the identification of a stem cell in a tissue is a major challenge of pivotal importance .
being able to detect the stem cell population allows for powerful approaches to study cell differentiation dynamics by , for example , lineage tracing ( barker et  al . , 2007 , busch et  al . , 2015 ) .
additionally , it provides a first step toward ex  vivo propagation of primary stem cells in organoid cultures ( lancaster et  al . , 2013 , sato et  al . ,
2009 ) , important for applications in regenerative medicine . moreover , stem cell populations relevant for disease progression , such as cancer stem cells , are promising targets for therapeutic intervention .
stem cells are typically rare , which makes their discovery by traditional population - based assays very difficult . for example
, it took decades of dedicated research to define the population of hematopoietic stem cells ( hscs ) ( eaves , 2015 ) , but it remains an open question how much heterogeneity exists within this subpopulation of bone marrow cells ( wilson et  al . , 2015 ) .
similarly , the discovery of intestinal stem cells ( van der flier and clevers , 2009 ) took years of work , and heterogeneity within this compartment remains under debate ( buczacki et  al . , 2013 ) .
the recent availability of single - cell mrna sequencing methods allows profiling of healthy and diseased tissues with single - cell resolution ( grn et  al . , 2015 ,
, 2015 , patel et  al . , 2014 , paul et  al . , 2015 ,
the transcriptome of a cell can be interpreted as a fingerprint , revealing its identity . however , biological gene expression noise ( eldar and elowitz , 2010 , raj and van oudenaarden , 2008 ) and technical noise because of amplification of minute amounts of mrna from a single cell ( brennecke et  al . , 2013 ,
2014 ) affects the readout and makes it a challenge to discriminate cell types based on their transcriptome . by sequencing large numbers of randomly sampled single cells from a tissue
these inventories can be screened for cell types of particular interest , such as stem cells .
an obvious strategy for the identification of the stem cell is the derivation of a lineage tree from single - cell sequencing data .
however , transcriptomes of randomly sampled cells only represent a snapshot of the system , and temporal differentiation dynamics can not be directly derived .
however , if the system of interest comprises all differentiation stages , such as the intestinal epithelium or the bone marrow , then attempts can be made to infer a lineage tree by assembling single - cell transcriptomes in a pseudo - temporal order .
existing approaches assume a continuous temporal change of transcript levels to assemble differentiation trajectories ( bendall et  al . , 2014 ,
here we present a method to identify rare and abundant cell types of a system and use these cell type classifications to guide the inference of a lineage tree .
we investigate the general properties characterizing the position of a cell type within the lineage tree and identify the number of branches and the transcriptome uniformity of a cell type as features correlating with the degree of pluripotency .
we show that our approach successfully recovers the identity of the stem cell in the intestine and in the bone marrow , two systems with a well described stem cell population .
we then use our method to predict multipotent cell populations in the adult human pancreas .
to develop a robust approach for the inference of differentiation trajectories , we used a previously published dataset from a lineage tracing experiment comprising the progeny of lgr5-positive mouse intestinal stem cells ( grn et  al . , 2015 ) .
this system is ideal for testing the inference of differentiation dynamics because the lineage tree is already well characterized ( figure  1a ) .
the continuously self - renewing intestinal epithelium is arranged in crypts and villi , with a small number of lgr5 + stem cells , also known as crypt base columnar cells ( cbcs ) , residing near the crypt bottom .
these cbcs give rise to rapidly proliferating transit - amplifying ( ta ) cells that migrate upward along the crypt - villus axis and develop into the terminally differentiated cell types ( barker , 2014 , van der flier and clevers , 2009 ) .
although absorptive enterocytes constitute the most abundant cell type , the secretory lineage comprises rare cells , such as mucus - producing goblet cells , hormone - secreting enteroendocrine cells , and antimicrobial paneth cells . labeled cells were collected 5  days after label induction using an lgr5-creert2 construct and a rosa26-yfp reporter with a loxp - flanked transcriptional roadblock ( figure  1b ) .
we first improved the robustness of the initial clustering step of our previously developed raceid algorithm ( grn et  al . , 2015 ) by replacing the k - means clustering with k - medoids clustering ( figure  s1 ) .
second , we noticed that the previously used gap statistic ( tibshirani et  al . , 2001 ) was not ideal for determining the cluster number .
although increasing the number of clusters in many cases leads to a growing gap statistic , the decrease of the within - cluster dispersion ( tibshirani et  al . ,
, we thus determine the cluster number by identifying the saturation point of the within - cluster dispersion .
together , these two changes lead to a more robust initial clustering of raceid2 ( experimental procedures ; figure  s1 ) . for the intestinal lineage tracing data ( experimental procedures )
, raceid2 recovered a larger group of lgr5 + stem cells ( cluster 2 ) and early progeny ( clusters 1 and 8) as well as the major mature cell types ; i.e. , enterocytes ( cluster 3 ) , goblet ( clusters 4 and 19 ) , paneth ( clusters 5 and 6 ) , and enteroendocrine cells ( cluster 7 ) ( figures 1c and 1d ) .
these cell types could be unambiguously assigned based on the cluster - specific upregulation of marker genes inferred by raceid2 ( table s1 ) .
one of the major challenges for the inference of differentiation pathways in a system with multiple cell lineages is the determination of branching points . to overcome this problem , we predefined the topology of the lineage tree by allowing differentiation trajectories linking each pair of clusters .
a putative differentiation trajectory links the medoids of two clusters , and the ensemble of all inter - cluster links defines the possible topology of the lineage tree . to minimize the effect of technical noise and , at the same time , the computational burden
, we first reduce the dimensionality of the input space requiring maximal conservation of all point - to - point distances . in a second step ,
we assign each cell to its most likely position on a single inter - cluster link . to find this position ,
the vector connecting the medoid of a cluster to one of its cells is projected onto the links between the medoid of this and all remaining clusters , and the cell is assigned to the link with the longest projection after normalizing the length of each link to one .
the projection also defines the most likely position of the cell on the link ( figure  2a ) , reflecting its differentiation state ( experimental procedures ) . if this strategy is applied to the intestinal data , then only a subset of links is populated ( figure  2b ) . to determine links that are more highly populated than expected by chance and are therefore candidates for actual differentiation trajectories , we computed an enrichment p value based on comparison with a background distribution with randomized cell positions ( figure  2b ; figure  s2a ) .
furthermore , we reasoned that the coverage of a link by cells indicates how likely it is that this link represents an actual differentiation trajectory and not only biased perturbations driving the transcriptome of a given cluster preferentially toward the transcriptome of another cluster without leading to actual differentiation events .
we defined a link score as one minus the maximum difference between the positions of each pair of neighboring cells on the link after normalizing the length of each link to one ( figure  s2b ) .
if this score is close to one , then the link is densely covered with cells with only small gaps in between . if the link score is close to zero , the cell density is only concentrated near the cluster centers connected by this link .
the computationally inferred intestinal lineage tree is consistent with the known lineage tree ( figure  1a ) .
secretory cell types ( clusters 4 , 5 , 6 , and 7 ) populate individual branches emanating from the central lgr5 + cluster , and absorptive enterocytes ( cluster 3 ) differentiate from the same group via a more abundant group of ta cells ( cluster 1 ) .
we compared the inferred lineage tree to the tree predicted by monocle ( trapnell et  al . , 2014 )
, a recent method for the derivation of branched lineage trees that does not rely on a predefined tree topology , and found that monocle could not resolve the different branches of secretory cells ( figure  s2 ) .
more precisely , we try to identify , from the lineage tree , the cell population with the highest degree of multipotency .
we noticed that different cell types showed a variable number of populated links to other clusters . the link score is reflected by the thickness of the line in our graphical representation ( figure  2b ) .
we also show links with a low link score because they are informative about the associated cell state .
for example , a cell type with many low - scoring links can fluctuate toward a diversity of fate biases , whereas cell types with only a few links are much more canalized .
these two scenarios reflect a more promiscuous transcriptome , such as expected for stem cells , versus a more confined transcriptome , as expected for a mature cell type . in our data , cluster 2 , which contains cells positive for lgr5 and other established stem cell markers ( ascl2 and clca4 ) ( figure  2c ) , was the most highly connected cluster .
another putative property of stem cells is the tendency to exhibit a more uniform composition of the transcriptome in comparison with differentiated cells .
mature cell types frequently express a small number of genes at very high levels , crucial for cell type - specific functions .
the transcriptome of paneth cells , for instance , is dominated by high numbers of lysozymes and other host defense genes .
the uniformity of the transcriptome is reflected by shannon s entropy ( shannon , 1948 ) , and this concept has previously been applied to study cellular differentiation ( anavy et  al . , 2014 , banerji et  al . , 2013 , piras et  al . , 2014 ) ( experimental procedures ) .
we anticipate that the transcriptome of a multipotent cell type is more uniform in each individual cell .
in addition , multiple state biases could coexist within this population that can give rise to diverse mature cell types upon external stimuli , or stochastically , leading to high entropy ( banerji et  al . , 2013 , ridden et  al . , 2015 ) .
for the intestinal lineage tracing data , both paneth and goblet cells had clearly reduced entropy compared with lgr5-positive cells , whereas the entropy of enterocytes and enteroendocrine cells was comparable with stem cells ( figure  2d ) .
we found that , for all analyzed datasets ( see below ) , the number of links discriminates better between multipotent and differentiated cells when rescaled by the entropy .
therefore , the simplest score that performs well in discriminating multipotent cells from the remaining cell types was a product of the median entropy ( after subtracting the minimal entropy observed in the system ) and the number of links of a cluster ( experimental procedures ) .
this score exhibits a clear maximum for cluster 2 comprising the lgr5 + stem cells ( figure  2d ) .
we named our algorithm stemid for the lineage tree inference and the derivation of this score .
next we wanted to test whether stemid could identify lgr5 + cells in a larger and more complex dataset comprising intestinal cells of various independent experiments conducted in our lab . in this dataset , we combined 3  weeks and 8  weeks of lgr5 lineage tracing data .
a subset of those was enriched in secretory cells by fluorescence - activated cell sorting ( facs ) on cd24 ( van es et  al .
, we also sorted non - traced cd24 + control cells ( experimental procedures ; figure  s3 ) .
raceid2 revealed the known intestinal cell types within this dataset based on cluster - specific expression of known cell type marker genes and subdivided these into stages of differentiation or maturation ( figures 3a and 3b ; figure  s3a ) .
a full list of differentially expressed genes for each cluster is given in table s2 .
for example , intestinal stem cells in cluster 7 , marked by high expression of lgr5 and clca4 ( figure  3b ) , were connected directly to all secretory branches , whereas ta cells ( cluster 5 ) primarily give rise to enterocytes ( cluster 10 ) ( figure  3c ; figures s3c and s3d ) .
interestingly , we observed two distinct differentiation trajectories for paneth cells ( clusters 13 and 14 ) , one via a dll1-positive common precursor of paneth and goblet cells ( cluster 1 ) and another one directly connecting stem cells ( cluster 7 ) or ta cells in cluster 5 , marked by upregulation of the cell - cycle gene pcna , directly to the mature paneth cell clusters . both the dll1-dependent ( van es et  al . , 2012 ) and the direct route ( farin et  al .
, 2014 , sawada et  al . , 1991 ) , which was observed after ablation of paneth cells , have been described .
we were not able to recapitulate this finding with a minimum spanning tree - based alternative approach ( figure  s3e ) .
we then computed the stemid score and found that the lgr5+/clca4 + cells ( cluster 7 ) exhibit the highest score ( figure  3d ) .
the second highest score was observed for cluster 21 , which represents a common progenitor to paneth and goblet cells .
the ta cells in cluster 5 , which our lineage inference identifies as progenitors with an enterocyte fate bias , acquire the third - highest stemid score .
noticeably , paneth cells in cluster 13 and mature goblet cells in cluster 2 show the same connectivity as the stem and progenitor cells in clusters 7 , 5 , and 21 , but rescaling by entropy helps correctly assign a mature state to these cells ( figure  s3f ) . in conclusion
, stemid could identify intestinal stem cells and distinguish progenitor populations from more mature intestinal cell types . to test the performance of stemid in a different biological system
, we applied the algorithm to single - cell sequencing data of mouse bone marrow cells .
these cells were selected based on physical interactions between doublets or larger groups of cells  and are thus not sampled randomly from all cell types in  the bone marrow .
this dataset was complemented with kitsca-1lincd48cd150 hscs ( kiel et  al . , 2005 )
cell types identified by raceid2 were dominated by the myeloid lineage and comprised hscs , erythroblasts , megakaryocytes , two groups of granulocytes ( neutrophils and eosinophils ) , macrophages , a small group of b lymphocytes , and several clusters representing progenitor stages of the myeloid lineage ( figures 4a and 4b ; figure  s6a ) .
a full list of differentially expressed genes for each cluster is shown in table s3 .
cluster 1 comprises almost exclusively sorted hscs ( figure  s4b ) . the inferred lineage tree ( figure  4c ; figures s6c and s6d ) indicates that hscs differentiate into multipotent progenitor cells ( cluster 5 ) but are also directly linked to mature lineages .
hscs and multipotent progenitors are both linked to megakaryocytes ( cluster 4 ) , eosinophils ( clusters 10 and 29 ) , macrophages ( cluster 28 ) , and two branches covering a spectrum of progenitor and mature states of the neutrophil ( clusters 11 , 3 , 2 , 14 , 12 , and 22 ) and erythroid lineage ( clusters 9 , 8 , 7 , 6 , and 13 ) , respectively .
the b lymphocytes are only directly linked to the hscs , suggesting that cluster 5 represents a myeloid progenitor population , and no lymphoid progenitors were present in our sample .
the inferred lineage tree is therefore consistent with the existence of a common myeloid progenitor population giving rise to erythrocytes , megakaryocytes , granulocytes , and macrophages ( orkin and zon , 2008 ) .
stemid determines the highest score for cluster 1 and , therefore , correctly recovers hscs among all cell types in the mixture ( figure  4d ; figure  s6 ) .
the second - highest score discriminates the multipotent myeloid progenitors ( cluster 5 ) from the remaining cell types , and the third - highest score was assigned to the earliest progenitor of the erythroblast lineage .
therefore , the level of multipotency also correlates with the stemid score of bone marrow - derived cells .
the high connectivity of cluster 1 provides evidence for early fate biases already in hscs .
moreover , the high entropy of hscs reflects a more uniform transcriptome in individual cells of this population .
the entropy distribution across all cells in this cluster is shifted in comparison with all other groups ( figure  5a ) . in general , the inter - cluster variability substantially exceeds the intra - cluster variability .
the narrow entropy distribution of cluster 1 also rules out a strong dependence on the cell cycle .
however , we also observed that 54 of the 276 hscs ( 20% ) show distinct fate biases , revealed by low expression of lineage - specific marker genes ( figure  5b ) , a finding that is consistent with a recent report based on lineage tracing ( peri et  al . , 2015 ) . because the sensitivity of single - cell sequencing is limited , this number is almost certainly an underestimation .
we note that most hscs ( 112 of 276 ) are assigned to the link with the multipotent progenitor ( cluster 5 ) .
we can not address whether the observed fate bias persists during differentiation or whether stochastic switching between distinct cell fates occurs during differentiation .
our observation is also consistent with a recent single - cell transcriptome analysis showing an unexpected heterogeneity of myeloid progenitor cell populations and suggests the existence of an early cell fate bias ( paul et  al . , 2015 ) .
we observe very similar sets of marker genes , as found in this study , but our lineage inference permits an analysis of the temporal dynamics of gene expression . as an example , we extracted all cells from the neutrophil branch ( clusters 1 , 11 , 3 , 2 , and 12 ) in pseudo - temporal order derived from the projection coordinates and clustered temporal expression profiles by using self - organizing maps ( experimental procedures ) .
a z - score of gene expression values along this trajectory reveals that the raceid2 clusters represent sets of cells with common modules of co - expressed genes and that gene expression within these modules changes smoothly over time ( figure  5c ) .
although ribosomal protein - encoding genes and other components of the translational machinery slowly decline during differentiation , other genes are transiently switched on in progenitor populations ( e.g. , elane ) or immature neutrophils ( e.g. , ngp ) or only upregulated in mature cells ( e.g. , retnlg ) .
finally , we note that the identification of the hsc population by stemid is robust to changing the contribution of this population to the mixed sample .
for example , when only ten hscs are randomly selected and all others are discarded from the dataset , stemid still assigns the highest score to the small hsc cluster ( data not shown ) . in summary
, stemid could successfully identify the stem cell type in a complex mixture of cells isolated from bone marrow .
the inferred lineage tree recovered known trajectories but suggested an early cell fate bias present already in hscs .
after having demonstrated that stemid can robustly identify the stem cell population in two distinct biological systems , we applied the algorithm to predict multipotent cell populations in a less characterized system : the human pancreas .
the pancreas consists of acinar cells that produce the digestive enzymes , ductal cells secreting bicarbonate to neutralize stomach acidity , and hormone - producing endocrine cells that regulate hormone metabolism ( jennings et  al . , 2015 ) .
it is unclear which multipotent cells maintain pancreatic homeostasis and can give rise to different mature cell types during regeneration upon injury .
although early studies have suggested that , in humans , these cell populations could reside within the exocrine compartment or that dedifferentiation of exocrine cells could give rise to endocrine cells ( bonner - weir et  al .
2015 ) , the identity of multipotent cell populations is still unclear ( jiang and morahan , 2014 ) .
we sequenced pancreatic cells from human donors ( experimental procedures ) , and application of raceid2 revealed all major cell types , including different subpopulations of acinar and ductal cells ; hormone - producing  ,  ,  , and pancreatic polypeptide producing ( pp ) cells ; and stellate cells ( figures 6a and 6b ; figures s5a and s5b ) .
a full list of differentially expressed genes for each cluster is shown in table s4 .
in particular , we discovered novel subpopulations of ductal cells . in one of these groups ( cluster 14 ) ,
the cell surface glycoprotein ceacam6 was significantly upregulated ( p  < 0.01 ; experimental procedures ) , whereas components of the ferritin protein ( fth1 , ftl ) , which is the major intracellular iron storage protein , were significantly upregulated ( p  < 0.01 ; experimental procedures ) in the other group ( cluster 4 ) ( figure  6c ) . the inferred lineage tree assigns a central position to the ductal cells ( figure  6d ; figures s7c 
distinct subtypes of ductal cells appear to give rise to different endocrine sub - types and acinar cells .
although differentiation trajectories link cluster 4 to acinar , pp , and  cells , cluster 14 is linked to  and  cells .
consistently , clusters 4 and 14 acquire the highest stemid score , indicating the highest level of multipotency among the cell types detected in this system ( figure  6e ; figure  s7f ) . the following ranks of the stemid score were occupied by other ductal sub - types and precursor cells that give rise to two sub - states of acinar cells .
interestingly , cluster 4 also directly connects to stellate cells . upon injury , these cells can switch to an activated state and migrate to the injured location to participate in tissue repair ( omary et  al .
, 2007 ) . to collect further evidence that cluster 4 is an endocrine progenitor cell , we plotted the expression of the cluster 4 marker fth1 and the  cell marker insulin ( ins ) in single cells residing on the differentiation trajectory connecting these two cell types .
the genes exhibited smooth , anti - correlated gradients suggestive of a continuous transition between these two cell types ( figure  6f ) . to independently validate this observation , we performed antibody staining against insulin and ftl in human pancreatic tissue sections .
we were able to detect individual cells co - expressing insulin and ftl within ductal structures , confirming the existence of cluster 4 cells ( figure  7a ) .
co - staining of glucagon revealed that these cells specifically produce insulin and not glucagon ( figure  7b ) , as suggested by our analysis ( figure  6c ) .
our results indicate that the ferritin - positive sub - population of ductal cells might differentiate into mature  cells .
in this study , we present an approach to identify stem cells using single - cell transcriptomics data . because the physiological state of a cell is an approximate reflection of its transcriptome , it is a reasonable assumption that cell types can be discriminated based on their transcriptome .
however , determining the stem cell identity among all rare cell types discovered also requires the derivation of a lineage tree . to address this task , we combined cell type identification by raceid2 with a tree reconstruction by guided topology .
we first introduce an improved version of our previous raceid algorithm ( grn et  al . , 2015 ) with a more robust initial clustering step .
the replacement of k - means by k - medoids leads to increased robustness of clustering for all datasets analyzed in the paper . for the complex intestinal dataset ( figure  3 ) ,
the fraction of clusters with jaccard s similarity of > 0.7 is 40% for k - means versus 73% for k - medoids .
the corresponding fractions are 58% versus 83% for the bone marrow data and 40% versus 90% for the pancreas data . to infer differentiation trajectories , we assign every cell onto a specific link between its cluster of origin and another cluster based on the longest projection of the vector connecting the cluster center with the cell position onto these links .
this adequately reflects how much a cell has moved from the most representative cell state in the same cluster ( the medoid ) toward another cell identity ( or vice versa ) .
if significantly more cells reside on a link than expected by chance , this provides strong evidence that cells of the cluster of origin exhibit a pronounced transcriptome bias toward another cell fate .
in addition , if a continuum of cell states covers a given link , as evidenced by a high link score , then this link represents a strong candidate for an actual differentiation trajectory .
significant links with reduced link scores , on the other hand , indicate plasticity of the connected cell types in a sense that the transcriptome of a cell type can , to some extent , fluctuate toward another fate .
the quality of our lineage inference is supported by the recovery of known differentiation trajectories in the intestinal epithelium and the bone marrow .
remarkably , we recovered a rare alternative differentiation pathway where lgr5 + cells differentiate directly into paneth cells without intermediate dll1 + progenitors ( farin et  al .
we could also show , for the intestinal and the bone marrow data , that stemid infers a lineage tree with substantially higher resolution in comparison with methods published previously ( haghverdi et  al .
, 2015 , trapnell et  al . , 2014 ; figure  s6 ) .
the derived lineage tree for the bone marrow suggested that , in contrast to the classical view of dichotomous differentiation via a hierarchy of increasingly restricted progenitor populations ( giebel and punzel , 2008 ) , a cell fate bias already exists at stages as early as the hsc stage ( figure  5b ) .
this observation is consistent with a recent single - cell transcriptome analysis revealing heterogeneity of the common myeloid progenitor cell population , indicating early fate bias ( paul et  al . , 2015 ) .
moreover , direct generation of progenitors restricted to the myeloid fate from mouse hscs has been described in the past ( yamamoto et  al . , 2013 ) , and the existence of unipotent cells within human hscs ( notta et  al . , 2016 ) and
classically defined mouse multipotent progenitor populations was shown recently ( peri et  al . , 2015 ) .
for both model systems , the stemid score , which quantifies very general properties of a cell type ( i.e. , the number of links and the entropy of the transcriptome ) , ranks raceid2-predicted cell types by their level of multipotency .
lgr5 + cbcs and sorted hscs acquire the highest score among all cell types of the intestine and bone marrow , respectively , demonstrating the performance of our algorithm .
we could further demonstrate the performance of stemid on two previously published datasets ( figure  s7 ) for cells from developing lung epithelium ( treutlein et  al . , 2014 ) and differentiating human radial glial cells ( pollen et  al . , 2015 ) .
potential problems for the stemid algorithm arise in the absence of intermediate progenitors or the occurrence of unrelated cell types . in the absence of intermediate progenitors , stemid infers a link to a more multipotent population . for example ,
it is known that a spectrum of progenitors will reside on this trajectory , and , as we have observed for the other lineages , an early fate bias toward lymphocytes could exist in hscs . in the absence of intermediate progenitors ,
a link to a more multipotent population reflects all information on the lineage relationship that can be extracted from the data .
if the stem cell itself is missing from the sample , stemid will identify the cell type with the highest level of multipotency .
the presence of unrelated cell types in the mixture could lead to false positive links .
however , because the feature space is high - dimensional , it is likely that none of the links between an unrelated cell type and the remaining lineage tree will be significantly populated .
we also argue that links of mature cell types to related progenitor or stem cell populations were identified with high specificity ( oftentimes only a single link in line with previous findings was detected ) .
this makes the occurrence of significant links between unrelated cell types unlikely . finally , we used stemid to screen human adult pancreatic cells for multipotent cell populations .
it is unclear which adult pancreatic cell types can give rise to the different mature pancreatic lineages during normal tissue turnover or regeneration .
although initial evidence suggested that multipotent cells within the ductal compartment could differentiate into endocrine cells both in humans and mice ( jiang and morahan , 2014 ) , subsequent lineage - tracing experiments produced contradictory results .
although mouse lineage tracing of carbonic anhydrase ii ( ca2)-positive ductal cells revealed that these cells give rise to  cells upon injury ( bonner - weir et  al . , 2008 ) , lineage tracing of sox9- , muc1- , or hnf1-positive cells could not confirm this finding ( furuyama et  al .
, 2011 , kopinke and murtaugh , 2010 , kopp et  al . , 2011 , solar et  al . , 2009 ) .
using stemid , we were able to predict distinct sub - populations of ductal cells with varying differentiation potential . although ductal cells marked by high levels of ceacam6 are predicted to differentiate into  ,  , and pp cells , another sub - population expressing high levels of the ferritin complex primarily appears to give rise to  cells and acinar cells .
we note that the latter sub - population does not express any of the markers used in previous lineage - tracing experiments , but we caution that expression of these genes might be too low to be reliably detected by single - cell mrna sequencing .
we further remark that  cell differentiation in the adult pancreas might not be conserved between human and mouse .
we provide the well documented r source code for raceid2 and the stemid algorithm at https://github.com/dgrun/stemid .
we hope that stemid will be useful for a better understanding of differentiation dynamics in a variety of systems .
for lineage - tracing experiments , we injected 0.4  mg tamoxifen into 3-month - old lgr5-creert2 c57bl6/j mice bred to rosa26lsl - yfp reporter mice .
crypts were isolated from mice as described previously ( sato et  al . , 2009 ) .
pancreatic cadaveric tissue was procured from a multiorgan donor program and only used when the pancreas could not be used for clinical pancreas or islet transplantation , according to national laws , and when research consent was present .
human islet isolations were performed in the islet isolation facility of the leiden university medical center according to a modified protocol originally described by ricordi et  al .
pancreatic tissue samples were fixed overnight in 4% formaldehyde ( klinipath ) , stored in 70% ethanol , and subsequently embedded in paraffin .
after deparaffinization and rehydration in xylene and ethanol , respectively , antigen retrieval was performed in citric buffer for 20  min .
primary antibodies were rabbit anti - ftl ( ab69090 ) , mouse anti - glucagon ( ab10988 ) , and guinea pig anti - insulin ( ab7842 ) .
alexa fluor - conjugated secondary antibodies against rabbit , mouse , and guinea pig immunoglobulin g ( igg ) ( life technologies ; a11008 , a10037 , and a21450 ) were used at a dilution of 1:200 .
nuclear counterstaining was done by embedding with dapi vectashield ( vector laboratories , h-1500 ) .
we used c57bl/6 female or male mice from 23 to 52  weeks bred in our facility .
experimental procedures were approved by the dier experimenten commissie of the royal netherlands academy of arts and sciences and performed according to the guidelines .
bone marrow was isolated from femur and tibia by flushing hank s balanced salt solution ( hbss , invitrogen ) without calcium or magnesium , supplemented with 1% heat - inactivated fetal calf serum ( fcs ) ( sigma ) .
the protocol was carried out as described previously ( grn et  al . , 2015 ) .
read mapping and quantification were done as described previously ( grn et  al . , 2015 ) .
the algorithm and follow - up analyses are described in full detail in the supplemental experimental procedures .
d.g . and a.v.o . conceived the study . d.g . developed the algorithm and performed all computational analyses .
single - cell sequencing of pancreatic cells and antibody staining were performed by m.j.m with the help of g.d .
single - cell sequencing of intestinal cells was performed by k.w . with the help of a.l .
 summaryadult mitotic tissues like the intestine , skin , and blood undergo constant turnover throughout the life of an organism . knowing the identity of the stem cell is crucial to understanding tissue homeostasis and its aberrations upon disease . here 
 we present a computational method for the derivation of a lineage tree from single - cell transcriptome data . by exploiting the tree topology and the transcriptome composition , 
 we establish stemid , an algorithm for identifying stem cells among all detectable cell types within a population . 
 we demonstrate that stemid recovers two known adult stem cell populations , lgr5 + cells in the small intestine and hematopoietic stem cells in the bone marrow . 
 we apply stemid to predict candidate multipotent cell populations in the human pancreas , a tissue with largely uncharacterized turnover dynamics . 
 we hope that stemid will accelerate the search for novel stem cells by providing concrete markers for biological follow - up and validation . 
Introduction
Results
Discussion
Experimental Procedures
Author Contributions