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Speaker: Wang guo-xin Date:06/19/12

Phyllotaxis as an example of the symbiosis of mechanical forces and biochemical processes in living tissue. Newell, A. C., P. D. Shipman, et al. (2008). Plant Signal Behavior 3(8): 586-589. Speaker: Wang guo-xin Date:06/19/12. Phyllotaxis.

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Speaker: Wang guo-xin Date:06/19/12

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  1. Phyllotaxis as an example of the symbiosis of mechanical forcesand biochemical processes in living tissue Newell, A. C., P. D. Shipman, et al. (2008). Plant Signal Behavior 3(8): 586-589. Speaker: Wang guo-xin Date:06/19/12

  2. Phyllotaxis • The arrangement of a plant’s phylla (flowers, bracts, stickers) near its shoot apical meristem (SAM). • Only partially understood. • The symbiosis of mechanical forces and biochemical processes.

  3. Phyllotaxis • Similar configurations in a wide variety of plants. • The almost-constant golden divergence angle, plastichrone ratio, the choices of parastichy numbers and the prevalence of Fibonacci sequences to which these numbers belong.

  4. Phyllotaxis • Auxin plays an important role in primordia formation. • A uniform concentration of auxin could give rise to an inhomogeneous quasi-periodic pattern of enhanced and depleted auxin zones.

  5. Overviews • Kuhlemeier and his group and Meyerowitzet al., • Arabidopsis. • The PIN1 proteins in each cell on the plant’s surface.

  6. Overviews {Smith, 2006 #1147}

  7. Overviews {Jonsson, 2006 #1148}

  8. Overviews • Regulated by the relative distributions of auxin in neighboring cells. • Proteins gravitate to and polarize in the cell walls. • The net effect is to drive auxin in the direction of its concentration gradient.

  9. Questions • No such surface deformations are treated in the model of Jönnson et al., • Growing tissue creates compressive stresses in the plant’s tunica.

  10. New mathematical model • Including the cooperation and competition of mechanical and biochemical processes. • Advantages of the observations in Arabidopsis that the pattern wavelength is large with respect to the cell diameter. • Both of the local auxin concentrations and surface deformation.

  11. New mathematical model • The exact way in which stresses influence biological tissue growth is still an open challenge to biologists. • The auxin-produced growth is proportional in a first approximation, to how much average tensile stress the local elemental volume feels.

  12. New mathematical model • Analyzing the model by imagining an annular region in the neighborhood of the SAM. • Representing the surface deformation and auxin fluctuation fields by a combination of quasi-periodic Fourier modes.

  13. New mathematical model • Assuming either or both of the PIN1-transport coefficient leading to reverse diffusion and the growth-induced circumferential stress are near critical values. • The job of theory is not only to identify the correct model from a mechanistic point of view but to find the simplest nontrivial model which captures most of the observed behaviors.

  14. Significant results • Cacti • If the circumferential stress in the formative region is subcritical but the PIN1 transport is supercritical, the surface deformation will be slaved to the phyllotactic configuration.

  15. Cacti ridges

  16. Significant results • Sunflower head. • The set of equations remains invariant under transformations which simulate moving radially outward in the sunflower head. • The pattern wavelength is an intrinsic constant only depending on plant parameters.

  17. Significant results

  18. Significant results

  19. Significant results Circumferential wave numbers m1, m2, m3 = m1 + m2, m4 = m1 + 2m2 are sequential members of the Fibonacci sequence.

  20. Conclusions • There are many other situations where the pattern is produced by a symbiosis between growth-induced mechanical forces and biochemical processes. • We might at last appreciate the symbiosis between mechanical and biochemical processes in producing self-organizing behavior in biological tissues on scales far larger than those of genes and cells.

  21. References • Smith RS, Guyomarc’h S, Mandel T, Reinhardt D, Kuhlemeier C, Prusinkiewicz P. A plausible model of phyllotaxis. ProcNatlAcadSci USA 2006; 103:1301-6. • Jönsson H, Heisler MG, Shapiro BE, Meyerowitz EM, Mjölsness E. An auxin-driven polarized transport model for phyllotaxis. ProcNatlAcadSci USA 2006; 103:1633-8.

  22. References • Dumais J, Steele CR. New evidence for the role of mechanical forces in the shoot apical meristem. J Plant Growth Regul 2000; 19:7-18. • Newell AC, Shipman PD, Sun Z. Phyllotaxis: Cooperation and competition between biomechanical and biochemical processes. J TheorBiol 2008; 251:421-39.

  23. References • Braam J. In touch: plant responses to mechanical stimuli. New Phytol 2005; 165:373-89. • Brouzés E, Farge E. Interplay of mechanical deformation and patterned gene expression in developing embryos. CurrOpin Genet Dev 2004; 14:367-74.

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