## Gut Stem Cell Replacement

Gut cell turnover is characteristically rapid and relies on stem cells in the crypts that lie between the intestinal villi. The prevailing view is that stem cell division is asymmetric with one daughter retaining a stem cell character; however, this pattern of stem cell turnover does not always apply. Using long-term lineage tracing, **Lopez-Garcia et al.** (p. 822, published online 23 September) showed that the loss of a stem cell was compensated for by the multiplication of a neighboring cell. The rate of stem-cell loss was found to be equivalent to the rate of cell division, indicating that symmetric cell division was the rule for gut stem cells and implying stochastic expansion, contraction, and extinction of clones occurs.

## Abstract

With the capacity for rapid self-renewal and regeneration, the intestinal epithelium is stereotypical of stem cell–supported tissues. Yet the pattern of stem cell turnover remains in question. Applying analytical methods from population dynamics and statistical physics to an inducible genetic labeling system, we showed that clone size distributions conform to a distinctive scaling behavior at short times. This result demonstrates that intestinal stem cells form an equipotent population in which the loss of a stem cell is compensated by the multiplication of a neighbor, leading to neutral drift dynamics in which clones expand and contract at random until they either take over the crypt or they are lost. Combined with long-term clonal fate data, we show that the rate of stem cell replacement is comparable to the cell division rate, implying that neutral drift and symmetrical cell divisions are central to stem cell homeostasis.

Theories of epithelial cell renewal place stem cells at the apex of proliferative hierarchies, possessing the lifetime property of self-renewal (*1*). In homeostasis, the number of stem cells remains fixed, imposing an absolute requirement for fate asymmetry in the daughters of dividing stem cells, such that only half are retained as stem cells. Fate asymmetry can be achieved either by being the invariant result of every division (intrinsic asymmetry) or by being orchestrated from the whole population, where cell fate following stem cell division is specified only up to some probability (population asymmetry) (*1*, *2*). These alternative models suggest very different mechanisms of fate regulation, yet their identification in normal tissues remains elusive.

In the intestinal crypt, the apex of the proliferative hierarchy is associated with the anchored cells of the crypt base (*3*). Heterogeneity in expression of fate-determining genes and in cell cycle characteristics has suggested that at least two populations (Lgr5^{+} and Bmi1^{+}) of crypt stem cells may exist (*4*, *5*). For neither population has the pattern of self-renewal been revealed.

Recent studies have provided evidence in support of intrinsic asymmetry by showing that crypt base cells are more likely to show an oriented spindle than cells higher in the crypt, and this correlates with asymmetric DNA segregation during division (*6*, *7*). However, the phenomenon of monoclonal conversion, whereby crypts become monophenotypic (clonal) with time after genetic marking of individual cells (*8*–*10*), presents an apparent experimental paradox. This observation rules out truly invariant modes of cell division involving multiple stem cells and has been explained by rare errors in intrinsic asymmetry (*11*–*13*). Hence, the consensus view remains that intestinal stem cells divide asymmetrically due either to inherent properties or environmental cues (*3*). Here we show that the dynamics of clonal growth leading to monoclonal conversion is directly related to the pattern of steady-state self-renewal.

Intestinal clones were induced by low-level Cre-mediated recombination in Ah*cre*^{ERt} animals (targeting potentially all the proliferative populations within the crypt with a single treatment) crossed to Cre-reporter strains as described previously, and were visualized in tissue whole mounts or sections [Fig. 1, A to J, and supporting online material (SOM) S-I]. With only 1.9 ± 0.7% of crypts containing labeled cells at 2 weeks after induction, the vast majority of clones were expected to derive from single cells. By imaging the crypt base, we first determined the proportion that have achieved monoclonal conversion (Fig. 1, I and J). Crypts can become monoclonal a short time after induction, such that ~50% are fully labeled within 8 weeks (Fig. 1K). The dynamics of monoclonal conversion can also be tracked by scoring the number of differentiated progeny that emerge from the crypts (Fig. 1, L to N, and fig. S1). After pulse labeling, cells exported from crypts form one to three clear migration streams on villi (Fig. 1, B and C). On the villus, clones comprised both Goblet and absorptive cell lineages, and within the crypt, clones contained Paneth cells. Each fully labeled crypt supports a clone width of *w*_{max }*=* 6.8 ± 1.3 cells (mean ± SD, *n* = 155) along the villus. As with the crypt base analysis, we found that 50% of clones were of full width (i.e., six cells or more) within 8 weeks, corresponding to 50% monoclonal crypts at this time point (Fig. 1M).

Monoclonal conversion rules out a simple model of tissue maintenance that originates from a population of long-lived stem cells following a strict pattern of asymmetric division, and can be explained by two classes of behavior. First, crypts could be maintained by a hierarchy in which a single stem cell generates, through a sequence of asymmetric divisions, stem cells with a more limited proliferative potential (*14*) (Fig. 2A). Second, tissue could be maintained by an equipotent stem cell population, in which stem cell loss is perfectly compensated by the multiplication of others (*15*–*17*) (Fig. 2B). Any detailed model of self-renewal will belong to one of these two classes (SOM S-II).

Although both behaviors predict attrition of surviving clones and drift toward monoclonality, the full range of clonal fate data allows us to discriminate between them. To understand how, we draw upon concepts from statistical physics applied to population dynamics. Within an equipotent cell population, ongoing replacement leads to “neutral drift” of the clonal population (*17*). In this case, if the stem cell pool were not limited by anatomical constraints, clonal evolution would settle into a characteristic behavior in which the size distribution acquires a “scaling form”: defining as the fraction of surviving clones that host *n* stem cells at a time *t* after induction (see SOM S-III) (*17*, *18*)(1)where 〈*n*(*t*)〉 denotes the average number of stem cells in a surviving clone. The scaling function, *F*(*x*), is “universal,” dependent only on the spatial organization of stem cells. From Eq. 1, it follows that, if is plotted against , the size distributions will follow the same curve irrespective of the time *t*. In the crypt, where the stem cell compartment is limited, scaling is transient and would eventually fail when a noticeable fraction of crypts become monoclonal.

By contrast, if replacement occurs hierarchically, then clones derived from the “master” stem cell will increase steadily in size, whereas those derived from its shorter-lived progeny will exhibit limited growth followed by loss. Crucially, the mixture of these two behaviors leads to binomial size distributions that do not scale (SOM S-V).

Clone size is impossible to measure in absolute terms in the intestine because of the constant migration and loss of cells. However, we can access indirectly: The cohesion of clones within the crypt, and the proportionality of the clone width emerging from the crypt to the villus (SOM S-I), show that clonal expansion is tied to the circumference at the crypt base. Therefore, the clone width, relative to that of fully labeled crypts, serves as a proxy for the fraction of labeled stem cells within the crypt. Formally, a clone of width *w* on the villus is associated with a clone covering a fraction *f*(*w*) = *w*/*w*_{max} of the circumference at the crypt base. The number of stem cells associated with a clone of width *w* is given by *n* = *f*(*w*)*N*_{stem}, where *N*_{stem} denotes the number of stem cells surrounding the crypt base. With this assignment, we find that for *t* ≤ 4 weeks, where the vast majority of crypts have yet to become monoclonal, the size distributions show scaling behavior (Fig. 2D), an unambiguous signature of neutral drift dynamics.

The growth rate, 〈*n*(*t*)〉, and the form of *F*(*x*) have the potential to offer further insight into the pattern of stem cell fate. In particular, if stem cells are organized into a one-dimensional arrangement, with cell replacement effected by neighboring stem cells (Fig. 3, A and B), then the average size of surviving clones grows as a square root of time, , with λ the stem cell replacement rate, and the scaling function is predicted to take the form (SOM S-III)

(2)

Referring to the experimental data, the coincidence of the scaling behavior with this universal (parameter-free) form, together with the observed square-root growth of the clone width over the same period (Fig. 2D, inset), reveals that stem cells are indeed being replaced laterally by neighboring stem cells in an effectively one-dimensional geometry. This behavior can accommodate both variability in replacement rates and potential stem cell replacement parallel to the crypt axis (SOM S-III.4 and S-III.5).

Because this pattern of stem cell fate emerges from the consideration of (universal) short-time dynamics, the long-term behavior, including the drift toward clonality, presents a powerful test of the model. By fixing just a single parameter, λ*/N*_{stem}^{2 }= 0.025 ± 0.003 per week (mean ± SEM), from a quantitative fit to the average clone width (Fig. 1M), we obtained an excellent agreement of theory (detailed in SOM S-IV and S-VI) with the measured monoclonal fraction (Fig. 1K) and clone size distributions over the entire time course (Fig. 3, C to H, and fig. S2). A similar analysis of clone fate as measured from the crypt base in the colon reveals the same neutral drift behavior (Fig. 3, I and J, and SOM S-VI).

These results reveal that stem cells of the small intestine and colon behave as an equipotent population following a pattern of neutral drift in which the loss of a stem cell is compensated by the multiplication of a neighbor. This process may be achieved through stochastic stem cell loss triggering self-renewal, or through overcrowding of the stem cell pool leading to loss. Further, analysis of sister cell orientation reveals that the frequent transverse cell divisions required for stem cell replacement occur at the crypt base (fig. S3).

Which cells constitute the stem cells, and what is their rate of loss? Current debate centers on the relationship between two crypt base populations, the Bmi1^{+} cells positioned around row 4 (*4*) and the columnar Lgr5^{+} cells that reside at the crypt base (*5*, *19*). Because both cell populations support long-lived clonal progeny, equipotency requires that Bmi1^{+} and Lgr5^{+} cells contribute to the same stem cell pool, with the cells generating each other. Such heterogeneity would not affect the scaling behavior in Eq. 2, as its effect would be resolved rapidly compared to one-dimensional drift around the crypt circumference (SOM S-III.4). If we estimate the number of stem cells on the basis of the total number of Bmi1^{+} and Lgr5^{+} cells (*4*, *5*, *19*), we can conclude that their total number is >16, suggesting that stem cells are replaced laterally by their neighbors at a rate λ ≈ 1 per day comparable to the measured cell division rate (*5*, *20*–*22*). Therefore, asymmetric cell division is not the sole, or even the most common, mode of stem cell division in the intestine: Symmetric stem cell division is not a rare event, but is a central aspect of homeostasis.

In place of a hierarchical arrangement, our results identify a pool of equipotent stem cells that is regulated by the behavior of neighbors. The pattern of stem cell regulation in the intestine provides an inherently flexible assembly in which any stem cell can be deployed to differentiate into one of a number of cell types, act to replace stem cells locally, and respond to changing environmental demand.

## Supporting Online Material

www.sciencemag.org/cgi/content/full/science.1196236/DC1

Materials and Methods

SOM Text

Figs. S1 to S3

References

## References and Notes

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- We thank H. Zecchini and R. Kemp at Cancer Research UK, Cambridge Research Institute (CRI), and the CRI Biological Resource Unit and Histopathology Core. This work was supported by Cancer Research UK (D.J.W.), Seneca Foundation (Region de Murcia, Spain) (C.L.-G.), the Engineering and Physical Sciences Research Council fellowship EP/F043325/1 (A.M.K.), and the Engineering and Physical Sciences Research Council Programme grant EP/F032773/1 (B.D.S.). A patent application on drug and toxicity testing has been submitted.