Patterning of the MinD cell division protein in cells of arbitrary shape can be predicted using a heuristic dispersion relation

Walsh, JC; Angstmann, CN; McGann, AV; Henry, BI; Duggin, IG; Curmi, PMG

Patterning of the MinD cell division protein in cells of arbitrary shape can be predicted using a heuristic dispersion relation

Walsh, JC Angstmann, CN McGann, AV Henry, BI Duggin, IG

Curmi, PMG

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Publication Type:: Journal Article
Citation:: AIMS Biophysics, 2016, 3 (1), pp. 119 - 145
Issue Date:: 2016-01-01

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Field	Value	Language
dc.contributor.author	Walsh, JC	en_US
dc.contributor.author	Angstmann, CN	en_US
dc.contributor.author	McGann, AV	en_US
dc.contributor.author	Henry, BI	en_US
dc.contributor.author	Duggin, IG https://orcid.org/0000-0003-4868-7350	en_US
dc.contributor.author	Curmi, PMG	en_US
dc.date.issued	2016-01-01	en_US
dc.identifier.citation	AIMS Biophysics, 2016, 3 (1), pp. 119 - 145	en_US
dc.identifier.uri	http://hdl.handle.net/10453/49136
dc.description.abstract	© 2016, Paul M. G. Curmi, et al. Many important cellular processes require the accurate positioning of subcellular structures. Underpinning many of these are protein systems that spontaneously generate spatiotemporal patterns. In some cases, these systems can be described by non-linear reaction-diffusion equations, however, a full description of such equations is rarely available. A well-studied patterning system is the Min protein system that underpins the positioning of the FtsZ contractile ring during cell division in Escherichia coli. Using a coordinate-free linear stability analysis, the reaction terms can be separated from the geometry of a cell. The reaction terms produce a dispersion relation that can be used to predict patterning on any cell shape and size. Applying linear stability analysis to an accurate mathematical model of the Min system shows that while it correctly predicts the onset of patterning, the dispersion relation fails to predict oscillations and quantitative mode transitions. However, we show that data from full solutions of the Min model can be used to generate a heuristic dispersion relation. We show that this heuristic dispersion relation can be used to approximate the Min protein patterning obtained by full simulations of the non-linear reaction-diffusion equations. Moreover, it also predicts Min patterning obtained from experiments where the shapes of E. coli cells have been deformed into rectangles or arbitrary shapes. Using this procedure, it should be possible to generate heuristic dispersion relations from protein patterning data or simulations for any patterning process and subsequently use these to predict patterning for arbitrary cell shapes.	en_US
dc.relation.ispartof	AIMS Biophysics	en_US
dc.relation.isbasedon	10.3934/biophy.2016.1.119	en_US
dc.title	Patterning of the MinD cell division protein in cells of arbitrary shape can be predicted using a heuristic dispersion relation	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	3	en_US
utslib.for	0605 Microbiology	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Strength - ithree - Institute of Infection, Immunity and Innovation
utslib.copyright.status	open_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	3	en_US

Abstract:

© 2016, Paul M. G. Curmi, et al. Many important cellular processes require the accurate positioning of subcellular structures. Underpinning many of these are protein systems that spontaneously generate spatiotemporal patterns. In some cases, these systems can be described by non-linear reaction-diffusion equations, however, a full description of such equations is rarely available. A well-studied patterning system is the Min protein system that underpins the positioning of the FtsZ contractile ring during cell division in Escherichia coli. Using a coordinate-free linear stability analysis, the reaction terms can be separated from the geometry of a cell. The reaction terms produce a dispersion relation that can be used to predict patterning on any cell shape and size. Applying linear stability analysis to an accurate mathematical model of the Min system shows that while it correctly predicts the onset of patterning, the dispersion relation fails to predict oscillations and quantitative mode transitions. However, we show that data from full solutions of the Min model can be used to generate a heuristic dispersion relation. We show that this heuristic dispersion relation can be used to approximate the Min protein patterning obtained by full simulations of the non-linear reaction-diffusion equations. Moreover, it also predicts Min patterning obtained from experiments where the shapes of E. coli cells have been deformed into rectangles or arbitrary shapes. Using this procedure, it should be possible to generate heuristic dispersion relations from protein patterning data or simulations for any patterning process and subsequently use these to predict patterning for arbitrary cell shapes.

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http://hdl.handle.net/10453/49136