Methods Of Analysing Homeostatic State In Cell Systems

  • Published: Mar 31, 2011
  • Earliest Priority: Sep 22 2009
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Methods Of Analysing Homeostatic State In Cell Systems Background to the Invention

This invention relates to methods which involve the analysis and prediction of cell growth behaviour such as proliferation and differentiation, and in particular, to methods for assessing changes in the growth behaviour of cells. This may be useful, for example, in identifying agents which alter growth behaviour, for example in carcinogenicity or toxicity screening and/or the development of cancer therapeutics. Adult tissues are maintained by stem and committed progenitor cells. In tissues that turn over, these cells must achieve a perfect balance between division and differentiation. Resolving the mechanisms that control balance represents a defining question in tissue stem cell biology. However, progress in resolving mechanisms of stem cell fate have been frustrated by the scarcity of reliable and specific molecular markers.

In homeostasis, it has been long-known that tissue turnover can occur via two distinct mechanisms of cell fate: i) stem cells can undergo perfectly asymmetric division, in which each and every cell division gives rise to one stem cell and one differentiated progeny, or iijcells can follow a pattern of population asymmetry in which cell divisions lead, on average, to one undifferentiated cell and one more differentiated cell. These two behaviours (a) encompass all pathways to homeostasis and (b) have been long- • known to stem cell researchers.

Prior art techniques for modelling cell proliferation and differentiation behaviour suffer from problems of complexity and are often unwieldy and difficult to apply across different systems. Furthermore, prior art models frequently involve attributing various behaviours or involvement to multiple cell classes including stem cells which can complicate matters further. Moreover, the involvement or role of cells such as stem cells in steady state behaviour is incompletely understood in the art, making it inherently difficult to model the biological systems. The present invention seeks to overcome problem (s) associated with the prior art.

Summary of the Invention The present inventors have shown that homeostasis of tissue places significant constraints on the possible mechanisms of cell fate leading to population asymmetry, and that this fact can be used to model and analyse cell growth behaviour. Thus the invention provides a method to analyse the homeostatic balance of cell tissue, which includes the following steps:

i) label one or more cells in a population

ii) incubate the cells for a time t

iii) determine the clone size distribution of labelled cells at time t

iv) determine if the clone size distribution of (iii) conforms to the scaling form:

Ρ = -Λ- /(η/{η(ή)), where

("(0)

Pn(t) is the probability of finding a surviving clone which has n progenitor cells at time†,

(«( ) denotes the average number of dividing cells in surviving clones at time t and

wherein if the clone size distribution conforms to the scaling form above, the cells are identified as being in a normal steady-state homeostatic balance; if the clone size distribution does not conform to the scaling form above, the cells are identified as not being in a normal steady-state homeostatic balance.

The invention further provides a method to identify if a cell is a committed progenitor cell or a three- dimensional stem cell population cell or a one- or two- dimensional stem cell population cell which comprises the following steps:

(i) label one or more cells in a population

(ii) incubate the cells for a time t

(iii) determine the clone size distribution of labelled cells at time t

(iv) compare the clone size distribution of (ii) to the scaling form:

pn(0 = j^-rf(n /(n(t))), where

("(0)

Pn(t) is the probability of finding a surviving clone which has n progenitor cells at time†,

(n( ) denotes the average number of dividing cells in surviving clones at time t and (v) determine if {η( ) - λί wnere ^ represents the cell turnover rate or if

(«(/)) = ^¾7 wjth χ †he s†em ce|| turnover rate or if («(/)) = Ar/ln( At) from †he comparison of (iv)

wherein

if the cells follow ("( )) - t then they are identified as committed progenitor cells or three- dimensional stem cell population type; and

if the cells follow ~ ^¾7 then they Qre ^Θη^Θ<:) as one-dimensional stem cell population type; and

if the cells follow («( )= ^/ln(At) thef| †hey Qre jden+ifjecj as two-dimensional stem cell population type.

The invention further provides a method of determining whether cells are committed progenitor cells or three- dimensional stem cell population type cells, said method comprising monitoring the non-universal short-time dependence.

In this scenario, the invention can be used to decide between committed progenitors and three dimensional stem cell population type cells using the measured non-universal short-time dependence. From the perspective of scaling and clonal evolution, the two patterns of behaviour cannot be discriminated. However, they can be compared to non-scaling behaviour - so dysregulation due to toxins or the proliferation of mutant clones is still analysable. Moreover, these two patterns of behaviour can be discriminated by looking af the short term behaviour which is non-scaling. For example, by looking literally at the first division and determining whether symmetric differentiation and multiplication occur with equal probability, and we have scaling, we infer that the regulation is internal. If, on the other hand, imbalance is observed - for example more proliferative two cell clones at short times than terminally differentiated, and we have scaling, we infer that it is externally regulated.

The expressions 'have scaling' or 'the data scale' or 'the data exhibit scaling' are used in their commonplace/textbook mathematical sense in which it is determined if the data fit to the predictions (descriptions) of the mathematical model provided herein.

Suitably said short-time data is obtained via the same measurements that provide the long-term data sets. The invention further provides a method of identifying a candidate modulator of cell proliferation or differentiation, comprising a method as described above wherein at least two samples of cells are labelled, wherein the first sample is contacted with the candidate modulator, and wherein a difference between the first and second samples of cells identifies the candidate modulator as a modulator of cell proliferation or differentiation.

The two samples of cells may be comprised by the same animal, explant, biopsy or other tissue sample provided that the cells can be treated separately with respect to the modulator (e.g. by topical application rather than systemic application since systemic application would be expected to affect all cells in an individual animal/explant/biopsy/other tissue sample). This has the advantage of reducing the number of animals/explants/biopsies/other tissue samples required.

Suitably the first and second samples of cells are comprised by first and second animals/explants/biopsies/other tissue samples. This has the advantage of keeping treatment of the first and second samples of cells separate.

The invention further provides a method of identifying a candidate modulator of cell proliferation or differentiation, comprising a method as described above, wherein the results are compared to a reference value for the cell type being examined, wherein a difference between the sample analysed and the reference value identifies the candidate modulator as a modulator of cell proliferation or differentiation.

The modulator may comprise any treatment such as genetic, environmental, infectious, chemical, physical eg. temperature or any other kind of treatment whose effect it is desired to assess. Typically the treatment will be application of a candidate modulator compound such as a chemical or pharmaceutical agent (eg. candidate drug) to the cells. Clearly this may need to be reapplied or 'topped up' depending on the incubation time, the stability, whether it is a transient or long-term treatment or other such considerations well within the abilities of the skilled operator. Application of the modulator will be by any suitable means, for example if the cells are comprised by an animal it may be by feed, by injection, by topical application (e.g. 'painting' the compound onto the skin of the animal) or any other suitable method. When the cells are cultured in vitro such as a biopsy, explant, primary culture or other technique, then suitably the candidate modulator may be added to the medium in which the cells are maintained. The modulator may be a genetic entity. For example it may be desired to investigate the effect of a particular genetic mutation or transgene on homeostatic state. In this scenario, suitably contacting the cells with the modulator would comprise introducing the mutation or transgene to the cells. For first and second populations of cells, the first (treated) population would be cells comprising the mutation or transgene; the second (untreated) population would be cells not comprising the mutation or transgene. In the examples this application of the invention is illustrated, for example with dominant negative mastermind like 1 protein.

In more detail, the invention provides a method of analysing the homeostatic state of a population of cells, which includes the following steps:

a) label one or more cells in the population

b) incubate the cells for a time†

c) determine the clone size distribution of labelled cells at time†

d) determine if the clone size distribution of (c) conforms to the scaling form:

Pn{t) where

Pn(t) is the probability of finding a surviving clone which has n progenitor cells at time t,

{«(/)) denotes the average number of dividing cells in surviving clones at time† and

wherein if the clone size distribution conforms to the scaling form above, the cells are identified as being in homeostatic balance; if the clone size distribution does not conform to the scaling form above, the cells are identified as not being in homeostatic balance.

In terms of 'analysing the homeostatic state', clearly each population of cells analysed may not actually be in homeostatic balance. This is of course one of the main benefits of the invention, to be able to tell whether or not the population of cells it in fact in homeostatic balance. A normal steady-state homeostatic balance means that the population being analysed is neither expanding (e.g. indicating dysregulated proliferation) nor contracting (e.g. indicating dysregulated cell loss). Thus the term "analysing the homeostatic state" may be taken to mean determining the homeostatic state or determining the homeostatic balance or investigating the homeostatic state and must not be interpreted as requiring the population of cells to be in balance - the answer to this is of course the most significant output of the methods of the invention.

Thus the answer to whether the cells are in homeostafic balance as determined in the method of the invention may be understood as determining whether or not the cells are in a normal steady-state homeostafic balance.

Analysing the homeostafic state may comprise detecting dysregulated proliferation. In this scenario finding that the cells are not in homeostatic balance corresponds to finding that the cells are accumulating (e.g. dysregulated proliferation).

Analysing the homeostatic state may comprise detecting dysregulated cell loss such as via apopotosis. In this scenario finding that the cells are not in homeostatic balance corresponds to finding that the cells are being lost (e.g. dysregulated apoptosis).

Typically the finding that the clone size distribution does not conform to the scaling form indicates that there is an imbalance; further test(s) or investigation(s) may be required to determine which type of imbalance (i.e. cell gain or cell loss).

In another aspect, the invention relates to a method as described above, further comprising

(e) determine if where λ, represents the cell turnover rate or if

(n(t)) = wj†h λ†he s†em ce||†umover ra†e or jf («(0) = wherein if the cells follow _ ^ , then they are identified as committed progenitor cells or three-dimensional stem cell population type; and

if the cells follow (nW) ~~ the they are identified as one-dimensional stem cell population type; and

if the cells follow («( ) = ^/ln(^ †nenney are identified as two-dimensional stem cell population type.

In another aspect, the invention relates to a method as described above further comprising

(f) determining whether cells are committed progenitor cells or three-dimensional stem cell population type cells by monitoring the non-universal short-time dependence.

In another aspect, the invention relates to a method of identifying a candidate modulator of cell proliferation, comprising (i) providing at least a first and second population of cells, wherein the first population is contacted with the candidate modulator;

(ii) analysing the homeostatic balance of said populations of cells as described above;

wherein a difference between the first and second populations of cells identifies the candidate modulator as a modulator of cell proliferation.

In another aspect, the invention relates to a method as described above wherein the population of cells is comprised by an adult tissue.

In another aspect, the invention relates to a method as described above wherein the cells are selected from oesophagus cells, gut cells, or epidermal cells.

In another aspect, the invention relates to a method as described above wherein the label is a genetically inheritable label.

In another aspect, the invention relates to a method as described above wherein the label comprises expression of a fluorescent protein induced by ere recombination. In another aspect, the invention relates to a method as described above wherein the cells are mouse cells and wherein the genetically inheritable label is Lgr5creERT/Rosa26 LSL confetti.

In another aspect, the invention relates to a method as described above wherein the cells are mouse cells and wherein the genetically inheritable label is AhcreER†/Rosa26 LSL EYFP.

Detailed Description of the Invention The long-term maintenance of tissue must conform to just two "universal" behaviours characterised by either cell autonomous (i.e. internal) regulation or external regulation. Within the context of the present invention, universal means that, under the condition of long-term homeostasis - a hallmark of adult tissue - any detailed pattern of cell fate will lead to a clonal evolution which is indistinguishable from one or other of these two classes: internal or external regulation.

More precisely, the behaviour of cell autonomous regulation follows a pattern of stochastic fate in which the probability of cell division leading to symmetric self-renewal is perfectly balanced by the probability that division leads to two differentiated cells. Significantly, this behaviour is achieved in a cell-autonomous manner, the product of internal regulation, leading to its recapitulation in culture. In the context of the present invention, cells of this type are referred to as committed progenitor cells.

Said pattern of cell behaviour applies for example to interfollicular epidermis cells or in primary cultures of glial cells derived from brain tumour tissue and in pancreatic beta cell population in islets. The external regulation behaviour involves cell division initiated by the loss (through differentiation, apoptosis, or otherwise) of neighbouring cells (or vice versa). In the context of the present invention, cells of this type are referred to as a stem cell population. Said behaviour, which belongs to a class of models known as the "voter model" in the statistical physics literature, and is distinct from that of committed progenitor cells in providing a mechanism both to maintain tissue in homeostasis and to repair and regenerate tissue.

Stem cell population pattern of behaviour represents a robust and ubiquitous feature of normal adult tissue maintenance. It applies preferably to adult tissue types, such as for example fhe stem cell compartment of interfollicular epidermis, the germ cell line in mouse, intestinal crypt (including the small intestine and colon) in mouse, and in drosophila midgut.

In both cases of population asymmetry, the long-term surviving clone size distribution, Pn(t), (defined as the probability of finding a surviving clone which has n progenitor cells at time t) takes the scaling form = -^Λη /{»«) where («(7)) denotes the average number of dividing cells in surviving clones at time†, and f(x) denotes a scaling function (defined explicitly below).

Within the context of fhe present invention, "surviving" refers to clones which host at least one progenitor cell type.

Operationally, this means that- if one makes a plot of (n(t))P„(t) vs. «/ «(/)), all data will collapse onto the same universal scaling curve defined by the function ( ) . Within the context of the present invention, long-term refers to times in excess of the typical time taken for cell turnover - specifically the average time between symmetric cell divisions, the reciprocal of the turnover rate. The two different classes of population asymmetry are differentiated by the specific definitions of («(/) and f(x) .

For cells that follow a pattern of internal regulation - the committed progenitor cell type — the average clone size grows linearly with time (n(t)) = λί, with the coefficient of proportionality, Λ , representing the cell turnover rate. The scaling function in this case is given simply as the exponential, f(x) = ex .

In contrast, cells that have a stem cell phenotype, characterised by external regulation, have a behaviour which depends on the effective "dimensionality"' of tissue - the registration of neighbouring stem cells. For example, in both intestinal crypt and the male germ line, tissue has a one-dimensional geometry. In the former, stem cells are restricted to the base region of the intestinal (or colonal) crypt and are arranged in an irregular one-dimensional array around the annulus of the crypt. Similarly, in spermatogenesis, the stem cells (contained within the undifferentiated spermatogonia population) adopt a quasi one-dimensional arrangement along the seminferous tubules of the testes - these cells adhere to the vasculature that forms an open network along the seminferous tubules. In these one-dimensional systems, the stochastic clonal fate conforms to a behaviour known in the mathematical physics literature as an annihilating random walk (a subclass of the voter model) with the average size of surviving clones growing as a square root of time, (n(t)) = ^πλί , with λ the stem cell turnover rate, and n = 3.14159265..., i.e. the universal constant. The corresponding scaling function is given by

Similarly, in a two dimensional tissue (such as an epithelia), in which cells are organized in a planar geometry, the average surviving clone size grows as (n( ) = /1η(Λ/) while, in common with committed progenitor cells, f(x) = ex . In a three-dimensional tissue, such as the islets of pancreatic beta cells, the average grows linearly (n( ) = t and f(x) = e" . Such behaviour can only be discriminated from committed progenitor fate by monitoring the non-universal short-time dependence. In practice, such short-time data would usually be accessible using the same measurements that lead to the long-term data sets.

The above mentioned mathematical models can be involved in various methods of analysis and prediction of homeostatic balance of cell tissue growth. In one embodiment, the invention relates to a method that involves the following steps:

-prepare cells for growth and allow for growth

-collect data of growth at time t

-compare data, preferably in the scaling form, to the results of the mathematical models above

-determine if cells are in a normal steady-state homeostatic balance or not

The invention therefore provides an immediate characterisation of normal tissue turnover - and therefore, also the facility to identify unregulated behaviour and potential premalignancy. The same method comprising the use of the above mentioned mathematical models allows the effects of modulator of growth, such as mutations, either spontaneous or engineered, pathogens, toxins, radiation or pharmacological agents, to be analysed by comparing the data collected. The modulators can be analysed by allowing them to impart their effect on the cells before or during growth, depending on operator choice.

For example, spontaneous or engineered premalignant clones with a growth advantage over the neutral drift of normal labelled stem cells can be readily identified by their departure from normal scaling. The quantitative effects of drugs that alter stem cell fate may be defined by treating with an agent and a control, for up to ten rounds of cell turnover, and comparing the respective evolution of labelling pattern.

A further advantage of said method is that it permits one to determine not only if said modulator affects the growth of the cells with respect to a norm, but whether it increases or decreases said growth of the cells, thus having a clear application in testing candidate pharmaceuticals for either regenerative applications such as liver regeneration, or degenerative applications, such tumour growth inhibition. In another embodiment, an identification of cell growth can determine which of two groups a type of cell belongs to: a committed progenitor type or 3- dimensional stemlike phenotype with respect to a 1- or 2- dimensional stem-like phenotype.

Thus the invention relates to a method which comprises the following steps:

-prepare cells for growth

-collect data of growth at time t

-compare data, preferably in the scaling form, to the results of the mathematical models above

-identify from the comparison to mathematical model results identified in (iii) if the cells are committed progenitor or stem cell population type.

Definitions

The term 'comprises' (comprise, comprising) should be understood to have its normal meaning in the art, i.e. that the stated feature or group of features is included, but that the term does not exclude any other stated feature or group of features from also being present.

Homeostasis

In tissues that turnover, it is thought that maintenance and repair is coordinated by stem cells. In homeostasis, tissue stem cells must achieve a perfect balance between self-renewal and differentiation. Resolving the factors that regulate this balance represents one of the defining questions of stem cell biology. By drawing upon concepts from non-equilibrium statistical mechanics and population dynamics, we show that homeostasis imposes stringent constraints on the available mechanisms of tissue maintenance, leading to the emergence of equipotency, and the development of just three classes of stem cell fate. These classes are characterized by robust signatures in long-term clonal evolution. This identification affords a functional classification of tissue stem cell types, and presents a unifying framework to interpret clonal fate data and mosaic-chimera studies. When benchmarked against several mammalian tissue types, we show that mechanisms of stochastic stem cell fate are strongly favored over the "classical" mechanism of invariant asymmetry.

In tissues that self-renew, the pathways of stem cell fate can be organized into two patterns of behaviour (Hogan and Watt, 2000) : In the first, stem cells follow a strict pattern of invariant asymmetry in which each and every cell division results in two cells with unequal fates: one cell remains in the stem cell compartment, while the other commits to differentiation. Such behavior can be controlled by extrinsic signals from the niche, as exemplified by the Drosophila germ line (Fuller and Spradling, 2007). Alternatively, tissues may be maintained by stem cells following a pattern of population asymmetry in which the balance between self-renewal and differentiation is achieved on a population basis. In this case, stem cells follow divergent fates with cell division leading to cell multiplication or loss with equal probability. In recent years, considerable emphasis has been placed on resolving the extrinsic molecular factors controlling stem cell fate and the spatial organization associated with the stem cell niche (Voog and Jones, 2010). Guided by the paradigm of invariant asymmetry the majority of studies have sought to identify the extrinsic molecular transcription factors that regulate stem cell fate. However, by addressing long-term lineage tracing data, several recent studies have argued that population asymmetry plays a central role in controlling stem cell fate. In the earliest of these investigations, the development of an inducible genetic labelling system allowed the acquisition of long-term clonal fate data at single cell resolution in murine interfollicular epidermis (IFE). Prior to this study, IFE was thought to represent a classic example of the stem/transit amplifying cell paradigm, with tissue maintained by long- lived, slow-cycling stem cells following a pattern of invariant asymmetry. By contrast, clonal fate studies revealed that, in normal homeostasis, IFE is maintained by a single equipotent cell population following a pattern of balanced stochastic fate in which cell division may give rise to two dividing cells, one dividing and one non-dividing cell, and two non-dividing cells (Clayton et al., 2007).

At first sight, the development of balanced stochastic fate in the maintenance of IFE may seem surprising. However, the condition of homeostasis places rigid constraints on tissue maintenance, significantly restricting the available patterns of stem cell fate, and leading in turn to robust signatures in clonal evolution. To understand why, it is helpful to consider first a "homogeneous" tissue in which all stem cells have sustained access to the same range of internal or environmental cues. In this case, homeostasis demands that the underlying stem cell population must be functionally equivalent (i.e. equipotent).

Under these stringent conditions, there emerge just three classes of stem cell fate (SOM): In the first, tissue is maintained by cells following a pattern of invariant asymmetry (Fig. 1 A) in which each and every division leads to asymmetric fate. A long-term lineage-tracing assay, based on inducible genetic labelling system, would reveal a mosaic of "proliferative units" each supported by a long-lived stem cell. If, on the other hand, self-renewal does not involve strict division asymmetry, then it must belong to just one of two classes of population asymmetry: If the size of the stem cell pool is not limited by anatomical constraints, cells may adopt a balanced stochastic fate, the product of cell-autonomous (or uncoordinated) regulation (Fig. I B). Alternatively, self-renewal may rely upon cell-extrinsic (or coordinated) regulation (Fig. 1 C) whereby stem cell multiplication is compensated by the loss of neighbors.

While invariant asymmetry allow individual cells to persist long-term, both mechanisms of population asymmetry lead to "neutral drift" (Box 1 ) in which ongoing clonal expansion is compensated by the contraction and loss of neighboring clones. Such neutral competition leads to long-term scaling of clone size distributions: Formally, defining Pn(t) as the fraction of surviving clones which host n(> l ) stem cells at a time t post-labelling, one may show that (SOM) where < n(t) >~ t denotes the average number of stem cells per surviving clone, F is the scaling function, and a is the growth exponent. From ( 1 ), it follows that, if <n(\) >Pn(tj is plotted against n/<n(t)>, the entire family of clone size distributions at different times collapse onto a single scaling curve. The growth exponent, a, and scaling function, F, are both "universal", independent of stem cell number, their rate of loss or division, etc., and dependent only on the coordination of stem cells in tissue (Box 1 ) . As such, they provide the means to discriminate between the two patterns of population asymmetry. Before turning to the ramifications and generalization of this classification, let us first address its practical application. Figure 2 shows clone fate data acquired from studies of three canonical tissue types; murine IFE, germ line, and intestinal crypt. All three are stereotypical of stem cell supported tissues in that they are rapidly turned over, and capable of long-term maintenance and repair. In all three cases, lineage tracing following inducible genetic labelling shows that tissue is maintained by an ever-diminishing clone number of ever-increasing size, a hallmark of neutral drift dynamics. Moreover, all three tissues reveal long- term scaling behavior, with cells in IFE belonging to the class of cell- autonomous regulation (Clayton ef al., 2007), while both spermatogenesis and intestinal crypt rely upon cell-extrinsic regulation in a linear or "one-dimensional" environment (Klein r al., 2010; Carlos-Lopez ef a/., 2010).

Signatures of stochastic stem cell fate can also be revealed using mosaic mouse models. In such systems, the same genetic label is used to mark a large fraction of cells, so single cell-derived clones can no longer be resolved. However, stem cells undergoing stochastic turnover will lead to progressive "coarsening" and aggregation of labelled domains (Fig. 3) . Once again, the dynamics of coarsening (density of interfaces, etc.) provide hallmarks of the underlying pattern of turnover (Snippert et al., 2010) . The identification of these restricted patterns of stem cell fate relied upon consideration of a seemingly idealized system in which an equipotent cell population resides in a spatially homogeneous environment. However, the majority of adult tissues are characterized by complex niche structures in which extrinsic factors such as intercellular matrix proteins and niche hub cells are believed to actively influence cell proliferation and differentiation. Moreover, mounting evidence suggests that many progenitor cell populations are characterized by heterogeneous expression of key cell fate determinants (Graf and Stadtfeld, 2008) . How can such environmental and genetic heterogeneity be reconciled with the apparent ubiquity of long term scaling? Providing stem cells are capable of moving through the range of gene expression levels and spatial locations within the niche, the. long term behavior of a stem cell population will acquire equipotency, i.e. while the levels of gene expression or location may leave particular cells primed for multiplication, quiescence, or loss, providing the bias is transient, cells will exhibit the same quantitative long term fate characteristics (Enver et al., 2009) . Such behavior is epitomised by the maintenance of the germ line where cells high in Nanos2/GFRal are primed for multiplication while cells high in Ngn3 are primed for differentiation (Nakagawa et al., 2010) . Yet long term lineage tracing studies show that both are capable of generating long-lived clones (Nakagawa et al., 2007; Sada et al., 2009). This type of "emergent equipotency" is easily extended to more complex and hierarchical regulatory networks (SOM).

As well as invariant asymmetry, this study has identified two distinct patterns of stochastic stem cell fate in cycling multicellular tissues, and it has explained why they consistently emerge despite the diverse range of tissue anatomies, physiologies, and molecular regulatory factors. Taken together, these three patterns of behavior offer a complete functional classification of stem cell types according to their fate characteristics. Although all three fate pathways are capable of long-term maintenance, only cell-extrinsic population asymmetry has the capacity for regeneration and repair without further regulation. As such, it is tempting to identify only this pattern of fate as representing a true stem cell phenotype.

Neutral drift in self-renewal by population asymmetry Neutral drift describes the spread of a neutral allele (in our case, a genetic label) in a population. Here we outline the characteristic scaling behaviors that emerge from the two general patterns of neutral drift dynamics.

Cell-autonomous self-renewal: In this case, cell fate is specified randomly with each stem cell division leading to multiplication or loss with equal probability - a critical birth-death process. With a division rate λ, the long-term ( t > \/A ) clone survival probability diminishes as p su , « 1/ At , while the average size of surviving clones grows as < «(/) >= \ /Pisurv )(t) « At . In the same limit, the clone survival probability acquires the characteristic scaling form ( 1 ), with the scaling function F(x) = exp[-x]. Cell -extrinsic self-renewal: Here the loss of a stem cell correlates with the multiplication of a neighbor. In this case, at the boundary of a labelled clone, the loss and replacement of a labelled stem cell (SL), or of its unlabelled neighbor (Su) , can lead to the following two fates: the outcome dependent on which of the cells, labelled or unlabelled, are lost. Such behavior is encountered in a broad class of problems where it is known variously as the "stepping stone model" in population genetics (Kimura and Weiss, 1 964) , a "Moran process" in population dynamics (Moran, 1962), and (inspired by treatments in which SL and Su represent voters with different political opinions) a "voter model" . As a paradigmatic model, the general class of voter models have been the subject of considerable attention, with studies in both 1he mathematics and physics literature. Although this process leads to same long term scaling behavior ( 1 ), as clonal boundaries are constrained by the spatial coordination of stem cells, the particular form of the scaling function and growth depend on the dimensionality of tissue. With stem cell loss rate, λ, the average size of persisting clones asymptotes to,

corresponding to a= l /2 in "tubular" ( I D) tissues, a= l in "volumnar" (3D) and "distributed" (>3D) tissues, and the marginal power law in "planar" (2D) tissues. Moreover, the asymptotic clone size distributions also vary with dimension with F(x) - exp[-7o 2 1 A] in I D and, as with the cell autonomous process, F(x) = exp[- ] in higher dimension.

Cells

In principle the invention can be applied to all tissues (i.e. to population(s) of cells within all tissues) which are normally in homeostatic balance. From a practical perspective, the tissue must permit identification of labelled clones as described extensively herein. Thus for example blood would be unlikely to be a suitable tissue since the cells float freely with no two- or three- dimensional constraints, making it extremely difficult or impossible to count cells of individual labelled clones after incubation. Thus the invention can be applied to any tissue for which labelled clones can be counted after incubation. Thus suitably the invention can be applied to any population of cells suchs as a tissue having a two or three dimensional structure. The mathematical model provides a powerful and robust statistical measure that has been seen to apply to a wide variety of tissue types, preferred examples of which are expressly mentioned.

In adult homeostatic tissues, the possible patterns of stem cell fate are greatly restricted. These patterns can be discerned straightforwardly by lineage tracing studies involving inducible labelling of individual cells, or from mosaic-chimera studies. Suitably the population of cells is a population of cells of an adult homeostatic tissue, (i.e. an adult tissue which is normally in homeostasis).

The invention provides a means to address effects of mutation, disease or drug treatment on such tissues. It may be applied to study cell fate in vivo in invertebrate and/or vertebrate organisms where suitable genetic markers exist. Examples include chimaeric or transgenic Drosophila, Zebrafish, mouse and humans. Suitably the cells are mammalian. More suitably the cells are mouse cells.

An ideal system is the "confetti" transgenic mouse in which ere activation results in genetic labelling of a wide range of cells and tissues with multiple colours of fluorescent protein.

Suitably the cell(s) may be comprised by a tissue. Such a tissue may be organotypic culture or may be an explant or biopsy or other suitable tissue or sample thereof. Such a tissue may remain in vivo in a test animal or human being studied. Target tissues for the above methods are preferably those which are normally proliferating, eg epithelia, testis, CNS, pancreatic beta cells, or in which proliferation is pathological, e.g. in regeneration following injury (e.g. liver), or due to induced or spontaneous premalignant change or cancer. Suitably the invention is also applied to human tissue/cell types corresponding to those non-human cell types mentioned herein.

The invention may be applied to adult tissue types. Suitably the cells are epithelial cells. Suitably the tissue comprises epithelium. Suitably the tissue comprises stratified squamous epithelium. This has the advantage of being easy to identify labelled clones within and has the further advantage of being easy to count cells within. Suitably the tissue comprises oesophagus.

Suitably the tissue comprises epidermis. The examples and disclosure herein is often focussed on epidermis but the principles and applications are the same in other tissues.

In particular the invention may be applied to epithelial tissue, epidermis (such as interfollicular epidermis), neurogenesis, oesophagus, gut (for example intestinal crypt; for example insect midgut such as fly midgut e.g. Drosophila midgut), pancreas cells, suitably cells comprised by said tissues.

The invention may be applied to interfollicular epidermis cells or in primary cultures of glial cells derived from brain tumour tissue and in pancreatic beta cell population in islets.

The invention may be applied to the stem cell compartment of interfollicular epidermis, the germ cell line in mouse, intestinal crypt (including the small intestine and colon) in mouse, and in drosophila midgut. The invention may be applied in vivo or in vitro.

If is advantageous to apply the invention to populations of cells in vivo since those cells are typically within a homeostatic system i.e. stably maintained tissue such as adult tissue.

In vitro applications

The invention may be applied in vitro. For example, the invention may be applied to populations of cells in organotypic culture, or in cell culture.

In most situations, stem cell behaviour in vitro will differ fundamentally from the in vivo system even for normal cells. This reduces the value of applying the invention to such systems. However, in the case of population asymmetry following from intrinsic regulation, the pattern of behaviour of normal cells may be conserved in culture. The invention is applicable to these systems. One example is keratinocytes. Another example is one of the two cell progenitor cell types seen in cultures derived from primary glioblastoma tumour samples. Indeed, these cells follow a balanced stochastic fate following from infernal regulation. It is a question of great interest how the fate of these cells can be altered with chemical agents and drug treatments. Therefore the invention is particularly applicable to such systems.

Therefore care must be taken in applying the invention to in vitro or cultured cell systems. In a restricted and appropriately qualified sense, cultured cells suitable for application of the invention but it is important for interpretation of the results that the invention is only applied to cultured cells which exhibit behaviour which can be regarded as normal, or which can be regarded as having achieved homeostatic balance (if this is balance follows an initial period of exponential growth, that is not a hindrance, but it is important to consider the data from the point at which homeostatic balance has been reached rather than including data from the exponential growth phase) .

For example the invention may be applied to cells within an explant (or organ) culture, such as a culture of freshly isolated tissue.

For example the invention may be applied to organotypic cultures in vitro, in which cells are grown in three dimensions allowing extrinsic regulation to be observed. In culture, stem cells tend to follow a pattern of non-homeos†a†ic behaviour in which cells expand geometrically until homeostasis is restored, while the restoration of homeostatic behaviour from organotypic cultures has been demonstrated in both primary cultures of keratinocyte stem cells and from intestinal crypt. Thus only those cultured systems which display homeostasis are suitable for the invention.

Labelling

The methods of the present invention preferably comprise labelling of cell(s), followed by incubation under conditions permissive of growth. Suitably cells may be labelled using one of the following techniques:

1 ) In vivo: The normal mechanism of tissue homeostasis can be identified with precision from studies using labels expressed within subpopulations of a given cell lineage in which the evolution of the distribution of labelled cells is tracked over time. Examples include- a) Inducible genetic labelling (e.g. floxed reporter with drug regulated ere).

Genetic labelling where the mutation is acquired progressively over time. Examples include, Spontaneous mutation (e.g. mitochondrial DNA mutations in human samples) or "leaky" expression from an inducible ere line without induction. b) Chimeras which give mosaic gene expression.

c) Short term labels, e.g. nucleotide analogues such as EdU, which can be tracked to give clone fate data over several cell divisions.

2) Explant (or organ) cultures of freshly isolated tissue, maintained for days to weeks, in which cells have either been labelled in vivo as in (1 ) here above , or are labelled ex vivo, e.g. with nucleotide analogues or retroviral or lentiviral vectors.

3) Organotypic cultures in vitro, in which cells are grown in three dimensions allowing extrinsic regulation to be observed. Cells may be labelled as in (2).

4) Transplantation studies in which cells or explants of tissue are grafted onto syngenic or immunocompromised animals after labelling using the methods described above. Alternatively established grafts may be characterized using cells expressing inducible genetic labels, introduced by viral vectors or by deriving cells from transgenic mice, or by pulses of nucleotide analogues given once the graft is established. Once labelled as above, the change in the size distribution of the clones or patches of labelled cells over time may be characterised. This is suitably done using any appropriate measuring technique such as manual counting or software-automated assessment. This is suitably performed over a time scale appropriate for the stem cell compartment in each tissue. This is preferably an imaging technique, e.g. fluorescent microscopy or immunohistochemistry. The data collected is then analysed for their scaling form compared to the results of the mathematical methods above.

The method of the invention requires cells to be labelled. Preferably labelling is via expression of a heritable genetic marker.

Typically this is expressed in a proportion of proliferative cells and their (differentiating) progeny. Examples include: chimeras, for example mice generated from genetically distinct strains by aggregation at blastocyst stage, mosaic markers, mutations induced by mutagens such as Ethyl nitrosourea, transgenic markers, such as β galactosidase or fluorescent protein or proteins. Markers that give single cell resolution are not essential but have the advantage of enabling more detailed insight into cell behaviour. The confetti mouse is an ideal labelling system for the invention and has the advantage of excellent resolution. An exemplary labeling system is hereditary expression of LacZ following induction of ere recombinase-loxP system under upstream sequence of Ngn3 (Nakagawa, Yoshida et al.. Dev. Cell, 2007; see Fig. 22). After "residence time" of ca. 2 months, clonal patches become resticted to those "rooted" in undifferentiated spermatogonia An exemplary labelling system is as for AhcreER†R26flDNM; this is further discussed in the examples. The labelled cells and their progeny are 'clones'. These are typically defined experimentally as clusters of labelled cells which appear in proximity to one another and therefore appear to have derived from a single labelled cell.

Labelling is carried out so as to label cells in the population at a useful frequency. This is sometimes called a 'clonal frequency'. The precise frequency varies depending on the cell population being studied. The important principle is that enough cells should be labelled so that clones appear often enough within the population so that data collection is practical. In principle no frequency of labelling is too low, but in practice too low a frequency means taking up operator time searching for labelled clones amongst unlabelled background cells. Thus a higher frequency (and therefore a greater number of clones per unit area or unit volume) is generally desirable to make analysis easier and to reduce the amount of tissue required (e.g. to reduce the number of test animals required) in order to collect enough data for suitably low error rates. However, the frequency should at the same time be low enough so that clones are on average adequately spaced to permit analysis. Too high a frequency of labelling results in too many clones too close together. This can confound the analysis if clones are so frequent that it is difficult to tell if clones were neighbours or 'ran together' during incubation. Thus the optimum labelling frequency is determined by the operator depending on the tissue being studied and the practicalities of collecting the data. The labelling frequency is easily adjusted by trial and error titrating the inducer/label accordingly. Guidance is given in the examples section of good starting points for amounts of inducer/label to be used in different applications.

The amount of raw data making up the clone size distribution (i.e. the number of clones for which cell numbers are counted) is in principle to be determined by the operator. When choosing the amount of data to collect, in principle more is better since larger datasets reduce error rates. In particular attention should be paid to the size of the error bars on the clone size distribution and enough data should be collected to reduce those error bars to a level acceptable to the skilled operator. This level will naturally depend on the application to which the invention is being put. In principle some studies may tolerate large error bars and therefore be conducted on advantageously small data sets, thereby reducing the labour and time for collection. Exemplary error rates for robust analysis are as in the accompanying examples and figures.

Further Applications of the Invention

The invention may be applied to analysis of clonal evolution of p53 mutant clones in mice following UVB irradiation, for example by applying it to studies such as that described in (Stochastic fate of p53-mutant epidermal progenitor cells is tilted toward proliferation by UV B during preneoplasia, A. M. Klein, D. E. Brash, P. H. Jones, and B. D. Simons Proceedings of the National Academy of Sciences 107, 270 (2010)) in order to infer the changes of cell fate in mutant clones.

The invention may be applied to study of an inducible system which leads to tumour initiation and involves a breakdown of conventional scaling behaviour.

Certain tumours are believed to be supported by clones of stem cells. The invention may be applied to decide if a tumour is supported by one or more clones of stem cells. For example, the tumour could be treated, then examined, and the number of clones growing back (if any) could be determined.

Brief Description of the Figures

Figure 1: Location and number of Lgr5 cells per crypt.

A) E-cadherin knock-in strategy in which the fluorescent protein monomer Cyan (mCFP) is fused to the C-terminus of Cdhl. B) Cellular localization of E-cadherin-mCFP fusion protein (white) in crypts of small intestine. C) E-cadherin-mCFP mice crossed with Lgr5-EGFP-Ires- CreERT2 mice. Left panel: whole-mount intestine scanned from crypt bottom to crypt-villus border (~125pm), right panel: lateral scan of semi-thick section (~50μΓη). E-cadherin-mCFP (white) allowed 3D reconstruction of tissue architecture, while Lgr5-GFP (green) visualizes intestinal stem cells. D) FACS analysis of intestine of Lgr5-EGFP-Ires-CreERT2 mice reveals 3 populations. GFPh' represents Lgr5 intestinal stem cells. E) Whole-mount intestine from E- cadherin-mCFP (white)/ Lgr5-EGFP-Ires-CreERT2 (green) mice. Lgr5-GFPh' population was visualized in red (false color), while E-cadherin-mCFP (white) marks cell borders. At the crypt base, all Lgr5+ cells were GFPhl. F) Counting in 3D reconstructions yielded 14±2 Lgr5hl cells per crypt in proximal small intestine. Scale bars; 50μηι. Figure 2: LgrS1" cells constitute an equipotent stem cell population. A) Confocal section at the crypt base with Lgr5 cells (green) and Paneth cells, with large granules, stained for lysozyme (red). All cells at crypt bottoms are either Lgr5hl cells or Paneth cells. B) Plating efficiency of Lgr5h' / Lgr5hl versus Lgr5hl /Paneth doublets as scored after a 7 day culture shows outgrowth of ~60% of Lgr5hl cells when paired with a Paneth cell. Insets: confirmation of sorting strategy by confocal microscopy; Lgr5hl in green and Paneth cell in red. Scale bars; 50μπι.

Figure 3: R26R-Confetti a stochastic multi-colour Cre-reporter.

A) R26R-Confetti knock-in strategy. Brainbow2.1 encoding 4 fluorescent proteins (Livet et al., 2007) was inserted into the Rosa26 locus. Upstream, the strong CAGG promoter, a LoxP-site and a neomycin resistance roadblock cassette, were inserted. B) Upon ere activation, the neomycin roadblock is excised, while the brainbow2.1 recombines in a random fashion to 4 possible outcomes. GFP is nuclear, CFP is membrane-associated and the other two are cytoplasmic. C) The R26R-Confetti knock-in line is a stochastic multi-colour Cre reporter in multiple tissues. Scale bars; 50μηι, except for pancreas, kidney and liver, ΙΟΟμιτι. Figure 4: Short-term clonal tracing analysis of individually labelled Lgr5u cells.

A) R26R-Confetti mice were crossed with Lgr5-EGFP-Ires-CreERT2 mice. Tracing was sporadically induced in single Lgr5hl cells (~ 1 Confetti colour in 6 crypts). Cytosolic GFP marks the Lgr5hl stem cell population. Panels from left to right: 1 ) Single plane-2D image of crypt with one YFP (white, false color) -labelled Lgr5hl cell. Background is DIC image; 2) 3D reconstruction of the same crypt showing Lgr5hl cells (green) and the traced cell (white). 3) Same, but GFP only. 4) Same but YFP only. Arrowheads point to Lgr5h' cells within a clone, arrows point to TA cells within clone that lost Lgr5hl activity. B) For 43 labelled clones, the total number of cells and numbers of Lgr5hl cells were scored. The matrix indicates the absolute number of clones scored for each given clone size and given number of Lgr5hl cells. Red hues represent relative frequencies of all scored events for given time-point. 100% is red; 0% is white. C) As A, but after 48hrs of tracing. In this crypt, RFP (red) revealed a tracing event. The red clone expanded to three Lgr5hl cells. By contrast, CFP (blue) revealed another tracing event in the same crypt, but where the clone lost Lgr5 expression. D) As B, but after 48hrs of tracing. E) As A, but after 72hrs of tracing. One Lgr5hl cells was labelled with YFP (white) and gorwn to a clone size of 6, of which 2 cells remained LgrS1". F) As B, but after 72hrs of tracing. G) Expansion of Lgr5hl cell numbers over time within clones with at least one Lgr5hi cell. The average size of these "surviving" clones gradually increases, yet the variability between individual clone sizes increases over time as well. Red hues represent relative frequency of Lgr5hl cell numbers per time-point. 100% is red; 0% is white. Scale bars; 25μηι. Figure 5: Long-term lineage tracing.

A) R26R-Confetti mice were crossed with Ah-Cre. xy plane images are shown at 1 week and 8 weeks after ere induction. Left panels are overview images. Right panels zoom in on crypts. Over time, labelled cell domains expand while neighbouring domains become extinct. Note that Paneth cells are long-lived and can reveal the "clonal history" of a crypt when derived from a clone that is extinct at the time of analysis. Inset; schematic representation of small intestine, indicating the two sectioning planes used for the analysis. B) xz-plane images of small intestine after R26R-Confetti activation reveal drift towards clonality over time. Non-clonal crypts are marked with a white-dashed circle. Scale bars; Ι ΟΟμιη. Figure 6: Progression towards monoclonality.

A) Schematic representation of the translation from actual data to quantitation of labelled domain sizes. Left panel shows the crypt base with Lgr5hl cells in false colour red, Lgr5 expression in green and E-cadherin-mCFP in white. Second panel is a schematic representation of the crypt base, in which three hypothetical labelled cell domains were visualized in red, yellow and blue. The red domain shows 7 labelled cells and encompasses 7/16 of the crypt base circumference. Two mitoses are shown; the first leads to the displacement and loss of the blue single-cell clone, and the second leads to the displacement of an unlabelled cell and the expansion of the yellow clone. The third panel illustrates the segregation of the crypt base into 16 equally spaced segments (sextadecals) corresponding approximately to the cellular composition of the crypt base stem cells. The process of Lgr5h' cell displacement following the symmetric duplication of a neighbouring Lgr5hl cell is shown for two clones, with the outcome shown in the final panel. B) The matrix indicates the absolute number of clones scored for each given domain size at each time-point post-induction. Red hues represent relative frequencies of all scored domain sizes per time-point. 100% is red; 0% is white. C) Frequencies of monochromatic crypts after given time-points post-induction.

Figure 7: Lgr5bi cells follow neutral drift dynamics.

A) A fit of the average number of Lgr5hl cells within surviving clones as predicted by the stochastic model of neutral drift dynamics (Solid line, Suppl. Information) to the experimental data (points, see Fig. 4G) leads to a stem cell loss rate of 0.74±0.4/day. The dashed curve shows a simple square root time dependence, which provides an increasing good approximation to the exact result. B) Cumulative clone size distribution, C„(t); i.e. the chance of finding a surviving clone with more than n stem cells, as measured by the Lgr5h' content within surviving clones. The lines show the size distribution as predicted by neutral drift dynamics with the stem cell loss rate fixed by the fit in A) (Suppl. information) while the points show experimental data from day 1 , 2, 3, 7 and 14 (Fig. 4G). Inset; at these early times, theory predicts that, if stem cell self-renewal follows from population asymmetry (the stochastic model), the cumulative clone size distribution, C„(t), should collapse onto a universal scaling curve when plotted as a function of n/<n(t)>, where <n(t)> denotes the average size of the surviving clones. Such behaviour is recapitulated by the experimental data, with the dashed curve representing the universal scaling function (2). C) The growth curve over time of Lgr5h' stem cell number within surviving clones as predicted by neutral drift dynamics with the stem cell loss rate of 0.74/day (obtained from Fig. 7A) and 16 stem cells per crypt. D) The corresponding frequency of monoclonal crypts over time as a percentage of surviving clones as predicted by neutral drift dynamics. E) Average size of labelled cell domains following long- term fate mapping of intestinal stem cells. Once again, with 16 stem cells per crypt, and an average stem cell loss rate of 0.74/day, the line shows the prediction following neutral drift dynamics (Suppl. information) while the points are obtained from experiment at 4, 7, 14, 28, 61 , 126 and 210 days post- induction (Fig. 6B and C). The corresponding frequency of monochromatic crypts (in which all progenitor cells are labelled with the same colour) is shown in the inset. F) Variability in clone size for partially labelled crypts at 4, 7, 14 and 28 days post-induction. The predictions made by neutral drift dynamics (lines, Suppl. information) match closely with the experimental data (points, Fig. 6B).

Figure 8 (related to Figure 1): E-cadherin-mCFP KI fusion protein maintains endogenous expression pattern and cellular localization. A) E-cadherin-mCFP KI strategy. mCFP was targeted at the endogenous STOP codon of Cdhl, thereby maintaining expression levels and pattern. B) Southern blot of targeted ES cells confirms proper integration into Cdhl locus. C) Expression pattern and cellular localization of E-cadherin-mCFP recapitulated the endogenous situation. Left panel; E-cadherin-mCFP (false colour white). Middle panel; bright field. Right panel; overlay (mCFP in false colour blue).

Figure 9 (related to Figure 4): Clonal evolution of labelled Lgr5bi cells at the crypt base remain cohesive. A) Bottom-view image of 7 day tracing of Lgr5-EGFP-Ires-CreERT2/ R26R- Confetti confirmed that clones tend to expand laterally around the perimeter of the crypt base while very few clones, if any, involve cells migrating through the apex of the crypt base. Lgr5- GFP is in green, Confetti colours in corresponding colours.

Figure 10 (related to Figure 5): At old age, neutral drift dynamics remain operative.

Neutral drift dynamics underlies intestinal self-renewal at all times. Even in mice of 40wks old, crypts drift towards clonality with the same broad time distribution. Scale bars; Ι ΟΟμιη.

Figure 11 (related to Figure 7): Computer generated R26R-Confetti tracing according to neutral drift dynamics. A) Numerical simulation illustrating neutral drift dynamics for eight crypts where the cells have been induced with an 80% probability after which any of the three colours (red:yellow:blue) can appear with equal probability. The on-going expansion, contraction, and loss of labelled patches results in a "coarsening" phenomenon leading to monoclonal ity of crypts at longer times. Figure 12 Conversion to monoclonality implies that stem cells are replaced in mouse intestinal crypts.

(A) Experimental schedule; clones were induced by a single pulse of β-napthoflavone (PNF) and tamoxifen (TM) in adult mice aged 1.5-9 months, and then visualised in small intestine and colon following chase periods of 2 weeks to one year through serial sectioning and wholemount imaging.

(B, C) Clonal progeny migrate in coherent streams on villi in wholemounted tissue emerging from partially-labelled (B) and fully-labelled crypts (C). Streams from single crypts are seen to split to occupy one (shown) or up to three villi (not shown).

(D,E) Clones contain both enterocytes and Goblet cells; (D) wholemount containing glu+ clone stained with Alcian blue to visualise Goblet cells (arrowheads), and (E), a sectioned EYFP+ clone stained with Periodic acid Schiff to visualise Goblet cells (full arrows). Positive Paneth cells are initially absent (v- arrows) but ultimately become labelled (see F).

(F-H) Schematic shows crypt-to-villis axis of clonal migration streams (brown) on the intestinal epithelium (grey). (F) Longitudinal section of 2 week-old clone; (G,H) serial sections of a clone migration stream showing a labelled 8 week-old clone. Paneth cells are labelled (v-arrows).

(I, J) Wholemounted tissue showing a partly labelled and a fully labelled crypt, respectively. Dashed circles indicate crypt boundaries; dotted lines show villi (v) out of the focal plane; 'c' marks adjacent crypts. Diagram shows the basal viewing perspective of the crypts (circles), of which one is clonally labelled (purple). (K) The fraction of fully labelled crypts over time shows conversion to monoclonality. The line shows a fit to neutral drift dynamics (see main text). Monoclonal conversion occurs at comparable rates irrespective of age at induction (legend).

(L) The number of labelled crypts per 104 villi decays over time post-labelling. Densities are normalised by their earliest time point (two and three weeks, respectively) to allow comparison of different cohorts (legend as in I).

(M) The average clone width increases during monoclonal conversion at all ages (legend as in 1). Theoretical curves in J and follow from the fit made in 1. (N) Representative stem cell labelling; the total labelled cross-section of villi remains constant, indicating that the labelled cells maintain a constant population (error bars = SEM).

Scale bars = 25μπι.

5 Figure 13 Short-time clone size distributions reveal a pattern of "neutral drift" in stem cell replacement

(A,B) Models of stem cell turnover in crypt: In (A), monoclonal conversion follows from turnover of a single, slow-cycling, asymmetrically-dividing "master" stem cell at the crypt base. Blue arrows show self-renewal through asymmetric division; grey arrows show divisions leading to differentiation and 10 upward migration. In (B), conversion arises from turnover of an equipotent stem cell population in which stem cell loss is compensated by the multiplication of other stem cells (blue arrows) resulting in random clonal expansion and contraction.

(C) Distribution of clone widths between 2-52 weeks post-labelling (each '+' translates to one clone). the short-term ( t≤4 weeks) clone size distributions,

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Figure 14 Model of neutral drift and monoclonal conversion in small intestine and colon.

(A) The neutral drift model in which Nstem equivalent stem cells surround the crypt base. The chance loss of a stem cell and its replacement at the clone edge leads either to the expansion of the labelled (blue) clone (case 1 ), or to its contraction (case 2). (B) A simulation based on this neutral drift model showing monoclonal conversion following the labelling of all stem cells by different colors.

(C-H) Clonal width distributions up to six months post-labelling alongside theoretical curves following from the neutral drift model with ¾y/vslem 2=0.025/week (see Fig. S2 for entire data set). (I,J) Clone size distribution as inferred from the fraction of crypt base labelled in colon. Clones were scored into four size categories as shown in (J). Curves follow from the neutral drift model with

Figure 15 (example 9 S I ) shows diagrams and photographs.

Figure 16 (example 9 S2) shows graphs.

Figure 17 (example 9 S3) shows photographs, diagrams and a bar chart.

Figure 18 shows photographs of cell clones.

Figure 1 shows a graph

Figure 20 shows a graph

Figure 21 shows a graph

Figure 22 shows an exemplary labelling system.

Figure 23 shows Clonal fate analysis in tail epidermis of induced AhcreERtR26flDNM mice. A: Clone size distribution 6 weeks after labelling. Cumulative frequency of multicellular clones containing at least one basal cell is expressed as a ratio to average clone size in each animal (<n>): red, black and green points are data from 3 animals, black curve is prediction of model shown in B. To interpret the graph, note that at the point arrowed, (x=n/<n>=0.9, y=40%), 40% of the clones have a size which is less than 0.9 of the average.

B: Data from all 300 clones is consistent with MAML mutation having no effect on proliferation rate of CP cells (green, average once per week). As with normal cells, 50% of proliferating cells are generated on average. However, cells that would normally undergo irreversible cell cycle exit revert to proliferation, dividing again after an average delay of 5 weeks. This suggests mutant cells are unable to commit to terminal differentiation, a hypothesis now under test in transcriptional and epigenetic studies of cultured primary cells from mutant mice.

Figure 24 shows Predictive power of the CP model. Clone size distribution after treatment with ATRA in tail epidermis. Clonal cell labelling was induced, and after a 3 month interval mice were treated with topical ATRA or vehicle only for three months. The histogram shows the observed clone sizes (error bars, s.e.m.), while the points indicate model predictions (red, control; blue, ATRA treated animals). This result indicates that during prolonged AT A treatment CP cells maintain the tissue by accelerated proliferation, whilst retaining their balanced stochastic fate.

Figure 25 shows fate of normal murine progenitor cells

Normal progenitor cell behaviour in murine esophageal epithelium as characterised by quantitative clonal analysis of clones labelled with Enhanced Yellow Fluorescent Protein. Division of cycling progenitor cells (green) generates either two progenitor cells, one progenitor and one post mitotic cell (red) or two post mitotic cells, with the probabilities shown. Progenitor cells divide every 5.4 days on average.

Figure 26 shows clone fate data from progenitor cells expressing DNM

Clonal expression of DNM was induced in EE progenitor cells and the number of basal cells per clones containing two or more cells scored as described in the text. Inset shows raw clone size distributions from days 3, 7 and 10 post clonal induction. Main panel shows data replotted after division of clone size (n) by the average clone size (<n>) for the corresponding time point. The collapse of all three curves onto a single curve indicates that the data scales with time.

Figure 27 shows effect of DNM expression on progenitor cell fate

A: Model of fate of DNM expressing cells

Mutant progenitors (green) divide asymmetrically every 1 .5 days (black arrow) to generate progenitors and cells with arrested differentiation (AD, red/green), which re- enter cycle every 15 days on average (red-green arrow).

B: Fit of model with clone fate data: curves show model prediction, points are data.

The invention is now described by way of example. These examples are intended to be illustrative, and are not intended to limit the appended claims.

Examples

Example 1: Studying the effect of a pharmacological agent on cell fate In a normal tissue.

The method of the invention may be applied to determine the effects of an agent on the murine small intestine. In this example it is desired to determine the fate of normal cells in this system. Thus in this example the population of cells is a population of mouse small intestine cells in vivo.

One or more cells in the population are labelled. In this example a genetic reporter such as that in the confetti mouse is induced at clonal density.

The cells are then incubated for a time t. The clone size distribution of labelled cells at time t is then determined. In this example the number of stem cells (e.g. cells high in expression of a stem cell marker such as Igr5) is determined over a time course ideally extending over 10 or more times the stem cell turnover time.

It is then determined if the clone size distribution conforms to the scaling form: P"(t) = (¾> (" ^'^' Whefe

Pn(t) is the probability of finding a surviving clone which has n progenitor cells at time t,

(«(/)) denotes the average number of dividing cells in surviving clones at time t and

wherein if the clone size distribution conforms to the scaling form above, the cells are identified as being in a normal steady-state homeostatic balance; if the clone size distribution does not conform to the scaling form above, the cells are identified as not being in a normal steady-state homeostatic balance.

Thus the quantitative cell fate data is analysed as described. The equivalence, fate, kinetics and regulation of stem cells may be inferred from the type of scaling observed.

Example 1 B: Effect of a candidate modulator of cell proliferation: The experiment is repeated with induced confetti mice treated with the agent

(candidate modulator), and if necessary a vehicle control. Quantitative clone fate analysis is repeated. If the agent has an effect on stem cell homeostasis, the scaling of the data will be disrupted. The method will reveal whether the agent causes excessive stem cell expansion (with a risk of malignant transformation) or stem cell depletion (predicted to cause tissue failure) .

Example 1C: Effect of a mutation on cell fate In a normal tissue:

In this example the candidate modulator may be regarded as a genetic mutant.

To determine the effect of a mutation on murine intestinal homeostasis, the confetti mouse may be bred onto a background mutant in a particular gene. Alternatively mice in which expression of a mutation is linked to that of a reporter gene, or in which cells expressing the mutant protein may be visualised, e.g. with an antibody that stains cells expressing the mutation may be used. In the later case the mutation is confined to clones of cells within the tissue. The effect of clones expressing a reporter or of mutant clones is then studied as described under above. This method may also be applied to determine whether a pharmacological mutation can rescue the effect of the mutation on cell fate. Example 1 D: Effect of a disease process on a normal tissue

The method described above may be applied to a disease model such as a mouse disease model (either transgenic or induced by an agent). The effects of the disease on cell fate may be determined as described. In addition the ability of a pharmacological agent to rescue the effect of the disease on cell fate may be determined.

Example 1: Detailed Protocol

A protocol for determining the effect of a pharmacological agent on the behaviour of mouse intestinal stem cells is described.

Resources required: Mice expressing an inducible genetic labelling system that will label intestinal stem cells. Examples are Lgr5creERT/Rosa26 LSLconfetti mice or AhcreERt/Rosa26 LSL EYFP mice (LSL indicates the presence of loxP flanked "stop" cassette preventing expression of the reporter in the absence of ere mediated recombination. The activation of ere at clonal frequency is achieved by treating mice with ere inducing drugs (Tamoxifen alone or βηαρίηοίΐανοηβ and Tamoxifen respectively) at doses previously determined by titration.

The protocol requires 20 mice as controls and 20 mice for experimental treatment.

Experimental Procedure:

Day 0: clonal labelling is induced by activation of ere to label intestinal crypt stem cells at clonal frequency (ie with one labelled stem cell per 6 or more crypts, each crypt containing approximately \ 6 stem cells, identified by their location in the cell positions 1 to 4 from the crypt base). Drug (candidate modulator) treatment of experimental animals is commenced.

Day 1 : Cull 4 experimental and animals, prepare intestinal epithelium for imaging and score the number of marker positive stem cells in clones in each animal using confocal microscopy (in normal mice the great majority of clones are single cells at this time point) .

Days 2, 4, 8 and 12: Cull 4 experimental and animals and repeat confocal imaging scoring stem cells per clone at each time point. The number of clones to be scored depends on the time point, typically rising from 50 clones at day 1 to 100 clones at later time points where there is a wider range of stem cells/clone.

Analysis: The data is analysed as described to determine if the clone size distribution scales with . time and if so what the scaling function is in control and experimental data sets.

Possible outcomes are;

Data scales in the same manner in control and experimental animals: In this case normal homeostatic stem cell behaviour is retained. The rate of stem cell division may increase or decrease (this is determined from the clone fate data) but intestinal homeostasis will be maintained in the long term in drug treated animals.

Experimental data scales but the scaling function is different from controls: This indicates an alteration in stem cell behaviour with drug treatment, the nature of which may be inferred from the scaling function. The nature of scaling may indicate intestinal homeostasis will be maintained in the long term in drug treated animals.

Data does not scale in experimental group: this would indicate a failure of homeostasis. Analysis of clone fate will reveal whether the outcome will be stem cell expansion, raising the possibility of future malignancy or stem cell depletion, which predicts that long term drug treatment will result in tissue failure. The protocol will define the effects of a drug on intestinal stem cells using 40 mice and an experimental program which can be completed in less than a month, including time for imaging and data analysis, representing a major advance on existing approaches.

Example 2: The effects of Notch Inhibition on CP cell fate Overview

Fig 23 shows a clonal experiment where the clones express both a reporter and a potentially oncogenic genetic inhibitor of Notch signalling, causing a breakdown of normal scaling associated with impaired terminal differentiation (cells that normally exit the cell cycle hang around in a "waiting" state and then drop back into cycle). Fig 24 shows how retinoic acid treatment accelerates proliferation but does not change scaling. This applies also to oesophagus. These are discussed in more detail below. Notch

The Notch signalling pathway regulates cell fate in many lineages in development and adult life (Bray, 2006). Signal transduction occurs when the Notch receptor is bound by ligands such as Jagged and Delta expressed on adjacent cells (Lindsell et al., 1995). The intracellular cytoplasmic domain of the receptor is cleaved from the transmembrane domain by□ secretase and translocates to the nucleus where it binds the transcription factor CBF1 (RBPJ-Ll), leading to the recruitment of transcriptional co- activators and the expression of Notch target genes (Furriols and Bray, 2001 ; Jarriault et al., 1995). In keratinocytes Notch activation both drives the differentiation of proliferating cells and regulates terminal differentiation (Blanpain et al., 2006; Lowell et al., 2000; Rangarajan et al., 2001 ) .

Consistent with these observations. Notch signalling has been found to be commonly disrupted in human non-melanoma skin cancer (Lefort et al., 2007; Thelu et al., 2002). Genetic ablation of Notch in transgenic mice, either in the epidermal basal layer as a whole or with a conditional ere allele resulting in mosaic recombination promotes tumour formation, due both to direct effects on keratinocytes and a systemic immune response, triggered by impaired epidermal terminal differentiation, which causes dermal inflammation and neoplasia associated with elevated levels of the cytokine TSLP (Demehri et al., 2009; Nicolas et al., 2003). Taken together these findings provide powerful evidence that Notch acts as a tumour supressor gene in both human and mouse epidermis. However, the fate of cells in notch mutant clones and how this changes during the preneoplastic process has not been defined quantitatively. In this project we will analyse the fate of cells in clones expressing a mutant Mastermind-like 1 (MAML1 ) protein that disrupts canonnical Notch signalling. Experimental Design

For quantitative clonal analysis of a conditional ere induced mutation it is essential for expression of the clonal reporter to be linked directly to expression of the mutant protein, so that all clones which express the reporter are actually mutated. Qualitative studies often use a reporter targeted to a separate locus from the mutant allele, but the variable efficiency of ere recombinase at different loci may result in a clonal fate data set contaminated by a subset of clones positive for the reporter but negative for the mutation. To study the effects of losing Notch signalling we have therefore opted to use a conditional transgenic strain (R26flDNM), developed by Warren Pear (Philadelphia), in which a conditional dominant negative mutant allele of the transcriptional cofactor MAML 1 (DNM) was fused to EGFP and targeted to the Rosa26 locus downstream of a LoxP flanked "STOP" cassette. This construct inhibits Notch signalling by blocking activation of RBPJU dependent transcription by all four murine Notch genes, and phenocopies deletion of RBPJa ( aillard et al., 2008; Maillard et al., 2004). Widespread expression of DNM in the epidermis results in the development of hyperkeratotic nodules, lesions resembling human actinic keratoses and SCC (Proweller et al., 2006). Importantly, epidermal DNM expression is readily dectable by staining for EGFP. An advantage of using a strain in which DNM is expressed from the Rosa26 locus is that it allows direct comparison with the conditional EYFP strain R26flEYFP, which we have used to characterise cell fate in normal epidermis (2,12).

R26flDNM mice will be crossed onto the AhcreERT strain, which we have characterised extensively (2, 12, (Kemp et al., 2004)). In this transgenic line, ere transcription is driven from the Cypl Al promoter which is inactive unless animals are treated with the. xenobiotic Dnapthoflavone (IHNF). Cre is also regulated post translationally by fusion to a tamoxifen regulated mutant oestrogen receptor. Simultaneous treatment with DNF and tamoxifen results in cre activity in IFE: titrating the dose of induing drugs results in recombination of 1 in 500 to 1 in 1000 basal cells, permitting analysis of discrete clones (2,12). Importantly, recombination does not occur in hair follicle cells in the bulge, the lower follicle or in the region between the bulge and the upper infundibulum (2 and unpublished observations). This allows us to analyse CP cell fate indepently of hair follicle stem cells (Jensen et al., 2009; Morris et al., 2004; Snippert et al., 2010; Tumbar et al., 2004).

In these experiments we will characterise the two epidermal sites where we have a quantitative insight into CP cell behaviour and which may be reliably wholemounted, the scale forming tail epidermis and the more typical epidermis of the ear. These locations differ significantly in the rate of CP proliferation (approximately once per week in the tail and once per month in the ear) and the proportion of CP cells undergoing symmetric cell division, allowing us to test whether the behaviour of Notch mutant clones depends on the kinetics of the surrounding wild type tissue or is cell autonomous (2, 12). In the same animals we will also be able to analyse clonal fate in oesophageal epithelium. Experimental plan

We will begin by crossing homozygous experimental R26flDNM or control R26flEYFP strains onto homozygous AhcreERT mice to generate heterozygous double transgenic animals. Doses of inducing drugs have already been titrated in to give recombination in circa 1 in 1000 basal cells in tail and ear IFE as assessed by confocal imaging of epidermal wholemounts stained for EGFP (2, (Braun et al„ 2003)). Next a cohort of 8 week old animals will be induced and 4 animals culled at each of a range of time points from 3 days to 1 year. The number of basal and suprabasal cells is assessed by scoring the number of cells in each of at least one hundred clones from each site by confocal imaging. Animals will be injected with EdU one hour before culling to assess proliferation in the wild type cells adjacent to the mutant clones. In addition blood samples will be taken to measure TSLP levels as a marker of potential systemic effects resulting from DNM expression, and cryosections of epidermis will be analysed for evidence of the associated dermal inflammation (Demehri et al., 2009).

In pilot experiments analysing the fate of mutant clones in tail epidermis from R26flDNMAhcreERT mice at 3 and 6 weeks after induction we have found a striking phenotype. Mutant clones expand more rapidly than those in R26flEYFPAhcreERT control animals but there is a substantial reduction in the number of stratified cells. Quantitative analysis reveals that the mutant CP cells divide at a normal rate and with a normal probabilty of generating proliferating daughter cells. However, in mutant clones, cells that would normally undergo terminal differentiation later revert back into cycle (Figure 23). This is consistent with previous reports that the cyclin dependent kinase p21 cipl is a direct Notch target in keratinoctes, and suggests Notch activation is required to lock basal cells out of cycle (Rangarajan et al., 2001 ). In the absence of Notch signaling, cells appear to exist in an intermediate state between proliferation and terminal differentiation, with a low probability of terminal differentiation and a high probability of resuming proliferation.

To test this hypothesis wild type and DMN basal keratinocytes will be isolated by flow sorting for the pan basal cell marker D l integrin and EGFP, RNA extracted and microarray analysis of amplified cDNA performed to identify transcriptional changes following DNM expression: basal cells sorted from age matched, clonally induced R26flEYFP animals will be used as a control. The array data will be interrogated to determine if regulatory cell cycle and differentiation genes are altered by DMN expression. Gene expression changes will be validated by in situ hybridisation and, where antibodies are available, immunostaining of wholemounts from induced animals. To confirm that changes in gene expression are linked to DNM primary cultures from epidermis of induced R26flDNM and control R26flEYFP mice, already established in the lab, will be transfected with siRNA directed against EGFP to determine if altered gene expression can be rescued by knockdown of the DNM-EGFP fusion mRNA. We are currently performing live cell tracking on wild type and recombined keratinocytes from experimental and control animals (see below under objective 2) to determine how cell behaviour in vitro is altered by DNM. We will use this assay to confirm whether cell fate can be rescued by DNM knockdown. Further cohorts of induced animals are now aging and will be analysed at time points up to one year unless the animals develop tumours and require sacrifice. The rate of growth and failure of terminal differentiation in the mutant clones is such that a high frequency of tumours is predicted unless signals from surrounding wild type cells slow clone growth. Should macroscopic skin lesions or tumours develop from the mutant clones these will be analysed by histology, gene expression and array CGH. Cells from the lesions will also be cultured to characterise their fate in colony forming assays and whether this is restored to normal by infection with viruses encoding EGFP shRNA.

In parallel with our analysis of epidermis we will also study oesophageal epithelium. Preliminary experiments show that we can achieve clonal density expression of DNM in R26flDNMAhcreERT mice and that this results in a substantial acceleration of clone growth. The data exhibit the same form of scaling as observed in tail epidermis, suggesting that DNM has similar effects on keratinocytes at both sites.

Thus it is demonstrated that quantitative clonal analysis can be used to define the effects of a specific mutation on CP cell fate. Moreover the invention may be used to study the link between altered clone behaviour and changes in gene expression in CP cells.

Example 3: The effects of activated Hedgehog signalling on CP cell fate

Basal cell carcincoma is the commonest malignancy in Caucasians and its incidence is rising rapidly in the UK and Europe (de Vries et al., 2004; Holme et al., 2000). Mutations resulting in constitutive activation of the Hedgehog pathway are frequent in BCC (Epstein, 2008). Epidermal expression of the Hedgehog effector Gli2 from a doxycycline regulated promoter in transgenic mice results in BCC, which regress when doxycycline is withdrawn but recur when the drug is reintroduced, arguing that Hedgehog activation has a key role in the pathogenesis of BCC (Hutchin et al., 2005). BCC were also was seen in a cre/lox model in which an activating mutation of the Smoothened gene (SmoM2*) fused to EYFP was targeted to the Rosa26 locus downstream of a LoxP flanked "STOP" cassette: BCC like lesions developed within 5 weeks of inducing ere activity (Mao et al., 2006). This R26flSM02*YFP strain was also used in a recent study that adressed the cellular origin of BCC (Youssef et al., 2010). Strikingly, induction of Smo2* expression in hair follicle stem cells with multiple hair follicle specific ere lines fails to induce BCC. In contrast clonal level expression of the mutant in the upper infundibulum or IFE using a tamoxifen regulated ere driven by a keratin 14 promoter resulted in BCC preferentially localised to tail and ear within 8 weeks of induction. Prior to the appearance of BCC, hyperplastic and dysplastic lesions were seen. This study argues that BCC may arise from IFE, either from an IFE stem cell population, or CP cells or both. We plan to investigate the quantitative changes in CP cell fate induced by Hedgehog mutation, whether mutant CP clones can evolve into preneoplastic lesions and BCC, and if this is so, the molecular and cell fate changes that occur during clonal evolution.

Experimental Design The R26flSM02*YFP strain is ideally suited for clonal analysis as the label EYFP is fused to the SM02* mutant protein and is readily detectable in recombined cells in epidermis (Mao et al., 2006; Youssef et al., 2010). In this model BCC in tail and ear epidermis, sites which are easily wholemounted, will facilitate this study.

Expermental Plan We will follow a similar plan to that outlined above (Example 2). Homozygous R26flSM02*YFP animals, obtained from the Jackson Laboratory will be crossed with homozygous AhcreERt animals. Doses of inducing drugs will be titrated to give clonal level recombination in ear and tail epidermis. A cohort of animals will be induced and clone sizes quantified by confocal imaging of immunostained wholemounts. The data will be analysed using Bayesian inference methods and a quantitative model of mutant CP fate at early time points developed. We will track the emergence and growth of preneoplastic lesions (first seen from 3 weeks post induction in KUcreERt mice) and determine whether the cellular dynamics of these lesions is consistent with SM02* mutant cell behaviour at earlier time points. Mutant and wild basal cells will be flow sorted and changes in transcription analysed by expression microarray. In addition we will laser capture preneoplastic lesions at later time points for expression microarray and array CGH analysis,†o enable us to correlate changes in cell fate dynamics with any additional genetic events. In addition we will examine proliferation and differentiation in wild type cells adjacent to clonal lesions to determine how normal cells respond to clones which violate homeostasis. These studies will give quantitative insights into the early stages of the evolution of the commonest form of NMSC.

Example 4: Fate of normal and preneoplastic CP cells in UVB irradiated epidermis

Analysis of the fate of PMC in UVB exposed epidermis suggests that they are derived from CP like progenitors with stochastic fate (4). PMC grow exponentially during UV irradiation, unless they exceed 1000 cells in size when growth slows, possibly due to signals from adjacent wild type cells. However, several important questions remain unresolved. Chronic UVB irradiation results in epidermal thickening and increased proliferation, but a quantitative analysis of the changes in normal cell fate induced by UVB has not been performed (Lu et al., 1999; Remenyik et al., 2003). Following the cessation of UVB exposure the limited data available suggests mutant cells revert to normal CP behaviour, but this prediction requires confirmation ( 1 1 ). Finally it remains unclear if the very low frequency with which PMC transform into carcinoma results from the low probability of an individual clone acquiring the necessary mutations or because only rare stem cell derived PMC are potentially tumourigenic. This is an important issue for cancer prevention, as CP type cells can be potentially eliminated by agents which increase probability of their generating differentiated progeny, whilst mutant stem cells will not be affected by such treatments. We plan to resolve these issues by performing quantitative fate tracking for wild type and P53 mutant cells during and after UVB irradiation. Experimental Design

For our initial experiments we will use the existing P53flR270H strain which carries a condition allele of a dominant negative form of P53 modelling Li Fraumeni Syndrome (Olive et al., 2004). Expression of the mutant protein increases UV induced cancer incidence in heterozygous mice (Wijnhoven et al., 2007). However, these mice lack a reporter to permit the isolation of intact mutant cells for molecular and cell culture analysis. We will therefore generate a new strain harbouring the commonest P53 mutant allele found in human NMSC, the gain of function R245W mutation (equivalent to R248W in humans) which has been shown to disrupt DNA damage repair (Song et al., 2007). The targeting construct (Fig. Generation of a conditional P53 R245W mutant mouse with an EGFP reporter. LoxP sites are shown as yellow triangles, numbers indicate exons. Following recombination the point mutant (*) P53 red will be expressed in place of the wild type allele (blue). The mutant is fused via a flexible linker to the E2A cleavable peptide followed by EGFP carrying a nuclear localisation sequence, to enable viable mutant cells to be isolated for further analysis. The Frt flanked puromycin selection cassette will be removed by Flp transfection of the targeted ES cells) is designed to maintain wild type levels of P53 prior to recombination. Following ere induction, wild type exons 7-1 1 of P53 will be removed, to be replaced by P53 carrying the R245W point mutation in exon 7. The C terminus of the mutant protein is fused via a flexible linker to the E2A cleavable peptide followed by EGFP carrying a nuclear localisation sequence (Engert et al., 2009; Trichas et al., 2008) . The E2A peptide ensures reliable reporting of expression of the mutant P53 without the risk of altered expression that can occur with the use of an internal ribosome entry sequence strategy. A Frt flanked puromycin selection cassette is included 3' of the reporter: this will be removed by Flp transfection of the targeted ES cells. The construct will be generated by DNA synthesis and recombineering techniques and will be extensively tested both prior to ES cell transfection and in the targeted ES cells for its ability to act as a dominant negative form of P53 (Song et al., 2007) . A consideration for this example is the possibility of UVB induced ere activity in the AhcreERt strain, as there is evidence that the CYP1 A1 (ie Ah) promoter is induced by UVB irradiation at similar dose levels to those we plan to use in this study (Fritsche et al., 2007). However as creERt activity also requires the presence of Tamoxifen, background clonal induction is likely to be at a low level, if it occurs at all. To confirm this is the case; uninduced R26flEYFPAhcreERT control animals will be exposed UVB in the schedule we we plan to use (0.6 x minimal erythema dose, MED five times per week for up to 12 weeks (Remenyik et al., 2003)). The background level of clonal induction will be determined by examining wholemounts harvested after 3, 6 and 12 weeks of UVB. Determination of the level of any ongoing clone induction due to UVB will allow us to correct for this in subsequent clone fate analysis.

Experimental plan

In parallel to generation of P53flR245W-GFP mice we will characterise the response of wild type CP cells to low dose UVB. AhcreERt R26flEYFP mice will be clonally induced and exposed to 0.6 MED UVB 5 times per week for 12 weeks. 4 mice per time point will be culled at 3 days, 1 3, 6 and 12 weeks, and wholemounts collected for analysis of clone size in tail and ear epidermis. We will also collect clone fate data at time points after cessation of UVB to track the changes in cell fate that occur as the epidermis recovers from UVB. The clone size data will be used to construct a quantitative model of CP fate in UV exposure which will be compared with unirradiated controls and our previous analysis of cell fate in p53 mutated cells in mouse and human UV exposed epidermis (1 1 ). These experiments will define the physiological response of the epidermis to low dose UVB. Next we will examine clonal fate in animals doubly heterozygous for AhcreERt and P53flR270H, induced to generate PMC, comparing clone sizes in un-irradiated and UVB exposed animals and also tracking clone fate post UVB treatment, testing the prediction that p53 mutant clones grow exponentially during UVB exposure but revert to balanced stochastic fate once UVB exposure ceases. Clones will be visualised by immunostaining epidermal wholemounts (Bertout et al., 2009) and the clone size distributions subjected to quantitative analysis (5). Once homozygous P53flR245W-GFP animals are available, they will be crossed onto the AhcreERt strain and the experiments above will be repeated. Fluorescent laser capture microdissection will be performed to isolate individual "outlier" clones which lie outside of the expected clone size distribution at a given time point or any macroscopic skin lesions which develop. These samples will be processed for transcriptional and genetic analysis, either by expression and genomic arrays or next generation sequencing. We will thus determine whether "outlier" clones express markers that could be used to identify corresponding lesions in human material.

The three mouse models developed here will form a resource for testing the ability of candidate cancer preventative agents to eliminate preneoplastic clones. The availability of quantitative models of the fate of mutant cells will greatly accelerate the identification of effective compounds. In addition, by correlating changes in cell fate with transcription, we will gain insights into potential molecular mechanisms that underlie CP cell fate choice. Example 5: Screen for pharmacological regulators of cell fate

We have screened candidate small molecule inhibitors for the ability to alter the fate of primary human epidermal stem and CP cells. Dishes of cells cultured at clonal density were fixed, stained and scored using an Olympus scanR automated microscope. To assess proliferation, cells were exposed to a pulse of EdU prior to fixation. CP cell behaviour dictates that as colony size increases the probability of a CP derived clone containing proliferating cells falls rapidly. In contrast the exponential growth of stem cells generates large colonies in which the majority of cells are in cycle. By 6 days of culture, stem and CP cells derived colonies can be clearly resolved. Two active agents were identified. Whilst having no effect on the number of colonies, Compound A increased the proportion of stem cells whilst Compound B strongly promoted the differentiation of stem cells into CP ceils. These screens will be extended to identify pharmacological agents which alter the probability of CP cell differentiation. To validate compounds identified in the screen, we are using time lapse microscopy of fluorescently labelled keratinocytes to visualise changes in cell fate directly. SiRNA transfection with lentiviral rescue will be used to confirm the specificity of agents whose targets are known. Where feasible, agents will then be investigated in vivo, using quantitative clonal fate analysis of epidermis and oesophagus in AhcreERTRosa26flEYFPmice according to the present invention, treated topically or systemically as appropriate. Example 6: Quantitative and predictive models for drug development

For many years in preclinical drug development has relied on a standard panel of in vitro assays. The cionogenicity assay tests the ability of an agent to decrease the number of cells which generate colonies containing 50 or more cells after 10-14 days in clonal density culture. This scoring rule excludes the colonies derived from CP type cells, which may represent the bulk of proliferating cells in tumours in vivo. Furthermore, all of the immortalised cancer cell lines we have tested so far lack the CP type population present in primary cultures of tumour cells. Standard xenograft models assay the action of drugs on stem like cells with regenerative potential but fail to resolve effects on CP type cells. Thus current methods may therefore miss agents with the potential to slow tumour growth via their effects on CP cells.

Clonal drug testing in human carcinoma cells

We will investigate the effects of existing anticancer drugs, and/or candidate modulators, on primary cultures of SCC, to determine if there is a difference in the sensitivity of stem and CP type cells to these agents. We will also seek to identify targeted compounds that promote the differentiation of malignant CP cells. Initial experiments will be performed at single time points using automated imaging and scoring. Confirmatory studies to allow the construction of a predictive model of the effects of each agent on cell fate will then be performed, allowing the most effective compounds to be rapidly identified.

Elimination of preneoplastic clones in vivo

The potential of agents for promoting preneoplastic CP cell differentiation will be tested in vivo using the methods of the invention. These will be applied topically and/or systemically and tested for their ability to eliminate P53 mutant clones in the epidermis and oesophagus. In such experiments, we hypothesise both normal and mutant CP clones will be driven to differentiate, causing non mutated stem cells to be mobilised. The result is the depletion of mutant clones and their replacement by normal CP cells derived from normal stem cells.

Pilot studies to establish the tolerability each of agent and where possible its pharmacodynamic efficacy will be performed. Clonal mutation will then be induced and the animals treated with agent and control for 3 and 6 average cell division times (in tail epidermis and oesophagus this corresponds to approximately 3 and 6 weeks). Small changes in cell fate result in significant alterations in clone size distributions (Klein et al., 2007) . The data will be used to construct a quantitative model of the effects of each agent. Agents predicted to substantially decrease the number of mutant clones will be tested in longer term experiments over a 3 month time course. Finally we will assay the ability of compounds to reduce the size of the largest and/or "outlier" clones in conditional P53 mutant mice exposed to UVB irradiation. These studies will provide a basis for future studies in humans with severely photodamaged epidermis who are at high risk of developing skin cancer.

In vivo clonal analysis for predictive testing of long term drug effects on epithelia

In addition to these studies on preneoplastic and malignant cells, we will exploit the power of clonal analysis according to the present invention to provide both quantitative insight into the effects of a drug on epithelial cell fate and predict the long term effects of drug treatment from a short term experiment. In a pilot study we investigated the effects of treating mouse tail epidermis with all trans retinoic acid (AT A) which is a powerful regulator of epidermal fate (Fisher and Voorhees, 1996). Two protocols were used: 1 ) treatment with ATRA or vehicle for 2 weeks, beginning immediately after induction of clonal labelling, or 2) induction followed by a three month interval followed by treatment with ATRA or vehicle alone for a further 3 months. Analysis of the animals treated for 2 weeks indicated the mean rate of cell division had increased from once every 6 days to once every 8 hours, but that the proportion of cells undergoing asymmetric cell division was unaltered. We used these parameters in the model to predict clone size in the long treatment protocol, finding the model to be highly effective at predicting clone size distribution at 6 months post induction (Figure 24). The ability to predict long term outcomes from short term experiments has the potential to accelerate drug testing, as the most promising compounds can be identified from short term experiments with as few as 6 animals per drug. We will extend these studies to investigational drugs with epithelial toxicity (e.g. BIBW2992, (Li et al., 2008)). The invention may thus be applied to lead compound testing.

Example 7: Application to Intestinal Crypts

Lgr5hl cells occur as a homogeneous population.

Lgr5hl stem cells in the small intestine divide approximately once per day (Barker et al., 2007). Quyn and colleagues have demonstrated that each Lgr5h' stem cell orients its mitotic spindle along its apical-basal axis (Quyn et al., 2010). In order to visualize crypt architecture at single cell resolution, we generated an E-cadherin-mCFP fusion knock-in allele (Fig. 1 A, B and Suppl. Fig. 1) and crossed this into the grS- EGFP-lres-CreERT2 Kl mouse strain. E-cadherin-mCFP mice were homozygous viable. The E-cadherin fusion protein allowed visualization of 3D crypt architecture to depths of 125 μτη (Fig 1 C), which revealed an almost perfect intermingling of Lgr5hl cells and Paneth cells (Fig 1 E).

FACS analysis demonstrated the existence of three different Lgr5-expressing populations based on GFP level (Fig. 1 D), of which only the GFPh'-cells yield long-lived intestinal organoid structures in-vitro (Sato et al., 2009). We next counted Lgr5h' intestinal stem cells in duodenal crypts of Lgr5-EGFP-Jres- CreERT2/ E-cadherin-mCFP mice. In the 3D reconstruction model (Fig. I E), essentially all non-Paneth cells at the crypt base were Lgr5-GFPh'. Conversely, no Lgr5-GFPhl cells were observed outside the crypt base. Crypts of the duodenum were found to contain 14±2 Lgr5hl cells (Fig. 1 F), similar to the numbers of Crypt Base Columnar cells as originally reported (Cheng and Leblond, 1974b).

In our initial in vitro experiments, less than 5% of single sorted Lgr5 intestinal stem cells could grow out into gut-like organoid structures (Sato et al., 2009). Recently, we noted that sorted heterotypic doublets (consisting of one Lgr5hl stem cell and one Paneth cell) displayed 25% plating efficiency (Sato et al., submitted). After further optimization, we reached a plating efficiency of approximately 60% when scored as exponentially growing organoids after 7 days (Fig. 2). In other words, more than half of Lgr5h' cells could grow out into an intestinal organoid when sorted together with a neighbouring Paneth cell. We interpreted this to imply that the majority of Lgr5hl cells have stem cell properties, at least when associated with a Paneth cell. Thus, we tentatively viewed each duodenal crypt to harbour a homogeneous population of 14 Lgr5hl intestinal stem cells. Multicolour lineage tracing of individual Lgr5 stem cells

To address how homeostatic self-renewal is controlled, we generated a Cre reporter allele termed R26R- Confetti. We integrated into the Rosa26 locus a construct consisting of the strong CAGG promoter, a LoxP flanked NeoR-cassette serving as transcriptional roadblock, and the original Brainbow-2.1 cassette (Livet et al., 2007) (Fig. 3A). After Cre-mediated recombination, the roadblock is removed and one of the four fluorescent marker proteins is stochastically placed under control of the CAGG promoter, allowing discrimination between the clonal progeny of neighbouring stem cells within the same niche (Fig. 3B). We validated fluorescent expression in multiple organs using the B-naphtaflavone (bNF)-inducible Ah~ Cre allele (Ireland et al., 2004). Cre induction in small intestinal crypts occurs at high efficiency, while less efficient induction of the Cre transgene occurs in a variety of other organs. The R26R-Confetti allele behaved as a stochastic multicolour cre-reporter generating nuclear green, cytoplasmic yellow, cytoplasmic red or membrane-bound blue cells (Fig. 3C). While the other three colours consistently appeared in near-equal ratios, nuclear GFP cells occurred at varying frequencies, yet always lower than the expected 25%.

Short-term clonal tracing analysis of individually labelled Lgr5hl cells Crypts drift towards clonality over time (Griffiths et al., 1988; Winton and Ponder, 1990), yet the kinetics of this process have not been documented at the single stem cell level. In the first of two tracing strategies addressing this issue, we analyzed the behaviour of clones developing from single Lgr5hl cells, stochastically initiated using the Lgr5-EGFP-Ires-CreERT2 allele in conjunction with the R26R-Confetti reporter. Analysis of stem cell clones was performed at various time points after Cre-activation by tamoxifen in 10 week-old mice, after which the progeny of these Lgr5hl cells were mapped in 3D- reconstructed crypts. Labelling occurred at a frequency of approximately one event per 6 crypts. All analyses were performed on crypts in the proximal segment of the duodenum.

Clone size was determined as the number of cells marked by a single fluorescent protein upon recombination of the R26R-Confetti allele. Cytoplasmic GFP intensity derived from the Lgr5 knock-in allele allowed the identification of Lgr5hl cells within a clone. Invariably, the identification of Lgr5hl cells by cytoplasmic GFP was confirmed by their location between Paneth cells. The first Confetti-marked stem cells were observed 24hrs after Cre induction (Fig. 4A). Most clones consisted of a single cell, of which 90% (34/38) could be identified as an Lgr5hl cell located between Paneth cells (Fig. 4B). Around 10% (5/43) of the marked stem cells had already undergone mitosis (Fig. 4B). After two days, most cells had divided at least once (Fig. 4C/D). We scored 101 two-cell clones for the presence of Lgr5 h' cells. Of these, 54 clones contained two Lgr5 1,1 cells, 10 contained a single Lgr5hl cell and 37 contained no Lgr5hl cell (Fig. 4D). Alongside the 101 two-cell clones, there were a further 37 larger clones with mixed Lgr5 expression, including one 7 cell-clone containing no Lgr5 1 cells, and others with four cells all of which were Lgr5hl. Apart from an overall expansion of clone size, this general pattern of behaviour (broad size distribution and divergent fates) was maintained at day 3 with the largest clone having as many as 10 cells (Fig. 4E and F). These results were indicative of the intestinal stem cells following seemingly divergent fates.

At later time points (day 7 and day 14), the rapid expansion and transfer of cells through the TA cell compartment to the villus made it challenging to reliably score their number. Therefore, we scored the number of Lgr5hl cells in each clone at days 1 , 2, 3, 7 and 14, while disregarding all other cell types within the clone. Thus, a 10 cell clone comprised of 4 Lgr5hl cells and 6 Lgr5'° cells translates to a clone of size 4, while a 10 cell clone in which all cells are Lgr5'° was considered "extinct". With this definition, the size distribution of surviving clones is shown in Figure 4G over the 14 day chase period. The data reveal a steady increase in the average clone size which compensates for the ongoing extinction of clones (Fig. 4G). Indeed, by day 14, the largest clone contained as many as 12 Lgr5h' cells, a figure approaching the 14 Lgr5h' cell average found in duodenal crypts. It was apparent that, even in the largest surviving clones, the labelled Lgr5h' cells were largely grouped together suggesting that, despite their rapid turnover, mixing of cells at the crypt base was limited (Suppl. Fig. 2 and Suppl. Movie 1 and 2). Furthermore, the morphology of these clones in the Lgr5hl compartment was consistent with a lateral expansion around the circumference of the crypt base while few, if any, cell divisions lead to clonal expansion through the base to the opposite side of the crypt. Long-term lineage tracing

In the second strategy, we aimed to mark all stem cells in crypts to document the drift towards clonality. The Lgr5 gene is expressed at low levels and, as a consequence, the Lgr5-EGFP-Ires-CreERT2 allele does not generate quantitative Cre activation upon a single tamoxifen induction. We therefore used the R26R-Conferti allele in conjunction with the Ah-Cre allele. The Ah-Cre transgene recombines LoxP sites efficiently in most cell types including the stem cells, yet is inactive in the long-lived Paneth cells (Ireland et al., 2004). Nevertheless, within the Paneth cell compartment, old unmarked Paneth cells are replaced by marked precursor cells over time (Ireland et al., 2005). Clonal analysis was performed at various time points after Cre-activation in 10 week-old Ah-Cre/R26R-Confetti mice, using "side-view" and "bottom- view" imaging of whole-mount intestine ("xy plane" and "xz plane" resp.; Fig. 5 A). Thus, the composition of many crypts could be captured in a single confocal image taken just above the crypt base, and for each crypt displayed as the biological equivalent of a "pie-chart". Analysis of the crypts in the time course provided visual snapshots of individual labelled domains of cells within crypts (Fig. 5B). Using these "bottom-view" images, we were able to extract quantitative data from week 1 to week 30, documenting the drift towards clonality (Fig. 5B). While only a small fraction of cells acquired the nuclear GFP label, 80% of the remaining cells were induced in approximately equal proportions, yellow:blue:red. At the earliest time point taken at 4 days post-labelling, the confocal section at the crypt base showed a striking, heterogeneous pattern of labelling

(Fig. 5B). At day 7, there was a significant expansion and coarsening of the labelled domains reflecting stem cell loss and lateral expansion of neighbouring clones (Fig. 5B). At later time points, we observed a continuing expansion of the average domain size alongside an ever-diminishing number of domains until crypts became fully labelled with one colour (monochromatic) or fully unlabelled (Fig. 5B). The first monochromatic crypts appeared as early as two weeks post-induction, while around 75% had become fully labelled at two months (Fig, 5B). Although the drift towards monoclonality continued, we noted the presence -albeit rare- of oligo-clonal crypts even at 18 and 30 weeks post-labelling (Fig. 5B, circles).

To describe quantitatively the drift towards clonality, we converted the sections from the crypt base into a labelled domain-size distribution (Fig. 6A). Specifically, we divided the circumference into 16 equal parts ("sextadecals"), reflecting the typical number of TA cells in a section near, but above, the crypt base (Potten and Loeffler, 1990). This assignment related proportionately to the stem cell content of a clone. For example, if we found a labelled domain of size 4 sextadecals - i.e. covering one quarter of the crypt circumference - this translated to one quarter of the crypt base stem cells being labelled in that colour. In this way, we could determine the labelled domain size distribution (Fig 6B) as well as the frequency of monochromatic crypts (Fig. 6C) over the 30 weeks chase period. On day 7, the domain size distribution was tilted towards smaller clone sizes with a peak around 3 to 4 sextadecals, i.e. clones covering 3/16 to 4/16 of the circumference (Fig. 6B). At two weeks, the weight of the distribution was gradually shifting towards larger clone sizes (Fig. 6B), with a small fraction of crypts (ca. 5%) already fully labelled (Fig. 6C). At 4 weeks, the average domain covered around 8 sextadecals, the half-filled crypt, in partially labelled crypts (Fig. 6B), while about 45% had become monochromatic (Fig. 6C). This trend continued out to the latest time point at 30 weeks when almost all crypts were monochromatic. This behaviour was consistent with competition between neighbouring stem cells leading to ever fewer yet larger clones and a steady progression towards monoclonality. This phenomenon was age-independent, as we observed the same drift towards clonality, when lineage tracing was initiated in 40-week old mice (Suppl. Fig. 3). Taken together, the short and long-term clonal fate data rule out a model in which all Lgr5hl cells are stem cells that segregate cell fate asymmetrically (Fig. 4B, D and F). Such a model would not be compatible with the previous observation -confirmed here- that crypts drift towards clonality (Griffiths et al., 1988; Winton et al., 1988). However, these early observations leave open the question of the functional homogeneity (i.e. equipotency) of the Lgr5hl population. Indeed, the divergence of clone fate seen in short-term lineage tracing, and the progression to monoclonality at longer times could be both accommodated within two very different frameworks. In the hierarchical model (1 ), the Lgr5hl cell compartment may be functionally heterogeneous with progenitor cells of limited proliferative potential supported by a single "dominant" stem cell following a strict pattern of invariant asymmetry such as proposed previously. Alternatively, in the stochastic model (2), tissue is maintained by an equipotent Lgr5h' stem cell population following a pattern of population asymmetry in which stem cell loss is compensated by symmetric self-renewal of a neighbouring stem cell.

At present, no marker or unique location has been identified which would distinguish a "dominant" Lgr5hi stem cell in the hierarchical model from its Lgr5hi progeny. Although, the validity of the model can thus not be addressed directly, several indirect conclusions can be drawn. First, for the model to be valid, the dominant stem cell has to be Lgr5hi, given that Lgr5-based tracing eventually leads to the marking of entire crypts. Second, the "dominant" stem cell has to divide in a strictly asymmetric fashion as a crypt can only harbour a single such cell. Third, because the kinetics of drift towards clonality differs from crypt to crypt, the dominant Lgr5hi stem cell should yield Lgr5hi progenitors, which can occur as relatively long-lived Lgr5hi cells (which persist for many months), but should also occur as short-lived Lgr5hi cells which disappear within days. Both long- and short-lived Lgr5hi progenitors should still be multipotent, again based on our previous tracing data (Barker et al., 2007).

In the stochastic model the situation is much less complicated. Only one type of Lgr5hl cell exists, 14 per crypt, all endowed with the potential for long-term sternness. Cell fate is determined after division of the Lgr5h' stem cell, potentially by competition for available niche space at the crypt base. Thus, homeostasis is obtained by neutral competition between equal stem cells and occurs at the population level. To evaluate the possibility that the stochastic model indeed underlies the homeostatic self-renewal in crypts, . we subjected our quantitative short- and long-term tracing data to a quantitative theoretical analysis. Mathematical analysis of short-term clonal evolution shows that stem cells follow neutral drift dynamics

In general, the ability to maintain tissue in long-term homeostasis places significant constraints on the properties of a stem cell population. In particular, it leaves open two patterns of stem cell fate: invariant asymmetry in which every stem cell division results in asymmetric fate (as exemplified by the hierarchical model), and population asymmetry in which the balance between self-renewal and differentiation is achieved on a population basis (as exemplified by the stochastic model) (Watt and Hogan, 2000). For the latter, since the size of the intestinal stem cell compartment remains roughly constant over time, it follows that balance of stem cell fate in crypts must follow from external regulation: the tissue responds to the loss of a nearby stem cell by symmetric cell division or vice versa. As a result, stem cells follow a stochastic pattern of behaviour known as "neutral drift dynamics". If, by chance, the last stem cell in a clone is lost, that particular clone becomes extinct. As a consequence, crypts inevitably drift towards clonality in the stochastic model. Evidence for population asymmetry and neutral drift dynamics has been reported recently for stem cells in mammalian testis (Klein et al., 2010). Two of us (AMK and BDS) have provided the theoretical underpinning for a study comparable to that of Klein et al. on intestinal crypt-villus dynamics (Lopez-Garcia et al., Submitted). Both of these studies relied upon long-term lineage tracing from which the "trails" of differentiating spermatocytes, and the migration streams of intestinal cells on the villi, were used to infer indirectly the dynamics of the underlying stem cell compartments.

With access to clonal fate data at single stem cell resolution, the present study allowed for a critical, direct analysis of the dynamics of the intestinal stem cell population. From the two studies mentioned above, several generic and robust features of neutral drift dynamics have emerged. First, after an initial transient evolution, the clone size distribution was predicted to acquire "scaling" behaviour: Formally, denoting as P„(t) the fraction of surviving clones which host n (>1 ) Lgr5hl cells at a time / post-induction, we can define a cumulative size distribution, Cn { ) = \— 2_,Pm ( » ' e- C»(t) simply records the chance of finding a clone with more than n stem cells after a time /. For the latter, "scaling" implies that the cumulative size distribution takes the form (Suppl. information), where («(')) denotes the average number of stem cells in a surviving clone, and F is the "scaling function". From (1 ), it follows that, when Cn{t) is plotted against « / «(/)), the entire family of size distributions at different times, t, collapses onto a single curve. The scaling function, F, is "universal", independent of stem cell number, their rate of loss or division, etc., and dependent only on the coordination of stem cells in tissue (see below). In crypts, since clone size cannot grow indefinitely, scaling behavior will be lost when crypts become monoclonal (Suppl. information).

By contrast, if homeostasis relies upon a stem cell hierarchy, clones derived from the dominant stem cell would increase steadily in size, while those derived from shorter-lived Lgr5hl cells would exhibit limited growth followed by loss. Significantly, the mixture of these two behaviors cannot lead to scaling (Klein et al., 2010). The growth, (n(t)), and form of F, offer further insight into the pattern of stem cell fate. If stem cells are organized into a one-dimensional arrangement, with cell replacement effected by neighboring stem cells, then the average size of surviving clones is predicted to acquire a square root time- dependence, < n(t) >» - fnAt , with λ the stem cell replacement rate, and the scaling function takes the form (Suppl. information, Bramson and Griffeath, 1980), (X) = exp(- c 2 /4) (2) Referring to Figure 7A and B, we indeed found that the cumulative clone size distribution from the short- term clonal assay showed a rapid convergence onto scaling behavior, while the average clone size followed a square root growth over the same period. Such scaling behavior is consistent with equipotency of all LgrS1" cells thereby arguing against the hierarchical model. Furthermore, the coincidence of the data with the universal (parameter-free) scaling function (2) further established that intestinal stem cells follow a pattern of neutral drift dynamics in which stem cell multiplication is compensated by the loss of neighboring stem cells. This leads to a lateral clonal expansion around the one-dimensional circumference defined by the crypt base (Fig. 6A), and consistent with the images obtained from whole-mounts (Fig. 5B). A fit of the predicted average clone size (w( ) (F'g- 7 A, solid line, Suppl. information) to the experimental data over the 14 days chase period (Figure 7 A, points) revealed a stem cell replacement rate of 0.74±0.04/day, a figure comparable with the cell division rate of the stem cells. As a result of this coincidence, we can conclude that, if asymmetric stem cell divisions take place at all, they make a negligible contribution to tissue homeostasis.

From the inferred rate of stem cell loss, we can use neutral drift dynamics to predict the long-term evolution of the average clone size and survival probability (Fig. 7C and D). With this result in hand, a further comparison of the clone size distribution with a more detailed analysis that includes the approach to scaling (Suppl. information) revealed an excellent agreement of theory (Fig. 7B, lines) with experiment at intermediate times (Fig. 7B, points).

Long term clonal evolution, coarsening, and the progression to monoclonality The long-term lineage tracing data provided a vivid demonstration of the "coarsening" phenomenon (i.e. the drift towards ever fewer, yet larger clones) predicted by neutral drift dynamics. It also presented an opportunity to study quantitatively the progression to monoclonality. The size distribution of contiguous labelled patches of stem cells generated in the R26R-Confetti system provided a signature of neutral drift dynamics, which can be compared to theory - a straightforward generalization of the clonal dynamics considered in the previous section to a multicolour mosaic system. Although the clone dynamics relates to an, as yet, unsolved problem in non-equilibrium statistical physics - the theory of a "coalescing random walk" (Ben-Nairn et al., 1996; Krapi vsky and Ben-Nairn, 1997; Wu, 1982) - the evolution could be generated straightforwardly by computer simulation, and the results compared with experiment (Suppl. Fig. 4 and Suppl. information). To extract quantitative insights from the experimental data, we required one further parameter, the number of stem cells in the crypt. Duodenal crypts harbor 14±2 Lgr5h' cells per crypt. In the following, we have assumed a figure of 16 stem cells per crypt to match the average number of TA cells in a crypt section near the base. However, within a relatively narrow range 14-18, a variable stem cell number would not significantly influence the quality of the fits discussed below. Taking the same stem cell loss rate from the short-term clonal analysis, Figure 7E shows a favourable agreement of neutral drift dynamics (solid line) with the measured average clone size (points) as well as the monochromatic crypt fraction (Fig. 7E, inset). In particular, the figure shows that, by two months, approximately 75% of the crypts became monoclonal (Fig. 7A, inset).

As with the short-term clonal assay, the average size dependence represented just one facet of a rich data set associated with the full clone size distribution. With the same two parameters in hand, the stem cell loss rate and stem cell number, an analysis of the size distribution showed an equally favourable agreement (solid lines) with the experimental data (points) at 4, 7, 14, and 28 days post-labelling (Fig. 7F). At longer times, the data were fully consistent with theory, but the numbers of non-clonal crypts had become too low to reach statistical significance. Experimental Procedures

Mice: E-cadherin-mCFP mice were generated using the construct in Fig. 1 A. The neomycin selection cassette was excised in vivo by crossing the mice with the PG -Cre mouse strain. E-cadherin-mCFP genotyping PCR primers: see Suppl. Table 1. E-cadherin-mCFP mice were bred with Lgr5-EGFP-Ires- CreERT2 mice. Double heterozygous mice of 10 weeks were used for experiments. R26R-Confetti mice were generated using the construct in Fig. 3 A. The brainbow 2.1 construct: (Livet et al., 2007). R26R- Confetti genotyping PCR primers: see Suppl. Table 1. R26R-Confetti mice were crossed with Lgr5- EGFP-Ires-CreERT2 or with Ah-Cre mice. Cre induction: 10 Week-old mice were injected with 5mg tamoxifen (single injection) or B-naphtoflavone (3x lOOmg in one day), respectively.

Tissue preparation for confocal analysis: For semi-thick sectioning of near-native tissue, organs were fixed in 4% Paraformaldehyde at room temperature for 20 minutes and washed in cold PBS. 1 cm2 of intestinal wall was put in a mold. 4% low melting point agarose (40 °C) was added and allowed to cool on ice. Once solid, a vibrating microtome (HM650, Microm) was used to make semi-thick sections ( 150μιη) (Velocity: l mm/s, Frequency: 65Hz, Amplitude: 0.9mm). Sections were directly embedded in

Vectashield (Vector Laboratories).

FACS analysis of Lgr5 populations and in vitro culture: LgrS+ cells were FACS analyzed as previously described (van der Flier et al., 2009). Crypts were dissociated with TrypLE express

(Invitrogen) with 2000 U/ml DNase (Sigma) for 30 min at 37°C. Dissociated cells were passed through 20μιη cell strainer (Celltrix) and washed with PBS. Cells were stained with CD24-PE antibody

(eBioscience) and Epcam-APC antibody (eBioscience) for 15 min at 4°C, and analyzed by MoFlo (DakoCytomation). Viable epithelial single-cells or doublets were gated by forward scatter, side scatter and pulse-width parameter, and negative staining for propidium iodide. Sorted cells were embedded in Matrigel. Crypt culture medium (Advanced DMEM/F 12 supplemented with Penicillin/Streptomycin, 10 mM Hepes, Glutamax, l x N2, I x B27 (Invitrogen), and 1 μΜ N-acetylcysteine (sigma) containing 50 ng/ml EGF, 100 ng/ml noggin, 1 g/ml R-spondin) were overlaid. Y-27632 (10 μΜ) was included for the first 2 days to avoid anoikis. Growth factors were added every other day and the entire medium was changed every 4 days. Organoid formation was analyzed 7 days after plating.

Microscope equipment: Images were acquired using a Leica Sp5 AOBS confocal microscope

(Mannheim, Germany) equipped with following lenses; lOx (HCX PL APO CS NA0.40) dry objective; 20x (HCX PL FLUOTAR L NA0.40) dry objective; 40x (HCX PL APO NA0.85) dry objective and a 63x (HCX PL APO NA 1 .30) glycerol objective.

Example 8: Neutral drift model of intestinal stem cell maintenance

The quantitative analysis of the lineage tracing data relies upon a model of intestinal stem cell fate involving "neutral drift dynamics", which was proposed to describe intestinal stem cell turnover in. The aim of the following supplementary sections is to elaborate on how the model is inspired by the current clonal fate data, and to elucidate the key elements of the theoretical and data analysis.

Whole-mount thick sections of tissue show the crypt base to be characterised by Paneth cells intercalated by narrower Lgr5hl progenitor cells. From the short-term clonal labelling study several important features emerge: Characterising clone size by their Lgr5h' cell content, the distribution of "surviving" clones (i.e. clones that host at least one Lgr5hl cell) reveals an ongoing expansion of the average clone size compensated by depletion in surviving clone density (Fig. 4). At the same time, the increasing width of the surviving clone size distribution suggests that Lgr5hl cells adopt seemingly "random" divergent fates (Fig. 4G). Taken together, such behaviour is consistent with maintenance of the Lgr5h' cell population following a pattern of population asymmetry. A second and important feature of the clonal evolution is the cohesion of labelled LgrS1" cells at the crypt base (Suppl. Fig. 2 and Suppl. Movie 1 and 2). Moreover, clones tend to expand laterally around the circumference of the crypt base while very few clones, if any, involve cells migrating through the apex of the crypt base. Finally, taking into account the close association of Lgr5 expression with Paneth cell contact (Fig. 1 E and 2A), we are led to consider a "quasi one-dimensional arrangement" of Lgr5hl stem cells, which follow the perimeter of the crypt base (Fig. 6A). Stem cell loss following displacement from the niche Paneth cells is compensated by the multiplication of neighbouring stem cells, and vice versa, leading to the conservation of stem cell number (Fig. 6A).

On this background, let us now consider the clonal evolution of a single labelled stem cell. Following this pattern of niche-based competition, if stem cell multiplication leads to the displacement of the labelled stem cell, the clone is lost. Conversely, if the labelled stem cell undergoes division, it may displace a neighbouring unlabelled cell leading to clonal expansion (see Fig. 6A, last three panels). In subsequent generations, the clone may again expand or contract depending on whether labelled cells at the boundary of the clone are lost or multiply. However, it is important to recognize that clonal growth and contraction, following this pattern of external regulation, can only occur at the boundary of the labelled clone. The loss and replacement of stem cells within a labelled fragment leave the clone size unchanged. As a result, clonally labelled domains of cells follow a pattern of neutral drift in which the boundary of the clone follows a "random walk". Clonal progression is arrested when the last cell in a clone is lost (leading to clonal extinction) or when the last cell in the crypt becomes labelled (leading to monoclonality and fixation of the clone).

Such behaviour is encountered in a broad class of problems where it is known variously as the "stepping stone model" in population genetics (Kimura, 1983), a "moran process" in population dynamics (Moran, 1962) and a "Voter model" in physics and mathematics (Bramson and Griffeath, 1980; Liggett, 1985; Korolev et al., 2010). As a paradigmatic model, the general class of Voter models have been the subject of considerable attention, with studies in both the mathematics and physics literature (Ben-Nairn et al., 1996). Indeed, for a general system following Voter model dynamics, it has been established that clonal evolution is characterised by long-term scaling behaviour in which the clone size distribution acquires the scaling form (1 ) discussed in the main text. In the one-dimensional arrangement, pertinent to the present system, the development of the long-term scaling behavior and the drift toward monoclonal ity can be developed in full from technical but straightforward mathematical analysis. In the following, we will reproduce the principal findings that relate to the analysis presented in the main text leaving a more detailed discussion to the literature (Lopez-Garcia et al., submitted).

Formally, the clone size distribution can be obtained from the Master equation,

Ι^Λ (ί) = Δ Λ (/) - (^ + ¾.., - 2<¾,)/¾(

λ at

- + <^_, - 2δηβ_ )pN m (0 + δηΑ , where p„(t) denotes the probability of finding a clone with n labelled stem cells (including n=0) at a time t following induction, λ denotes the stem cell replacement rate, and Nslem denotes the total number of stem cells (labelled and unlabelled) in the crypt. Defining the one-dimensional lattice translation operator, E„, = em k with k m - m k E-\— 2 denotes the lattice Laplacian. δ„,„ denotes the Kronecker delta symbol taking the value of unity when m=n and zero otherwise, while S(t) denotes the Dirac delta function being non-zero only at t=0 and integrating to unity. The first term on the right hand side of the equation describes a "random walk" of the clone size associated with the ongoing loss and expansion of labelled stem cells at the clone boundary, the second term accommodates the extinction of a clone due to the loss of the last stem cell, while the third term is associated with the fixation of a clone when all the cells in a crypt become fully labelled. Finally, the last term encodes the initial condition, translating to one labelled stem cell per crypt.

By constructing the Green function associated with the lattice Laplacian (Ben-Nairn et al., 1996), and employing the method of images, one may show that the Master equation has the general time-dependent solution, while the monoclonal fraction is given by,

and the extinction probability takes the form,

To make contact with the experimental data, we must now construct the surviving clone size distribution obtained following the exclusion of extinct clones, i.e. Pn(t) =— - .Although the full time-dependent distributions are easily resolved numerically from the expressions above, further analytical simplification can be made at long times. In particular, at times 1 « At « Ns 2 lem , the surviving clone size distribution acquires the scaling form,

1

F{n l < n{t) >),

< n(t) > where F(x) = exp[- /zx2/4 J denotes the scaling function and, in the same limit, denotes the average size of surviving clones. From the expression for P„(t), it follows that the cumulative clone size distribution acquires the scaling form, Cn(t) = F(n/ < n(t) >), utilised in the main text.

In the opposite limit, At » N2 lem , the majority of crypts have become fully clonal, In this limit, the clone size distribution, /?,,^, is dominated by the lowest term in the sum. Here we find that,

A(t)

P„(0 = sm(rni/Ni1em), \≤n≤NMm - l

cot( /2Nslem) while PN (0 = 1 - .4(0 with

A{t) = 4 cos2(^/2Nttem)exp[-4Atsin2(^/2Nittm)}

The sinusoidal form of P„(t) of the partially labelled crypt at long times reflects the persistence of clones which are nearly half-filled. Clones that are close to extinction or saturation are precarious, easily arrested by loss or fixation. Conversely, clones that cover half of a crypt can afford to drift without risk of loss. Statistics of clonal evolution in the densely labelled confetti mouse system

Having described the clonal evolution of single labelled cells, in the following section, we will consider the more challenging problem of the multicolor Confetti mouse system. As in the main text, to develop intuition, it is helpful to consider a fictitious "Confetti"-mouse system in which each and every cell in a crypt is labelled by a different colour. Intuitively, it is easy to see that the progression to monoclonality will lead to a coarsening phenomenon in which the gradual extinction of labelled clones is compensated by the expansion of others - neutral competition. It is also clear that the statistics of the ensemble of individual clonal patches is equivalent to the problem described in the previous section. It is curious to note that the joint statistics of the multiple colour system represents a largely unsolved problem in non-equilibrium statistical physics - the problem of "coalescing random walkers" (Krapivsky and Ben-Nairn, 1 97).

In reality, the Confetti mouse system is essentially limited to just four colours, yellow, blue, red and "unlabelled". (The induction rate of the nuclear GFP in the densely labelled system is negligible and can be safely ignored). Therefore, on induction, the densely labelled system is characterised by an initially heterogeneous distribution of labelled clone sizes in which neighbouring cells of the same colour appear by chance. Moreover, distinct clones of the same colour can appear several times in a single clone. Nevertheless, although the evolution of clone sizes will differ quantitatively in its characteristics, the qualitative features are maintained: coarsening of the clone size distribution leading to monochromatic ity of the crypt. Needless to say, the statistics of the coarsening process represent a yet more challenging, and unsolved theoretical problem, beyond the scope of the current work. However, we can infer the dynamics of the multicolor system in full straightforwardly from numerical simulation.

For completeness we simply note here that, to explore the clone size evolution described in the main text, we followed the dynamics of randomly induced crypt segments following the pattern of neutral dynamics described in the previous section. More specifically, we induced cells at a labelling frequency of 4 in 5, with each colour, yellow, blue, and red, drawn with equal probability, matching that found in the experimental system. Here, for the reasons outlined in the main text, we took a stem cell number of Ns,em= 16. To develop the numerical simulation, we chose to update randomly chosen cells by exchanging their colour by one of their neighbours reflecting the outcome of stem cell loss following multiplication.

With 1 ,000,000 crypts monitored in the simulation, the relevant clonal distributions were fully converged allowing comparison with the results of the long-term lineage tracing experiment. The results of the comparison are described in example 7. Microscope settings and image analysis:

Fig. IB: (image 512 x 512 pixels, 8 bits, 63x, airy 1.5) In a semi-thick section of near native fixed intestine, mCFP was excited using a 458nm laser and collected between 465-600 nm.

Fig. 1C, left panel: (XYZ stack 512 x 512pixels, 8 bits, 63 steps, 2μηι stepsize, 63x). In a whole-mount of near native fixed intestine, fluorescence was excited using a 2-photon laser at 880 nm. mCFP was collected using external/ non-descanned detector with 480/30 nm bandwidth and 505nm longpass filter. EGFP was collected using external/ non-descanned detector with 530/50 nm bandwidth and the same 505nm LP filter. 3D representation was created using Volocity (Improvision Ltd.).

Fig. 1C, right panel: (XYZ stack 1024 x 1024 pixels, 12 bits, 32 steps, 1.5μπι stepsize, 63x). In a semi- thick section of near native fixed intestine, fluorescence was excited using a 2-photon laser with settings as in Fig. I C, left panel.

Fig. IE: (XYZ stack 1024 x 1024, 12 bits, 37 steps, 2.5μιη stepsize, 63x). In a whole-mount of near native fixed intestine, fluorescence was excited using a 2-photon laser with settings as in Fig. 1 C. left panel. Fig. 3, 6: Images of at least 1024 x 1024 pixels and 12 bits were acquired with one of the three dry lenses, xy-plane images were created by scanning semi-thick sections of near native fixed intestine, xz-plane images were created by scanning whole-mounts of near native fixed intestine. Scans were performed in series for XFP excitations. nuclearGFP, the argon laser 488 nm line; for EYFP 514 nm line; for RFP a red diode laser emitting at 561 nm, and blue mCFP was excited using a laserline at 458 nm. In general GFP fluorescence was collected between -498-51 Onm, airy 1 ; EYFP fluorescence was collected between

-521 -560 nm, airy 1 ; RFP fluorescence was collected between -590-650 nm, airy 1 ; mCFP fluorescence was collected between -466-495 nm, airy 1 .5. DIC was obtained while using 488 nm laser through transmission gate. The acquired images were processed with Image J and photoshop.

Fig. 4: XYZ stacks, 1024 x 1024 pixels and 12 bits were acquired with in general the 63x glycerol objective, xy-plane images were created by scanning semi-thick sections of near native fixed intestine and used for visual snapshots, xz-plane images were created by scanning whole-mounts of near native fixed intestine and used for analysis. Scans were performed in series for XFP excitations. Lgr5 driven EGFP and nuclearGFP, the argon laser 488 nm line; for EYFP 514 nm line; for RFP a red diode laser emitting at 561 nm, and blue mCFP was excited using a laserline at 458 nm. In general EGFP fluorescence was collected between -498-51 Onm, airy 1 ; EYFP fluorescence was collected between -521 -560 nm, airy 1 ; RFP fluorescence was collected between -590-650 nm, airy 1 ; mCFP fluorescence was collected between -466-495 nm, airy 1 .5. DIC was obtained while using 488 nm laser through transmission gate.

Quantitative data analysis - Counting Lgr5hl cells:

3D representations were created using Volocity (Improvision Ltd.). 4 separate XYZ stacks per mouse were scanned per part of small intestine (duodenum, jejunum and ileum). Using Image J, average Lgr5- GFPhi signals were calculated from at least 10 Lgr5-GFP positive cells at the entire base of crypts per XYZ stack. Threshold was set at 66% of this particular stack average. GFP signals above this threshold were visualized in red. RGB overlays showed Lgr5-GFP in green, mCFP in white and GFP signals above threshold in red. The numbers of Lgr5hl cells per crypt (each cell with regions above threshold) were counted in Z-stacks, and multiple counts of the same cell in different slices were avoided by marking cells in each plane with a custom Image J plug-in.

Average number of Lgr5hl cells per crypt was calculated over more than 75 counted crypts out of 8 different Z-stacks per intestinal part obtained from 2 mice at l Owks of age. Same holds true for standard deviation.

Quantitative data analysis - Short-term tracing of Lgr5hl cells: The acquired images were processed with Image J and photoshop or Volocity. Lgr5 driven EGFP was separated from Confetti nuclearGFP based on cellular localization. Lgr5hl threshold was defined as described above. Numbers of Lgr5h' cells per crypt were counted as well as number of cells belonging to one clone (all positive for one of the Confetti colors). In addition, of each cell within a clone its relative crypt position was scored (located at the entire crypt base, around +4 or >+4) and whether it belonged to the Lgr5hl population or not.

Quantitative data analysis - Long-term tracing of intestinal stem cells: xz-plane images, obtained from wholemount intestine, were processed in Image J and photoshop.

Analysis of the clone and labeled domain size distributions were conducted using simulations based on Fortran codes and X GRACE. Theoretical analysis of the one-dimensional neutral drift model is described in example 8 above.

Example 9: Intestinal stem cell study

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 labelling system, we show that clone size distributions conform to a novel scaling behaviour 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 neighbour, 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 (/). 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) (I, 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 Bmil +) 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 following 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 (1 -13). Hence the consensus view remains that intestinal stem cells divide asymmetrically either due 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 using low level Cre-mediated recombination in Ahc eERt animals (targeting potentially all the proliferative populations within the crypt with a single treatment) crossed to Cre- reporter strains as described previously, and were visualised in tissue whole mounts or sections (Fig. 12A-J, SOM S-l). With only 1.9±0.7% of crypts containing labelled cells at 2 weeks post-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. 121-J). Crypts can become monoclonal a short time after induction, with some 50% fully-labelled within 8 weeks (Fig. 12K). The dynamics of monoclonal conversion can also be tracked by scoring the number of differentiated progeny that emerge from the crypts (Fig. 12L-N, Fig. 14). Following pulse labelling, cells exported from crypts form one to three clear migration streams on villi (Fig. 12B,C). On the villus, clones were comprised of both Goblet and absorptive cell lineages, and within the crypt, clones contain Paneth cells. Each fully- labelled crypt supports a clone width of wmax=6.8+\ .3 cells (mean ± standard deviation, «=155) along the villus. As with the crypt base analysis, we found that 50% of clones were of full-width (i.e. 6 cells or more) within 8 weeks, corresponding to 50% monoclonal crypts at this time point (Fig. 12M).

Monoclonal conversion rules out a simple model of tissue maintenance originating from a population of long-lived stem cells following a strict pattern of asymmetric division, and can be explained by only two classes of behaviour. 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. 13A). 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. 13B). Any detailed model of self-renewal will belong to one of these two classes (SOM S-II). Although both behaviours predict attrition of surviving clones and drift towards 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 (77). In this case, if the stem cell pool were not limited by anatomical constraints, clonal evolution would settle into a characteristic behaviour in which the size distribution acquires a "scaling form": defining P„(t) as the fraction of surviving clones which host n stem cells at a time t post-induction (see SOM S-1II (17, 18)) where («(/)) 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 (1 ), it follows that, if («( )-Ρ«( is plotted against the size distributions will follow the same curve irrespective of the time /. 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, while those derived from its shorter-lived progeny will exhibit limited growth followed by loss. Crucially, the mixture of these two behaviours leads to binomial size distributions that do not scale (SOM S-V).

Clone size is impossible to measure in absolute terms in intestine because of the constant migration and loss of cells. However, we can access P„(t) 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), shows that clonal expansion is tied to the circumference at the crypt base. Therefore, the clone width, relative to that of fully-labelled crypts, serves as a proxy for the fraction of labelled 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/wmax 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)Nstl,m, where Nstan denotes the number of stem cells surrounding the crypt base. With this assignment, we find that for t<A weeks, where the vast majority of crypts have yet to become monoclonal, the size distributions show scaling behaviour (Fig. 13D), an unambiguous signature of neutral drift dynamics.

The growth rate, (n(t)), and the form of Fix), have the potential to offer further insight into the pattern of stem cell fate. In particular, if stem cells are organised into a one-dimensional arrangement, with cell replacement effected by neighbouring stem cells (Fig. 14A,B), then the average size of surviving clones grows as a square root of time, (/!(0) * /Λ7, with λ the stem cell replacement rate, and the scaling function is predicted to take the form (SOM S-III),

F(x) = (πχ /2)exp[-/Ec2 /4] (2) Referring to the experimental data, the coincidence of the scaling behaviour with this universal (parameter-free) form, together with the observed square root growth of the clone width over the same period (Fig. 13D, inset), reveals that stem cells are indeed being replaced laterally by neighbouring stem cells in an effectively one-dimensional geometry. Note that this behaviour can accommodate both variability in replacement rates, and potential stem cell replacement parallel to the crypt axis (SOM S1I1.4-5).

Since this pattern of stem cell fate emerges from the consideration of (universal) short time dynamics, the long-term behaviour, including the drift towards clonality, presents a powerful test of the model. By fixing just a single parameter, A /Vs,ein 2=0.025±0.003/week (mean±sem), from a quantitative fit to the average clone width (Fig. 12M), we obtain an excellent agreement of theory (detailed in SOM S-IV,VI) with the measured monoclonal fraction (Fig. 12K) and clone size distributions over the entire timecourse (Figs. 14C-H, Fig. 16). A similar analysis of clone fate as measured from the crypt base in colon reveals the same neutral drift behaviour (Fig. 141,J; 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 neighbour. This process may be achieved through stochastic stem cell loss triggering self-renewal, or through over-crowding 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. 17). Which cells constitute the stem cells, and what is their rate of loss? Current debate centres on the relationship between two crypt base populations, the Bmil+ cells positioned around row 4 (4), and the columnar Lgr5+ cells that reside at the crypt base (5, 19). Since both cell populations support long-lived clonal progeny, equipotency demands that Bmi l+ and Lgr5+ cells contribute to the same stem cell pool with the cells generating each other. Such heterogeneity would not affect the scaling behaviour in Eq. (2), as its effect would be resolved rapidly compared to one-dimensional drift around the crypt circumference (SOM S-I1I.4). If we estimate the number of stem cells on the basis of the total number of Bmi l + and Lgr5+ cells (4, 5, 19), we can conclude that their total number is in excess of 16, suggesting that stem cells are replaced laterally by their neighbours at a rate ^l/da 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 intestine: symmetric stem cell division is not a rare event, but is a central aspect of homeostasis.

In summary, in place of a hierarchical arrangement, our results identify a pool of equipotent stem cells that is regulated by the behaviour of neighbours. The pattern of stem cell regulation in 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.

References to Example 9

I . F. M. Watt, B. L. Hogan, Science 287, 1427 (2000).

2. S. J. Morrison, J. Kimble, Nature 441, 1068 (2006). 3. D. H. Scoville, T. Sato, X. C. He, L. Li, Gastroenterology 134, 849 (2008).

4. E. Sangiorgi, M. R. Capecchi, Nat Genet 40, 915 (2008).

5. N. Barker et al., Nature 449, 1003 (2007).

6. C. S. Potten, G. Owen, D. Booth, J Cell Sci 115, 2381 (2002).

7. A. J. Quyn et al. , Cell Stem Cell 6, 175 (2010).

8. D. J. Winton, M. A. Blount, B. A. Ponder, Nature 333, 463 (1988).

9. D. F. Griffiths, S. J. Davies, D. Williams, G. T. Williams, E. D. Williams, Nature 333, 461 (1988).

10. H. S. Park, R. A. Goodlad, N. A. Wright, Am J Pathol 147, 1416 ( 1995).

1 1. C. Booth, C. S. Potten, J Clin Invest 105, 1493 (2000).

12. M. Loeffler, A. Birke, D. Winton, C. Potten, J Theor Biol 160, 471 (1993).

13. . Loeffler, T. Bratke, U. Paulus, Y. Q. Li, C. S. Potten, J Theor Biol 186, 41 (1997).

14. D. J. Winton, B. A. Ponder, Proc Biol Sci 241, 13 (1990).

15. . Bjerknes, Biophys J 48, 85 (1985).

16. E. D. Williams, A. P. Lowes, D. Williams, G. T. Williams, Am J Pathol 141, 773 ( 1992).

17. A. M. Klein, T. Nakagawa, 1. R., S. Yoshida, B. D. Simons, Cell Stem Cell 7, 214-224 (2010).

18. A. . Klein, D. P. Doupe, P. H. Jones, B. D. Simons, Phys Rev E Stat Nonlin Soft Matter Phys 76, 021910

(2007).

19. N. Barker et al., Cold Spring Harb Symp Quant Biol 73, 351 (2008).

20. H. S. Al-Dewachi, N. A. Wright, D. R. Appleton, A. J. Watson, Virchows Arch B Cell Pathol 18, 225

(1975).

21. H. S. Al-Dewachi, D. R. Appleton, A. J. Watson, N. A. Wright, Virchows Arch B Cell Pathol Incl Mol

Pathol 31, 37 (1979).

22. C. S. Potten, Int J Radiat Biol Relat Stud Phys Chem Med 49, 257 (1986).

23. N. A. Wright, M. Irwin, Cell Tissue Kinet 15, 595 (1982).

Example 10: Scaling and Applications

In a "homogeneous cell population", balance between division and differentiation significantly restricts available patterns of cell fate. These constraints afford a simple classification of progenitor cell types which lead to robust and testable experimental signatures.

Here we define classification and identify signatures in experimental clonal data across a range of tissue types including Interfollicular epidermis; Spermatogenesis; Intestinal crypt.

Consisting of a single lineage, the keratinocyte, mammalian epidermis provides simple model system. Behaviour is stereotypical of stem cell systems: continuously turned over and capable of regeneration following injury. Interfollicular epidermis considered a "classic" s†em/TA cell system i.e. it shows division asymmetry.

Exemplary labeling according to the invention may include pulse-labeling study using inducible ere recombinase-loxP system. This provides access to clone fate data in homeostatic tissue across a range of times. Figure 18 shows how the clones may appear.

Basal layer clone fate data shows inexorable increase in average size of an ever- diminishing clone population (Fig 19). Broad distribution of clone size corresponds to divergent fates, leading to long-term scaling behaviour as shown in the equation above (Fig. 20).

Clonal evolution is governed by a single rate limiting 'process' (Fig. 21 ).

Epithelium of small intestine ordered into crypts and villi which turnover every 3-5 days. In this system an exemplary label (marker) is inducible Lgr5-LacZ expression (eg. as in Barker, Clevers, et al., 2007). (Lgr5+) stem cells reside at the base of the crypt and generate all epithelial lineages. Intestinal stem cells follow pattern of population asymmetry with external regulation.

Despite the (potential) complexity of niche architecture, analysis of clonal fate characteristics reveal that adult tissues are maintained by turnover of a homogeneous cell population following one of two patterns of population asymmetry; in both cases, homeostasis is achieved through expansion of ever-diminishing clonal population and signalled by scaling.

Thus the invention offers advantages compared to prior art techniques including that it is superior to (and may undermine the utility of) labeling-retaining assays; enables analysis of mechanisms controlling resistance to mutation; and facilitates the study of (conserved) biomolecular pathways responsible for achieving stochastic regulatory control.

Example 11: A dominant negative mastermind like 1 mutant blocks commitment to terminal differentiation in oesophageal progenitor cells

Notch signalling is required for the normal differentiation of cells in stratified squamous epifhelia, including the murine oesophagus. It is unclear how Notch alters the fate of normal progenitor cells and the extent to which Notch acts directly on cells or indirectly by triggering epithelial inflammation. Here we investigate the effects of transgenic blockade of canonical Notch signalling in adult murine oesophageal progenitor cells in which a dominant negative mastermind like 1 protein (DNM) has been induced at clonal density. This approach demohstrates that loss of Notch has direct effect on cell fate without associated inflammation. The size distribution of clones expressing DNM scales with time, and the entire clone fate data set is consistent with a model in which cell division rate is increased but cells which would normally commit irreversibly to terminal differentiation re-enter cycle. These results indicate a requirement for Notch for cells to become post mitotic and demonstrate the existence of an intermediate state of "arrested differentiation" in vivo.

Murine oesophageal epithelium (EE) consists predominantly of layers of keratinocytes and is flat and featureless (Fig. 25A) (Goetsch, 1 10). Proliferation is confined to cells in the basal layer (Messier and Leblond, 1960) . On commitment to terminal

differentiation, basal cells exit the cell cycle and migrate into the first suprabasal cell layer, after which they undergo a series of morphological changes which culminate in their being shed at the tissue surface (Seery, 2002). We have recently used inducible genetic labelling to track the fate of proliferating cells in EE over a one year time course. This study revealed that following division, cells may adopt one of three fates, dividing to give either two cycling or two post mitotic cells or one of each. We observed that, at late time points, the entire clone size distribution scales with time (i.e. the probability of finding a clone size n at time t is the same as finding a clone size 2n at time 2t) . Such scaling indictates that one rate limiting process, the division of a single population of proliferating cells, determines clone size. The data thus excludes the model in which slow cycling stem cells and a more rapidly proliferating transit amplifying cell population maintain the population. The entire clone fate data set fits quantitatively with a remarkably simple paradigm in which all cycling basal cells are identical, and divide to generate daughters with one of the three fates at random. The probabilities of the symmetric fates are balanced to achieve tissue homeostasis across the population (Fig. 25).

This observation raises the question as to the molecular mechanisms that underlie the cell fate choice and differentiation of oesophageal progenitors. A candidate regulator of these processes is the Notch signalling pathway which regulates cell fate in many lineages in development and adult life (Bray, 2006). Signal transduction occurs when the Notch receptor is bound by ligands such as Jagged and Delta expressed on adjacent cells (Lindsell et al., 1995). The intracellular cytoplasmic domain of the receptor is cleaved from the transmembrane domain by γ secretase and translocates to the nucleus where it binds the transcription factor CBF1 (RBPJ-K), leading to the recruitment of transcriptional co-activators and the expression of Notch target genes (Furriols and Bray, 2001 ; Jarriault et al., 1 95).

There is strong qualitative evidence linking Notch signalling with keratinocyte differentiation in squamous tissues. In epidermal keratinocytes Notch activation both drives the differentiation of proliferating cells and regulates the later stages of terminal differentiation (Blanpain et al., 2006; Lowell et al., 2000; angarajan et al., 2001 ). In keeping with these findings, loss of Notch signalling is also associated with squamous carcinoma development in humans and mice (Lefort et al., 2007; Thelu et al., 2002) (Demehri et al., 2009; Nicolas et al., 2003). More recently, loss of Notch signalling has been reported to be associated with decreased expression of the terminal

differentiation marker filaggrin in murine esophagus, an increase in staining for the proliferation associated antigen Ki67 and loss of expression of Notch 3 in murine EE (Ohashi et al., 2010). However, the interpretation of this study is complicated as the transgenic ere strain used to inhibit cannonical Notch signalling by inducing a floxed allele of a dominant negative mastermind-like 1 protein (DNM) was active in all squamous tissues. Widespread loss of Notch signaling may lead to inflammation via the cytokine TSLP, so it is unclear whether the esophageal phenotype is due to cell autonomous effects of loss of Notch signalling, immune mediated effects or a combination of the two.

Collectively these results provide qualitative evidence for a role of Notch in EE progenitor cell fate. Here we investigate the effect of loss of Notch signalling in cells induced to express DNM at clonal density. This allows the effect of the mutation on cell fate†o be determined without the overlay of immune mediated effects. Quantitative analysis of clone size distributions reveals that the normal scaling behaviour of EE progenitors is lost, and gives new insights into a requirement for Notch in commitment to terminal differentiation. In the absence of Notch cells which would normally

differentiate and then stratify out of the basal cell layer re-enter the cell cycle demonstrating the existence of intermediate states in commitment in vivo. The effect of this alteration in fate is exponential clone expansion and the replacement of wild type EE with mutant cells.

Clonal analysis of DNM mice

For quantitative clonal analysis of a conditional ere induced mutation it is essential for expression of the clonal reporter to be linked directly to expression of the mutant protein, so that all clones which express the reporter are actually mutated. Qualitative studies often use a reporter targeted to a separate locus from the mutant allele, but the variable efficiency of ere recombinase at different loci may result in a clonal fate data set contaminated by a subset of clones positive for the reporter but negative for the mutation. To study the effects of losing Notch signalling we therefore opted to use a conditional transgenic strain (R26,IDNM) , in which a conditional dominant negative mutant allele of the transcriptional cofactor MAML 1 (DNM) was fused to EGFP and targeted to the Rosa26 locus downstream of a LoxP flanked "STOP" cassette. This construct inhibits Notch signalling by blocking activation of RBPJK dependent transcription by all four murine Notch genes, and phenocopies deletion of RBPJK (Maillard et al., 2008; Maillard et al., 2004) . Widespread expression of DNM in the epidermis results in the development of hyperkeratotic nodules, lesions resembling human actinic keratoses and SCC (Proweller et al., 2006). Importantly, epidermal DNM expression is readily dectable by staining for EGFP. An advantage of using a strain in which DNM is expressed from the Rosa26 locus is that it allows direct comparison with the conditional EYFP strain R26flEYFP, which we have used to characterise cell fate in normal esophagus (see Fig. 25) .

R26flDNM mice were crossed onto the AhcreERT strain, which we have characterised extensively generating animals doubly heterozygous for both alleles ((Kemp et al., 2004)) . In this transgenic line, ere transcription is driven from the Cyp l A l promoter which is inactive unless animals are treated with the xenobiotic pnapthoflavone (βΝΡ). Cre is also regulated post translationally by fusion to a tamoxifen regulated mutant oestrogen receptor. Simultaneous treatment with NF and tamoxifen results in cre activity in IFE: titrating the dose of induing drugs results in recombination of 1 in 500 to 1 in 1000 basal cells, permitting analysis of discrete clones.

A cohort of 8 week old animals was induced with NF and tamoxifen. Three animals culled at each of a range of time points from 3 to 10 days. Wholemounts of EE were prepared, stained for EGFP and imaged by confocal microscopy (Doupe et al., 2010). The number of basal cells and suprabasal cells in each of 100 clones per clones from at least 3 animals was recorded at each time point. In addition blood samples were taken to measure TSLP levels as a marker of potential systemic effects resulting from DNM expression (Demehri et al., 2009). There was no change in TSLP levels from baseline, indicating that clonal level induction had not triggered a systemic immune response and arguing that the effects on cell fate were due to the direct effect of DNM on progenitors.

The clone size distributions are shown in Fig. 26 (inset). The data is found to scale with time, demonstrated by all three data sets collapsing onto a common curve when the average number of basal cells per clone is plotted against the average clone size at that time point (Fig. 26 main figure). The probability of finding a clone of size n at time t, P_n(t), is thus P_n(t)=( l /<n(†)>)f(n/<n(†)>), where <n(t)> is the average size and f is a scaling function. This result means that the clonal evolution is resolvable and involves only one time scale, in this context the division rate of a single cell population of progenitors expressing the DNM protein.

Further analysis shows that the entire clone size data set is consistent with a model in which all progenitor cell divisions are asymmetric and generating cells which are either progenitors or cells with arrested differentiation (AD) (Fig. 27 A, B). The average cell division time of the mutant cells is 1 .5 days. The AD cells do not leave the basal layer, but revert back into cycle after a random length of time: the average time cells spend in the AD state is 15 days. This analysis argues that Notch signalling is required for irreversible commitment to terminal differentiation and points to existence of intermediate states between proliferation and terminal differentiation. These insights can only be gained from quantitative clonal analysis and highlight the utility of this approach in the investigation of the effects of a potentially oncogenic mutation on clonal fate. Strikingly, these can be uncovered by an alteration in normal scaling of clone size in data gathered from just nine mice over a two week time course. Thus the benefits of the invention are demonstrated.

Methods

The R26,IDNM and AhcreERt strains have been described. Doubly transgenic heterozygous mice were administered intraperitoneal doses of pnapthoflavone and Tamoxifen to induce recombination. Three animals were culled at each time point. Circulating TSLP levels were determined by ELISA, (R and D systems).

Immunostaining for EGFP was performed on esophageal whoiemounts, as described (Doupe et al., 2010).

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All publications mentioned in the above specification are herein incorporated by reference. Various modifications and variations of the described aspects and embodiments of the present invention will be apparent to those skilled in the art without departing from the scope of the present invention. Although the present invention has been described in connection with specific preferred embodiments, it should be understood that the invention as claimed should not be unduly limited to such specific embodiments. Indeed, various modifications of the described modes for carrying out the invention which are apparent to those skilled in the art are intended to be within the scope of the following claims.

CLAIMS

1. A method of analysing the homeostatic state of a population of cells, which includes the following steps:

a) label one or more cells in the population

b) incubate the cells for a time†

c) determine the clone size distribution of labelled cells at time†

d) determine if the clone size distribution of (c) conforms to the scaling form: ΡΛ = -ΑττΆη/(η(ί))), where

(»( )

Pn(t) is the probability of finding a surviving clone which has n progenitor cells at time t,

(n(t)) denotes the average number of dividing cells in surviving clones at time t and

wherein if the clone size distribution conforms to the scaling form above, the cells are identified as being in homeostatic balance; if the clone size distribution does not conform to the scaling form above, the cells are identified as not being in homeostatic balance.

2. A method according to claim 1 , further comprising

(e) determine if where λ, represents the cell turnover rate or if

(«( ) = Λ& wi†h λ the stem cell turnover rate, or if (»(')> = ^/ln(*

wherein if the cells follow _ , then they are identified as committed progenitor cells or three-dimensional stem cell population type; and

if the cells follow ~ †nen†nev are identified as one-dimensional stem cell population type; and

if fhe cells follow {n(^) ~ At / n(At) †nen†nev are identified as fwo-dimensional stem cell population type.

3. A method according to claim 2 further comprising

(f) determining whether cells are committed progenitor cells or three-dimensional stem cell population type cells by monitoring the non-universal short-time dependence.

4. A method of identifying a candidate modulator of cell proliferation, comprising

(i) providing at least a first and second population of cells, wherein the first population is contacted with the candidate modulator;

(ii) analysing the homeostatic balance of said populations of cells according to any of claims 1 to 3;

wherein a difference between the first and second populations of cells identifies the candidate modulator as a modulator of cell proliferation.

5. A method according to any preceding claim wherein the population of cells is comprised by an adult tissue.

6. A method according to claim 5 wherein the cells are selected from oesophagus cells, gut cells, or epidermal cells. 7. A method according to any preceding claim wherein the label is a genetically inheritable label.

8. A method according to claim 7 wherein the label comprises expression of a fluorescent protein induced by ere recombination.

9. A method according to claim 7 wherein the cells are mouse cells and wherein the genetically inheritable label is Lgr5creERT/Rosa26 LSL confetti.

10. A method according to claim 7 wherein the cells are mouse cells and wherein the genetically inheritable label is AhcreERt/Rosa26 LSL EYFP.

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