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One overarching principle of eukaroytic development is the generative spatial emergence and self-organization of cell populations. As cells divide and differentiate, they and their descendants form a spatiotemporally explicit and increasingly compartmentalized complex system. Yet despite this compartmentalization, there is selective functional overlap between these structural components. While contemporary tools such as lineage trees and molecular signaling networks provide a window into this complexity, they do not characterize embryogenesis as a global process. Using a four-dimensional spatial representation, major features of the developmental process are revealed. To establish the role of developmental mechanisms that turn a spherical embryo into a highly asymmetrical adult phenotype, we can map the outcomes of the cell division process to a complex network model. This type of representational model provides information about the top-down mechanisms relevant to the differentiation process. In a complementary manner, looking for phenomena such as superdiffusive positioning and sublineage-based anatomical clustering incorporates dynamic information to our parallel view of embryogenesis. Characterizing the spatial organization and geometry of embryos in this way allows for novel indicators of developmental patterns both within and between organisms.
Article was previously submitted to PeerJ as a peer-reviewed submission, but was rejected. Reviewer comments were addressed and article rewritten for submission to special issue of BioSystems (Computational, Theoretical, and Experimental approaches to Morphogenesis, in memoriam of Dr. Lev V. Beloussov)
Supplemental File 1: Circular network topologies comparing connections among subtrees and tree levels
The x-axis features a series of circular networks based on the number of above threshold connections between cells at different levels of the tree in a 7 level (128-cell condition) tree.
Rows in descending order: no difference in tree level (0), difference of one level (1), difference of two levels (2), difference of between 3 and 7 levels (3-7).
Columns from left to right: all connections between cells in the AB sublineage only (intra-AB), all connections between cells in the P1 sublineage only (intra-P1), all connections between cells where one cell is from the AB sublineage and the other cell is from the P1 sublineage (inter-AB-P1).
Supplemental File 2: Heat map of the clique analysis for a 7 level (128-cell condition) tree
Each row represents a unique clique generated from a connectivity matrix of the 7 level tree. The heat map columns represent the number of members in the generated cliques from each octopartite subtree (8 categories). Color coding scheme is presented in the legend to the right of the map.