� � � � � � � Phototaxis in Volvox 18.S995 - L28 the beating of thousands of flagellated cells despite the organ at a frequency that likely coevolved with the organism’s flagel flagellar beating of the organisms, the authors measured the fluid velocities produced by the flagella and modeled the mo thors identified a theoretical optimal spinning frequency and tested the finding experimentally by observing how well the , flagellar beating and spinning are linked adaptations. By better understanding dunkel@mit.edu how simple organisms coordinate multicellular processes, the findings may provide insight into key evolutionary steps fied Nissle to 2- to 3-day–old mice Francis McCubbin et al. (pp. 11223– modified Nissle pretreatment. The tified apatite grains in thin sections can be occupied by fluorine, chlorine, tive amounts of fluorine, chlorine, and March (pp. 11260–11264) modified
� � � � Fidelity of adaptive phototaxis Knut Drescher, Raymond E. Goldstein 1 , and Idan Tuval Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom Edited by Harry L. Swinney, University of Texas, Austin, TX, and approved May 6, 2010 (received for review January 28, 2010) www.pnas.org/cgi/doi/10.1073/pnas.1000901107 PNAS ∣ June 22, 2010 ∣ vol. 107 ∣ no. 25 ∣ 11171 – 11176 PNAS June 22, 2010 � vol. 107 � no. 25 � 11147–11650 In This Issue Proceedings of the National Academy of Sciences of the United States of America www.pnas.org Moving to the light To optimize photosynthesis, algae such as Volvox carteri swim toward or away from sunlight. To execute this motion, known as phototaxis, these microorganism colonies must coordinate the beating of thousands of flagellated cells despite the organ - ism’s lack of a central nervous system. Using analytical and empirical methods, Knut Drescher et al. (pp. 11171–11176) demonstrate that V . carteri spins about its swimming direction at a frequency that likely coevolved with the organism’s flagel - lar kinetics to maximize photoreactivity. To characterize the flagellar beating of the organisms, the authors measured the fluid velocities produced by the flagella and modeled the mo - tion with hydrodynamic equations. Using the model, the au- thors identified a theoretical optimal spinning frequency and tested the finding experimentally by observing how well the algae swam in media with increased viscosities that inhibited Multicellular colony Volvox carteri . the organism’s ability to spin. According to the authors, the ex- periments demonstrated that with a decreased rotation rate the algae were unable to execute phototaxis as accurately as before, suggesting that in V . carteri , flagellar beating and spinning are linked adaptations. By better understanding how simple organisms coordinate multicellular processes, the findings may provide insight into key evolutionary steps that eventually led to higher organisms with central nervous systems. — T.J. dunkel@math.mit.edu fied Nissle to 2- to 3-day–old mice Francis McCubbin et al. (pp. 11223– modified Nissle pretreatment. The tified apatite grains in thin sections can be occupied by fluorine, chlorine, tive amounts of fluorine, chlorine, and March (pp. 11260–11264) modified
Knut Drescher MPI Marburg Idan Tuval Mediterranean Ray Goldstein Institute for Cambridge Advanced Studies dunkel@math.mit.edu
� � � � � � � Why is Volvox interesting ? • germ-soma differentiation • interesting asexual reproduction ‘technique’ • metachronal waves • locomotion the beating of thousands of flagellated cells despite the organ • phototaxis at a frequency that likely coevolved with the organism’s flagel flagellar beating of the organisms, the authors measured the fluid velocities produced by the flagella and modeled the mo thors identified a theoretical optimal spinning frequency and tested the finding experimentally by observing how well the dunkel@math.mit.edu , flagellar beating and spinning are linked adaptations. By better understanding how simple organisms coordinate multicellular processes, the findings may provide insight into key evolutionary steps fied Nissle to 2- to 3-day–old mice Francis McCubbin et al. (pp. 11223– modified Nissle pretreatment. The tified apatite grains in thin sections can be occupied by fluorine, chlorine, tive amounts of fluorine, chlorine, and March (pp. 11260–11264) modified
Evolution of multicellularity Chlamydomonas Eudorina Volvox reinhardtii elegans carteri Gonum Pleodorina Volvox pectorale californica aureus Short et al, PNAS 2013 dunkel@math.mit.edu
Volvox carteri somatic cell cilia 200 ㎛ daughter colony from germ cell http://www.youtube.com/watch?v=fqEHbJbuMYA dunkel@math.mit.edu
Asexual reproduction & inversion dunkel@math.mit.edu 2014 Goldstein lab
Volvox carteri somatic cell cilia 200 ㎛ daughter colony from germ cell ... and can dance Drescher et al (2010) PRL dunkel@math.mit.edu
Volvox carteri somatic cell cilia 200 ㎛ daughter colony Drescher et al (2010) PRL dunkel@math.mit.edu
Volvox carteri 200 ㎛ 10 ㎛ Chlamydomonas reinhardtii dunkel@math.mit.edu
Chlamydomonas alga 10 ㎛ 10 ㎛ ~ 50 beats / sec speed ~100 μ m/s Goldstein et al (2011) PRL dunkel@math.mit.edu
Chlamydomonas dunkel@math.mit.edu Merchant et al (2007) Science
Model organism for studying meta-chronal waves Brumley et al (2012) PRL dunkel@math.mit.edu
Superposition of singularities 2x stokeslet = stokeslet symmetric dipole rotlet -F F F p ( r ) = ˆ r · F 4 π r 2 + p 0 v i ( r ) = (8 π µ ) − 1 [ δ ij + ˆ r i ˆ r j ] F j r r − 1 r − 2 r − 2 flow ~ ‘pusher’
Volvox carteri swimming speed ~ 100 ㎛ /sec PIV 100 ㎛ ⌃ � � �� ⇧ ⌅⇧� ⌃ ⇤ ⌥ ⌫ � ⌦ � / ⌃ � � / ⇤ / ⇤ ⌥ ⇥ / ⌃�⌥ ⌃ � ⇤ � � � ⇣⌃ �⌥� ⌥ ⇥ ⇥ / ⌅ � � ⌥�⌃ ⇤ � � ⌥⇤ � ⇣ � / ⇤ / ⇥ / ⇤ ⌃ � ⇥ � ⇤ Drescher et al (2010) PRL dunkel@math.mit.edu
How does Volvox achieve phototaxis ? Approach: • light response of individual cells • effects of size & spinning frequency • mathematical modeling • check predictions of model dunkel@math.mit.edu
Experimental setup r: 200 μ m.) Fig. 1. Geometry of V. carteri and experimental setup. ( A ) The beating fla- gella, two per somatic cell ( Inset ), create a fluid flow from the anterior to the posterior, with a slight azimuthal component that rotates Volvox about its posterior-anterior axis at angular frequency ω r . (Scale bar: 100 μ m.) ( B ) Studies of the flagellar photoresponse utilize light sent down an optical fiber. dunkel@math.mit.edu
Spectra of light sources r: 200 μ m.) bright-field 𝝁 >620, 100 fps dunkel@math.mit.edu
Photo-response at different intensities 0.25Hz dunkel@math.mit.edu
Adaptive photo-response serves as a measu is u 0 ¼ 81 μ m ∕ s fo 1 𝜈 m tracers Fig. 2. Characteristics of the adaptive photoresponse. ( A ) The local flagella- generated fluid speed u ð t Þ ( Blue ), measured with PIV just above the flagella 10µm from cilium during a step up in light intensity, serves as a measure of flagellar activity. The baseline flow speed in the dark is u 0 ¼ 81 μ m ∕ s for this dataset. Two time scales are evident: a short response time τ r and a longer adaptation time u(t) = average -30° ... +30° τ a . The fitted theoretical curve ( Red ) is from Eq. 4 . ( B ) The times τ r ( Squares ) and τ a ( Circles ) vary smoothly with the stimulus light intensity, measured in terms of PAR. Error bars are standard deviations. dunkel@math.mit.edu
Adaptive photo-response serves as a measu is u 0 ¼ 81 μ m ∕ s fo to diffuse the length of the flagellum 2+ 𝜐 r : Ca -diffusion (?) (for L ∼ 15 μ m, D ∼ 10 − 5 cm 2 ∕ s), 𝜐 a : unknown suggesting that the photocurrent triggers dunkel@math.mit.edu
Photo-response model photo-response serves as a measu variable is u 0 ¼ 81 μ m ∕ s fo by u ð t Þ ∕ u 0 ¼ 1 − β p ð t Þ ð photoresponse variable that is p ¼ ð s − h Þ H ð s − h Þ − p; τ r _ τ a _ h ¼ s − h; h ð t Þ ¼ s 1 e − t ∕ τ a þ s 2 ð 1 − e − t ∕ τ a Þ ; p ð t Þ ¼ ð s 2 − s 1 Þ s : stimulus input variable ð e − t ∕ τ a − e − t ∕ τ r Þ : 1 − τ r ∕ τ a h : hidden biochemistry variable dunkel@math.mit.edu
Heuristic response model dunkel@math.mit.edu
Let’s try to be more quantitative ... dunkel@math.mit.edu
Frequency dependence of photo-response Fig. 3. Photoresponse frequency dependence and colony rotation. ( A ) The normalized flagellar photoresponse for different frequencies of sinusoidal stimulation, with minimal and maximal light intensities of 1 and 20 μ mol PAR photons m − 2 s − 1 ( Blue Circles ). The theoretical response function (Eq. 5 , Red Line ) shows quantitative agreement, using τ r and τ a from Fig. 2 B for 16 μ mol PAR photons m − 2 s − 1 . ( B ) The rotation frequency ω r of V. carteri dunkel@math.mit.edu
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