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Polarity in cells and sheets

Polarity in cells and sheets

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Polarity in cells and sheets

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  1. Polarity in cells and sheets Frances Taschuk 14 April 2008

  2. E. coli cell division • Like many other prokaryotes, E. coli cells reproduce by binary fission • The plane of division is determined by the location of a ring of FtsZ protein • So how does FtsZ end up in the middle of the cell?

  3. Modeling Min protein locations • Localization of FtsZ determined by Min protein system – MinC inhibits FtsZ polymerization • Min protein localization involves polar oscillations – modeled by Meinhardt and de Boer • Nucleoid occlusion also contributes to localization

  4. The Min proteins • MinD – ATPase on cytoplasmic side of membrane • Recruits MinC and MinE from cytoplasm to membrane • MinE – displaces MinD from membrane – binds at flank of MinD accumulation • (MinC – inhibits FtsZ polymerization)

  5. Oscillation of MinC/D On average, MinC concentration is highest at each end of cell

  6. Modeling oscillations • Reaction-diffusion model using local self-enhancement and long range antagonism • Assumptions: • FtsZ, MinD, MinE produced at constant rate • All 3 diffuse rapidly • All associate with membrane by self-enhancing process • MinE displaces MinD • (not stated specifically in paper) Colocalization of MinC with MinD – ie, MinD treated as inhibiting FtsZ

  7. Simulation and Results Calculate numerical solutions by turning these into difference equations, eg: FtsZ – blue MinD – green MinE - pink

  8. Start from homogeneous state •

  9. Re-finds center after division

  10. Consistent with observations of extended FtsZ- filaments MinD-GFP localization

  11. What about sporulation? • Bacillus subtilis produces endospores through an asymmetrical division • Additional influence of SpoIIE protein causes FtsZ to spiral to separate rings near cell poles • One is chosen for division – mechanism unknown

  12. Multicellular systems • Cells in multicellular organisms must organize their individual polarity to form higher-order structures • Cell polarity: apical vs basal-lateral orientation • Planar cell polarity: cell orientation within a sheet such as the epithelium

  13. Drosophila as model system • Displays planar cell polarity in back bristles, wing hairs, and photoreceptors of the eye

  14. Mathematical modeling of wing cell polarity • In Science, 2005 • Signaling between cells is contact-dependent • The authors propose that enough is known about the proteins involved to explain phenomena such as domineering nonautonomy. • Can be modeled as a reaction-diffusion system using partial differential equations

  15. The feedback loop • Loop amplifies initial asymmetry, resulting in polarized distributions of planar cell polarity proteins • Fz recruits Dsh to membrane, Pk and Vang to adjacent cell’s membrane. • In each cell, Pk and Vang block local recruitment of Fz/Dsh Fz = frizzled Dsh = dishevelled Pk = Prickle-spiny-legs Vang = Van Gogh/strabismus

  16. System of 10 nonlinear partial differential equations representing proteins and complexes Parameters unknown, so chose ones that produced certain hair pattern phenotypes - not highly sensitive to precise values Includes directional bias – actual mechanism unknown The model

  17. Showed localization to correct membrane Able to explain autonomous mutations vs nonautonomous domineering mutations Autonomous: cells with abnormal Dsh or some abnormal Fz functions do not affect polarity of nearby cells Nonautonomous domineering: mutant Fz unable to recruit Vang to adjacent cell Results

  18. Autonomy of mutations fzR52 – nonautonomous – does not recruit Vang-YFP fzF31 – autonomous – Fz still recruits Vang-YFP

  19. References Meinhardt,H., de Boer, P. A. J. 2001. Pattern formation in Escehericihia coli: a model for the pole-to-pole oscillations of Min proteins and the localization of the division site. PNAS 98:25 14202-14207. Amonlirdviman, K, et al. 2005. Mathematical modeling of planar cell polarity to understand domineering nonautonomy. Science 307, 423-424. Images: