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.