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?

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

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

Start from homogeneous state /DC1/8http:// /DC1/8

Re-finds center after division

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

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 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 Displays planar cell polarity in back bristles, wing hairs, and photoreceptors of the eye

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 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

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

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

References Meinhardt,H., de Boer, P. A. J 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: Amonlirdviman, K, et al Mathematical modeling of planar cell polarity to understand domineering nonautonomy. Science 307, Images: