single cells). Another group repeated this experimental approach for FSCs, and reported an average of only 2.1 (rather than 4.5) different lineage colors at 9d because FSC lineages were labeled at a much lower frequency (Fadiga & Nystul, 2019) (Kalderon et al., 2020). An FSC lineage has to be labeled to be counted (Fig. 4A, bottom).
3. Locations of all stem cells
A fundamental cornerstone for further exploration of stem cell behavior is to determine the locations of all stem cells. The strategy that has dominated mouse stem cell investigations is to use a promoter that can target Cre recombinase activity to as precise a subset of cells as possible and evaluate the resultant lineages. Inevitably, however, targeting is not to a single cell location. For example, targeting with conditional Lgr5-Cre and a suitable tamoxifen regimen for activating Cre at clonal density generally leads to marking of any of about 14 cells occupying circumferential positions in crypts of the small intestine that are in contact with Paneth cells and occupy distinct locations along the major developmental axis, commonly distinguished by numbers (for example, +1, +2 and +3) (Fig. 1B). Subsequent lineage analyses have generally shown that the number of stem cell lineages observed at a later time is lower than the number of marked Lgr5-positive cells, assessed shortly after marking, so it is not possible to conclude that every marked Lgr5-high cell was a stem cell. This is inevitable for paradigms exhibiting population asymmetry, especially for long time periods. Moreover, because lineage tracing permits only one viewing time per sample, it is not possible to relate the location of each single labeled cell seen in one cohort of animals shortly after labeling to the lineage outcomes seen in a later cohort.
So, what is the solution? A strategy that was employed for FSCs was simply to use the location of cells in a stem cell lineage (temporally defined by initial marking several days earlier). Importantly, though, only those stem cell lineages where there is a single candidate stem cell location maintaining the lineage should be considered (Fig. 5).
Figure 5. Determining stem cell locations using the single candidate location approach.
(A) Possible stem cell locations are first prioritized. Here, the anterior domain (“A”) is excluded because cells there do not divide (ECs in a germarium, Paneth cells in a crypt). Prime candidate territory (“M”) here (rectangle with three columns of four cells) corresponds to the middle domain of a germarium or the most basal cells in a crypt excluding Paneth cells. Each row shows possible appearances of colored stem cell lineages. In each case, the blue stem cell lineage includes labeled cells in more than one column of this domain; any may be a stem cell, so those lineages are not informative. However, the single (top) or multiple (middle) red and green cells within domain M are confined to a single column, providing evidence for stem cells residing in the right and center columns, respectively. In the bottom example there are no red cells in domain M, so the red cells in a less likely but possible stem cell location “P” become candidates (P corresponds to Fas3-positive territory at the posterior of a germarium or cells in +4 or higher positions of crypts). For FSC lineages there were relatively few examples of this type, indicating that few if any stem cells reside in this domain and that the red cells are simply the most recent derivatives of a lineage no longer containing a stem cell. Single candidates in “M” must be (and were) observed at higher frequencies than this background of stem cell lineages en route to extinction to provide strong evidence of corresponding stem cell locations. In ovarioles, labeled FSCs also produce new labeled ECs (colored cells in domain “A”). The location of EC-producing stem cells can be deduced by applying the single candidate method to EC-containing lineages. Here, the green lineage in top and bottom examples provides evidence for EC-producing stem cells in column 2 of the prime domain. (B, C) Examples from Reilein et al., (2017) of FSC lineages with single candidate FSC locations in (B) layer 1 (“B”), just anterior to the border of Fas3 staining (dotted white line) and (C) layer 2 (“BR”), one cell further anterior; other colors appear in additional FSCs in other z-sections.
There are two inherent limitations to this approach. First, some stem cell lineages may no longer include a stem cell, especially in population asymmetry paradigms, so a labeled derivative cell might mistakenly be considered as a stem cell (a background of potential false positives). Convincing evidence of a specific stem cell location therefore rests on finding a common candidate stem cell location at a frequency higher than the background frequency of potential false positives. Second, it is necessary to know enough about the tissue being studied to define the domain where a stem cell could conceivably be found (“candidate stem cell territory”). The approach is illustrated in concept by Fig. 5A and described in detail for FSCs.
FSCs must reside in the germarium because all egg chambers necessarily progress through an ovariole. Somatic cells in the anterior half of the germarium (“A” in Fig. 5) do not divide (Kirilly, Wang, & Xie, 2011) and cannot therefore be a major source of continued FC production because more than 5 FCs are produced every 12h (Reilein et al., 2018). In the mouse intestinal crypt this would be equivalent to ignoring non-dividing labeled Paneth cells as a plausible source of most stem cell activity (Gehart & Clevers, 2019). Prime candidate FSC territory is the most anterior region containing dividing cells in the germarium (“M” for middle of the germarium in Fig. 5) because developmental progression is generally towards the posterior (Fig. 2B). More posterior somatic cells (“P” in Fig. 5), within the region of strong expression of the membrane protein Fas3 (Fig. 1A, Fig. 2B), appear mostly to be FCs associated with germline cysts. This region is not, however, discounted; it will be considered after prime candidate territory. The equivalent location in the mouse intestinal crypt might be +5 positions and upwards, with prime candidate stem cell territory being between +1 and +4 on the basis of generally upward migration and the expression patterns of Lgr5 and other markers (Fig. 1B).
Reilein et al (2017) scored all (225) multicolor FSC lineages among 50 ovarioles, 9d after marking, to identify those with only a single candidate FSC in prime candidate territory. Among those lineages, the single candidate marked FSC nucleus was found in different z-sections with similar frequency, always close to the germarial wall; in other words, at all circumferential locations of the germarium. This is equivalent to equal prevalence in each row of cells in Fig. 5A. Next, the authors considered all FSC lineages where candidate FSCs were confined to a single anterior-posterior (AP) plane or ring (one column of territory “M” in Fig. 5A). Sometimes there was a single marked cell; other times, there were two or more marked cells in the same AP plane. Such candidate FSCs were found mostly in “layer 1” (immediately anterior to the border of strong Fas3 staining; 24 lineages) or one cell further anterior (“layer 2”; 19 lineages) (Fig. 5B, C; like the red and green cells in “M” in Fig. 5A). Less frequently, they were one cell further anterior (“layer 3”). So, the single candidate approach showed that FSCs mostly reside in two AP planes and without any known radial restriction. There are an average of about eight somatic cells in layer 1, and six in layer 2, and two in layer 3, leading to an estimate of 14 FSCs in layers 1–2 and another two in layer 3.
Fewer than 10% (15/225) of FSC lineages included labeled cells in the posterior half of the germarium but with no candidate FSC in layers 1–3 (as for the red lineage in the bottom example of Fig. 5A). This territory (“P” in Fig. 5) is much larger than the layer 1–3 region and includes FCs associated with two germline cysts. In some ovarioles the most anterior labeled cells were outside the germarium, clearly indicating prior FSC loss (as in Fig. 3H). These were seen at a frequency of about 5% for each egg chamber location (first, second, third etc.), providing a measure of false positive frequency. It is therefore likely that the lineages with labeled cells only in the posterior half of the germarium (“P” territory) also lacked FSCs and were on their way to extinction because they were seen at the same frequency as the background of false positives (5% per cyst). Thus, it appears that the Fas3-positive cells in the germarium (Fig. 1A, Fig. 2B) are all or mostly FCs. By contrast, the single candidate stem cells appearing in layer 1 were found at over three times the frequency that could reasonably be expected for lineages that have lost their last FSC(s).
Combining multiple approaches and reality checks
The three different strategies described led to the elucidation of FSC locations, a time-course of FSC turnover and three independent estimates of total stem cell numbers. Each approach has systematic limitations, principally related to the challenges of scoring all stem cell lineages over an optimal time period for stem cells maintained by population asymmetry. It is important to assess those limitations and to compare deductions with related observations as a reality check. FSCs provide an illustrative example.
The old model suggested that each of two FSCs per germarium gives rise to one FC daughter per cycle of egg chamber budding- two founder FCs per egg chamber (Nystul & Spradling, 2007). This cannot be reconciled with an observation of four or more different colors of FCs, derived from marked FSCs, in a single egg chamber (Reilein et al., 2017) or the estimated average contribution of 5–6 founder FCs to each new egg chamber (Reilein et al., 2018). It also cannot be reconciled with the required amplification of FC numbers before budding (Kalderon et al., 2020). The assertion of just two FSCs also required some reproducible asymmetry that could lead to only two of the several somatic cells in an AP plane having different properties. No radial asymmetries have been noted in germaria, the single candidate FSC approach identified FSCs at equal frequencies along the circumference of the germarial wall and live imaging showed cells in those locations to circulate back and forth radially, sometimes exchanging positions (Reilein et al., 2017), all providing evidence of radial equivalence. Moreover, cells in the same AP plane share common morphologies, with extensive projections across the width of the germarium and common patterns of gene expression (Hartman et al., 2015; Reilein et al., 2017). Those observations do not, of course, exclude stochastic heterogeneity over time.
Might the estimate of about 16 FSCs occupying all radial locations in two principal AP planes be closer to the truth, but also not accurate? One possibility is that not all layer 1 cells are FSCs. The method used to identify FSC locations does not guarantee that all cells in layer 1 are FSCs and the estimate of about 16 FSCs in total from other approaches has significant uncertainties, so it is possible that some layer 1 FSCs may be FCs. However, the single candidate FSC approach provides compelling evidence that a significant fraction of layer 1 cells are FSCs and the estimates of about 16 FSCs in total cannot plausibly be too high by more than 3 or 4 cells. Moreover, when marked FSCs lack Wnt pathway activity they all accumulate in layer 1 and are largely maintained over periods (12d) far in excess of FC lifetimes (Melamed & Kalderon, 2020). Thus, a significant proportion of the FSC population clearly resides in layer 1 and a large fraction of layer 1 cells must be FSCs. At the other end of the spectrum, the very limited proliferation observed in layer 3 (Melamed & Kalderon, 2020), together with the relatively low frequency of single candidate FSCs found in this location (Reilein et al., 2017), makes the assertion of active FSCs in this location less certain.
Application of FSC approaches and key lineage principles to other paradigms
Mouse gut crypt stem cells
The exact locations and number of all stem cells in mouse intestinal crypts remain unresolved (Beumer & Clevers, 2020). There are about 14 cells with Lgr5 expression above a certain threshold (Lgr5-high), in locations from the base up to +3 or +4, some of which clearly can initiate Lgr5-Cre stem cell lineages (Fig. 1B) (Snippert et al., 2010). However, some Lgr5-high cells in the 0 to +4 domain were found to be quiescent Paneth cell precursors, which did not produce stem cell lineages under unperturbed conditions (Buczacki et al., 2013). Additional Cre drivers that mainly target cells at the +4 position within the crypt has shown that at least a subset of those cells are active stem cells, producing persistent ribbons of derivatives, and that some of the targeted cells do not overlap with the Lgr5-high population (Gehart & Clevers, 2019; Li et al., 2014; Sangiorgi & Capecchi, 2008). A widely quoted deduction of just six active stem cells per crypt of the small intestine resulted from examination of the proportions of crypts with zero, mixed and full (“clonal”) representation of continuously generated lineages over time (Kozar et al., 2013). The deduction was dependent on fitting to a model with some idealized assumptions and requiring a non-trivial measurement of an independent parameter (rate of clone labeling). Also, the time period over which stem cell function was assayed cannot be chosen with that approach and is effectively quite long because the key raw data concern the rates of extinction of lineages and conversion to full crypt occupancy. It is likely that assays over shorter periods would capture more active stem cells.
In intestinal crypts, the most abundant stem cell derivatives, enterocytes and their dividing precursors, consistently move out of the crypt to the villus within two days (Gehart & Clevers, 2019; Tetteh et al., 2016). This allows a temporal definition of stem cell lineages as those that retain labeled crypt enterocyte derivatives more than 2d (or slightly longer to be safe) after marking, directly analogous to the criterion used for FSCs. Hence, each of the three approaches applied to FSCs could equally be applied to mouse intestinal stem cells, whether initial marking of cells is targeted or random. Stem cell number could be estimated using the single stem cell output approach (Fig. 3), measuring the average proportional contribution to all crypt enterocytes and their precursors 4d after low frequency marking. Moreover, by using a ubiquitously expressed conditional Cre, Lgr5-Cre and other drivers (like Bmi1-Cre) separately, additional information concerning heterogeneity might be revealed.
The number of enterocyte-producing lineages per crypt could also be counted directly over various time periods, starting at around 4d, using a high-frequency multicolor lineage labeling strategy (Fig. 4). Multicolor lineage tracing was previously achieved at appropriately high density (few cells with no label) using the near-ubiquitous Ah-Cre and lineages were scored over a variety of different time periods to illustrate stem cell turnover, but were not used to estimate stem cell numbers (which would be improved by using more colors (Fig. 4)) (Snippert et al., 2010).
The single candidate stem cell approach could be used to measure the frequency of stem cell lineages containing candidate stem cells in only one “horizontal” layer (from the base of the crypt upwards), exactly as outlined for FSCs (Fig. 5). This should reveal the relative proportion of stem cells in different layers. Limitations cited for FSCs would also apply to this paradigm but all three approaches might be expected to complement current understanding, especially by emphasizing shorter time periods sufficient to define stem cells but with limited stem cell loss, and by examining all crypt cells, rather than just those targeted by a selective Cre driver.
Mouse interfollicular epidermal stem cells
While the spatial organization and dynamics of FSCs in germaria, and mouse intestinal stem cells in crypts are notably similar, these features are very different in the mouse epidermis, as are some of the unresolved issues concerning stem cells. Here, dividing cells are confined to a basal layer and produce derivatives that migrate apically through multiple layers (Fig. 1C) (Blanpain & Simons, 2013; Rognoni & Watt, 2018). Stem cells must therefore reside in the basal layer and lineage studies typically target cells of the basal layer (for example, using K14-Cre). Efforts to resolve whether some or all basal cells are stem cells, and if there are distinct stem cell populations, have used the limited repertoire of conditional Cre transgenes that target (generally overlapping) subsets of basal cells.
An early landmark study proposed the existence of a single stem cell population with no transit-amplifying cells in the basal layer (Clayton et al., 2007). Later studies inferred distinct stem cell and progenitor identities from the relative longevity of lineages derived from different basal cell populations and supported the proposed hierarchy with mathematical modeling (Mascre et al., 2012; Sanchez-Danes et al., 2016). However, different rates of extinction are also compatible with two independent or partially overlapping stem cell communities (with different numbers of competing stem cells, different division rates and frequencies of stem cell “differentiation”). Moreover, a subsequent study suggested that the observed lineage dynamics can also fit a model of a single stem cell population (Piedrafita et al., 2020). Other studies have shown spatial segregation to different regions of the epidermis, notably tail scale and inter-scale regions, of stem cells with distinguishable characteristics, such as cell cycling time, and dedicated to the production of different terminal derivatives (Gomez et al., 2013; Rognoni & Watt, 2018; Roy et al., 2016; Sada et al., 2016). It would be extremely useful to explore additional strategies that might report hierarchical relationships directly, provide more information on the proportion of all, or a specific subdivision of basal cells, that are stem cells and where each type of stem cell is located.
The epidermis does not, like individual Drosophila ovarioles or mouse intestinal crypts, have discrete, independent physiological units as originally proposed (Potten, 1974), precluding simple application of the single-cell output approach or counting differently colored lineages within a single physiological unit. The identification of stem cells might, nevertheless, be aided by generating lineages at low density using either a universally-expressed or transcriptionally restricted conditional Cre and then scoring the location of “single candidate stem cells” after a variety of time intervals. Crucially, samples could be stained with a variety of markers that collectively reveal several potential indicators of heterogeneity within the marked cells themselves and in their immediate environment (Fig. 6A, B). The strategy allows for exploration of many potentially useful molecular (Involucrin, Lgr6, Integrins, different Keratins, melanocyte markers and signaling pathway reporters that can reveal heterogeneous spatial cues) and morphological markers (scale regions, hair follicles) simultaneously, rather than requiring multiple highly specific Cre drivers, which are currently not available (Huang et al., 2021; Sada et al., 2016). By requiring the presence of at least one labeled cell in layers above the basal layer, all “single candidates” would definitively be identified as upstream of derivative cells (and therefore provisionally considered stem cells). A lineage with more than one basal cell can also be scored as a “single candidate” if all marked cells share a certain characteristic (just as 2 or more FSCs in a single AP layer provides evidence of at least one stem cell with that characteristic), increasing the frequency of informative clones. The frequency of stem cell locations relative to heterogeneous positional markers is always key information and may reveal some unanticipated specificity for stem cells targeted by the chosen Cre driver.
Figure 6. Epidermal stem cell locations, hierarchies and resolution of symmetric and asymmetric division outcomes.
(A, B) Epidermal basal cells (circles) present a continuum with few inherent positional landmarks. Marked lineages (red outlines) could be examined relative to a variety of molecular markers (green and blue). (A) At relatively early times after sparse labeling, lineage-labeled cells (red outlines) will often be isolated enough to be “single candidates”. Supra-basal cells (not shown) would give evidence that the lineage had produced derivatives. Each “single candidate” gives information about stem cell location relative to other molecular (green or blue) or morphological (star, oval) markers. Three possibilities are illustrated. Labeled cells may mostly be adjacent to cells expressing the green marker, or adjacent to certain morphological landmarks (oval) or express the blue marker and be adjacent to another landmark, such as a hair follicle (star). These location characteristics can be scored also for lineages with more than one marked basal cell (as “single candidates”) if all basal cells share the same characteristic. (B) At later times, most surviving lineages (red outlines) will contain many basal cells. Red lineages originating (from early timepoints) in colorless cells may later include green cells (top left), whereas orange lineages initiated in green cells by a different Cre may not include colorless cells (top right) if colorless stem cells produce proliferative green cells. Lineages may avoid certain territories, potentially maintained by different stem cells (adjacent to the hair follicle) but not others (adjacent to the oval), revealing boundaries of spatial domains maintained by certain stem cells. (C) Cartoons illustrate division outcomes for two-cell progeny of a labeled basal cell. Asymmetric (top) and Symmetric (middle and bottom) division outcomes can only be inferred if it is assumed that division and differentiation are coupled, with all differentiated derivatives (yellow) projected out of the basal layer and all cells remaining in the basal layer being stem cells (blue). However, if division and differentiation are separate events (“uncoupled”), the path to each 2-cell outcome (top, middle or bottom row) can proceed (solid arrows) through an initially symmetric division. Moreover, the identity of basal cells is uncertain at the time of observation (denoted by green color) because each basal cell may have either divided again (stem cell) or moved upwards (differentiated cell) if further development had been allowed (dashed arrows). Definitive assignment of symmetric or asymmetric outcomes requires live imaging or observing lineages of more than 2 cells using a lineage technique that marks the daughters of the initial stem cell division with different colors. Moreover, capturing all differentiation events requires also examining single marked cells (bottom).
The approach of using multiple markers to substitute for morphological positional information inherent in other paradigms could also provide direct evidence regarding hierarchical relationships, which lie at the heart of the most cogent current ambiguities. For example, measuring the frequency of K14-Cre lineage labeling of Inv-positive cells, and of Inv-Cre labeling of Inv-negative cells in various locations (relative to morphological and molecular markers) would clarify whether there is a strict directional hierarchy or some degree of equilibration amongst Inv-positive and Inv-negative basal cells (Fig. 6B) (Mascre et al., 2012; Sanchez-Danes et al., 2016). Similarly, large lineage patches might show clear boundaries between regions harboring two potentially distinct stem cell populations or, instead, evidence of intermingling and equilibration between the two (Fig. 6B).
Finally, the epidermis is ideally suited to scoring differentiation of a basal cell without any division because it takes at least a week for progression through higher layers before cells die or are lost. Clones with no marked basal cells have generally not been systematically scored in past analyses (Clayton et al., 2007; Mascre et al., 2012). Scoring a week after sparse labeling of basal cells could report for most marked cells whether they divided (two or more marked cells anywhere) or differentiated before division (a single marked cell in upper layers). Whether the latter behavior can be attributed only to stem cells or also to some cells that may be committed to differentiate (without further division) might be resolved by marking cells initially with a method that requires cell division. The results could provide information about the temporal separation of division and differentiation, and their relative likelihood for the specific population of cells labeled (dictated by the chosen Cre driver).
Lifelong persistence of stem cells
This review has emphasized the imperative of capturing all upstream sources of derivative cells by including the use of experimental time periods that exceed the lifetime of derivative cells by only a small margin. What evidence reveals whether the upstream cell population persists for a lifetime or whether it is replenished by another set of more upstream cells? Some mouse intestinal and epidermal lineages persist for two or more years, showing that at least some of the targeted, identified stem cell population persist for a lifetime. However, only a small fraction of lineages persists (Clayton et al., 2007; Lopez-Garcia, Klein, Simons, & Winton, 2010; Mascre et al., 2012; Sada et al., 2016; Snippert et al., 2010), so this evidence cannot rule out substantial replenishment of the stem cell population by upstream cells.
What is a potential general solution for demonstrating long-term self-replenishment of stem cell communities? One possibility is to label stem cell lineages at high density in a cohort of animals, using a multicolor strategy for clarity, verify labeling of the majority of stem cell lineages at a short time interval in a cohort of samples, and then measure any subsequent decline in the proportion of physiological units (ovarioles for FSCs, crypts for intestinal stem cells and basal cells for epidermal stem cells) that are fully labeled, extending towards a whole lifetime (Fig. 7). The approach relies on being able to label the stem cell population that is being tested at very high efficiency and sparing whatever cell population is a potential candidate for being upstream. For intestinal stem cells, the test could include all lineages initiated in Lgr5-high cells, essentially testing whether +4 cells that remain unlabeled because of low Lgr5 expression and contribute only modestly over the short-term might eventually replace lineages initiated in Lgr5-high cells (Li et al., 2014). A related test, which may also be relevant to epidermal stem cells, could instead target only dividing cells for labeling (over an extended time period) to examine long-term replacement by initially highly quiescent cells.
Figure 7. Testing for replenishment of a stem cell population.
(A, B) Labeling is cleanly targeted with high efficiency to a population of cells that are found to be stem cells (colored circles) in samples analyzed at an intermediate time, without marking any cells that are conceivably upstream of the stem cell (white circles). (A) If all stem cells are initially labeled there will be no unlabeled cells in the stem cell compartment at the intermediate time. At later times (close to a lifetime) a single lineage color will likely dominate (sometimes two or more colors may still be present). There will be no unlabeled (white) stem cell lineages (top line) unless the stem cell population is at least partially replenished (second line). (B) In practice, labeling may be very efficient (say 80%) but not uniform, so some samples will include unlabeled stem cells at intermediate times and only (or largely) unlabeled stem cells at very long times. The test is therefore whether the proportion of samples with any unlabeled stem cell lineages increases over time (from a baseline of 20%, determined from the proportion of unlabeled stem cells at the intermediate time, in this example).
For FSCs, the only plausible upstream candidates are non-dividing ECs in the anterior half of the germarium (Fig. 1A, Fig.2B). When recombinant multicolor FSC lineages were generated at high efficiency (with parental genotypes remaining in about 2/9 of FSCs, assessed at 9d), the majority of ovarioles (20/29) observed 31d after marking (a significant fraction of an adult Drosophila lifetime) contained only marked recombinant cells throughout the FSC region (Reilein et al., 2017). The cells were originally marked by mitotic recombination and therefore necessarily derive from the dividing FSC population, sparing the quiescent EC population (as illustrated in Fig. 7). Thus, there appears to be no widespread replacement of the FSCs in layers 1–3 over a lifetime; rather, the defined FSC population maintains itself. Similar tests have been conducted for mouse prostate stem cell populations (Wuidart et al., 2016).
In practice, these tests may often not be clean enough (labeling the entire defined stem cell population but no candidate upstream cells) to exclude any replenishment of stem cells. Indeed, there likely is replenishment at a low rate from quiescent cells in germaria (ECs) and crypts, especially in response to some stresses within the range of experience in the natural habitat. This should not provide a barrier to naming cells that produce the bulk of all derivative cells during a lifetime without substantial depletion as stem cells.
Heterogeneity and hierarchies
In a population asymmetry paradigm, it is expected that different stem cells will have different lifetimes, but the lifetime of each stem cell is stochastic and cannot be predicted (Jones, 2010). Indeed, a significant fraction of stem cells in such a community will have lifetimes only marginally greater than derivative cells and some may differentiate before they divide. Thus, some stem cells behave almost like derivative cells but the key difference is that their loss is not pre-determined and certain; it is a matter of chance. The relatively common argument that those cells surely cannot be stem cells because they neither last very long nor show the key characteristic of dividing and differentiating, is false. An individual stem cell need not divide and differentiate; only the community of stem cells must survive for a lifetime to serve its function.
Lineage data showing variable stem cell lifetimes, characteristic of population asymmetry, can always also be rationalized in terms of a hierarchy of functionally distinct cells with longer-lasting stem cells replenishing shorter-lived intermediates. Such models can be made progressively more elaborate to fit raw lineage data. It is therefore never possible to exclude all hierarchical models. However, such a model should only be preferred if it is specific and supported by convincing evidence of a hierarchy. In the absence of such evidence, the simplest model of population asymmetry and stochastic differences in behavior should be preferred. Importantly, the observation of heterogeneous properties among members of a stem cell community is not necessarily evidence of a functional hierarchy. As discussed in the next sections, this is because the acquisition of different properties may be dynamic and stochastic, with all options available to each member of the stem cell community.
Stem cell heterogeneity: diverse products
Tissues typically contain multiple cell types that turn over, raising two general questions. First, are the different cell types supported by one, two or more distinct stem cell populations? Second, if one stem cell population supports more than one type of derivative, when does diversification take place? The general expectation is that diversification occurs principally beyond the stem cell domain, taking advantage of substantially different signaling environments in geographically distinct locations or by sorting among near-equivalent neighboring cells through lateral inhibition mechanisms. However, it is also theoretically possible for a given type of stem cell to produce alternative products directly. In that situation, what determines the output from a stem cell? Answers require studying lineages that derive from single stem cells over both very short periods to measure immediate behavior and long periods of time to capture potentially diverse outputs, as demonstrated for FSCs.
Early studies of products of cells marked in adults showed that Escort Cells (ECs), which surround developing germline cysts in the anterior half of the germarium (Fig. 1A, Fig. 2B), are replenished in adult ovaries (Decotto & Spradling, 2005; Kirilly et al., 2011; Margolis & Spradling, 1995). Some ovarioles included both marked FCs and ECs, while others had only one of those cell types labeled, raising the question of whether there are distinct stem cells for ECs and for FCs. The key initial tests were of two types. First, cells were marked at very low frequency to ensure that lineages almost always derived from a single cell (using an infrequent color combination in multicolor clones is very useful for this). Many such lineages contained both FCs and at least one EC, showing that a single stem cell can produce both ECs and FCs (Reilein et al., 2017). Second, lineages were examined over an extended time course. The proportion of FC-containing ovarioles with no marked ECs declined from over 50% at 9d to almost zero by 22d, suggesting that all FC-producing stem cells (FSCs) can produce ECs if they persist long enough (Reilein et al., 2017).
The basis for an FSC producing an EC versus an FC turned out to be the precise location of an FSC. ECs are anterior to FSCs and each new EC must therefore derive directly from an anterior (layer 2 or 3) FSC (rather than a layer 1 FSC), a process that was captured in a few instances by live imaging (Reilein et al., 2017). A new FC might, in theory, be recruited from any FSC location because germline cysts pass through the entire FSC territory. However, Reilein et al (2017) found that lineages containing FSCs only in layer 1 frequently included a very recently produced FC (contacting a stage 2b cyst), whereas lineages containing only layer 2 or 3 FSCs mostly did not. The data strongly suggested that FCs derive directly, only or mainly, from layer 1 FSCs. Thus, the nature of the derivative cell depends on the precise position of the stem cell from which it directly derives. Further studies showed that the FSC domain spans a declining gradient of Wnt signaling from anterior to posterior and a converse gradient of JAK-STAT pathway activity. Differentiation to an FC is promoted by high Wnt and low JAK-STAT pathway activity, whereas the converse is true for differentiation to a FC, providing a clear molecular rationale for different outcomes at different locations (Melamed & Kalderon, 2020; Reilein et al., 2017; Sahai-Hernandez & Nystul, 2013; Vied, Reilein, Field, & Kalderon, 2012; X. Wang & Page-McCaw, 2014).
Mouse intestinal stem cells support production of a variety of secretory cells in addition to absorptive enterocytes (Fig. 1B). Diverse cell production has been attributed to differences in Wnt, Notch and EGFR signaling but the positional source of these signaling differences is not entirely clear (Gehart & Clevers, 2019). It is therefore unclear whether the precise location of the differentiating stem cell might play a role. Paneth cells, unlike other derivatives, reside near the base of crypts in the steady state. It is commonly stated that all non-stem cell derivatives are first formed at around the +5 position and that Paneth cells subsequently migrate downwards (Gehart & Clevers, 2019). While disruption of Ephrin signaling and other genetic components leads to aberrant positioning of Paneth cells in the steady state (Batlle et al., 2002; Genander et al., 2009), those and other studies do not document active migration of Paneth cells or its disruption. Paneth cell precursors have been deduced to lie in a range of locations from 0 to +4 (Buczacki et al., 2013). It therefore seems appropriate to explore the possibility that Paneth cell precursors might, by analogy to the conversion of FSCs to ECs, derive directly, sometimes or predominantly, from stem cells below the +4 or +5 location.
Dynamically heterogeneous behavior in a single stem cell community
Does direct conversion of layer 1 FSCs to FCs and anterior FSCs to ECs mean that there are two distinct stem cell populations present? That would only be the case if each stem cell and stem cell descendants stayed in the same AP location. There was, in fact, a tendency for lineages to contain only marked ECs or only marked FCs shortly after stem cell marking (Reilein et al., 2017). However, when FSCs were marked at low frequency to label only a single FSC initially, and lineages containing two or more FSC derivatives were examined 3d later, only one third were confined to a single AP layer (Reilein et al., 2017). Moreover, as described earlier, production of both ECs and FCs becomes increasingly common over time. Thus, although the instantaneous properties of FSCs in different AP locations are different, an FSC or its FSC progeny can move to a different AP layer within a fairly short time and adopt new layer-specific properties. So, the range of possible behaviors of a single FSC is the same, no matter what its location. The heterogeneity within the stem cell population is dynamic and all FSCs are interchangeable members of a single community, aptly given a single name.
One could still ask whether FSCs should be classified as FC-biased (layer1) and EC-biased (layers 2/3). An objective answer is possible by adhering to the approach previously outlined to ascertain stem cell location with respect to FC production. Applying the same logic to clones that include at least one EC (Fig. 5A), single-layer candidate stem cells were confined to the posterior FSC layer (10 examples) or anterior FSC layers (13 examples) with similar frequency, mandating the conclusion that stem cells for ECs are located roughly equally in both posterior and anterior layers. Thus, by using an objective strategy for defining the location of source cells, the stem cell locations for FCs and for ECs were indistinguishable. Cells in both major AP layers are therefore appropriately named FSCs without any further distinctions. All FSCs maintain EC production as well as FC production even though the immediate differentiation potential of anterior FSCs is exactly opposite to that of posterior FSCs.
FSCs also display marked heterogeneity in division rates, with more posterior FSCs dividing faster (Melamed & Kalderon, 2020; Reilein et al., 2017). This is again a malleable property, rather than a rigid heritable behavior, with derivatives of a single marked cell showing EdU incorporation frequencies characteristic of their current locations and JAK-STAT signaling strength contributing significantly to this positionally graded property (Melamed & Kalderon, 2020). It has been estimated that the greater production of new FSCs in layer 1 than in anterior layers roughly balances the greater rate of FC production to EC production (measured at four to one), so that there need be no net flow of FSCs in the AP direction (Reilein et al., 2018). Net flow would inevitably mean that FSCs in one location have a greater average half-life than in another AP location.
It is often stated that intestinal stem cells have a longer half-life if they are in deeper crypt locations, based on the results of a relatively short-term (3d) live imaging experiment (Ritsma et al., 2014). The conclusion might seem almost inevitable if stem cells are only lost directly through differentiation from higher (+3 or +4) locations, especially if division rates are also higher at deeper levels. However, the same study provided clear evidence that individual cells can move in either vertical direction within the 0 to +4 domain, opening up the possibility that the potential for long-term survival of cells at the top of the stem cell domain might be much greater than measured in short-term studies. There is also some ambiguity over how many of the Lgr5-high cells studied were stem cells (since this layer might contain a mixture of stem and derivative cells) and whether other, potentially more stable stem cells at higher locations (+4) (Li et al., 2014) were excluded (Ritsma et al., 2014). Explicit measurement of “single-candidate” stem cell locations over different time intervals might alter current conclusions about the relationship between longevity and stem cell location. The FSC case study presents an explicit precedent for different outcomes of short and longer-term studies with regard to the characteristics of a stem cell in a given location, largely producing only FCs or only ECs (short-term) or both (long-term). In general, relatively rapid exchange of stem cell locations within a heterogeneous niche signaling environment provides an opportunity for a diversity of behaviors with similar or equal opportunity for each member of the stem cell community.
Mechanisms of Population Asymmetry and consequences for stem cell competition
The earliest depictions of stem cell maintenance portrayed repeated asymmetric outcomes for each stem cell division. When more than one active stem cell is present within a developmental unit there is an alternative to invariant single-cell asymmetry, whereby each stem cell may act differently, provided the sum of all stem cell behaviors maintains the stem cell population and produces derivative cells. That organization, generally termed population asymmetry, encompasses a variety of theoretical arrangements, ranging from the purest stochastic model where each stem cell is equally likely to duplicate or differentiate (become a derivative cell), and others where there is only occasional stem cell duplication (Blanpain & Simons, 2013; Jones, 2010; Lopez-Garcia et al., 2010). Individual stem cells are often said to undergo neutral competition under conditions of population asymmetry, meaning that any two stem cells labeled at random have equal chances of surviving or amplifying. Elucidating genetic factors that bias competition is especially important for understanding how pre-cancerous mutations arising in stem cells may be maintained and amplified (Frede, Adams, & Jones, 2014; Reilein et al., 2018; Snippert, Schepers, van Es, Simons, & Clevers, 2014; Vermeulen et al., 2013; White & Lowry, 2015).
Although the definitions of population asymmetry and neutral competition are couched in terms of experimental outcomes determined by lineage analyses, the most significant biological questions concern the mechanisms underlying stem cell behavior. The two fundamental properties of stem cells are cell division and production of derivative cells. So, a central mechanistic question is whether those two behaviors are independent or coupled, and hence whether they can be regulated independently to affect competition. Division and differentiation are necessarily coupled in stem cells maintained by invariant single cell asymmetry. Experiments must determine whether the two processes are linked for stem cell communities maintained by population asymmetry.
The question is not easy to address. In essence, a lineage technique must be able to report when a stem cell last divided (fixed by a timed recombination event), when a daughter cell became a derivative cell (reported by location in some paradigms) and that the parent cell was indeed a stem cell (based on elapsed time or selective labeling). This was possible for FSCs because the accumulation of egg chambers budding at regular intervals produces a chronological history of FSC to FC differentiation that can be assayed at a single time from the appearance of a fixed ovariole. Cells were marked at low frequency and analyzed 3d later so that all FSC derivatives remained in the ovariole (Reilein et al., 2018). In the multicolor labeling system that was used, two daughters resulting from a recombination event always have complementary colors (“twin-spots”: B pairs with GR, G with BR: GR and BR also pair) (Fig. 2B). Recombination in an FC necessarily yields FCs with both complementary twin-spot colors on the same egg chamber, whereas recombination in an FSC can lead to an unpaired FC color (Fig. 2B). That device was used as an internal control for precise temporal definition of marked cells as FSCs, revealing what portion of an ovariole contained derivatives of marked FSCs (rather than FCs) after 3d. A lineage in the FSC-derivative region that contained only one FC patch and no FSCs (like the green lineage in Fig. 2B) reported an FSC that differentiated without any FSC division subsequent to FSC marking. For those lineages, the location of the marked FC patch revealed the time of differentiation. The time between differentiation to an FC and the FSC division that marked the FSC lineage at 0d was found to be highly variable, showing that FSC division and differentiation are not temporally coupled (Reilein et al., 2018). It was also shown by using a variety of genetic alterations that FSC division and differentiation can be regulated largely independently (Melamed & Kalderon, 2020; Reilein et al., 2018).
An important consequence of division-independent differentiation is that genetic changes that alter the division rate of one stem cell will necessarily strongly affect competition with neighboring normal stem cells. This connection was demonstrated mathematically for a stem cell population of a fixed size and has been shown experimentally for many genetic alterations that increase or decrease the division rate of FSCs (Melamed & Kalderon, 2020; Reilein et al., 2018; Z. A. Wang, Huang, & Kalderon, 2012; Z. A. Wang & Kalderon, 2009). The same organization of the stem cell community, which necessarily promotes survival and amplification of fast-dividing stem cell variants, is shared by mouse intestinal stem cells (Morrissey & Vermeulen, 2014; Ritsma et al., 2014; Snippert et al., 2014; Vermeulen et al., 2013), and may be very important in early steps in the development of some cancers. If, on the other hand, the division and differentiation of individual stem cells are coupled, even within a stem cell community governed by population asymmetry, a genetic change that increases division rates would promote divisions leading to stem cell duplication and stem cell loss equally, with no net effect on competition and survival, so long as the total stem cell population remains constant (Reilein et al., 2018).
Although population asymmetry necessarily involves some symmetric stem cell duplications, presentation of different modes of population asymmetry in terms of the fraction of divisions outcomes that are symmetric can be deceptive as an accurate embodiment of stem cell behavior. The population asymmetry exhibited by epidermal stem cells is often described in those terms, with two major studies reporting that about 80% of stem cell division outcomes are asymmetric (Clayton et al., 2007; Mascre et al., 2012). That fraction is considerably higher than the expectation of 50% if all division outcomes were entirely stochastic. The asymmetric division outcome frequency was estimated principally by fitting to a mathematical model, combining data on the rate of extinction of lineages and estimations of division rates, rather than a potentially more definitive approach of directly measuring outcomes of stem cell divisions.
Even when individual division outcomes are examined in fixed specimens (Roy et al., 2016), there are significant inherent limitations. To specify the results of a division, the identity of both daughters must be deduced. Cells in supra-basal locations can be identified confidently as derivative cells. However, the precise location of all stem cells is not known and a differentiation event may hypothetically occur long after division (until proven otherwise), followed by a potentially variable time before movement out of the basal layer. Hence, it cannot be assumed that a cell in the basal layer is a stem cell. Instead, the identity of a basal cell daughter can only be established after it either divides or moves out of the basal layer. Thus, the observed outcomes for two marked cells can only be attributed to asymmetric or symmetric (duplicating or differentiating) divisions if it is assumed that differentiation is always coupled to cell division. If no such assumption is made, there are other routes to the same observed outcomes, including the possibility that every stem cell division is initially duplicative (Fig. 6C). Importantly, subsequent events may prove provisional assignment of asymmetric or symmetric outcomes to be incorrect. If a twin-spot labeling technique can be employed (Griffin et al., 2009; Zong, Espinosa, Su, Muzumdar, & Luo, 2005), it would be possible to score lineages of more than 2 cells and, in most cases, deduce the identities of the two differently-colored daughters of the first, labeling division. Equally important, trying to capture the relationship between stem cell division and differentiation by reporting only observation of division outcomes is systematically flawed because it ignores instances of differentiation without any division (Fig. 6C); similar logic applies to fitting long-term lineage results to models that permit differentiation only as a consequence of division. Thus, phrasing outcomes in terms of asymmetric vs symmetric divisions can be mis-leading with regard to the actual processes (one or two steps) and the numerical deductions themselves may often be flawed by an implicit assumption of coupled division and differentiation.
For both mouse epidermal and intestinal stem cells, the most direct evidence concerning the outcome of individual stem cell divisions derives from live imaging. For intestinal stem cells results were not reported quantitatively with regard to division outcomes but a large fraction of symmetric, duplicative outcomes is evident from the raw data and, crucially, division and differentiation were generally not temporally coupled (Ritsma et al., 2014). Prior short-term lineage studies interpreted results only in terms of symmetric and asymmetric division outcomes, even though some of the raw data gave clear evidence of single derivative cells from a marked Lgr5-hi cell (Snippert et al., 2010); continuous observation clarified and corrected the former impression conveyed of coupled division and differentiation (Ritsma et al., 2014).
For epidermal stem cells, the fraction of symmetric outcomes for pairs of daughters was reported as 56% and 66% from live imaging of two different skin locations (much higher than the 20% deduced from indirect lineage study deductions, and consistent with independent daughter cell fates); crucially, differentiation was not generally temporally coupled to division (Mesa et al., 2018; Rompolas et al., 2016). These conclusions are not constrained by the inherent limitations for measuring asymmetric or symmetric outcomes in lineage studies, and suggest there is no special mechanism that imposes a preference for asymmetric division outcomes. Rather, a stem cell divides and each daughter has an equal chance of subsequently differentiating, just as currently believed for mouse intestinal stem cells and Drosophila FSCs. Altogether, establishing whether stem cell division and differentiation are coupled provides key insights into population asymmetry mechanisms and the impact of proliferation rate on competition, whereas characterization according to the frequency of symmetric versus asymmetric divisions can easily be flawed and may carry with it an explicit or implicit assumption that division and differentiation are coupled.
Live imaging has another advantage over lineage studies because it allows detailed observation of neighboring cells to supplement observations strictly focused on a single cell lineage. Those observations have begun to shed light on how coupling of stem cell division and differentiation is achieved at the population level when it is apparently stochastic and uncoupled when viewed cell-autonomously (Mesa et al., 2018). An important initial finding was that the division of one stem cell is promoted by differentiation (exit from the basal layer) of a neighbor, with no evidence of the converse causal connection (Mesa et al., 2018).
Conclusions
It is both intriguing and important to probe how each type of adult stem cell maintains a specific set of derivative cells throughout life under normal and adverse conditions. Insights for each paradigm may be important for developing tissue-specific regenerative therapies or for understanding and countering cancer development, while the study of several paradigms may allow appreciation of common principles and stimulate new hypotheses. To realize those goals, it is essential to use universal definitions, and apply appropriate methods rigorously, tailoring them to the specific attributes and challenges of each paradigm. I have argued in favor of a straightforward universal definition of adult stem cells as a community that reflects their basic physiological function of maintaining a supply of derivative cells. I have also outlined several strategies and important principles for defining and investigating adult stem cells through lineage analyses, using FSCs to illustrate the repeatedly key considerations of sampling all stem cells comprehensively, examining outcomes over a variety of time periods and using low-density and high-density labeling for different purposes. The FSC case study also illustrates how early assumptions, based on prevailing expectations, can easily lead to false conclusions. The strategies outlined for FSCs have not generally been used to investigate mammalian stem cells but could usefully complement traditional approaches to answer some outstanding questions regarding stem cell numbers, locations and basic behaviors. Eventually, live imaging under non-invasive, physiological conditions with suitable markers will likely become the richest source of information.
Stem cell investigations increasingly incorporate single cell expression analyses and associated inferences of potential developmental paths. It is important to keep in mind that the only way to determine adult stem cell identity is by thorough experimental evaluation of cell behavior over time, avoiding the potential pitfall of assuming that cells with significantly different expression profiles must be physiologically different. Many adult stem cell communities appear to be very fluid, with individual cells changing location, gene expression patterns and behavior over time, thereby embracing significant heterogeneity into a single population without a rigid functional hierarchy. Drosophila FSCs exhibit exactly those properties. FSCs also illustrate how regulation of stem cell division and differentiation by extracellular signals that are graded over the stem cell domain inevitability results in a range of gene expression patterns over the whole stem cell community (Hartman et al., 2015; Melamed & Kalderon, 2020; Reilein et al., 2017). It seems reasonable to forecast that thorough functional analyses of various other adult stem cell communities will mostly show them also not to be fragmented according to specialized tasks signaled by distinct gene expression profiles, but instead to act as a single large community of component cells with fluid expression profiles, sharing extensively in those tasks. Perhaps the general design feature of incorporating heterogeneity into a fluid community permits more reliable and durable execution of physiological stem cell function. Comprehensive and open-minded functional studies using cell lineage and live imaging techniques have been instrumental in our evolving conception of adult stem cells from a small number of specialized, long-lived and potent cells at the top of a rigid hierarchy to a larger, more diverse but inclusive community that maintains healthy tissues.
Acknowledgments
I thank Valentina Greco, Alice Heicklen, David Melamed, Rachel Misner and Amy Reilein for comments on the manuscript, and Amy Reilein for execution of all Figures. Research supported by the National Institutes of Health (RO1 GM079351 to D.K.).
Research in the laboratory of DK on Drosophila FSC biology was supported by NIH RO1 GM079351.
Footnotes
Conflicts of Interest/Competing Interests: None
Declarations
Ethics approvals: Not applicable
Consent to participate: Not applicable
Consent for publication: Not applicable
Availability of data and material: Not applicable
Code availability: Not applicable
Author’s contributions: Not applicable
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