Proliferation Networks and Epithelial Tissues

From Cell Division to Network Topology

The fruitfly wing is an amazing example of self-assembly.

Starting from a small disc of 30 cells, the wing forms through many rounds of division until it is a large tissue with some 30,000 cells. During this time the wing also manages to create important architectures, from the cobblestone like regularity of cell shapes, to laying down the pattern of veins, to controlling overall organ size and shape. Many researchers study this system as a model for multicellular organism development. At the same time, the wing belongs to a category of tissues that is common throughout the animal kingdom (and similar to plants) called epithelial tissues. As a result it shares many interesting properties with other multicellular organisms and gives us a clue about the evolution of multicellular systems.

We are interested in the link between local and global, i.e. how do the local decisions of a cell result in high-level tissue structure? And vice-versa, can high-level tissue structure give us clues about how cells take decisions? Our approach involves looking at tissue as an expanding network (graph) of cell connections and using different techniques to understand the properties of this graph. We have a series of papers on this topic, that captures most of our work.

Together with our long-time collaborators, Dr Matt Gibson (Stower's Institute) and Dr. Norbert Perrimon (Harvard Medical School) we are investigating this system. This work was led first by Ankit Patel, an applied math student who graduated in 2009, and then by William ("Tyler") Gibson, a biophysics student who graduated in 2011.

Nature, August 2006, Abstract:

The predominantly hexagonal cell pattern of simple epithelia was noted in the earliest microscopic analyses of animal tissues, a topology commonly thought to reflect cell sorting into optimally packed honeycomb arrays. Here we use a discrete Markov model validated by time-lapse microscopy and clonal analysis to demonstrate that the distribution of polygonal cell types in epithelia is not a result of cell packing, but rather a direct mathematical consequence of cell proliferation. On the basis of in vivo analysis of mitotic cell junction dynamics in Drosophila imaginal discs, we mathematically predict the convergence of epithelial topology to a fixed equilibrium distribution of cellular polygons. This distribution is empirically confirmed in tissue samples from vertebrate, arthropod and cnidarian organisms, suggesting that a similar proliferation-dependent cell pattern underlies pattern formation and morphogenesis throughout the metazoa.

PLOS Computational Biology, June 2009, Abstract:

Cell division is one of the key mechanisms driving organismal growth and morphogenesis. Yet many aspects of the relationship between local cell division (how a cell chooses an orientation to divide) and global tissue architecture (e.g. regular versus irregular cells) remain poorly understood. We present a computational framework for studying topological networks that are created by cell division; this framework reveals how certain tissue statistics can be used to infer properties of the cell division model. Recently it has been observed that five diverse organisms show almost identical cell shape distributions in their proliferating epithelial tissues, yet how this conservation arises is not understood. Using our model we show that the low variation observed in nature requires a strong correlation between how neighboring cells divide and that although the statistics of plants and fruitflies are almost identical, it is likely that they have evolved distinct cell division methods.

Cell, Feb 2011, Abstract:

For nearly 150 years, it has been recognized that cell shape strongly influences the orientation of the mitotic cleavage plane (e.g.,Hofmeister, 1863). However, we still understand little about the complex interplay between cell shape and cleavage-plane orientation in epithelia, where polygonal cell geometries emerge from multiple factors, including cell packing, cell growth, and cell division itself. Here, using mechanical simulations, we show that the polygonal shapes of individual cells can systematically bias the long-axis orientations of their adjacent mitotic neighbors. Strikingly, analyses of both animal epithelia and plant epidermis confirm a robust and nearly identical correlation between local cell topology and cleavage-plane orientation in vivo. Using simple mathematics, we show that this effect derives from fundamental packing constraints. Our results suggest that local epithelial topology is a key determinant of cleavage-plane orientation, and that cleavage-plane bias may be a widespread property of polygonal cell sheets in plants and animals.


The Emergence of Geometric Order in Proliferating Metazoan Epithelia,
Matt Gibson, Ankit Patel, Radhika Nagpal, Norbert Perrimon
Nature, 442(7106):1038-41, Aug 31, 2006 (nature link) , (pdf), (supplement)

Epithelial topology. Problems and Paradigms
Radhika Nagpal, Ankit Patel, Matt Gibson
BioEssays 30(3):260-266, March 2008 (pdf)

Modeling and Inferring Cleavage Patterns in Proliferating Epithelia
Ankit Patel. Doctoral Thesis, Harvard University, Nov 2008. (pdf)

Modeling and Inferring Cleavage Patterns in Proliferating Epithelia.
Ankit Patel, William Tyler Gibson, Matt Gibson, Radhika Nagpal
PLoS Comput Biol 5(6):e1000412, June 2009 (open access)

Topological biases and feedbacks in proliferating tissues
William Tyler Gibson, Doctoral Thesis, Harvard University, Sept 2011. (pdf)

Control of the Mitotic Cleavage Plane by Local Epithelial Topology
William Tyler Gibson, J. Veldhuis, B. Rubinstein, H. Cartwright, N. Perrimon, W. Brodland, Radhika Nagpal, and Matthew C. Gibson
Cell Volume 144, Issue 3, 414-426, 4 February 2011. (pdf)
featured in Cell highlights (" Funky shapes and Pushy neighbors")