Recent evidence points to the presence of torsion in FtsZ bonds. In addition, experiments with FtsZ mutants on surfaces resulted in new aggregates that cannot be explained by older models for FtsZ dynamics. We use an interaction model for FtsZ derived from molecular dynamics simulations and expand a fine-grained lattice model used to describe FtsZ aggregates on a surface. This new model includes different anchoring angles for the monomers and allows bond twist, two ingredients that oppose each other resulting in a more dynamic and interesting system. We study the role and importance of these conflicting elements and how the aggregates are characterized by the different interaction parameters.