Rectified and Ramifying Representations for the Purpose of Theoretical Expediency

One aim of the DevoWorm project is to take a tree structure (in this case a cell lineage tree from an embryo) and extract distributed structural information. This is done to find previously undiscovered patterns in early development (embryogenesis). One way in which this can be accomplished is by building undirected complex networks to represent the relationships between three-dimensional cellular position in a point model of the embryo. Indeed, rather than a branching tree, we are left with a much larger tree with a significant number of cycles. This allows us to examine previously undiscovered interactions between cells based on proximity (such as juxtacrine and paracrine signalling).

A tree with a cycle, indeed. Popular meme or research problem?

Now these ideas have been made concrete in the form of a poster and presentation that describe the methodology and results of representing approximations of cell nuclei in the embryo as a connected network. This work has been featured at the Network Frontiers Workshop (Northwestern University) and the Midwest Regenerative Medicine Meeting (Washington University, St. Louis). Here is the poster in slide form:

Notice how this approach is both geometrically vivid and extensible to different modes of development. The graphs and statistics were rendered in Gephi, and other computation was done in MATLAB and R. Our next steps include developing customized modules in Gephi for drawing differentiation trees, developing hybrid directed acyclic graph (DAG)/undirected network graph structures, and refining the network construction methodology.

We are also working on a methodology called the scalable interactome, which simply involves using graphs to visualize and extract information at multiple spatial and temporal scales. One current example of this is OneZoom explorer, which renders the tree of life in a fractal manner. This can be extended to exploring the fractal and complex geometric nature of the embryo itself.

A slightly different view of human evolution and rejection of human exceptionalism. COURTESY: OneZoom Tree of Life.

"Miscellaneous Polyhedra" by Carol Branch (no pun intended).

With that nod to complexity, I would be remiss if I did not mention the old SimCity dictum? A gratuitous image of fractals and reference to a Wil Wright easter egg is the perfect way to end this post.