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

View Article: PubMed Central - PubMed

ABSTRACT

Embryonic development proceeds through a series of differentiation events. The mosaic version of this process (binary cell divisions) can be analyzed by comparing early development of Cionaintestinalis and Caenorhabditis elegans. To do this, we reorganize lineage trees into differentiation trees using the graph theory ordering of relative cell volume. Lineage and differentiation trees provide us with means to classify each cell using binary codes. Extracting data characterizing lineage tree position, cell volume, and nucleus position for each cell during early embryogenesis, we conduct several statistical analyses, both within and between taxa. We compare both cell volume distributions and cell volume across developmental time within and between single species and assess differences between lineage tree and differentiation tree orderings. This enhances our understanding of the differentiation events in a model of pure mosaic embryogenesis and its relationship to evolutionary conservation. We also contribute several new techniques for assessing both differences between lineage trees and differentiation trees, and differences between differentiation trees of different species. The results suggest that at the level of differentiation trees, there are broad similarities between distantly related mosaic embryos that might be essential to understanding evolutionary change and phylogeny reconstruction. Differentiation trees may therefore provide a basis for an Evo-Devo Postmodern Synthesis.

No MeSH data available.


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).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC5037352&req=5

biology-05-00033-f001: 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).

Mentions: In summary, lineage and differentiation trees differ from conventional graphs in that one axis represents the timing of developmental events. Both the lineage tree and the differentiation tree for the same mosaic organism are both rooted, planar, ordered binary trees, but differing only along their ordinal axis (perpendicular to the time axis). See Figure 1C for a visual example. They are therefore isomorphic in the graph theoretical sense [27]. Two isomorphic differentiation trees that look the same except for changes in their timing along the vertical axis have been hypothesized to describe heterochrony [10,13]. When two trees are not isomorphic, we shall say that they differ in “topology”. One example of this is that lineage trees of mutants often differ in topology [10,28,29,30].


Quantifying Mosaic Development: Towards an Evo-Devo Postmodern Synthesis of the Evolution of Development via Differentiation Trees of Embryos
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).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5037352&req=5

biology-05-00033-f001: 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).
Mentions: In summary, lineage and differentiation trees differ from conventional graphs in that one axis represents the timing of developmental events. Both the lineage tree and the differentiation tree for the same mosaic organism are both rooted, planar, ordered binary trees, but differing only along their ordinal axis (perpendicular to the time axis). See Figure 1C for a visual example. They are therefore isomorphic in the graph theoretical sense [27]. Two isomorphic differentiation trees that look the same except for changes in their timing along the vertical axis have been hypothesized to describe heterochrony [10,13]. When two trees are not isomorphic, we shall say that they differ in “topology”. One example of this is that lineage trees of mutants often differ in topology [10,28,29,30].

View Article: PubMed Central - PubMed

ABSTRACT

Embryonic development proceeds through a series of differentiation events. The mosaic version of this process (binary cell divisions) can be analyzed by comparing early development of Cionaintestinalis and Caenorhabditis elegans. To do this, we reorganize lineage trees into differentiation trees using the graph theory ordering of relative cell volume. Lineage and differentiation trees provide us with means to classify each cell using binary codes. Extracting data characterizing lineage tree position, cell volume, and nucleus position for each cell during early embryogenesis, we conduct several statistical analyses, both within and between taxa. We compare both cell volume distributions and cell volume across developmental time within and between single species and assess differences between lineage tree and differentiation tree orderings. This enhances our understanding of the differentiation events in a model of pure mosaic embryogenesis and its relationship to evolutionary conservation. We also contribute several new techniques for assessing both differences between lineage trees and differentiation trees, and differences between differentiation trees of different species. The results suggest that at the level of differentiation trees, there are broad similarities between distantly related mosaic embryos that might be essential to understanding evolutionary change and phylogeny reconstruction. Differentiation trees may therefore provide a basis for an Evo-Devo Postmodern Synthesis.

No MeSH data available.