There might be a misunderstanding in the first part. The rotation of filament does not drive macroscopic rotation or spiral formation. What we describe in the text was the switch to turn to the left was governed by the filament rotation, but the real formation of a spiral is driven by the locomotion of the filament. The cited paper described the clumping of Anabaena cylindria in a dense culture. The clumping or aggregation in Arthrospira (Ohmori group) is mediated by cAMP, but A. cylindrica might be different. I have been using Anabaena for about 40 years, but I have never seen Anabaena filaments form a spiral on agar plates. Spiral formation and clumping are different phenomena. It is difficult to discuss the relationship (if any) between clumping and rotation.
When the cells form spirals, there are two components to this process: the formation of spirals and their macroscopic sense of rotation: clock- or counterclockwise. In the discussion it is assumed that the rotation of the filaments is crucial for both of these components. If this would be true, then no spirals should be observed in non-rotating filamentous gliding cyanobacteria. However, this is not the case. Anabaena spec. a non-rotating species can generate spirals (see Figure X; Mucilage secretion and the movements of blue-green-algae. Protoplasm 1968, 65, 223–238). This means that the sense of rotation may only be responsible for the direction of the spiral but not for its emergence in the first place. It would be good if the authors would distinguish between these two phenomena and discuss them accordingly.