Magnetotactic bacteria assemble chains of magnetosomes, organelles that contain magnetic nano-crystals. A number of genetic factors involved in the controlled biomineralization of these crystals and the assembly of magnetosome chains have been identified in recent years, but how the specific biological regulation is coordinated with general physical processes such as diffusion and magnetic interactions remains unresolved. Here, these questions are addressed by simulations of different scenarios for magnetosome chain formation, in which various physical processes and interactions are either switched on or off. The simulation results indicate that purely physical processes of magnetosome diffusion, guided by their magnetic interactions, are not sufficient for the robust chain formation observed experimentally and suggest that biologically encoded active movements of magnetosomes may be required. Not surprisingly, the chain pattern is most resembling experimental results when both magnetic interactions and active movement are coordinated. We estimate that the force such active transport has to generate is compatible with forces generated by the polymerization or depolymerization of cytoskeletal filaments. The simulations suggest that the pleiotropic phenotypes of mamK deletion strains may be due to a defect in active motility of magnetosomes and that crystal formation in magneteosome vesicles is coupled to the activation of their active motility in M. gryphiswaldense, but not in M. magneticum.