A mathematical model of the formation and contraction of the prokaryotic Z-ring in vivo was developed, based on the polymerisation and membrane anchor binding activity of the FtsZ protein as measured in vitro. From a set of kinetic parameters that are estimated from the experimental literature, the model, which is referred to as Critical Accumulation of Membrane-bound FtsZ Fibres (CAM-FF), predicts one of three cell division outcomes: i) division proceeds to completion, ii) division is initiated but stalls prior to completion, and iii) division is not initiated. CAM-FF was validated by the accurate prediction of the effect of deletion of the membrane anchor proteins ZipA and FtsA, and was used to predict an order of efficiency of the biochemical targets for antibacterial drug design as follows: FtsZ polymerisation > ZipA/FtsA availability > FtsZ GTP-binding. The temperature-sensitivity of the ftsZ84 mutant was also analysed using CAM-FF and it was found that an acquired ATPase activity of the FtsZ84 protein (FtsZ G105S) could explain the temperature-sensitivity of cell growth. At lower temperatures where the ATPase activity is low, a functional Z-ring is able to form and contract. However, at 42 °C the increase in the ATPase rate causes the Z-ring to disassemble and cell division is inhibited. On purification of the FtsZ G105S mutant protein, a significant ATPase activity was observed in vitro that was absent in the wild-type FtsZ protein. Therefore, the ATPase activity is not an experimental artifact, as was previously thought. The ZapA and ZipA roteins were also purified, and the FtsA protein was overexpressed for subsequent purification, in preparation for crystallography and in vitro cell division reconstitution studies. A set of linear DNA molecules with defined length and GC content was designed and produced for the investigation of polymer hysteresis in flow.