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

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Polarity in cells and sheets

Frances Taschuk

14 April 2008

e coli cell division
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?
modeling min protein locations
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
the min proteins
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)
oscillation of minc d
Oscillation of MinC/D

On average, MinC concentration is highest at each end of cell

modeling oscillations
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
simulation and results
Simulation and Results

Calculate numerical solutions by turning these into difference equations, eg:

FtsZ – blue MinD – green MinE - pink

start from homogeneous state
Start from homogeneous state
  • http://www.pnas.org/cgi/content/full/98/25/14202/DC1/8
what about sporulation
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
multicellular systems
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
drosophila as model system
Drosophila as model system
  • Displays planar cell polarity in back bristles, wing hairs, and photoreceptors of the eye
mathematical modeling of wing cell polarity
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
the feedback loop
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

the model
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
results
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
autonomy of mutations
Autonomy of mutations

fzR52 – nonautonomous – does not recruit Vang-YFP

fzF31 – autonomous – Fz still recruits Vang-YFP

references
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:

http://www.nature.com/nrm/journal/v6/n11/images/nrm1745-f1.jpg

http://www.nature.com/nrm/journal/v6/n11/images/nrm1745-f3.jpg

http://www.nature.com/nrmicro/journal/v3/n12/images/nrmicro1290-f1.jpg

http://www.pnas.org/cgi/reprint/96/9/4971.pdf

http://www.pnas.org/cgi/content/full/98/25/14202/DC1/6

http://www.nature.com/nrmicro/journal/v1/n2/images/nrmicro750-f1.gif

http://dev.biologists.org/cgi/content/full/129/11/2749/FIG2

http://www.mshri.on.ca/mcneill/planar.html

http://web.wi.mit.edu/rebay/pub/research/images/wteye.jpg

http://www.bohemianscientist.org/images/blog07/03/drosophila.jpg