Granule formation at the macroscale.

(A) Images showing cultures at 30, 86, and 252 days of growth. (B) Slices through mature granules, showing cyanobacteria in green and yellow cores containing solid precipitates. (C) Images of aggregate formation in a glass beaker, at 0, 200, and 2000 minutes (see Movie S2). (D) Time-projected, composite image showing aggregate growth through coalescence of two smaller particles (indicated by triangle and square), with a larger particle (indicated by star). Arrows show the trajectory of the small particles. Insets at top show individual images before (0min) and after (80min) the coalescence event, respectively (see Movie S2 and S3 for example coalescence events). (E) Maximum particle size within field of view, plotted against time. Different colours indicate data from separate experiments. Coalescence events cause visible ‘steps’ in the maximum particle size (red and blue arrows). An aggregate ‘tightening’ event is also visible in the data – see still images taken before and after ‘tightening’ event. Inset shows the distribution of aggregates’ speed.

Collection of beads at the microscale.

(A) Still images of F. draycotensis filaments (red) and polystyrene beads (white) at (i) the beginning and (ii) end of a 6-hour video (see Movie S5). (B) The cluster size distribution for the polystyrene beads as a function of time (shown in different colours), from two independent time-lapse experiments (dashed or solid lines). (C) Time-projected composite images showing a bundle of filaments and beads transported by their activity. Time is false-coloured from purple (0min) to yellow (40min) and is applied to the beads (left) or filaments (right). (D) Example image showing EPS concentrated within a bead cluster. EPS is stained with fluorescently labelled lectin (green), filaments are light red and beads are dark red. (E) Three different examples of entangled filament-filament (left) or filament-bead (middle, right) clusters, featuring long, looped filaments.

A physical model of cyanobacteria as an active elastic filament.

(A) Sketch of a simulated cyanobacterial filament. Gliding on the surface is encoded by local forces and moments distributed along the filament length. The filament can bend, twist, and (minimally) stretch, with friction due to surrounding viscous fluid. The coupled rotational and translational directions of the forces are prescribed for a de-coordinated reversal. (B) Time-composite images of (i) a buckling F.draycotensis filament and (ii) an exemplar simulated filament. False-colour shows time as indicated. Scale bars 100 µm. (C) Images of (i) a F. draycotensis filament and (ii) a simulated filament forming a plectoneme (see also Movie S7). (D) Experimental observations of the length distributions of a filament population (blue), and instances of buckling (red) and plectoneme-forming (green) filaments within the population. Dashed vertical lines indicate thresholds for buckling (red) and twisting (green) instabilities predicted by the analytical model (see Methods and SI). (E) A ‘phase space’ for plectoneme formation. Only certain values of length and stiffness (K) result in well-behaved plectonemes, as opposed to straight, buckled, or knotted filaments (see also Figure S3 and Movie S8). (F) Time series of images from model simulations of pairs of flexible filaments (K=0.1), gliding on each other with the orange filament undergoing de-coordinated reversal. (i) Short filaments (200 µm) separate and (ii) long ones (500 µm) tangle via plectoneme formation (see also Movie 9 and Movies 10-12 for simulated and experimental entanglements, respectively).

Shorter cyanobacterial filaments do not collect particles.

(A) Gliding speed and filament length data for three populations of filaments: long (blue) and shortened (orange) F. dray-cotensis, and Pseudanabaena (green) (see Movie S13). (B-D) Images of the endpoint (12 hours after initiation) of the macro-beaker collection/aggregation assay for the same three populations. (E) Time evolution of the largest particle area visible in the beakers for the three populations, coloured as in (A).