Fluid Dynamics and the Evolution of Biological Complexity R E Goldstein DAMTP Cambridge II. Evolutionary Transitions to Multicellularity Phil. Trans. 22, 509-518 (1700) (1758) Volvox as a Model Organism A. Weismann (1834-1914) Perhaps second only to Darwin in impact: Advocated germ-plasm theory (anti-Lamarck). 1892: Significance of Volvocine green algae 1. Extant collection, spanning from unicellular to differentiated multicellular 2. Readily obtainable in nature 3. Studied from differing perspectives (biochemical, developmental, genetic) D.Kirk (1998) 4. Broad ecological studies 5. Recent enough that genome may retain traces of genetic changes in organization 6. Evidence of repeated genetic changes 7. Amenable to DNA transformation And, for theorists, it is the proverbial “spherical cow” A Family Portrait Chlamydomonas Gonium pectorale Eudorina elegans reinhardtii Pleodorina Volvox carteri Volvox aureus californica Germ-soma differentiation daughter colonies somatic cells Evolutionary Aspects • Multicellular volvocalean algae may have evolved from a common ancestor similar to the extant Chlamydomonas reinhardtii. • The transition from less complex forms to more complex forms such as Volvox occurred more than once. • Lineages exhibiting different developmental programs are interspersed with each other and with non-Volvox species. Chlamydomonas reinhardtii Eudorina Eudorina Eudorina Volvox Volvox Volvox Germ-Soma Differentiation: regA gene In e.g. Chlamydomonas, the “ancestral” life cycle is: vegetative → reproductive → vegetative Palintomy: reproductive cells first grow and then divide by multiple fission. 8 cells 8 colonies Grows 2d d=3 divisions In e.g. Volvox, there is terminal differentiation, and after birth of daughter colonies, somatic cells undergo programmed cell death (apoptosis) “Somatic regenerator” mutants (R. Starr, 1970) led to discovery that there is a single gene (regA) whose mutation gives rise Reg phenotype, in which somatic cells spontaneously revert to reproductive ones. In other words, the role of regA in wild-type cells is to suppress all aspects of reproductive cell development. It is off in gonidia, on in somatic cells. The Diffusional ottleneckB Metabolic requirements scale with surface Diffusion to an somatic cells: ~R2 absorbing sphere Currents ⎛ R ⎞ 2 CC=∞ ⎜1 − ⎟ IRm = π4 β ⎝ r ⎠ IDCRd = 4π ∞ 2- PO4 and O2 tes yieldaestim bottleneck radius ~50-200 μm (~Pleodorina, start of germ-soma differentiation) DC Organism radius R R = ∞ b β Life Cycles of the Green and Famous division maturation inversion of gonidia hatching of juveniles cytodifferentiation and expansion Hatching of Daughter Colonies (V. barberi) Structure of Flagella & the Flagellation Constraint Microtubule Organising Centre Chromosomes Basal bodies are microtubule organizing centres …flagella are resorbed during cell division (no multi-tasking) (Bell & Koufopanou, ’85,’93) Stirred, not Shaken Broken Colonies Deflagellated Colonies Flagellated Colonies (2006)] PNAS Colchicine, a flagellar regeneration inhibitor (binds to tubulin, prevents microtubule polymerization) Consistent with “Source-sink hypothesis” Bell & Koufopanou (‘85,’93) Inhibitor Liberated Deflagellation Deflagellation Liberated of flagella germ cells +Inhibitor +Inhibitor +Inhibitor [Solari, Ganguly, Michod, Kessler, Goldstein, regeneration Still medium Bubbled medium Bubbled Microscopy & Micromanipulation micro- micro- manipulator manipulator motorized microscope stage Stirring by Volvox carteri 1 mm Pseudo-darkfield (4x objective, Ph4 ring) Tools of the trade – preparation micropipette Measuring Volvox Flows , July 2006 (Backscatter) Physics Today Sujoy Ganguly, U. Arizona & U. Cambridge Time-exposure of Volvox carteri near a surface A Closer View Fluorescence Even Closer (Flagellar Motions Visible) Fluorescence Even Closer (Locally Chaotic Advection) Fluorescence Fluid Velocities During Life Cycle Hatch Division Daughter Pre-Hatch This is “Life at High Peclet Numbers” Solari, et al. (2006) Flagellar-Driven Flows and Scaling Laws Specified shear stress f at surface ⎡⎛ R 3 ⎞ ∞ ⎤ u= − U⎜ c − ⎟P cos θ − A( ) r P cosθ r ⎢⎜ 3 ⎟ 1 ()∑ l l ()⎥ ⎣⎝ r ⎠ l =2 ⎦ ⎡⎛ R 3 ⎞ ∞ ⎤ u= − U⎜ d + ⎟P1 cos θ + B( ) r1 P cosθ θ ⎢⎜ 3 ⎟ 1 ()∑ l l ()⎥ ⎣⎝ 2r ⎠ l =2 ⎦ πf R U = 8η Po ,yw ,Short, Solari, Gangulers, Kessler & GoldsteinPNAS (2006) Metabolite Exchange r 2 Acrivos & Taylor (1962) u⋅ ∇ c = D ∇ c heat transport from a solid sphere: current ~ RPe1 / 3 Magar, Goto & Pedley (2003) prescribed tangential velocity in a model of “squirmers” 2 1 / 2 2Ru ⎛ R ⎞ ⎛ 4ηD ⎞ Pe=θ ≈⎜ ⎟ ; R = ⎜ ⎟ ≈10mμ < R D ⎜ R ⎟ a ⎜ π f ⎟ b 1 / 2 ⎝ a ⎠ ⎝ ⎠ current ~ RPe 2 ∂C ∂ C cale: sreya lyBoundar ur ≈ D 2 ∂y ∂y 1− / 2 ε ⎛UR ⎞ ε C C ~ ⎜ ⎟ ~ Pe1− / 2 U ≈ D R ⎝ D ⎠ Rε ε2 The Peclet number scales as: 2 1 / 2 2Ru ⎛ R ⎞ ⎛ 4ηD ⎞ θ ⎜ ⎟ Pe= ≈⎜ ⎟ ; Ra = ⎜ ⎟ ≈10mμ < b R D ⎝ Ra ⎠ ⎝ π f ⎠ Bottleneck Bypassed (!) ∂C C I= − DR2 Ω d ≈ 4πDR2 ∞DC≈ 4π RPe1 /~ 2 2 (! R ) a ∫ ∞ ∂r Ra The Advantage of Size Phenotypic Plasticity I. Q: If colonies are deprived of nutrients, how do they adjust? A: By growing larger (!) Still medium Bubbling medium Q: If colonies are deprived of nutrients, how dothey adjust? Q: Ifcoloniesaredeprived ofnutrients,how A: By growing longerflagella andbeatingthemfaster(!) A: Bygrowing Flagella length (dilution) Phenotypic Plasticity II. Flagella length (still) Beating rate (dilution) Flow rate/10 (dilution) Up velocity (dilution) Up velocity (still) Hydrodynamic Coupling of Volvox Flagella Regrowth after deflagellation Changing beat frequency 125 frames/sec, phase contrast Regulated self-assembly!.