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

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 Comput. Biol., 2008, 4, 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 revise some of the model parameter values 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.