Mutations are an inevitable consequence of cell division. Similarly to how DNA sequence differences allow inferring evolutionary relationships between organisms, we and others have recently demonstrated how somatic mutations may be exploited for phylogenetically reconstructing lineages of individual cells during development in multicellular organisms. However, a problem with such “phylogenetic fate maps” is that they cannot be verified experimentally; distinguishing actual lineages within clonal populations requires direct observation of cell growth, as was used to construct the fate map of Caenorhabditis elegans, but is not possible in higher organisms. Here we employ computer simulation of mitotic cell division to determine how factors such as the quantity of cells, mutation rate, and the number of examined marker sequences contribute to fidelity of phylogenetic fate maps and to explore statistical methods for assessing accuracy. To experimentally evaluate these factors, as well as for the purpose of investigating the developmental origins of connective tissue, we have produced a lineage map of fibroblasts harvested from various organs of an adult mouse. Statistical analysis demonstrates that the inferred relationships between cells in the phylogenetic fate map reflect biological information regarding the origin of fibroblasts and is suggestive of cell migration during mesenchymal development.
A goal of biology addresses how the fertilized egg, through a limited repertoire of cell division, cell migration, and cell death, develops into an organism composed of many cells of different types. Among the best tools for investigating this question are “fate maps.” Fate maps depict what each part of the embryo eventually becomes and, conversely, allow for backward tracing of cell lineage at later stages of development (Clarke and Tickle 1999; Stern and Fraser 2001).
Most famously, Sulston et al. (1983) used a microscope to painstakingly map the fate of all of the cells of Caenorhabditis elegans—an accomplishment facilitated by the worm's transparency, brief embryogenesis, and limited number of cells. For more complex organisms, whose development cannot be so easily monitored, lineage studies have relied on marking cells with dyes (Honig and Hume 1989) or genetic reporters (Eloy-Trinquet et al. 2000; Zong et al. 2005), so that progeny of particular cells become identifiable later on. This approach reveals which cells are descended from a common progenitor, but cannot distinguish how those cells are related to one another, because, for a clone of even just a few cells, there is a nearly uncountable number of possible pedigrees (Salipante and Horwitz 2007). Thus, cell marking studies in higher organisms cannot discriminate cell lineage in the same way as has the fate map based on direct observation of cell division that has proven so useful for understanding development in the worm (Sulston 2003).
To overcome this obstacle, we (Salipante and Horwitz 2006) and Frumkin et al. (2005) have recently proposed an approach to mapping lineages that we have termed “phylogenetic fate mapping,” on the basis of retrospectively deciphering the order of mutations accumulating in individual cells as they divide. (A related approach has tracked cellular ancestry via changes in DNA methylation (Kim and Shibata 2004; Kim et al. 2005; Wu and Guo 2008). In principle, fate maps can be likened to a “tree of life,” where the origin of each cell traces back through its progenitors to the fertilized egg. Because DNA replication occurring during cell division inevitably introduces errors, the genome of one cell likely contains unique differences that distinguish it from other cells (Drake et al. 1998), thus offering a record of cellular lineage in which cells with the most closely related patterns of mutation share the most recent common ancestry. If it were possible to sequence the genome of individual cells in a multicellular organism, then it would be possible to reconstruct each cell's lineage with the use of phylogenetic (or similar) algorithms, in the same way that comparing DNA sequences between different species has allowed for inferring evolutionary history (Felsenstein 1988).
It is not yet possible to sequence the genome of individual cells, but we previously demonstrated (Salipante and Horwitz 2006) that examination of a few dozen polyguanine repeat sequences—abundant throughout the genome and particularly vulnerable to mitotic mutations altering their length—could be used phylogenetically to reconstruct an artificial lineage of mouse fibroblasts cultured over several months time and also to generate a “proof-of-principle” fate map of single cells harvested from a mouse. Frumkin et al. (2005) performed similar experiments, cataloging length-altering mutations among a variety of short tandem repeat (“microsatellite”) DNA sequences, to reconstruct the lineage of cultured human cancer cells.
A problem with fate maps, in general, is that, short of observational studies possible only in simple organisms like the worm, there is no “gold standard” for determining actual lineages in higher organisms, so appropriate methods need to be developed for evaluating accuracy of phylogenetic fate maps. Here we employ computer modeling of somatic cell division to identify factors influencing the fidelity of phylogenetic fate maps and to establish statistical methods for evaluating their accuracy. To test conclusions drawn from these simulations, and also to explore the developmental origins of mesenchymal lineages, we have additionally constructed a phylogenetic fate map of fibroblasts taken from various anatomical locations from an adult mouse.
MATERIALS AND METHODS
We performed initial, exploratory analyses using the neighbor-joining method as implemented in SplitsTree4 (Huson 1998), or the Bayesian method without ordered character states as implemented in MrBayes 3.1.1 software (Ronquist and Huelsenbeck 2003), as previously described (Salipante and Horwitz 2006), but with the allcompat (strict consensus) option selected. When running the standard discrete evolutionary model, the Bayesian algorithm uses four priors. The “statefreq” and “shape” priors define the probability of transition between particular mutation states, and were set to default parameters, resulting in an equal probability of transition between all states. The final two priors, “topology” and “brlens,” constrain the simulation to specific topologies and branch lengths, respectively. Again, we selected default parameters, placing no constraints for either of these priors. For all subsequent analyses, the Bayesian method was used. All Bayesian phylogenies were calculated from at least 200 trees after convergence had been reached, as defined by the diagnostic average standard deviation of split frequencies between the two parallel runs falling below 0.02. Trees were edited with MEGA 3.1 (Kumar et al. 2004) for clarity. The scale bar of the experimental phylogenetic reconstruction was converted into “number of cell divisions” by dividing by the average mutation frequency of an allele per mitosis, assuming the same estimated mutation rate of cultured mouse fibroblasts (Salipante and Horwitz 2006).
SiMouse is a Perl script based on the EvolveAGene program (Hall 2005). SiMouse simulates mitotic error during division of diploid mouse cells and is available upon request from the authors. The program accepts a user-defined series of tract lengths for autosomal mononucleotide repeat markers and assigns this genotype as the “root” of the phylogeny. The user also selects the number of cells to be produced in the final lineage tree and the average branch length (the average number of mutations between nodes).
The program creates a bifurcating phylogeny with random topology, utilizing the following assumptions:
Cells have an equal probability of becoming quiescent or continuing to divide, with branch lengths either set to one or permitted to vary from between one to twice the user-selected value.
The user defines a mean mutation rate and its standard deviation, and the program assigns a relative mutation frequency for each locus by sampling from a corresponding normal distribution. We set the mean mutation rate to 4.1 × 10−3 and the standard deviation to 3.3 × 10−3 per allele, on the basis of values that we previously quantified for polyguanine mononucleotide repeat tracts in mouse cells. (Salipante and Horwitz 2006).
Each marker mutates independently. Beginning with the root sequence at the base of the phylogeny, the program mutates sequences at each node, introducing mutations at particular markers at the designated mutation frequencies.
The type of mutation is modeled after experimental observation of the behavior of mononucleotide repeats. For each mutation that is introduced, the size of the change in tract length is proportional to those observed for mouse cells [probability of a single-base change = 0.66, probability of a two-base change = 0.34 (Boyer et al. 2002)].
When a mutation does occur, there is an equal probability that a repeat tract will expand or contract.
The simulated genotypes for each cell in the phylogeny are recorded in a tab-delineated output file.
Our experimental studies rely on fragment-length polymorphism genotyping, by which it is not possible to associate an autosomal allele with a particular genotype signal. Therefore, if mutational events affect different alleles but result in repeat sequences that are of the same length, the genotyping products would be indistinguishable from one another. To account for this limitation, we assume that the fewest number of mutations possible have occurred, in other words, that all identical genotypes are the result of the same mutational event. We have correspondingly made the same assumptions of parsimony when preparing the simulated data for analysis.
For all simulations, we used an input file containing 126 diploid markers, half of which were homozygous, and half of which were heterozygous, with the alleles separated by 1 bp in length. We executed data simulations under three different conditions and for each condition simulated three independent lineages. Thus, a total of three phylogenetic reconstructions were performed for trees containing 126 markers and six reconstructions for all other numbers of markers:
Variable number of markers and variable number of mutations per branch. We simulated lineages containing 32 cells with average branch lengths of 1, 1.5, 6, 13, or 19. All 126 markers, or pairs of 63, 50, 40, 30, 20, or 10 markers were randomly sampled without replacement from each simulation and used to produce phylogenetic fate maps of the simulated cells. The number of mutations per marker per branch is a product of the mutation rate of cells and the number of cell divisions which have occurred per branch, and we therefore interpreted our results with respect to both of those variables. The “branch-length” scale was converted to number of cell divisions by (average branch length)/(average mutation rate per locus × number of markers), where the mutation rate was 8.2 × 10−3 per cell division and the number of markers was 126. Similarly, the branch-length scale was converted to “relative mutation rate” by (average branch length/(number of cell divisions per branch × number of markers))/(average mutation rate per locus), where the number of cell divisions per branch was set to three and other variables were the same as before.
Variable number of markers and variable number of cells. We ran simulations with an average branch length of six and containing 16, 32, 64, or 128 cells in the lineage. All 126 markers, or pairs of 63, 50, 40, 30, 20, or 10 markers, were randomly sampled without replacement from each simulation and used to produce phylogenetic fate maps of the simulated cells.
Randomly sampled cells from a larger data set. We simulated lineages containing 256 cells with an average branch length of 1.5. For each of the three simulations, all 256 cells, or a subset of 16, 32, 64, or 128 cells, were randomly sampled without replacement. For each sampling of cells, all 63, 50, 40, 30, 20, or 10 markers were randomly sampled without replacement from each simulation and used to produce phylogenetic fate maps.
Bayesian phylogenetic reconstructions were performed as described, and we evaluated accuracy by quantitatively scoring each inferred cell lineage tree for topological similarity to the known phylogeny using a pairwise tree-comparison algorithm (Nye et al. 2006). Because spurious, unassociated similarities in a data set artifactually result in some baseline degree of topological similarity between even randomly generated trees, we found it necessary to rescale the experimental topological similarity scores. We obtained a baseline topological percentage similarity by randomizing data sets containing an appropriate number of cells for each condition tested (in which the number of cells, but not the number of markers examined, was found to influence the baseline topological similarity score), where randomization of data was accomplished by randomly assigning genotypes at each locus to cells other than their place of origin. We then created phylogenetic trees from the scrambled data and calculated their topological percentage similarity to the true tree as before, to determine the baseline topological similarity. Percentage accuracy of phylogenetic reconstructions was calculated by [(percentage of similarity between known tree and inferred tree − baseline percentage of similarity)/(100 − baseline percentage of similarity)] × 100. We synthesized a total of 56 trees from randomly scrambled data and used the mean topological similarity for the baseline.
For visualization purposes, three-dimensional functions were fitted to data by the lowest sum of the squared absolute errors method as implemented by a specialized algorithm (http://zunzun.com), and functions were modeled using the R statistical computing language and environment (http://www.r-project.org).
Statistical methods for determining accuracy:
We evaluated statistical methods for estimating phylogenetic fate map accuracy using data simulations and phylogenetic reconstructions from lineage simulation condition 1.
To evaluate Bayesian posterior probability as an estimator of accuracy, we quantified how well the posterior probabilities of clades on an inferred lineage correlate with the frequency that those clades exist on the actual lineage. The fraction of clades within given deciles of posterior probability values that were present in the known phylogeny was quantified using a specialized Perl script. All phylogenetic reconstructions were used for the analysis.
To evaluate delete-half jackknifing as an estimator of accuracy, we determined how the degree of topological similarity between pairs of jackknifed trees corresponds to the degree of similarity between trees containing twice as many markers and the known tree. Topological similarity between trees was determined using a pairwise tree-comparison algorithm (Nye et al. 2006) and rescaled as described above.
Heart, lungs, spleen, kidneys, biceps, and quadriceps of an adult 129X1/SVJ mouse were freshly harvested. Tissues were roughly minced with a scalpel, forced through sterile 40-mesh tissue dissociation screens (Sigma, St. Louis), and incubated in a tissue culture plate containing 1 ml 0.25% trypsin/1 mm EDTA solution (GIBCO, Grand Island, NY) at 37° in 5% CO2 for 30 min. After incubation, plates were washed with 1 ml normal media [DMEM/10% FBS with penicillin (100 IU/ml) and streptomycin (100 μg/ml)], transferred to sterile microcentrifuge tubes, and centrifuged at 420 × g for 10 min. The pellets were resuspended in normal media and transferred at a clonal dilution to culture plates for the first phase clonal expansion. After eight to nine doublings had occurred, fibroblast colonies were examined by phase contrast microscopy for appropriate histology and were exposed to 0.25% trypsin/1 mm EDTA solution. Colonies used for internal controls (heart 1, heart 2, and heart 3) were each transferred to two wells of a six-well culture dish and grown as separate cultures (A and B), and all other isolates were transferred to a single six-well culture dish. Cells were propagated for an additional two to six doublings and were then harvested for DNA using the QIAamp DNA micro kit (QIAGEN, Valencia CA).
Estimation of experimental fate map phylogeny:
For jackknifing analysis, four sets of paired trees were produced by randomly sampling 43 markers without replacement from the full panel of 87 markers. The topological agreement between trees was determined and rescaled as described above. For Bayesian posterior probability regression analysis, all 87 markers or subsets of 83, 80, 77, 73, 70, 67, 63, or 60 markers were randomly sampled and used to produce Bayesian phylogenetic reconstructions. Nine random samplings were taken for each condition, and the average posterior probability for all branches on the trees was calculated. Both jackknifing and posterior probability analyses were performed using genotype data for all cells.
Oligonucleotides (purchased from ABI for NED-labeled primers and Operon for all other labels) are listed in supplemental Table 1 at http://www.genetics.org/supplemental/. All reverse primers carried the “pigtail” sequence 5′-GTTTCTT-3′, which has been shown to prevent genotyping artifacts due to the terminal deoxynucleotidyl transferase activity of Taq DNA polymerase (Brownstein et al. 1996). Five-microliter PCR amplifications containing 9 ng genomic DNA each were carried out for 42 cycles using Taq DNA polymerase (QIAGEN), and PCR fragments were resolved with an ABI PRISM 3100 genetic analyzer. All genotypes were repeated in triplicate. Electropherograms were initially processed with ABI GeneScan Analysis 3.7 and Genotyper software before analysis using the PeakSeeker program (J. M. Thompson and S. J. Salipante, unpublished results, source code available on request). All genotype calls were manually confirmed prior to phylogenetic reconstruction.
Factors influencing accuracy of phylogenetic fate maps:
The accuracy of conventional phylogenetic reconstructions based on DNA or protein sequences is a function of the number of taxa, the amount of sequence information available from each taxon, and the number of mutations separating one taxon from another (Hall 2005; Rokas and Carroll 2005). In contrast to traditional phylogenetics, where these parameters are largely inherent to evolutionary history, for phylogenetic fate maps, most factors are under experimental control; the number of taxa corresponds to the number of cells chosen for analysis. DNA sequence information comes in the form of microsatellite repeat markers, which are so abundant throughout the genome that as many as necessary can be chosen for analysis. The mitotic mutation frequency could, at least in principle, be regulated by conducting studies with organisms genetically predisposed to mutation or exposed to mutagens. To understand how the number of markers, cells, and mutations influence accuracy of phylogenetic fate maps, we initially performed computer simulations with synthetically generated lineages.
We created a program modeling mitotic mutation of autosomal marker sequences on the basis of parameters experimentally observed for polyguanine tracts in mouse cells (Boyer et al. 2002; Salipante and Horwitz 2006). The user specifies the number of cells, the mean number of mutations per branch of the tree, and the mutation frequency; the program generates lineage trees while correspondingly modeling the evolution of marker genotypes.
We first determined which of two commonly used phylogenetic algorithms (Hall 2005), the Bayesian or the neighbor-joining method, more faithfully reconstructs computer-modeled cell lineage trees. The Bayesian method is a character-based approach that infers the most likely population of phylogenetic relationships by maximizing those relationships with respect to an evolutionary model, whereas the neighbor-joining method establishes relationships by algorithmically quantifying the fraction of differences between taxa. We produced phylogenetic fate maps of simulated genotype data using both approaches and compared deduced trees to the actual lineage. Although the two performed nearly equally well under most conditions, the Bayesian method proved more accurate than neighbor joining in reconstructing trees involving lower numbers of mutations per branch (not shown), in agreement with our earlier studies analyzing lineages of cultured cells (Salipante and Horwitz 2006). We therefore performed fate map reconstructions using the Bayesian method.
Next, we estimated how many polyguanine markers are needed to construct accurate phylogenetic fate maps. In our model, we set the rate of length-altering mutation of polyguanine markers at 8.2 × 10−3 per cell division, on the basis of our previous studies of cultured mouse fibroblasts (Salipante and Horwitz 2006). In Figure 1A, we have plotted accuracy as a function of the number of markers genotyped and the mean number of cell divisions for each branch of the lineage tree. The height of the surface plot represents how well phylogenetic reconstructions agree with the actual lineage tree. As might be expected, adding more markers improves accuracy, and, with enough markers, accuracy reaches 100%. The highest possible resolution for a fate map is one in which the sampled cells are separated by just a single mitosis, and, by extrapolating from our modeling studies, we predict that to produce a perfect map at this level of resolution would require 300 markers, whereas only 170 markers should be needed to generate a map with 90% accuracy.
We then determined how mutation rate influences accuracy of an inferred lineage. In Figure 1B we have plotted accuracy as a function of the number of markers genotyped (where we have set the mean number of mitoses per branch equal to three). At a mutation frequency about four times greater than what we actually observed in cultured fibroblasts, the plot shows that further increases in mutation rate offer relatively minimal improvement in accuracy. However, varying the mean number of mitoses per branch of the tree also affects how mutation rate influences accuracy. At the highest possible resolution (not shown), corresponding to just one cell division for each branch of the tree, the inflection point (after which little gain in accuracy comes from further increases in mutation rate) corresponds to a mutation rate of ∼12 times what we experimentally observed in cultured fibroblasts. In contrast, for a tree with an average of 13 cell divisions per branch (not shown), the experimentally observed mutation rate coincides with the inflection point relating accuracy to mutation rate. In general, a higher mutation frequency facilitates construction of a higher resolution fate map, but, depending upon the desired resolution, there is also an optimally efficient mutation frequency, beyond which limited gains in accuracy are attained.
A potential issue concerns revertant and parallel mutations. In the first case, a marker may appear “wild type” but has actually undergone at least two mutations, where the final mutation has changed the marker back to its initial state. In the second case, two markers may have arrived at identical states, but are unrelated through common descent. Our data simulation model allows for an equal probability of expansion or contraction of markers; thus, simulated data sets contain both reversion and parallel mutations, and it is expected that such mutations will occur in experimental cell lineage trees, as well. To address the effects of reversion and parallel mutation, we performed additional simulations of cell lineage trees under conditions where reversion mutations and parallel mutation are not allowed and determined how well reconstructions of those lineage trees compared with the known tree. Comparing these simulations to results obtained for lineages simulated under our usual model (not shown), no difference was observed in the accuracy of the reconstructed trees (P = 0.675), indicating that the inability to distinguish parallel and reversion mutations from stepwise mutations does not significantly impact the quality of phylogenetic fate map reconstruction.
We then modeled varying the total number of cells but found that it had no effect on accuracy (Figure 1C). We conclude that our simulations are likely applicable to fate maps incorporating large numbers of cells. In practice, however, an organism is composed of a certain number of cells, only a subset of which are practical to examine for phylogenetic fate mapping. Because the population of cells isolated for analysis is small compared to the trillions of cells of a higher organism, this process is akin to random sampling. Therefore, the greater the number of cells sampled, the higher the probability of obtaining two closely related cells, and consequently, the lower the average number of mutations per branch. Under actual experimental conditions, decreasing the number of cells analyzed should improve overall accuracy, because it increases the observed number of differences between cells. We tested the effects of constructing fate maps from randomly sampled subsets of cells embedded in a larger cell lineage tree (Figure 1D) and found that decreasing density of cell sampling improves accuracy similarly to increasing the average number of mutations per marker.
Evaluating accuracy of phylogenetic fate maps:
A conventional application of phylogenetics is evolutionary biology, where, just as with cell lineage history, independent means for validating results are seldom available. Assessment of accuracy has therefore relied on statistical methods for assessing the accuracy of phylogenetic trees (Hillis 1995). Consequently, we took a statistical approach to evaluating the accuracy of simulated phylogenetic fate mapping data.
The posterior probability associated with Bayesian phylogenetic reconstruction is one such measure of accuracy (Huelsenbeck et al. 2001). We have plotted how well the posterior probability of clades reflects their presence in the known lineage (Figure 2A), when modeled for trees with different mean numbers of mutations distinguishing cells, ranging from an average of only 1.5 mutations per branch of the lineage tree to as many as 19. In general, posterior probability underestimates accuracy and does so most markedly for either low values of posterior probability or when the number of mutations separating taxa is low. As mutation rate increases, the correlation between accuracy and posterior probability improves, and the two measures become nearly indistinguishable when the mutation frequency reaches 19 changes per branch. Bayesian posterior probability thus provides a conservative estimate of the accuracy of a phylogenetically reconstructed cell lineage tree.
Another means for assessing the accuracy of a phylogenetic fate map involves “jackknifing” (Lapointe et al. 1994), where nonoverlapping subsets of markers are used to construct paired phylogenetic trees that can be compared to one another. The principle behind this approach is that, given enough markers, there should be sufficiently redundant information such that independent panels of markers will generate identical trees. We determined how well accuracy correlates with the amount of similarity between jackknifed trees and plotted this relationship for different numbers of mutations separating taxa (Figure 2B). Jackknifing also underestimates accuracy, particularly when there are few mutations distinguishing cells. Further, the lengthy computation times required to produce Bayesian phylogenies prohibits the use of jackknifing to evaluate confidence of individual nodes, and it can therefore only be practically used to gauge the overall accuracy of a phylogenetic fate map.
Fate map of mouse fibroblasts:
To experimentally evaluate conclusions drawn from the preceding computer simulations, and also to investigate the origins of mesenchymal lineages, we attempted to construct a fate map of individual fibroblasts sampled at various anatomical locations throughout a mouse.
We isolated individual fibroblasts by dissecting connective tissues from different organs. To obtain sufficient DNA from a single cell for genotyping multiple markers by PCR, the genome must first be amplified. We previously accomplished this task (Salipante and Horwitz 2006) using “whole-genome amplification” (Klein et al. 1999) of single cells. Here we employed a different approach in studies conducted with fibroblasts, because they can be readily cultured. We isolated single fibroblasts and expanded each cell into a small colony of clonally related cells by briefly growing them in vitro (for ∼15–20 population doublings). Although cells may accrue additional mutations during this time, the majority of cells in the expanded population will not be mutated at any given locus, and DNA obtained from them should represent an average genotype approximating the originally isolated cell (Salipante and Horwitz 2006). In effect, by passing fibroblasts through a single cell “bottleneck,” we should be able to observe patterns of mitotic mutation present at the time they are isolated.
We used capillary electrophoresis to determine the length of the polyguanine tract for 87 PCR-amplified autosomal markers in DNA extracted from each of 34 clonally expanded fibroblasts (a total of 2958 genotypes, repeated in triplicate). Overall, 47/87 markers demonstrated a length-altering mutation in at least one allele from each of the samples, and every isolate was uniquely identifiable on the basis of its pattern of somatic mutation (supplemental Table 2 at http://www.genetics.org/supplemental/).
We then phylogenetically reconstructed the lineage tree using a Bayesian approach (Figure 3), thus revealing relationships between fibroblasts sampled from different tissues of an individual mouse. We included three internal controls (heart-1A/B, -2A/B, and -3A/B), in which a single fibroblast colony was split into two separate cultures early during its in vitro clonal expansion (after nine cell doublings). As expected, each member of the pair groups more closely to its partner than to other isolates on the fate map, yet each subclone still remains distinguishable by one or two mutations, indicating that the method can resolve even the history of their last few divisions.
As the simulation studies have demonstrated, both the average Bayesian posterior probabilities and the amount of similarity between jackknifed trees correlate with accuracy of the phylogenetic reconstruction, and these independent metrics may be used to quantify accuracy of the inferred tree. The average posterior probability of the phylogenetic map of fibroblasts is 26.1%, and, by the jackknifing method, the average similarity between pairs of jackknifed trees is 10.2%, standard error of mean (SEM) = 1.5%. Simulation studies using equivalently sized phylogenies constructed from randomized genotype data (not shown) predict an average posterior probability of 13.2% and average similarity for pairs of jackknifed trees of 0%, SEM = 0.618%. For the posterior probability, we propose adding a “correction factor” to compensate for underestimation of tree accuracy, as apparent from simulation studies. In our tree of fibroblasts, the mean number of mutations per marker is 1.38 (SEM = 0.11), and, in our simulations, when the mean number of mutations equals 1.5, accuracy is uniformly underestimated by 31.8% for Bayesian posterior probabilities <65%. By applying this correction, we therefore conservatively estimate accuracy for the experimental tree as 51.1%. (The simulation studies showed that similarity between jackknifed pairs of trees also underestimates accuracy, but not by a readily determinable amount.) We conclude that about half of lineage relationships inferred in the fate map have actually transpired in the organism. Although there are insufficient genotype data to generate an accurate tree, the phylogenetic reconstruction nevertheless contains nonrandom, biologically relevant information regarding relationships between fibroblasts. Moreover, the Bayesian algorithm assigns a posterior probability to each branch of the tree, indicating which lineages are more likely to be correct than others.
Our simulations indicate that analyzing subsets of cells has an effect similar to that of increasing the average number of mutations, thereby improving accuracy of the reconstruction. Consequently, we generated fate maps in which we analyzed just a subset of the most genetically divergent cells. Specifically, we excluded isolates that are less than either five or six mutations different from the center of the phylogeny (as determined by midpoint rooting), leaving only 24 and 14 cells, respectively, to be included in the inferred tree. The accuracy (based on posterior probability with the correction factor applied) of these limited fate maps (supplemental Figure 1 at http://www.genetics.org/supplemental/) increases to 61.9 and 71.0%, respectively. Pruning the tree in such a manner increases accuracy, albeit at the expense of supplying information about fewer lineages.
Our modeling studies have indicated that accuracy is a function of how many markers are analyzed. We performed a regression analysis of the fibroblast data, using random subsets of available markers, to investigate the relationship between the number of markers examined and the accuracy of the phylogenetic fate map (Figure 4). The average posterior probability of the experimental fate map decreases as fewer markers are included in the analysis. Unfortunately, it was not possible to extend the regression analysis to <60 markers, because too many unresolved branches of the lineage (“polytomies”) under those conditions confounded the scoring algorithm. The data fit a linear regression over the range of conditions available for testing, which, on the basis of our studies of simulated data, do not accurately portray the curvilinear relationship between number of markers examined and accuracy. Our extrapolation must therefore be taken as conservative, and we calculate that for this particular lineage map, ∼300 polyguanine markers would be required for a perfect map (where all uncorrected posterior probabilities are ≥65%).
The method that we have taken for mapping cell lineages on the basis of somatic mutation bears similarity to phylogenetic reconstructions of evolutionary relationships between organisms. Other than through the direct observation of cell division during development—infeasible for higher organisms—no experimental approach, cell marking included, can discriminate the actual cell lineage tree from among the nearly limitless number of all possible ancestries. Consequently, deciphering cell lineages must be accomplished retrospectively, just as with studies of evolution, where statistical phylogenetic methods are well-established.
To investigate what factors contribute to accuracy of phylogenetic fate maps, we have simulated mitotic mutation of microsatellite DNA markers, modeling conditions that we have previously experimentally observed in mouse cells. Not surprisingly, we find that more markers lead to better accuracy and that there is an optimally efficient number, depending upon lineage histories, beyond which additional markers offer diminishing returns. Somewhat less obviously, accuracy also improves with mutation frequency up to a threshold that varies as a function of the number of mitoses separating the sampled cells, after which greater mutation frequencies exert relatively smaller influences. We did not model extremely high (and consequently biologically implausible) mutation frequencies, where we expect mutation rate to negatively influence accuracy. (Consider that if mutation frequency were equal to one, then every marker would change length during each cell division, effectively randomizing information.) We also found that the density of sampling influences the overall accuracy of a tree indirectly through its effects on how closely related any two cells are likely to be; the more cells that are sampled, the more likely it is that two will share a recent common ancestry that will be more difficult to resolve, because there has been less opportunity for somatic mutation to individualize their genomes.
Another consideration is that embryonic development involves both cell proliferation and differentiation. During proliferation, the mass of cells is similar to that of the ancestral population and, thus, the mutations occurring in this stage are shared among most cells. After differentiation, different cell lineages may share these ancestral variations like the ancestral polymorphisms among populations or species. Stem cells, in particular, could have lower mutation rates than nonstem daughter cells. Indeed, this forms the basis of the “immortal strand hypothesis” (whereby stem cells retain the template strands and only daughter cells inherit DNA mutated through replication errors), for which there is conflicting evidence regarding its validity (Lansdorp 2007; Rando 2007). Ignoring this complication, for the time being, likely negatively influences the accuracy of branch lengths, but may not affect overall topology.
In contrast to conventional phylogenetics, it is possible to prospectively modify parameters influencing accuracy through appropriate experimental design. Polyguanine and other microsatellite DNA repeat sequences are sufficiently abundant in the genome of most organisms, such that cost imposes the only real limitation on how many can be genotyped. Eventually, as DNA sequencing becomes more economical (Bentley 2006), it may be possible to forego the use of markers and to simply determine the composition of long stretches of the genome within each cell to identify somatically arising single base substitutions or other types of mutations. More immediately, control of the mutation frequency could be possible through exposure to mutagens or manipulation of the genetic background. Frameshift mutagens, such as intercalating agents (Ferguson and Denny 1990), and genetic (Kolodner and Marsischky 1999) or chemically-induced (Clark and Kunkel 2004) inhibition of DNA mismatch repair, in particular, increase mutation rate in mononucleotide and other microsatellite repeats.
In fact, the mutation rate may not be constant across different lineages. For example, it might be useful to apply phylogenetic fate mapping to the study of cancer and metastases, where the mutation rate may be increased due to defective DNA mismatch repair. Alternatively, some tissues are more mitotically active than others, such as comparing epidermis to brain. Variation in mutation and growth rates between particular populations of cells will exert local effects on the fidelity of phylogenetic inferences for specific lineages within the larger cell fate tree—a circumstance that we have not modeled here. In general, though, increasing mutation rate does improve accuracy of the reconstruction.
Frumkin et al. (2005) previously modeled the effects of varying the number of cell divisions that comprise lineage trees, using mutation frequencies calculated for conventional microsatellite markers, which mutate less frequently than the polyguanine mononucleotide tracts we modeled. They concluded that ∼150,000 markers would be required to produce perfect fate maps in a wild-type mouse. Our vastly lower estimate of ∼300 markers reflects, at least in part, the higher mutation frequency of polyguanine mononucleotide repeats that we have incorporated into our models. However, in reconstructing the lineage of DNA mismatch repair-deficient cells, which exhibit elevated mutation rates, Frumkin et al. predicted that just a few hundred markers are required for good accuracy, and they actually experimentally achieved perfect reconstructions of cultured mismatch repair-deficient cancer cells using far fewer markers.
We constructed a phylogenetic fate map of fibroblasts sampled from different tissues of a single mouse to determine how well theoretical predictions match up against experimental data. Given that there is no simple experimental approach allowing for verification of accuracy, we borrowed from statistical methods employed with conventional phylogenetics. Our studies with simulated data indicate that either the Bayesian posterior probability or jackknifing comparisons allow for assessment of the accuracy of phylogenetic fate maps. Both are conservative, but the Bayesian approach is preferable, because the amount by which it underestimates accuracy is fairly predictable and therefore potentially correctable. The Bayesian approach also evaluates the confidence associated with each bifurcation of the tree. Due to logistical factors, we did not genotype the ∼300 markers that we estimated from our modeling studies to be required to achieve perfect accuracy for cells separated by a single mitosis. Nevertheless, with analysis of 87 polyguanine markers we achieved a map that, by both jackknifing and Bayesian posterior probability metrics, was significantly better than random and therefore contains biologically relevant information regarding cell lineage. Both the theoretical studies and analysis of data subsets indicate that limiting the tree to cells with the most divergent genotypes produces a tree with greater accuracy overall. Although the in vivo mutation rate of mouse cells remains uncharacterized, by performing a regression analysis on the basis of subsets of actual marker genotypes for all the cells from the actual fibroblast tree, we project that ∼300 markers—reassuringly, the same number that we predicted in modeling studies—are necessary to generate a fibroblast fate map with perfect accuracy. Not all microsatellite markers mutate with the same frequency (Salipante and Horwitz 2006), however, and we did not detect mutations for about half of the markers genotyped in fibroblasts. If it were possible to identify genomic sequences reliably prone to mutation, then only 162 polyguanine markers would be needed to generate an accurate fate map of the fibroblasts that we sampled.
Previously, we used whole-genome amplification to generate sufficient quantities of DNA from single cells for multiple PCR-based genotyping reactions (Salipante and Horwitz 2006). However, the various methods of whole-genome amplification are each vulnerable to artifacts (Dietmaier et al. 1999; Hughes et al. 2005) that could decrease the resultant quality of phylogenetic fate maps. Here we demonstrate an alternative to whole-genome amplification, in which we have cultured single fibroblasts briefly as clonal isolates for a few generations to extract enough genomic DNA to complete multiple PCR genotyping reactions. Many types of cells, including hepatocytes (Tateno and Yoshizato 1999), adipocytes (Sugihara et al. 1987), astrocytes (Mbarek et al. 1998), renal tubular cells (Springate and Taub 2007), and epithelial cells from colon (Follmann et al. 2000), prostate (McKeehan et al. 1984), and mammary glands (Soule and McGrath 1986) can grow in primary cell culture, if not immortally, then for at least a few generations. And for those cell types that may be terminally differentiated or otherwise incapable of reentry into the cell cycle, another possibility involves expression of a conditionally immortalizing gene from a DNA tumor virus, such as the SV40 T-antigen. Several lines of transgenic mice expressing a temperature-sensitive SV40 T-antigen are available (Jat et al. 1991; Vicart et al. 1994). Under permissive conditions, the T-antigen becomes active, facilitating the cultured growth and immortalization of many different types of primary cells isolated from these mice, even from normally quiescent lineages. Looking forward to the ultimate generation of high density phylogenetic fate maps, a trade-off with use of clonal expansion of single cells is that it requires that the cells be living at the time of their dissection, as opposed to whole-genome amplification, where cells could be isolated from fixed tissues with methods such as laser capture microdissection (Callagy et al. 2005).
Finally, as a biological question, the source of fibroblasts is uncertain, and evidence supports their origin from primitive mesenchyme during embryogenesis (Brand-Saberi and Christ 2000), ongoing local generation (Hay 1995) within organ epithelia (the “epithelial-mesenchymal transition” model), and, perhaps most surprisingly, from hematopoietic stem cells derived from bone marrow (Friedenstein et al. 1970; Ogawa et al. 2006). Although we hesitate to draw conclusions from a phylogenetic fate map exhibiting low overall accuracy, our experimental map of fibroblasts exhibits features suggestive of cell migration. It should be possible to detect migration in phylogenetic fate maps by identifying isolates which are separated by only a few mutations, but that were sampled from anatomically distant locations. The highest-confidence grouping on the inferred lineage tree, with a 90% posterior probability, which can be considered credible, is for a fibroblast harvested from the right lung and another from the spleen and that are separated by only four cell divisions. Furthermore, cells from the spleen are distributed throughout the branches of the tree, whereas fibroblasts from other organs tend to cluster more closely. These observations are suggestive of cell mobility at some point during the development of mesenchyme. Following fertilization and until at least late gastrulation, cells in the embryo migrate and mix with one another (Lawson et al. 1991; McMahon et al. 1983; Soriano and Jaenisch 1986). Mesenchymal stem cells appear to migrate at even still later stages of development (Mendes et al. 2005). Mixture of a common fibroblast precursor pool, followed by clonal expansion, could account for our findings. Alternatively, it is possible that cell migration has taken place in the adult. The migration of fibroblast precursors with limited replicative potential through the bloodstream could also explain the fate map, and the phylogenetic diversity of fibroblasts present in the spleen may be a consequence of its role in filtering blood—a function of this organ heretofore thought to be limited to blood cells (Kraal and Mebius 2006). Of course, these hypotheses must be tested and confirmed, either by use of conventional cell lineaging techniques or by the production of higher-confidence phylogenetic fate maps.
We thank B. Hall, G. McVicker, J. Kidd, and R. Rohlfs for discussion and help with software and H.-H. Lee for help with cell isolation. This work was supported by National Institutes of Health (NIH) grants DP1OD003278 and R01DK078340 (to M.S.H.); F30AG030316 (to S.J.S.); and NIH T32GM007266, Poncin Fund, and Achievement Rewards for College Students Fellowship grants to the University of Washington Medical Scientist Training Program (for S.J.S.).
Communicating editor: M. W. Feldman
- Received August 22, 2007.
- Accepted December 5, 2007.
- Copyright © 2008 by the Genetics Society of America