A model of membrane contraction predicting initiation and completion of bacterial cell division

Abstract

Copyright and reuse:The Warwick Research Archive Portal (WRAP) makes the work of researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.Copies of full items can be used for personal research or study, educational, or not-forprofit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. Publisher's statement:http://dx.doi.org/10.1039/C3IB20273A A note on versions: The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP url' above for details on accessing the published version and note that access may require a subscription. Bacterial cell division involves a complex and dynamic sequence of events whereby polymers of the protein FtsZ assemble at the division plane and rearrange to achieve the goal of contracting the cell membrane at the site of cell division, thus dividing the parent cell into two daughter cells. We present a mathematical model (which we refer to as CAM-FF: Critical Accumulation of Membrane-bound FtsZ Fibres) of the assembly of the contractile ring in terms of the accumulation of short linear polymers of FtsZ that associate and dissociate from the cell membrane. In prokaryotes, the biochemical function of FtsZ is thought to underpin the assembly and at least the initial kinetic force of ring contraction. Our model extends earlier work of Surovtsev et al. [PLoS Computational Biology, 2008, 4, 7, e1000102] by adding (i) the kinetics of FtsZ accumulation on cell membrane anchor proteins and (ii) the physical forces required to deform the cell against its surface tension. Moreover, we provide a more rigorous treatment of intracellular diffusion and we update some of the model parameters in light of the experimental evidence now available. We derive a critical contraction parameter which links the chemical population dynamics of membrane-bound FtsZ molecules to the force of contraction. Using this parameter as a tool to predict the ability of the cell to initiate division, we are able to predict the division outcome in cells depleted of key FtsZ-binding proteins.

Biological Insights from a Simulation Model of the Critical FtsZ Accumulation Required for Prokaryotic Cell Division

“…We have developed a model of this key phase of cell division 7 and showed that the results are consistent with the division behaviour observed following the loss of expression of FtsA or ZipA, two components of the Escherichia coli divisome complex. This strongly suggests that the simulation model is a reliable tool to probe the early stages of cytokinesis which critically depend on the Z-ring and its membrane interactions.…”

“…The model has been implemented in Mathematica 8 as detailed in our previous paper. 7 In this paper we present the predicted wild-type behaviour and the predicted effects of various perturbations to key biochemical parameters and contrast those predictions with available experimental data.…”

“…Despite a number of simplifications, CAM-FF makes accurate predictions of cell division behaviour. 7 However, the estimates of timescales of the process, while correct in terms of relative ordering, are too short, for reasons that are discussed below. The model has been implemented in Mathematica 8 as detailed in our previous paper.…”

Mathematical Models of Microbial Growth and Metabolism: A Whole-Organism Perspective

“…Prior to cell division, the cell elongates to approximately twice its original length while its genetic material is replicated. Once this is complete, filamentous temperature sensitive (Fts) proteins, chief among which is FtsZ, assemble to form the cell division apparatus (divisome) by polymerizing and thus forming the socalled Z-ring, which localises to the middle of the cell [37][38][39] . New cell envelope material is synthesised and the two chromosomes are pulled apart.…”

“…One good example is the model of bacterial metabolism, where the state variables are metabolite concentrations, gene expression levels, transcription factor activities, metabolic fluxes, and biomass concentration 25 . However, in many cases the aim is not to describe the whole organism but instead to focus on specific subsystems of the cell, such as the assembly of the Z-ring 37 , or the electron transport chains of mitochondria 51 and purple non-sulfur bacteria 52 . Depending on the specific properties of the given biological network under consideration, different formalisms can be employed to simulate its dynamic behaviour.…”