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Recent work on distinct multicellular organisms has revealed a hithertounknown type of biological noise; rather than a regular arrangement, cellularneighborhood volumes, obtained by Voronoi tessellations of the cell locations,are broadly distributed and consistent with gamma distributions. We propose anexplanation for those observations in the case of the alga $Volvox$, whosesomatic cells are embedded in an extracellular matrix (ECM) they export. Both asolvable one-dimensional model of ECM growth derived from burstytranscriptional activity and a two-dimensional "Voronoi liquid" model are shownto provide one-parameter families that smoothly interpolate between theempirically-observed near-maximum-entropy gamma distributions and thecrystalline limit of Gaussian distributions governed by the central limittheorem. These results highlight a universal consequence of intrinsicbiological noise on the architecture of certain tissues.

Stochastic Voronoi Tessellations as Models for Cellular Neighborhoods in Simple Multicellular Organisms