In this work, we aim to understand the behaviour of filaments and bundles of filaments in the presence of diffusible cross-linkers; we posit that these are analogues of the structures present in the Z-ring, with special focus on E. coli. Then, we study these structures by constructing a mathematical model based on statistical mechanics, and analysing its behaviour under different ranges of parameters. We show that the ring-like geometry of the division plane is conducive to constriction, and that this effect can be potentialised by the dynamics of depolymerisation. Furthermore, we show that percolating bundles of filaments are also capable of constriction, and that percolation is necessary but not sufficient for a contractile force to arise. Finally, we investigate how such a model can originate percolating bundles of filaments and how to maximise the contractile potential of such bundles. Concomitantly, we investigate the mutant ftsZ84, an E. coli mutant with uncommon properties that might help us understand the relationship between FtsZ assembly and bacterial cell division, by using a new experimental approach. Though the results prove inconclusive, we were able to confirm that the activity of this mutant agrees with the published literature.