Department of Applied Mathematics and Theoretical Physics ∗ Electronic Address: [email protected] A fundamental issue in evolutionary biology is the emergence of multicellular or- ganisms from unicellular individuals. The accompanying differentiation from motiletotipotent unicellular organisms to multicellular organisms having cells specializedinto reproductive (germ) and vegetative (soma) functions, such as motility, impliesboth costs and benefits, the analysis of which involves the physics of buoyancy,diffusion, and mixing.
In this talk, I discuss recent results from an investigation of the uni- to mul- ticellular transition in a model lineage: the volvocine green algae. These rangefrom Chlamydomonas, a unicellular, biflagellated, photosynthetic green alga lessthan 10 microns in size to Volvox, a colonial organism that can reach 1 mm across,composed of thousands of somatic cells (structurally like Chlamydomonas) on thesurface of a sphere which contains a small number of germ cells. An importantissue is thus the relationship between metabolic requirements and environmentalmetabolite exchange with increasing size.
For organisms whose body plan is a spherical shell, the current of needed nu- trients grows quadratically with radius, whereas the rate at which diffusion aloneexchanges molecules grows linearly, leading to a bottleneck radius beyond which thediffusive current cannot meet metabolic demands. How has nature dealt with thisconundrum? Organized beating by the somatic cells’ flagella clearly allows theseorganisms to swim, but could the resultant fluid flow play a role in the metabolicactivity? In other words: Is there a link between motility, mixing, and multicellu-larity? I describe two approaches to this problem.
First are experiments that quantify the role of advective dynamics in enhancing productivity in germ-soma differentiated colonies. We found [1] that that deflag-ellated colonies lose productivity relative to normal colonies, but forced advectionreturns productivity to normal. Imaging of fluid motion around colonies revealsflows with very large characteristic velocities U extending to length scales compa-rable to the colony radius R. For a typical metabolite diffusion constant D,theassociated Peclet number P e = 2U R/D ≫ 1; advection dominates diffusion, withstriking augmentation at the cell division stage. Second, we have found [2] thatthe flagella-driven advection generates a boundary layer of concentration of a dif-fusing solute, and that concentration gradient produces an exchange rate which isquadratic in the radius, as required, thus circumventing the bottleneck and facili-tating evolutionary transitions to multicellularity and germ-soma differentiation inthe volvocine green algae.
[1] C.A. Solari, S. Ganguly, J.O. Kessler, R.E. Michod, and R.E. Goldstein, Proc.
Natl. Acad. Sci. (USA) 103, 1353 (2006).
[2] M.B. Short, C.A. Solari, S. Ganguly, T.R. Powers, J.O. Kessler, R.E. Michod, and R.E. Goldstein, Proc. Natl. Acad. Sci. (USA) 103, 8315 (2006).


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