# Quantifying Mosaic Development: Towards an Evo-Devo Postmodern Synthesis of the Evolution of Development via Differentiation Trees of Embryos

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

#### Higher-Order Patterns and Organization by Differentiation

## 2. Materials and Methods

#### 2.1. Description of Datasets, Ciona Intestinalis

^{6}µm

^{3}. In the original acquisition of the data, a tracer enzyme was used to identify each cell body in a whole embryo. All data (cell identities and volumetric measurements) from each embryonic stage were integrated into a single data structure in order to determine line of descent based on a reference lineage tree [8], confidence intervals, and differentiation tree order.

#### 2.2. Description of Datasets, Caenorhabditis elegans

^{+}marker. Three-dimensional (spatial) position, diameter, and nomenclature (identity) for all cells are extracted from observations of 261 embryos. These variables are then averaged over every observation of a specific cell type. Discrete GFP

^{+}regions are segmented from microscopy images using computer vision techniques, and are used to construct an optimal spherical representation (see [55]). Due to the nature of the quantification of the C. elegans data, corresponding volumetric data of the whole embryo (as we have for Ciona in Figure 2) is not available. This spherical representation is based on identification of the centroid and annulus for these segmented regions from florescence signal intensity. While this is not an exact measure of diameter for the entire cell, it provides a reasonable approximation. The positional data is translated to have its origin at the location of the P0 cell, and is used to produce a three-dimensional spatial representation of the embryo. In this representation, orientation along A-P axis is reversed so that negative values are closer to the anterior end.

#### 2.3. Methods for Collecting Secondary Data

^{+}marker. These techniques allow for approximation of volume by calculation of cell volume as a proportion of total embryo volume in Ciona and cell volume as a calculation of a sphere based on an approximation of cell diameter for C. elegans.

#### 2.4. Finding Biologically-Meaningful Asymmetric Divisions

_{i, j,}C

_{s}is the smaller daughter cell volume in the unordered pair C

_{i, j,}and h is the threshold. A range of t values (0.05, 0.25, 0.50) are calculated for cells as a percentage of volume in the Ciona embryo (Table S2). A range of t values (0.01, 0.025, 0.05) are calculated for a spherical approximation of cell volume in the C. elegans embryo (Table S3). This difference criterion (G) is compared to the difference in volume between C

_{i}and C

_{j}in the following manner:

#### 2.5. Ratio Between Larger and Smaller Daughter Cells

#### 2.6. Differentiation Trees

#### 2.7. Differentiation Code and Tree Classification

#### 2.8. Composite Differentiation Code

^{+}nuclei. This composite differentiation code was used to estimate the C. elegans differentiation tree topology (Figures S2A and S2B), and can be found in Table S5.

#### 2.9. Power Regression Formula

#### 2.10. Hamming Distance Calculation

_{i}and y

_{i}are binary strings of the same length (depth in the tree) compared pairwise, k is the length of both strings, and DH counts the number of differences between the two strings in terms of bits. This calculation can be done for the same cell, in regards to its positions in the lineage and differentiation trees, between different cells in the same tree, that are at the same depth, or between cells at the same depth in trees of two different organisms.

#### 2.11. Three-Dimensional Representation of Hamming Distances in C. elegans

#### 2.12. CAST (Cell Alignment Search Tool) Analysis

_{i}= 0 for the small cell in an asymmetric division or for a contraction wave in a regulating embryo [10,13,14], or b

_{i}= 1 for the larger cell or an expansion wave. When it is easier to think in terms of letters rather than binary numbers, one may substitute C = 0 and E = 1. BLASTing works on the nucleotide or amino acid sequence, represented by letters, so the CAST analogy to BLAST is clearer when the differentiation code is expressed in letters.

#### 2.13. Graphs and Analysis

## 3. Results

#### 3.1. Introduction to Analysis

#### 3.2. Within-Species Embryonic Variation

^{3}), while the other phase (B), cell volume exhibits much less variation (standard deviation = 0.10 µm

^{3}). While the boundary between phases is somewhat arbitrary, we can say that longer lived cells (with a lifetime of roughly 70 min or older) exhibit less variability in cell volume. Although we cannot establish a direct link to tissue formation, given currently available data, it provides at least some evidence for cellular sublineages that behave somewhat differently from the rest of the embryo.

^{2}= 0.91, p > 0.001). In general, the longer the lifetime of a cell, the smaller its volume. In identifying 11 selected outlier cells (points greater than 2.5 standard deviations away from the main data series trend line), we can see that eight (8) of these cells are descendants of P1 (clustered in the MS lineage). Only a single outlier in Figure 4 is descended from AB (ABar). Overall, however, the variation observed in C. elegans is much less than in Ciona.

^{2}= 0.70, p < 0.001), while Figure 6 yields a much stronger relationship for C. elegans (R

^{2}= 0.97, p < 0.001). While there are more outliers in the Ciona example, this could be due to a number of technical factors such as more precise temporal measurements for the C. elegans example and differences in how the volume measurement is approximated between these species.

#### 3.3. Cellular Variation Across Lineage Trees

^{2}= 0.60, p < 0.001. An identical bivariate comparison in C. elegans yields a linear regression of similar strength (R

^{2}= 0.56, p < 0.001). In both cases, we can see that overall, cell volume decreases as lineage depth increases, but it is noteworthy that the curve is nonlinear for Ciona (Figure 7) while linear for C. elegans (Figure 8). This is consistent with the decrease in volume over developmental time that was shown in Figure 5 (Ciona) and Figure 6 (C. elegans).

#### 3.4. Comparison of Lineage and Differentiation Trees

#### 3.5. Intra-Specific Comparisons Using Isometric Graphs

#### 3.6. CAST Analysis of Differentiation Codes

#### 3.7. Interpretation of Results

## 4. Discussion

#### 4.1. Analytical Caveats

^{+}nuclei to estimate cell volume in C. elegans. While the datasets used are comparable in some ways, they do not serve us particularly well in others. This limitation is particularly true for the lack of size variation amongst C. elegans daughter cell pairs. Our estimates for smaller and larger divisions would be improved by data on whole cell size, or cell volume data that resembles the method of segmentation for Ciona. For example, our method of estimating C. elegans cell size may misclassify some pairs of cells by not capturing the true extent of their shape and size. This is particularly true of cell polarity exhibited during the two and four-cell stage in C. elegans [64]. It is of note that there would be a similar issue with defining size by segmenting the cell membrane, as the complexities of cell shape are also hard to capture in an absolute manner.

#### 4.2. Discussion of Within-Species Cellular Variation

#### 4.3. Differentiation Trees and Comparative Development

#### 4.4. Overarching Features of Mosaic Embryogenesis

#### 4.5. Broader Evolutionary Implications

#### 4.6. A Toy Model of an Idealized Mosaic Embryo

## 5. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Driesch, H.A.E. The potency of the first two cleavage cells in the development of echinoderms [translation of 1891 German version]. In Great Experiments in Biology; Gabriel, M., Fogel, S., Eds.; Prentice-Hall: Englewoods Cliffs, NJ, USA, 1955; pp. 210–214. [Google Scholar]
- Wilson, E.B. Experimental studies in germinal localization: II. Experiments on the cleavage-mosaic in Patella and Dentalium. J. Exp. Zool.
**1904**, 1, 197–268. [Google Scholar] [CrossRef] - Lawrence, P.A.; Levine, M. Mosaic and regulative development: Two faces of one coin. Curr. Biol.
**2006**, 16, R236–R239. [Google Scholar] [CrossRef] [PubMed] - Waddington, C.H. Principles of Embryology; George Allen & Unwin Ltd.: London, UK, 1956. [Google Scholar]
- Vogt, W. Mosaikcharakter und Regulation in der Frühentwicklung des Amphibieneies. Verh. Dtsch. Zool. Ges.
**1928**, 32, 26–70. (In German) [Google Scholar] - McCain, E.R.; Cather, J.N. Regulative and mosaic development of Ilyanassa obsoleta embryos lacking the A and C quadrants. Invertebr. Reprod. Dev.
**1989**, 15, 185–192. [Google Scholar] [CrossRef] - Cunha, A.; Azevedo, R.B.R.; Emmons, S.W.; Leroi, A.M. Developmental biology: Variable cell number in nematodes. Nature
**1999**, 402, 253–253. [Google Scholar] [PubMed] - Nishida, H.; Stach, T. Cell lineages and fate maps in tunicates: Conservation and modification. Zool. Sci.
**2014**, 31, 645–652. [Google Scholar] [CrossRef] [PubMed] - Meinertzhagen, I.A. Eutely, cell lineage, and fate within the ascidian larval nervous system: Determinacy or to be determined? Can. J. Zool.
**2005**, 83, 184–195. [Google Scholar] [CrossRef] - Gordon, N.K.; Gordon, R. Embryogenesis Explained; World Scientific Publishing Company: Singapore, 2016. [Google Scholar]
- Rochlin, K.; Yu, S.; Roy, S.; Baylies, M.K. Myoblast fusion: When it takes more to make one. Dev. Biol.
**2010**, 341, 66–83. [Google Scholar] [CrossRef] [PubMed] - Idema, T.; Dubuis, J.O.; Kang, L.; Manning, M.L.; Nelson, P.C.; Lubensky, T.C.; Liu, A.J. The syncytial Drosophila embryo as a mechanically excitable medium. PLoS ONE
**2013**, 8, e77216. [Google Scholar] - Gordon, R. The Hierarchical Genome and Differentiation Waves: Novel Unification of Development, Genetics and Evolution; World Scientific & Imperial College Press: Singapore; London, UK, 1999. [Google Scholar]
- Gordon, N.K.; Gordon, R. The organelle of differentiation in embryos: The cell state splitter. Theor. Biol. Med. Model.
**2016**. [Google Scholar] [CrossRef] [PubMed] - Essam, J.W.; Fisher, M.E. Some basic definitions in graph theory. Rev. Mod. Phys.
**1970**, 42, 272–288. [Google Scholar] [CrossRef] - Gordon, R. On Monte Carlo algebra. J. Appl. Probab.
**1970**, 7, 373–387. [Google Scholar] [CrossRef] - Wang, L. Directed Acyclic Graph. In Encyclopedia of Systems Biology; Dubitsky, W., Wolkenhauer, O., Cho, K.-H., Yokota, H., Eds.; Springer: Berlin, Germany, 2013; p. 574. [Google Scholar]
- Wikipedia Planar Graph. Available online: https://en.wikipedia.org/wiki/Planar_graph (accessed on 28 March 2016).
- Bonichon, N.; Gavoille, C.; Hanusse, N.; Poulalhon, D.; Schaeffer, G. Planar graphs, via well-orderly maps and trees. Graphs Comb.
**2006**, 22, 185–202. [Google Scholar] [CrossRef] - Riordan, J. The numbers of labeled colored and chromatic trees. Acta Math.
**1957**, 97, 211–225. [Google Scholar] [CrossRef] - Jacobson, G. Space-efficient static trees and graphs. In Proceedings of the 30th Annual Symposium on Foundations of Computer Science, Research Triangle Park, NC, USA, 30 October–1 November 1989; pp. 549–554.
- Crescenzi, P.; Penna, P. Strictly-upward drawings of ordered search trees. Theor. Comput. Sci.
**1998**, 203, 51–67. [Google Scholar] [CrossRef] - Di Battista, G.; Eades, P.; Tamassia, R.; Tollis, I.G. Algorithms for drawing graphs: An annotated bibliography. Comput. Geom. Theory Appl.
**1994**, 4, 235–282. [Google Scholar] [CrossRef] - Rusu, A.; Clement, C.; Jianu, R. Adaptive binary trees visualization with respect to user-specified quality measures. Proc. Int. Conf. Inf. Vis.
**2006**, 10, 469–474. [Google Scholar] - Garg, A.; Goodrich, M.T.; Tamassia, R. Planar upward tree drawings with optimal area. Int. J. Comput. Geom. Appl.
**1996**, 6, 333–356. [Google Scholar] [CrossRef] - Sulston, J.E.; Schierenberg, E.; White, J.G.; Thomson, J.N. The embryonic cell lineage of the nematode Caenorhabditis elegans. Dev. Biol.
**1983**, 100, 64–119. [Google Scholar] [CrossRef] - Wikipedia Graph Isomorphism. Available online: https://en.wikipedia.org/wiki/Graph_isomorphism (accessed on 28 March 2016).
- Hedgecock, E.M. Cell lineage mutants in the nematode Caenorhabditis elegans. Trends Neurosci.
**1985**, 8, 288–293. [Google Scholar] [CrossRef] - Sternberg, P.W.; Horvitz, H.R. Gonadal cell lineages of the nematode Panagrellus redivivus and implications for evolution by the modification of cell lineage. Dev. Biol.
**1981**, 88, 147–166. [Google Scholar] [CrossRef] - Vandenberg, L.N.; Levin, M. A unified model for left-right asymmetry? Comparison and synthesis of molecular models of embryonic laterality. Devel. Biol.
**2013**, 379, 1–15. [Google Scholar] [CrossRef] - Goldstein, B. On the evolution of early development in the Nematoda. Philos. Trans. R. Soc. Lond. B Biol. Sci.
**2001**, 356, 1521–1531. [Google Scholar] [CrossRef] [PubMed] - Gordon, R. Walking the tightrope: The dilemmas of hierarchical instabilities in Turing’s morphogenesis. In The Once and Future Turing: Computing the World; Cooper, S.B., Hodges, A., Eds.; Cambridge University Press: Cambridge, UK, 2015; pp. 150–164. [Google Scholar]
- Koonin, E.V. Towards a postmodern synthesis of evolutionary biology. Cell Cycle
**2009**, 8, 799–800. [Google Scholar] [CrossRef] [PubMed] - Metz, J.A.J. Thoughts on the geometry of meso-evolution: Collecting mathematical elements for a postmodern synthesis. In Mathematics of Darwin's Legacy; Chalub, F.A.C.C., Rodrigues, J.F., Eds.; Springer: Basel, Switzerland, 2011; pp. 193–231. [Google Scholar]
- Björklund, N.K.; Gordon, R. Surface contraction and expansion waves correlated with differentiation in axolotl embryos. I. Prolegomenon and differentiation during the plunge through the blastopore, as shown by the fate map. Comput. Chem.
**1994**, 18, 333–345. [Google Scholar] [CrossRef] - Shapiro, E.; Biezuner, T.; Linnarsson, S. Single-cell sequencing-based technologies will revolutionize whole-organism science. Nat. Rev. Genet.
**2013**, 14, 618–630. [Google Scholar] [CrossRef] [PubMed] - Veeman, M.; Reeves, W. Quantitative and in toto imaging in ascidians: Working toward an image-centric systems biology of chordate morphogenesis. Genesis
**2015**, 53, 143–159. [Google Scholar] [CrossRef] [PubMed] - Stach, T.; Anselmi, C. High-precision morphology: Bifocal 4D-microscopy enables the comparison of detailed cell lineages of two chordate species separated for more than 525 million years. BMC Biol.
**2015**. [Google Scholar] [CrossRef] [PubMed] - Hudson, C.; Yasuo, H. Similarity and diversity in mechanisms of muscle fate induction between ascidian species. Biol. Cell
**2008**, 100, 265–277. [Google Scholar] [CrossRef] [PubMed] - Wikipedia Synapomorphy. Available online: https://en.wikipedia.org/wiki/Synapomorphy (accessed on 30 March 2016).
- McGhee, G.R. Convergent Evolution: Limited Forms Most Beautiful; MIT Press: Cambridge, MA, USA, 2011. [Google Scholar]
- Bao, Z.R.; Zhao, Z.Y.; Boyle, T.J.; Murray, J.I.; Waterston, R.H. Control of cell cycle timing during C. elegans embryogenesis. Dev. Biol.
**2008**, 318, 65–72. [Google Scholar] [CrossRef] [PubMed] - Ho, V.W.; Wong, M.K.; An, X.; Guan, D.; Shao, J.; Ng, H.C.; Ren, X.; He, K.; Liao, J.; Ang, Y.; et al. Systems-level quantification of division timing reveals a common genetic architecture controlling asynchrony and fate asymmetry. Mol. Syst. Biol.
**2015**. [Google Scholar] [CrossRef] [PubMed] - Tiraihi, A.; Tiraihi, M.; Tiraihi, T. Self-organization of developing embryo using scale-invariant approach. Theor. Biol. Med. Model.
**2011**. [Google Scholar] [CrossRef] [PubMed] - Arata, Y.; Takagi, H.; Sako, Y.; Sawa, H. Power law relationship between cell cycle duration and cell volume in the early embryonic development of Caenorhabditis elegans. Front. Physiol.
**2015**. [Google Scholar] [CrossRef] [PubMed] - Ginzberg, M.B.; Kafri, R.; Kirschner, M. On being the right (cell) size. Science
**2015**. [Google Scholar] [CrossRef] [PubMed] - Sulston, J.E. C. elegans: The cell lineage and beyond. Biosci. Rep.
**2003**, 23, 49–66. [Google Scholar] [CrossRef] [PubMed] - Roubinet, C.; Cabernard, C. Control of Asymmetric cell division. Curr. Opin. Cell Biol.
**2014**, 31, 84–91. [Google Scholar] [CrossRef] [PubMed] - Bordzilovskaya, N.P.; Dettlaff, T.A.; Duhon, S.T.; Malacinski, G.M. Developmental-stage series of axolotl embryos [Erratum: Staging Table 19-1 is for 20 °C, not 29 °C]. In Developmental Biology of the Axolotl; Armstrong, J.B., Malacinski, G.M., Eds.; Oxford University Press: New York, NY, USA, 1989; pp. 201–219. [Google Scholar]
- Nieuwkoop, P.D.; Björklund, N.K.; Gordon, R. Surface contraction and expansion waves correlated with differentiation in axolotl embryos. II. In contrast to urodeles, the anuran Xenopus laevis does not show furrowing surface contraction waves. Int. J. Dev. Biol.
**1996**, 40, 661–664. [Google Scholar] [PubMed] - Brodland, G.W.; Gordon, R.; Scott, M.J.; Björklund, N.K.; Luchka, K.B.; Martin, C.C.; Matuga, C.; Globus, M.; Vethamany-Globus, S.; Shu, D. Furrowing surface contraction wave coincident with primary neural induction in amphibian embryos. J. Morphol.
**1994**, 219, 131–142. [Google Scholar] [CrossRef] [PubMed] - Nakamura, M.J.; Terai, J.; Okubo, R.; Hotta, K.; Oka, K. Three-dimensional anatomy of the Ciona intestinalis tailbud embryo at single-cell resolution. Dev. Biol.
**2012**, 372, 274–284. [Google Scholar] [CrossRef] [PubMed] - Tassy, O.; Dauga, D.; Daian, F.; Sobral, D.; Robin, F.; Khoueiry, P.; Salgado, D.; Fox, V.; Caillol, D.; Schiappa, R.; et al. The ANISEED database: Digital representation, formalization, and elucidation of a chordate developmental program. Genome Res.
**2010**, 20, 1459–1468. [Google Scholar] [CrossRef] [PubMed] - Aniseed Aniseed Data: C. intestinalis. Available online: http://www.aniseed.cnrs.fr/aniseed/download/download_data (accessed on 28 March 2016).
- Bao, Z.R.; Murray, J.I.; Boyle, T.; Ooi, S.L.; Sandel, M.J.; Waterston, R.H. Automated cell lineage tracing in Caenorhabditis elegans. Proc. Natl. Acad. Sci. USA
**2006**, 103, 2707–2712. [Google Scholar] [CrossRef] [PubMed] - Cirino, P.; Toscano, A.; Caramiello, D.; Macina, A.; Miraglia, V.; Monte, A. Laboratory Culture of the Ascidian Ciona intestinalis (L.): A Model System for Molecular Developmental Biology Research. Available online: http://comm.archive.mbl.edu/BiologicalBulletin/MMER/cirino/CirTit.html (accessed on 14 August 2016).
- Bianchi, L.; Driscoll, M. Culture of Embryonic C. elegans Cells for Electrophysiological and Pharmacological Analyses. Available online: http://www.ncbi.nlm.nih.gov/books/NBK19713/ (accessed on 28 March 2016).
- Granville, V. Developing Analytic Talent: Becoming a Data Scientist; Wiley: Hoboken, NJ, USA, 2014. [Google Scholar]
- Wikipedia GIMP. Available online: https://en.wikipedia.org/wiki/GIMP (accessed on 28 March 2016).
- Alicea, B.; Gordon, R. C. intestinalis Embryonic Differentiation Tree (1- to 112-cell stage). Available online: https://figshare.com/articles/C_intestinalis_Embryonic_Differentiation_Tree_1_to_112_cell_stage_/2117152 (accessed on 28 March 2016).
- Alicea, B.; Gordon, R. C. elegans Embryonic Differentiation Tree (10 Division Events). Available online: https://figshare.com/articles/C_elegans_Embryonic_Differentiation_Tree_10_division_events_/2118049 (accessed on 28 March 2016).
- Hobert, O. Neurogenesis in the Nematode Caenorhabditis elegans. Available online: http://www.ncbi.nlm.nih.gov/books/NBK116086/ (accessed on 28 March 2016).
- Hobert, O. Neurogenesis in the nematode Caenorhabditis elegans. In Comprehensive Developmental Neuroscience: Patterning and Cell Type Specification in the Developing Cns and Pns; Rubenstein, J.L.R., Rakic, P., Eds.; Elsevier Academic Press: San Diego, CA, USA, 2013; pp. 609–626. [Google Scholar]
- Goldstein, B.; Hird, S.N.; White, J.G. Cell polarity in early C. elegans development. Development
**1993**, Supplement, 279–287. [Google Scholar] - Bhatla, N. C. elegans Cell Lineage. Available online: http://wormweb.org/celllineage#c=P0&z=1 (accessed on 28 March 2016).
- Nishida, H. Cell lineage analysis in ascidian embryos by intracellular injection of a tracer enzyme. III. Up to the tissue restricted stage. Dev. Biol.
**1987**, 121, 526–541. [Google Scholar] [CrossRef] - Rose, L.; Gonczy, P. Polarity establishment, asymmetric division and segregation of fate determinants in early C. elegans embryos. WormBook
**2014**, 1–43. [Google Scholar] - Packard, G.C. On the use of log-transformation versus nonlinear regression for analyzing biological power laws. Biol. J. Linn. Soc.
**2014**, 113, 1167–1178. [Google Scholar] [CrossRef] - Hamming, R.W. Error detecting and error correcting codes. Bell Syst. Tech. J.
**1950**, 29, 147–160. [Google Scholar] [CrossRef] - Wikipedia BLAST. Available online: https://en.wikipedia.org/wiki/BLAST (accessed on 28 March 2016).
- Needleman, S.B.; Wunsch, C.D. A general method applicable to the search for similarities in the amino acid sequence of two proteins. J. Mol. Biol.
**1970**, 48, 443–453. [Google Scholar] [CrossRef] - Alicea, B.; Portegys, T.; Gordon, R. Information isometry technique reveals organizational features in developmental cell lineages. bioRxiv
**2016**. [Google Scholar] [CrossRef] - Bossinger, O.; Schierenberg, E. Early embryonic induction in C. elegans can be inhibited with polysulfated hydrocarbon dyes. Dev. Biol.
**1996**, 176, 17–21. [Google Scholar] [CrossRef] [PubMed] - Sternberg, P.W.; Horvitz, H.R. The genetic control of cell lineage during nematode development. Annu. Rev. Genet.
**1984**, 18, 489–524. [Google Scholar] [CrossRef] [PubMed] - Lyczak, R.; Gomes, J.E.; Bowerman, B. Heads or tails: Cell polarity and axis formation in the early Caenorhabditis elegans embryo. Dev. Cell
**2002**, 3, 157–166. [Google Scholar] [CrossRef] - Banks, K. Thunderbirds, pterosaurs and tumblers: The biomechanics of flight. Harv. Sci. Rev.
**2011**, 31–33. [Google Scholar] - Azevedo, R.B.R.; Lohaus, R.; Braun, V.; Gumbel, M.; Umamaheshwar, M.; Agapow, P.M.; Houthoofd, W.; Platzer, U.; Borgonie, G.; Meinzer, H.P.; et al. The simplicity of metazoan cell lineages. Nature
**2005**, 433, 152–156. [Google Scholar] [CrossRef] [PubMed] - Lambie, E.J. Cell proliferation and growth in C. elegans. BioEssays
**2002**, 24, 38–53. [Google Scholar] [CrossRef] [PubMed] - Brauchle, M.; Baumer, K.; Gönczy, P. Differential activation of the DNA replication checkpoint contributes to asynchrony of cell division in C. elegans embryos. Curr. Biol.
**2003**, 13, 819–827. [Google Scholar] [CrossRef] - Kipreos, E.T. C. elegans cell cycles: Invariance and stem cell divisions. Nat. Rev. Mol. Cell Biol.
**2005**, 6, 766–776. [Google Scholar] [CrossRef] [PubMed] - Labouesse, M.; Mango, S.E. Patterning the C. elegans embryo: Moving beyond the cell lineage. Trends Genet.
**1999**, 15, 307–313. [Google Scholar] [CrossRef] - Geard, N.; Bullock, S.; Lohaus, R.; Azevedo, R.B.R.; Wiles, J. Developmental motifs reveal complex structure in cell lineages. Complexity
**2011**, 16, 48–57. [Google Scholar] [CrossRef] - Yamada, A.; Nishida, H. Control of the number of cell division rounds in distinct tissues during ascidian embryogenesis. Dev. Growth Differ.
**2014**, 56, 376–386. [Google Scholar] [CrossRef] [PubMed] - Gonczy, P.; Rose, L.S. Asymmetric cell division and axis formation in the embryo. WormBook
**2005**, 1–20. [Google Scholar] [CrossRef] [PubMed] - Ogura, Y.; Sasakura, Y. Ascidians as excellent models for studying cellular events in the chordate body plan. Biol. Bull.
**2013**, 224, 227–236. [Google Scholar] [PubMed] - Lemaire, P. Evolutionary crossroads in developmental biology: The tunicates. Development
**2011**, 138, 2143–2152. [Google Scholar] [CrossRef] [PubMed] - Lu, K.; Cao, T.; Gordon, R. A cell state splitter and differentiation wave working-model for embryonic stem cell development and somatic cell epigenetic reprogramming. BioSystems
**2012**, 109, 390–396. [Google Scholar] [CrossRef] [PubMed] - West, G.B.; Brown, J.H.; Enquist, B.J. A general model for the origin of allometric scaling laws in biology. Science
**1997**, 276, 122–126. [Google Scholar] [CrossRef] [PubMed] - West, G.B. The origin of universal scaling laws in biology. Phys. A
**1999**, 263, 104–113. [Google Scholar] [CrossRef] - Kuratani, S. Modularity, comparative embryology and evo-devo: Developmental dissection of evolving body plans. Dev. Biol.
**2009**, 332, 61–69. [Google Scholar] [CrossRef] [PubMed] - Atchley, W.R.; Hall, B.K. A model for development and evolution of complex morphological structures. Biol. Rev.
**1991**, 66, 101–157. [Google Scholar] [CrossRef] [PubMed] - Alicea, B.; Gordon, R. Toy models for macroevolutionary patterns and trends. BioSystems
**2014**, 122, 25–37. [Google Scholar] [CrossRef] - Lecointre, G.; Le Guyader, H. The Tree of Life: A Phylogenetic Classification; Harvard University Press: Cambridge, UK, 2006. [Google Scholar]
- Gibson, D.G.; Glass, J.I.; Lartigue, C.; Noskov, V.N.; Chuang, R.-Y.; Algire, M.A.; Benders, G.A.; Montague, M.G.; Ma, L.; Moodie, M.M.; et al. Creation of a bacterial cell controlled by a chemically synthesized genome. Science
**2010**, 329, 52–56. [Google Scholar] [CrossRef] [PubMed] - Hutchison, C.A.; Chuang, R.-Y.; Noskov, V.N.; Assad-Garcia, N.; Deerinck, T.J.; Ellisman, M.H.; Gill, J.; Kannan, K.; Karas, B.J.; Ma, L.; et al. Design and synthesis of a minimal bacterial genome. Science
**2016**. [Google Scholar] [CrossRef] [PubMed] - Palyanov, A.; Khayrulin, S.; Larson, S.D.; Dibert, A. Towards a virtual C. elegans: A framework for simulation and visualization of the neuromuscular system in a 3D physical environment. In Silico Biol.
**2011**, 11, 137–147. [Google Scholar] - Szigeti, B.; Gleeson, P.; Vella, M.; Khayrulin, S.; Palyanov, A.; Hokanson, J.; Currie, M.; Cantarelli, M.; Idili, G.; Larson, S. OpenWorm: An open-science approach to modelling Caenorhabditis elegans. Front. Comput. Neurosci.
**2014**. [Google Scholar] [CrossRef] [PubMed] - Schulze, J.; Schierenberg, E. Evolution of embryonic development in nematodes. EvoDevo
**2011**. [Google Scholar] [CrossRef] [PubMed] - Castillo-Davis, C.I.; Hartl, D.L. Genome evolution and developmental constraint in Caenorhabditis elegans. Mol. Biol. Evol.
**2002**, 19, 728–735. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**A demonstration of how binary codes produce different classifications of each cell in C. elegans embryos according to two different binary tree orderings. (

**A**) Five nodes and their left/right (L/R) ordering in the C. elegans lineage tree; (

**B**) a binary lineage code classification for these same nodes (cells) in the lineage tree, with 0 representing nodes that branch to the left, and 1 representing nodes that branch to the right; (

**C**) the same five nodes as shown in A and B, but reordered to reflect their relative cell volumes, small daughter cells to the left (0) and large daughter cells to the right (1). This is reflected in their differentiation code classification; (

**D**) a demonstration of how the Hamming distance metric is calculated for the “distance” between the lineage code and the differentiation code for a given cell (X and X’). Only the path in the tree is shown, from the root (top) to the given cell (bottom). Represented as a decimal number, the Hamming distance (see Methods) is the number of differences (or flipped bits) between X and X’ (labeled in red).

**Figure 2.**Embryo volume per cell stage of embryogenesis for Ciona. Volume (measured in cubic microns) is averaged over a number of observations (N). N (stage) is given in Table S1.

**Figure 3.**The log-linear relationship between cell volume (log

_{10}of cell volume in µm

^{3}) and the cell lifetime (linear) of individual cells for Ciona embryo (raised at 18–20 °C) based on all cells between the one-cell stage and the 112-cell stage (N = 225). Cell volume is normalized as a percentage of total embryo volume. Some data points are overlapping, and are divided into two categories. (

**A**) Blue dots (n = 209), x-axis interval 10.5–70.5 min; (

**B**) red dots (n = 16), x-axis intervals 72–103.5 min. The mean value for category A is 0.20, and the mean value for category B is 0.19, shown on the graph as two horizontal gray lines.

**Figure 4.**The relationship between cell volume and the cell lifetime of individual cells for the pre-hatch C. elegans embryo (raised at 25 °C), based on 96 cells (N = 96). Cell volume (µm

^{3}) extrapolated from cell diameter after normalization to P0 (1-cell stage). Main data series is blue, selected outliers are red. The data from the outliers is not included in the lower least squares fit, and vice versa.

**Figure 5.**An analysis of cell volume versus lifetime in Ciona, based on all cells between the one-cell stage and the 112-cell stage (N = 224). Cell volume is normalized as a percentage of total embryo volume, and lifetime is the duration of the period of time between a cell’s creation via division and its division into two daughter cells. Trendline (black) is based on a power function.

**Figure 6.**An analysis of cell volume in C. elegans versus lifetime (as calculated by Bao et al. [55]), based on 192 cells (N = 192) from a subtree of the AB lineage. Cell volume is extrapolated from nuclear diameter and is normalized as a percentage of total embryo volume Lifetime as in Figure 5. Trendline (black) is based on a linear function.

**Figure 7.**Comparison of cell volume versus lineage depth for Ciona. The graph includes 382 cells from the two-cell stage to the 112-cell stage. Lineage depth is determined by the number of division events from the one-cell stage (depth of 0).

**Figure 8.**Comparison of relative cell volume versus lineage depth for C. elegans. Graph includes 558 cells from the pre-hatch embryo. Lineage depth is determined by the number of division events from the one-cell stage (depth of 0).

**Figure 9.**Maximum, mean, and minimum values (black dots from top to bottom) for smaller cell volume to larger cell volume ratios for Ciona summarized by lineage depth (values per division event).

**Figure 10.**Maximum, mean, and minimum values (black dots from top to bottom) for smaller cell volume to larger cell volume ratios for C. elegans summarized by lineage depth (values per division event).

**Figure 11.**An isometric graph showing the Hamming distance of the differentiation tree from the lineage tree in Ciona (N = 213). The H abbreviation stands for Hamming distance. The position of a point representing a cell is based on the depth of its node in the differentiation tree. The positions of all points are rotated 45 degrees clockwise from a bottom-to-top differentiation tree ordering (where the 1-cell stage is at the bottom of the graph). Each cell is colored with its Hamming distance. Along a given line, the cells appear in their order, left to right, in the differentiation tree. For example, cells A.5.1 and A.5.1* at depth 4, where the total number of cells is 16 (ranging from 0 to 15), means cell A.5.1 is at the extreme left side of the differentiation tree, and cell A.5.1* is at the extreme right side of the differentiation tree. The other cells are spaced in between. The pattern of Hamming distances suggests that the relationship between the two orderings is nonrandom and therefore has some underlying anatomical importance.

**Figure 12.**An isometric graph showing the Hamming distance of the differentiation tree from the lineage tree in C. elegans (N = 230). The H abbreviation stands for Hamming distance. The position of a point representing a cell is based on the depth of its node in the differentiation tree. The positions of all points are rotated 45 degrees clockwise from a bottom-to-top differentiation tree ordering (where the one-cell stage is at the bottom of the graph). Each cell is colored with its Hamming distance. See the legend of Figure 11 for other details.

**Figure 13.**The differentiation tree of the axolotl (Ambystoma mexicanum) up to neural plate formation (stages 8–12 raised at 20 °C). All cell types are presumptive. Red branches to the left labelled with the letter C indicates a contraction wave, while green branches to the right labelled with the letter E indicates an expansion wave. The time axis (vertical) is represented in two ways: (1) on the left, are hours since fertilization for embryos raised at 20 °C, (2) on the right are stage numbers based on distinctly recognizable morphological features [49]. Regarded as a vector, the vertical component of each edge represents the duration of each wave. The ordinal axis is horizontal in this figure. Note each numbered wave may pass through one tissue and continue into an adjacent tissue and so, for example, E3 begins in endodermal tissue and then continues into mesodermal tissue. From [10] with permission of World Scientific Publishing. The differentiation codes based on the named tissues (boxes) and unnamed intermediate tissues (black dots) with unique differentiation codes are determined from this tree and shown in Table S6.

**Table 1.**Number and proportion of cell divisions above confidence interval threshold (see Methods) for asymmetric cell divisions, based on Equation (2). Data represents all divisions (N = 117) in a pre-gastrulation Ciona fate lineage tree.

Ciona | Confidence Interval h | ||||
---|---|---|---|---|---|

0.05 | 0.1 | 0.25 | 0.50 | TOTAL | |

Number of volume asymmetric cell divisions | 103 | 82 | 48 | 23 | 117 |

Proportion of total | 0.88 | 0.7 | 0.41 | 0.2 | 1.0 |

**Table 2.**Number and proportion of cell divisions above confidence interval threshold (see Methods) for asymmetric cell divisions. Data represents all divisions (N = 257) in a pre-hatch C. elegans lineage tree.

C. elegans | Confidence Interval h | ||||
---|---|---|---|---|---|

0.005 | 0.01 | 0.025 | 0.05 | TOTAL | |

Number of volume asymmetric cell divisions | 203 | 151 | 80 | 22 | 257 |

Proportion of total | 0.79 | 0.59 | 0.31 | 0.09 | 1.0 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Alicea, B.; Gordon, R.
Quantifying Mosaic Development: Towards an Evo-Devo Postmodern Synthesis of the Evolution of Development via Differentiation Trees of Embryos. *Biology* **2016**, *5*, 33.
https://doi.org/10.3390/biology5030033

**AMA Style**

Alicea B, Gordon R.
Quantifying Mosaic Development: Towards an Evo-Devo Postmodern Synthesis of the Evolution of Development via Differentiation Trees of Embryos. *Biology*. 2016; 5(3):33.
https://doi.org/10.3390/biology5030033

**Chicago/Turabian Style**

Alicea, Bradly, and Richard Gordon.
2016. "Quantifying Mosaic Development: Towards an Evo-Devo Postmodern Synthesis of the Evolution of Development via Differentiation Trees of Embryos" *Biology* 5, no. 3: 33.
https://doi.org/10.3390/biology5030033