How Do You Know Cells Have Depth

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Estimating Prison cell Depth from Somatic Mutations

• Dan Frumkin,
• Rivka Adar,
• Shalev Itzkovitz,
• Tomer Stern,
• Shai Kaplan,
• Gabi Shefer,
• Irena Shur,
• Lior Zangi,
• Yitzhak Reizel,
• Alon Harmelin,
• Yuval Dor,
• Nava Dekel,
• Yair Reisner,
• Dafna Benayahu,
• Eldad Tzahor,
• Eran Segal,
•  [ ... ],
• Ehud Shapiro
• [ view all ]
• [ view less ]

Estimating Cell Depth from Somatic Mutations

• Adam Wasserstrom,
• Dan Frumkin,
• Rivka Adar,
• Shalev Itzkovitz,
• Tomer Stern,
• Shai Kaplan,
• Gabi Shefer,
• Irena Shur,
• Lior Zangi,
• Yitzhak Reizel

x

• Published: May nine, 2008
• https://doi.org/10.1371/periodical.pcbi.1000058

Figures

Abstract

The depth of a cell of a multicellular organism is the number of cell divisions information technology underwent since the zygote, and knowing this basic cell property would help accost primal bug in several areas of biology. At present, the depths of the vast majority of human and mouse cell types are unknown. Hither, nosotros show a method for estimating the depth of a cell by analyzing somatic mutations in its microsatellites, and provide to our knowledge for the first time reliable depth estimates for several cells types in mice. According to our estimates, the average depth of oocytes is 29, consequent with previous estimates. The average depth of B cells ranges from 34 to 79, linearly related to the mouse historic period, suggesting a rate of ane cell sectionalization per 24-hour interval. In contrast, various types of adult stem cells underwent on boilerplate fewer cell divisions, supporting the notion that adult stem cells are relatively quiescent. Our method for depth estimation opens a window for revealing tissue turnover rates in animals, including humans, which has important implications for our knowledge of the body under physiological and pathological weather.

Author Summary

All the cells in our trunk are descendants of a single jail cell – the fertilized egg. Some cells are relatively close descendants, having undergone a small number of cell divisions, while other cells may be hundreds or even thousands of divisions deep. So far, science was unable to provide even gross estimates for the depths of the vast bulk of human and mouse cells. In this study, nosotros show that precise depth estimates of cells can be obtained from the analysis of non-hazardous mutations that spontaneously accumulate during normal evolution. The concept behind the method is simple: deeper cells tend to acquire more mutations and "drift away" from the original Dna sequence of the fertilized egg. Knowing how deep cells are is the cardinal to many key open questions in biology and medicine, such as whether neurons in our brain can regenerate, or whether new eggs are created in adult females.

Citation: Wasserstrom A, Frumkin D, Adar R, Itzkovitz S, Stern T, Kaplan S, et al. (2008) Estimating Cell Depth from Somatic Mutations. PLoS Comput Biol 4(5): e1000058. https://doi.org/10.1371/periodical.pcbi.1000058

Editor: Philip East. Bourne, University of California San Diego, United states of america of America

Received: October 22, 2007; Accepted: March 13, 2008; Published: May nine, 2008

Copyright: © 2008 Wasserstrom et al. This is an open-access commodity distributed nether the terms of the Creative Commons Attribution License, which permits unrestricted utilize, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: This research was supported by The Israel Academy of Science and Humanities (Bikura), past The Yeshaya Horowitz Association through The Center for Complexity Scientific discipline, by a enquiry grant from Dr. Mordecai Roshwald, by a grant from the Kenneth and Sally Leafman Appelbaum Discovery Fund, by the estate of Karl Felix Jakubskind, past The Clore Middle for Biological Physics, and past a inquiry grant from The Louis Chor Memorial Trust. AW received support from the Kahn Family Center for Systems Biology of the Human Jail cell.

Competing interests: The authors take alleged that no competing interests exist.

Introduction

Directly observation of jail cell divisions, which was used to reconstruct the cell lineage of the 959 somatic cells of Caenorhabditis elegans [1] implicitly yielded likewise the depths of these cells. However, directly observations cannot be done for humans and mice since they are opaque and have a tremendous number of cells [ii]. Instead, calculations based on cell numbers, proliferation kinetics and diverse theoretical assumptions have been used to estimate the depths of homo [3] and mouse [4] oocytes (approximately 25 cell divisions in both), and of human sperm (approximately 30 divisions at age fifteen with additional 23 divisions per yr thereafter [three]). The evolutionary-biological science concept of a molecular clock [five] – a relatively constant rate of molecular development – has besides been suggested for estimation of cell depths using either epigenetic [6] or genetic [7] mechanisms. An association between depth and increase in methylation was demonstrated in cell populations of endometrial glands [6]. Mutations in microsatellites (MS; repetitive Dna sequences) have been used to clarify histories of human being colorectal tumors, estimating that tumor cells underwent on average well-nigh 2,300 divisions since the first of tumor progression and 280 divisions since the final clonal expansion [7],[8]. All the same, the depths of the vast majority of human and mouse cells are unknown, and no systematic method for their estimation has been proposed so far.

Results

Correlation Between Genetic Distance and Prison cell Depth

Our work develops the notion of genetic molecular clocks into a quantitative method for depth estimation of single cells of any type. When a cell divides, its DNA is replicated with almost perfect fidelity, yet somatic mutations occur in every jail cell division [9]. These somatic mutations, which were previously shown to encode the prison cell lineage tree [9], also encode precise data regarding cell depth. The thought is simple: deeper cells tend to acquire more mutations, hence genetic altitude from the zygote and jail cell depth are strongly correlated (Figure 1A). In principle, any mutation may assist for depth assay, yet mutations in MS are particularly well suited for depth analysis given that MS are highly abundant in human and mouse [ten], and slippage mutations (which insert or delete repeated units) in MS occur at relatively high rates [x] and are coupled to cell division [x]. Moreover, animals with mutations in cardinal mismatch repair (MMR) genes display very high mutation rates in MS [11],[12].

Figure 1. Cell depth analysis.

(A) The depth of a cell is the number of divisions it underwent since the zygote. The figure shows a tiny part of the prison cell lineage tree of an organism – a binary tree representing the verbal design of prison cell divisions of its developmental history from a single cell to its electric current state. The tree depicts not only the lineage relations between cells, but also their depths, obtained by projecting them to the depth axis. A correlation between genetic distance and prison cell depth is shown in a small fraction (five MS alleles) of the genome. Each allele is assigned a relative allelic value – a whole number equal to the difference between the number of repeats of that allele and the number of repeat units of the corresponding allele in the zygote. Mutations are coloured in red. (B) Reckoner simulations of MS mutations and depth estimations based on a maximum likelihood approach. Cells at various depths were simulated accumulating MS stepwise mutations according to wild-blazon and MMR-deficient mutation rates (p = ii.v*10^−five and p = 0.01, respectively). Depth interpretation errors were scored according to the log (base 2) of the ratio between the estimated and faux depths.

https://doi.org/x.1371/journal.pcbi.1000058.g001

Computer Simulations

We use the zygote genome equally a reference against which mutations are determined (Figure 1A). Each analyzed cell is assigned an identifier [nine], a vector representing the mutations that the cell accumulated at a set up of analyzed alleles. To assess the theoretical potential of depth analysis using genomic MS we performed estimator simulations based on information nosotros previously obtained regarding the numbers of MS and their mutation rates in man and mouse [ix]. We faux wild-type and MMR-deficient mutational behaviour on cells at diverse depths and estimated their precision using a maximum-likelihood approach (come across Materials and Methods). As expected, increasing the number of analyzed alleles, using faster mutation alleles, or analyzing deeper cells – each improves depth interpretation score (Figure 1B; a boundary instance occurs in wild-type simulations in depth 10 cells, in which fault increases with increasing number of alleles, come across Materials and Methods). Using the entire ready of genomic MS in wild-type human and mouse enables to estimate the depth of cells (at least ten divisions deep) with precision greater than 95% (Figure 1B). In MMR-deficient organisms, 100 alleles are sufficient to estimate depths of cells (at least 10 divisions deep) with precision greater than seventy% (Figure 1B).

A Method for Estimating Cell Depth from Somatic Mutations

These simulations presume that the mutational behaviour of MS alleles is elementary, consistent, and completely known to the states. In practice this is not the case: although some macro-properties of MS mutational behaviour are known [10], the precise behaviour of each MS allele is unknown, and is not readily obtainable. Instead of attempting to decipher the mutational behaviour of every allele in our gear up of MS, nosotros employed a model-complimentary approach, which utilizes global backdrop of the set, thus masking the idiosyncrasies of specific alleles. We previously showed that when reconstructing the lineage relations betwixt a set of cells of an ex vivo cultured prison cell tree (CCT) with known depths, there is a linear correlation between the reconstructed and actual depths [9]. Here we continued to investigate this relation, which is the basis of assigning actual depths in our suggested method. A description of the method is shown in Effigy two: a scale CCT is created and reconstructed using the Neighbour-Joining (NJ) algorithm [13] using the altitude office 'Absolute-distance' (Effigy 2A; this distance mensurate has previously been suggested to scale linearly with time [14]). A multiplier – a number representing the ratio between the reconstructed and actual depths – is obtained (Figure 2B), and is consequently used for in vivo depth estimations (Figure 2C).

Effigy 2. Estimating cell depths from somatic mutations.

(A) Our method for in vivo jail cell depth interpretation employs a calibration system based on a cultured cell tree (CCT) – an ex vivo tree with known topology and well-estimated edge lengths. A CCT created from an Mlh1−/− mouse cell line (of similar background to the mice in which nosotros performed depth analyses) is shown. CCT leaves (M1–M10) were analyzed over a panel of about 100 MS loci, and a tree was reconstructed using the method described in ref. [9] (Neighbor-Joining [NJ] phylogenetic algorithm and 'Absolute-distance' distance function were used; come across Materials and Methods). Reconstructed depths of all leaves (except for M2, an outlier omitted from assay) were very similar, with a standard departure of less than viii% of the hateful. (B) Linear correlation betwixt actual and reconstructed depths of human and mouse CCTs. Circles represent CCT nodes; numbers indicate multipliers in each CCT. (C) A multiplier obtained from a CCT is used to calibrate the depths of cells in the reconstructed cell lineage tree.

https://doi.org/10.1371/journal.pcbi.1000058.g002

The Method Is Well Supported

Successful depth estimation based on our suggested method depends on the fulfilment of 3 weather condition: (i) there is a practiced linear correlation between reconstructed and bodily node depths in CCTs; (two) this correlation is like between similar experiments, i.e. a multiplier obtained from the correlation in one experiment can be used in another; (3) this multiplier tin be reliably transferred from ex vivo to in vivo experiments. Beneath we show that each of these conditions is indeed fulfilled. Figure 2B shows a linear correlation in man CCTs [nine] (R^two = 0.94 and 0.87 for CCTs A and C, respectively) and a newly-created mouse CCT. Multipliers of human CCTs are very similar – 411 and 421 for CCTs A and C, respectively. Depth estimations of nodes from i CCT based on a fit obtained from the other CCT are extremely precise: the average error when estimating the depth of a node from CCT A based on a fit obtained from CCT C is 6.iv%±four.1% (and eleven%±11% vice versa, for the estimation of CCT C nodes based on a fit obtained from CCT A). The multiplier of mouse CCT is dissimilar (256), reflecting the differences between mutational behaviour of our human and mouse MS sets. To further demonstrate that multipliers tin be transferred between similar experiments, we performed computer simulations in which a multiplier obtained from 1 randomly generated tree was used to estimate depths of cells of other like random trees. These simulations prove that when 100 alleles (with mutation rate p = i/100) are analyzed, depths of xc% of the samples are estimated with mean error of less than 30% (data non shown). To show that ex vivo and in vivo mutation rates are consistent we analyzed the percent of mutations in a set of 130 MS alleles in the mouse CCT samples and multiple samples obtained from four Mlh1−/− mice. The correlation coefficient (r = 0.44) was found to be highly significant (p<10^−six).

Next we checked whether depth analysis is sensitive to the number of analyzed cells and the specific choice of analyzed alleles. To test the sometime, we generated random copse with l leaves and simulated MS stepwise mutations at various rates. Nosotros reconstructed the trees, with increasing subsets of leaves (three–50). Depth estimates of a single leaf (included in all subsets) varied by less than 5% between reconstructions demonstrating that our method is robust to the number of analyzed cells (data not shown). To test the latter, we calculated a fit for the mouse CCT by bootstrapping the information thou times (run into Materials and Methods), obtaining a mean fit of 251±28. This demonstrates that the obtained multiplier (256) is not sensitive to the specific option of alleles.

Depth Estimations of Cells In Vivo

Nosotros practical the method and estimated depths of 163 cells of diverse types sampled from four MMR-deficient (Mlh1−/−, see [15]) mice anile 5.5–40 weeks (Table 1 and Table S1). Identifiers of analyzed cells (run into Table S4) were obtained elsewhere [16],[17] (Text S1 describes materials and methods for obtaining identifiers cells from mice aged 5.5–thirteen weeks). Each identifier [9] represents the mutations that the corresponding cell sample caused at the fix of loci in comparison to the zygote. Experiment mice take a dual genetic background (C57Bl/6 X 129SvEv), therefore the ii alleles of each MS locus are potentially heterozygous, and are considered to mutate completely independent. Our analysis of eight oocytes isolated from the right ovary of a v.v week erstwhile mouse showed that their average depth is 29 cell divisions (Figure 3A), slightly higher than previous estimates of about 25 prison cell divisions [4]. The average depth of four types of developed stem cells (satellite, kidney, mesenchymal, hematopoietic) from mice five.5–xiii weeks old ranged from 24–40 cell divisions. These results, when contrasted to the observed depth of differentiated cells such as B-cells (see below), lend support to the view that a general trait of stem cells is their relative quiescence [eighteen]. Satellite cells are adult stem cells positioned nether the basal lamina of muscle fibers, which are responsible for the remarkable regenerative capacity of adult skeletal muscle [19]. Depths of satellite cells isolated from various muscles and myofibers ranged from xiv to 75. This wide range of depths suggests that the progenitors of some cells were activated due to events of muscle repair [twenty] or that satellite cells are a heterogeneous population, for example with respect to the rate of cell division [21]. Nevertheless, the boilerplate depths of satellite cells were quite similar (38, 28 and 36; Figure 3B) even though they were sampled from mice at dissimilar ages (5.5w, 10w and 13w, respectively). This suggests that well-nigh of the satellite prison cell population in diverse muscles and myofibers originated during embryonic evolution, without extensive proliferation in adult life under normal circumstances, and confirms that satellite cells are mitotically quiescent in mature muscle [22]. In dissimilarity, in that location was a linear correlation betwixt the boilerplate depth of B-cells and mouse age (R² = 0.97; Effigy 3B). The slope of the linear correlation (6.3) suggests that the turnover charge per unit of splenic B-cells (or progenitors) is nearly one time per day in adults mice. Moreover, B-cells were deeper than satellite cells in 10–xiii week old mice (statistically pregnant in 10 weeks, but non in xiii weeks). Comparison of lung epithelial cells and tumor cells (from various tumor foci) isolated from a forty week old mouse showed that tumor cells are significantly deeper than epithelial cells (average depths 237 and 117, respectively; Frumkin D., et al., submitted). Two possible explanations for this big difference are that tumor cells separate more than apace than normal epithelial cells, or that the tumor founder cell was deeper than the epithelial cells, creating a shift for the entire tumor cell population. Some other possible explanation is that tumor cells learn mutations faster than wild type cells. While this may exist true in general, it is unlikely in this specific example, since both normal and tumor cells in our Mlh1−/− mice are completely deficient in mismatch repair.

Figure three. In vivo depth estimations.

Depth estimates of various cells sampled from mice aged v.five–xl weeks. (A) Box plots of depths according to cell blazon and mouse age. Box (blue) displays the middle 50% of the data from the lower to upper quartiles (median is cherry-red). Ends of vertical lines (whiskers) indicate minimum and maximum data values, unless outliers (marked by '+') are nowadays, in which instance the whiskers extend to a maximum of 1.5 times the inter-quartile range. Stars depict cell types with statistically significant different boilerplate depths (p<0.05). (B) Average depths of satellite cells and B cells as a function of mouse age. While depths of satellite cells did not correlate to age, depths of B cells showed a linear correlation (R² = 0.97) to age, corresponding to near one cell division per day. Mistake bars denote standard errors of the mean.

https://doi.org/x.1371/journal.pcbi.1000058.g003

The DNA of analyzed cells was amplified either by ex vivo civilization or past whole genome amplification (WGA; see Table ane). Although mutations might occur in civilization, analysis of cell clones is with high probability identical to assay had it been performed on the clone'south founder cell ([9]; fixation for a mutation during cell culture would be largely undetectable because there are no bottlenecks during the procedure). Even so, WGA might generate artefact mutations [23] leading to increased depth estimates. Our command experiments show that WGA introduces 0.9–1.2% artefact mutations (in GenomiPhi and GenomePlex, respectively; [16]). We recalculated cell depths assuming these artefact mutation levels in WGA samples, obtaining depths smaller by 18% on average, see Materials and Methods).

Discussion

In conclusion, nosotros developed a method for estimating depths of cells in vivo complementary to our previous method for lineage analysis [nine], and applied it to various types of mouse cells. The method is composed of two independent steps: beginning, relative depths are assigned to sampled cells, which are and then transformed to accented depths using an external scale system in the grade of a CCT. Each CCT is applicable only to the assay of in vivo cells of similar background to those of the CCT. Culling calibrations are besides possible, for example, by the fluorescent labelling of cells followed by analysis of their intensity (which dilutes approximately by half in each jail cell division [24]). Similar depth estimates (16% difference on boilerplate, data not shown) tin can be obtained independent of tree reconstruction simply by correlating the number of mutations and cell depth. In futurity, calibration may be discarded altogether if reliable in vivo depths estimates tin can exist obtained for a certain group of cells, using any method, which tin can then exist used for internal calibration with other cells.

Horwitz and colleagues also recently developed a method for cell lineage analysis based on somatic mutations in polyguanine repeat DNA sequences [25], very like to our previous method [ix]. They reconstructed a tree of jail cell samples from a seven-calendar month erstwhile wildtype mouse, in which branch lengths correspond to the number of jail cell divisions. In light of the recent rapid technological advances in high-throughput genomic analysis, we also believe that the direction of this methodology is heading towards the assay of wild-blazon organisms, including humans. All the same, now our preference was to analyze MMR-deficient mice because MS in these mice have elevated mutations rates, which enable analyzing a relatively small number of MS with repeat units of two letters (due east.g. 'Ac') and more. Such MS are preferable over mononucleotide sequences because their PCR stutter patterns are much reduced, making analysis more precise and thus more reliable. Analysis of wildtype organisms based on such MS is non practical at nowadays, as it would crave analysis of thousands of MS loci. While not platonic, we believe our assay may give a lot of useful and reliable data since MMR-deficient humans [11] and mice [12] accept been shown to develop normally.

The reconstructed tree obtained past Horwitz and colleagues [25] is unrooted, hence it is not possible to infer the depth of their analyzed cells. Analysis of unrooted copse enables to infer the number of cell divisions between any two samples which is the sum of cell divisions from each sample to their common ancestor (this could exist referred to as "depth of cell lineage since 10", X being their common ancestor). In our assay nosotros infer the identifier of the zygote with loftier precision (based on tail DNA, see [16]), which enables to reconstruct a rooted tree. Based on this, we can estimate the depth of single cells, and use the term "depth" as shorthand for "depth of prison cell lineage since the zygote".

Our depth estimations of oocytes were highly similar to previous reports, providing an independent confirmation for the precision and definiteness of our method. Withal, depth estimations may exist imprecise to some extent due to various factors, such as the stochastic nature of mutations, differences betwixt ex vivo and in vivo mutation rates, and different mutation rates betwixt dissimilar tissues. In this case of the latter, obtaining tissue-specific mutation rates would enable to perform a compensation step, thus minimizing the error in depth estimations. Beyond the potential of static depth assay at a specific timepoint, iterative depth assay at various timepoints can reveal the turnover rates of various tissues under physiological and pathological conditions [26]. For example, depths of a stable tissue which does not turnover is expected to remain abiding with time, while depths of not-stable tissues are expected to increase at a rate dependant on the turnover charge per unit. An alternative method for qualitatively obtaining relative cell turnover rates betwixt tissues was previously suggested based on retrospective birth dating of cells [26]. Similarly, analysis of injected stable isotopes was used to make up one's mind the turnover rate of claret in mice and rats [27]. Our method enables performing precise depth analysis in a non-invasive fashion, which may shed light on several open fundamental questions, such as whether there is regeneration of neurons [28] and oocytes [29] and the in vivo dynamics of stem cells.

Materials and Methods

Mouse CCT

Mlh1−/− MEF cells (obtained from Michael Liskay, OHSU) were grown in medium composed of DMEM low glucose (Gibco) supplemented with 10% Fetal Bovine Serum, 1% Non-essential amino acids, and Gentamycin (70 µg/ml). The CCT was created as previously described [nine]. Cell division charge per unit was estimated as 1 division per day according to the frequency of routine plate passages. CCT leaves (M1-M10) were genotyped in our prepare of MS loci using an automated procedure as previously described [9], except that capillary bespeak assay was performed automatically with a new calculator algorithm nosotros designed [16]. We reconstructed the CCT with a set of 95 MS loci (see Tables S2 and S3 for list of loci and cell identifiers, respectively) using our previous method for lineage reconstruction [9], except that the altitude office was 'Absolute Distance'. In this function the distance betwixt ii samples is the average distance betwixt their allelic values in all alleles which were analyzed in both samples. The multiplier of homo and mouse CCTs is the slope of the linear regression between actual and reconstructed depths of CCT nodes. When bootstrapping was performed, alleles from each CCT nodes were sampled with replacement, creating pseudo-identifiers of the aforementioned size as the original identifiers. The CCT was reconstructed based on the pseudo-identifiers, and multipliers were calculated.

Computer Simulations

Identifiers of cells at various depths were simulated based on a symmetric stepwise mutation model, according to which each MS allele mutates with probability p, and mutations are either +1 or −1 (each with probability p/2). Both wild-blazon (p = 2.v*10^−five) or MMR-deficient (p = 0.01) mutation rates were tested. Depths of faux cells were estimated using the algorithm described beneath. Estimation score (fold of deviation) was divers as follows: score = |log₂ (estimated_depth / real_depth)|. Ordinarily, increasing depth improves (lowers) the score. However, in shallow cells with slow mutation rates (e.m. cells x divisions deep in wild-blazon simulations) there are ordinarily no mutations, hence the estimated depth is nada and the score increases with depth since the departure between the estimated and existent depths increases.

Algorithm for Depth Estimation (for Computer Simulations)

This algorithm was used for estimating depths of cells in computer simulations (in the case the mutational behaviour of MS is elementary and completely known). Nosotros assume that the mutational behaviour of each MS allele is defined by a Probability Vector (PV; p_i is the probability of the allele to mutate by i MS repeats in each prison cell partitioning; Σp_i = 1). For every MS allele, given its initial value (number of repeats) at the root, fill a table whose rows are indexed by number of repeats, whose columns are indexed by depth (starting at ane and ending at the maximum believable depth of a leaf), and whose (i,j) entry gives the probability that at depth j its value is exactly i. This table can be prepared (in accelerate and stored) using dynamic programming, cavalcade after column, using the PV for the item MS allele. If there are several alleles with the same PV, so only i table per PV needs to be prepared. Then, given a cell identifier, for every depth d, take product of the entries in the tables, where for each MS allele the entry taken is the one in cavalcade d and the row corresponding to the value of the MS allele in the cell. This production is our estimate of the likelihood that the foliage is at depth d. The estimated depth is d with maximum likelihood.

Ex Vivo – In Vivo Correlation

Only alleles which were successfully amplified and analyzed in at least 20% of mouse CCT and Mlh1−/− samples were analyzed. We generated 10^half-dozen random permutations of the per centum of mutations in the in vivo samples, obtaining a correlation coefficient for each permutation. No permutation resulted in a higher correlation coefficient.

Selection of MS for In Vivo Studies

The loci for in vivo studies were chosen according to the post-obit criteria: (i) loci with a large number of repeats, in attempt to obtain fast mutating loci. Loci with different mutation rates hold different information, and the best loci for depth assay are those with the highest mutation rates (unpublished analysis); (two) loci which are amplified well using our primers yielding high quality signals; (iii) loci whose signal can hands exist analyzed (eastward.g. their two alleles are sufficiently far apart).

In Vivo Depth Interpretation

A lineage tree was reconstructed for each Mlh1−/− mouse (using NJ and the 'Absolute Altitude' role), and for each cell the reconstructed depth was obtained, which is the sum of edge lengths in the reconstructed tree. The estimated depth of each cell was its reconstructed depth multiplied by the multiplier obtained from the mouse CCT. We calculated the 95% conviction interval of the regression coefficient, and used its lower and upper premises every bit multipliers for obtaining the 95% conviction interval of the depth approximate of each cell. Depth recalculations assuming WGA artefact mutations were calculated equally follows: for each WGA sample m randomly chosen mutated alleles (g = 0.9% or m = i.two% of analyzed signals for GenomiPhi or GenomePlex WGA samples, respectively) were changed to zero, and depths were recalculated. This was repeated 100 times, and a modified depth (hateful depth over repetitions) was obtained for each sample.

Supporting Information

Acknowledgments

We thank Uriel Feige for suggesting the algorithm for estimating fake depths and Amit Mishali for the design and preparation of the figures. Ehud Shapiro is the Incumbent of The Harry Weinrebe Professorial Chair of Estimator Science and Biology and of The French republic Telecom – Orange Excellence Chair for Interdisciplinary Studies of the Paris "Centre de Recherche Interdisciplinaire" (FTO/CRI).

Writer Contributions

Conceived and designed the experiments: AW DF RA GS IS LZ YR YD ND YR DB ET ES ES. Performed the experiments: AW DF RA GS IS LZ Yr AH YD ET. Analyzed the information: AW DF RA SI TS ES ES. Contributed reagents/materials/analysis tools: SK GS IS LZ YR AH YD ND Twelvemonth DB ET. Wrote the paper: AW DF RA SI GS YR YD ND DB ET ES ES.

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Source: https://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.1000058

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