This thesis comprises two parts, both concerned with the study of Escherichia coli bacterial suspensions. The first part investigates E. coli motility whilst the second part explores E. coli growth in the presence of the antimicrobial peptide pexiganan. In Part 1 I measure the three-dimensional diffusion of non-motile cells in an active suspension of E. coli, using Differential Dynamic Microscopy (DDM). It is found that tracer diffusivity is enhanced linearly as a function of the bath activity, defined as the product of the number density of active bacteria and their average speed. The absolute enhancement is measured to be 1:8 ± 0:1 times smaller that that published previously in the vicinity of a surface, in agreement with theoretical predictions of enhanced diffusion by far-field advection. The diffusivities of non-motile mutants with and without paralysed flagella are enhanced to the same extent, despite a difference in hydrodynamic radii. In addition, the protocol for growing, preparing and measuring motile E. coli is optimised using DDM. In Part 2 I investigate how E. coli density in liquid media supplemented with pexiganan influences the measurement of its Minimum Inhibitory Concentration (MIC). Growth curves, peptide bioassays and single cell microscopy are used. It is found that population density drops rapidly when pexiganan is introduced, but regrowth occurs within 24 hours at sub-MIC concentrations. The shape of the density curve is explained by peptide depletion linked to cell death and immediate recovery of cells exposed to the peptide. As expected from these findings, the system displays a substantial inoculum effect, quantified with a fitted power law. Substantial variation is seen between replicate MIC assays; an inherent property of the system which derives from the drop to small numbers of viable cells before regrowth. Finally, I show that DDM measurements of E. coli motility in antimicrobial peptides can provide an alternative, high-throughput density curve.