ABSTRACT
In this paper, we will introduce a method for calculating and visualizing the information content of embryogenesis called the information isometry technique. We treat cell lineage trees as directed acyclic graphs (DAGs) that can be subject to reordering using various criteria. When we compare alternative orderings of these graphs, they reveal subtle patterns of information. We use one such alternative criteria (e.g. a differentiation code) to sort cells at each level of the tree. Both axial- and differentiation-based orderings can by characterized using a binary classifier to quantify the order of particular cells at each level of a given tree. We calculate a Hamming distance to compare these orderings and reveal differences that result from these ordering criteria. We also introduce a method of visualization through the construction of isometric graphs, or a series of colored points forming isometric lines with each representing a level of the original lineage tree. We show that these graphs reveal biologically significant patterns through comparisons between randomly generated lineage/differentiation trees and the Caenorhabditis elegans lineage/differentiation tree. As a collective indicator of distance between various cell lineage orderings, isometric graphs can reveal a number of emergent patterns within cell lineages and between sublineages, including the relative information content of specific subtrees. These patterns of information content reveal the informative nature of alternative ordering criteria with respect to important trends in development.
