Introduction

Cyanobacteria form a diversity of macroscopic structures in aquatic and terrestrial ecosystems. Aggregates and granules can form in aquatic environments, including lakes, open ocean, and bioreactors [1–6], while biofilms and mats are found on rocks or sediments in environments including hot springs and tidal flats [7]. Macrostructures often contain different bacterial species in multiple distinct layers [7–9]. The metabolic activities of resident microorganisms generate gradients of light, oxygen and redox potential, and cycling of key metabolites such as hydrogen and sulfur [4, 5, 10–15]. Therefore, cyanobacterial macrostructures form key habitats enabling microbial transformations of (in)organic matter and thought to have played a key role in the original oxygenation of the Earth’s atmosphere [7, 10, 16].

Macrostructure morphologies may be smooth or pustular, and may also generate protruding laminated structures known as stromatolites [7, 17]. Cyanobacterial mat sections transferred to the laboratory show vertical and conical growth through accumulation and burial of organics [1, 8, 17–20]. Mats can also incorporate inorganic or nutrient-rich sediment particles, aiding in sediment stabilisation [21, 22] and mineral deposition [23]. Similarly, marine cyanobacterial aggregates can attach to and incorporate air-borne dust [24]. Cyanobacteria can act as adsorbing, passive surfaces [7, 25, 26], contributing to these macrostructures through adsorption and flocculation. However, other mechanical drivers of particle incorporation and determinants of macrostructure morphology remain unknown.

Environmental macrostructures are often specifically associated with motile, filamentous species of cyanobacteria [2, 7, 24]. Genes associated with gliding motility – particularly those involved in the synthesis and secretion of motility-enabling polysaccharides – are present across nearly all filamentous cyanobacteria [27]. The extracellular polysaccharides, secreted during gliding motility and broadly known as ‘slime’, can also act as a flocculating agent and cause attachment of filaments to each other and to organic substances [25, 26]. Diverse filamentous cyanobacteria form different types of macrostructures in the laboratory [3, 4, 28], but the exact role of gliding motility in the formation dynamics of macrostructures is unclear. Therefore, the cyanobacterial factors influencing macrostructure formation and eventual morphology remain an open question [7, 8, 17] and the ‘engineering’ of cyanobacterial granules for biotechnological applications remains empirical and unpredictable [2, 5].

Here, we studied macrostructure formation in detail, using a motile filamentous cyanobacterium (Fluctiforma draycotensis, from the Cyanobacteriales order) that reproducibly forms macroscopic granules (‘macrostructures’) under laboratory conditions. This allowed us to track structure formation across macro- and microscopic lengthscales, and timescales from seconds to days. We discovered an emergent behaviour where filament gliding motility generates dynamic collection of solid particles, which are incorporated into granular macrostructures. Combining experiments with a novel physical model of filament propulsion and mechanics, we identified that this behaviour depends on filament length and flexibility, and showed that shortened filaments do not collect particles to form granular structures. A contrasting short motile filamentous species (from order Pseudoanabenales, whose lineage diverged from Cyanobacteriales approximately two billion years ago), also does not perform particle collection, as predicted by our model. We thus establish a clear role for gliding motility and filament physical properties in dictating macrostructure formation and morphology. These insights and future analyses of presented model systems, will enable better understanding of environmental cyanobacterial macrostructures and their engineering for biotechnologies.

Results

Macrostructure formation is driven by gliding motility and particle collection

We studied macrostructure formation first in a microbial community dominated by a motile, filamentous cyanobacterium, F. draycotensis (order Cyanobacteriales) [4] (see Methods). This species shows a form of gliding motility characteristic of many filamentous cyanobacterial species, involving surface-attached back-and-forth movement, principally along the long axis of the filament [29] (Movie S1). The filaments also rotate around their long axis as they move, with the rotation tightly coupled to forward translation [29]. We focused on the repeatable emergence of macrostructures in F. draycotensis cultures as a model system, then explored another cyanobacterial culture dominated by an alternative motile, filamentous species, Pseudanabaena sp. (order Pseudanabaenales). For both static and gently shaken F. draycotensis cultures, macrostructures formed within 1-2 days of culture initiation and persisted over the lifetime of the culture, which can be up to several months (Figure 1A and Methods). Mature macrostructures formed under static conditions were highly robust to agitation by swirling or shaking, and comprised an envelope of cyanobacterial filaments surrounding a mm-scale solid yellow core that is enriched in iron compared to the media (Figures 1B and S1). Yellow flocculate iron precipitates were observed to form in non-inoculated media, but they always remained sub-mm and readily dispersed upon minimal agitation (Figure S2). Macrostructures were not observed in cultures containing a mutant, non-motile F. draycotensis, or cultures containing only the other community members without F. draycotensis (Figure S2). These results show that macrostructure formation in this system is driven by the motility of the filamentous cyanobacteria.

Fig. 1.

To understand the formation of these granular macrostructures with embedded particles, we imaged a dilute, homogenised culture in a glass beaker of diameter ≈ 4 cm, over a period of ≈ 48 hours (Figure 1C and Methods). We repeatedly observed the emergence of highly motile granular structures, which reproducibly grew to a diameter of 1 mm within 24 hours (Movie S2). Specifically, small yellow particles first appeared at the bottom of the beaker, often surrounded by visible bundles of cyanobacteria filaments. These particles moved with, and were actively collected by, cyanobacterial filaments (Movies S2, S3). Increasingly larger granular structures were formed through coalescence of two or more smaller structures, which appear yellow or green depending on the density of cyanobacteria around the structure (Figure 1D and Movie S3). We quantified the size and speed of macroscopic structures over the course of a 33-hour filming period (Figure 1E and Methods). The size increase over this period is mainly due to the macrostructure formation dynamics, as the biomass doubling time in F. draycotensis cultures is in the order of one week [4]. We find that structures of 1 mm diameter form after about 20 hours, and move at speeds of 1-4 µm/s (Figure 1E, inset), comparable to measured gliding speeds for individual F. draycotensis filaments [29].

In later stages, larger structures were often visibly green due to their dense covering of cyanobacteria (Figure 1A). Macrostructures could also become denser through collected particles and filaments ‘tightening’ (Figure 1E). We found that particle collection by cyanobacteria was not selective for the yellow precipitate particles, and polystyrene macroscopic spheres (430 µm diameter) were similarly collected if provided, pointing to a physically rather than chemically-mediated process (Movie S4).

Particle collection is associated with buckling instabilities

We next investigated how particle collection happens mechanistically at the microscopic level, and which specific motility behaviours displayed by F. draycotensis are relevant. We took timelapse videos at the microscale, using fluorescence microscopy and microscopic polystyrene beads (48 µm diameter, see Methods), and observed their dynamic collection (Movie S5). In a representative example shown in Figure 2A, initially homogenously distributed beads were collected into one of two large (≈ 100 µm) clusters after 6 hours, incorporating 60% of the beads within the field of view. The time evolution of cluster size distribution at this microscopic length scale is reproducible (Figure 2B).

Fig. 2.

We observed bead collection in these microscopic timelapse experiments via at least two specific motility behaviours. First, beads were directly transported upon becoming stuck to filaments, or bundles of filaments, performing ‘normal’ back-and-forth gliding motility (Figure 2C). Secondly, buckling and plectoneme formation in a filament were observed to transport and collect beads (Movie S5, S6). Buckling can occur when a gliding filament de-coordinates during a reversal. Rotation-translation coupling can then lead the filament to form a multiply twisted loop called a plectoneme [29]. We frequently observed that filament clusters (with or without beads) contained filaments that were longer than the population average, and were buckled, sometimes forming loops or plectonemes (Figure 2E). Beads encountered by unbuckled gliding filaments were not always transported, but when transported beads encountered another bead cluster, they generally stayed together. A fluorescent lectin, which is known to stain filamentous-cyanobacteria-associated slime [14, 29, 30], stains these bead aggregates (Figure 2D). These observations suggest that slime-mediated filament motility, combined with buckling, and plectoneme formation, drives particle collection and cohesion of bead clusters.

Filament physical properties determine buckling, plectoneme formation and entanglement

To test the hypothesis that buckling and plectoneme formation play an important role in particle collection, we sought a better understanding of how these relate to the motility and physical properties of the filaments. We developed a dynamical 3D model for slender filaments that move through local active gliding forces and torques. In this model, each filament is characterised by its centreline position and local orientation, and the filament can bend and twist as it glides on the surface to which it adheres, with its dynamics set by the surrounding viscous fluid (see Figure 3A, Methods and Supporting Information, SI). The essential novelty of this model is that the filament itself is active and out of equilibrium, and additionally, the forces and torques are applied locally along its centreline, and not at its extremities as in previous steady-state mechanical studies of elastic, twistable filaments such as DNA [31–33] (see Methods and SI).

Fig. 3.

We used measured gliding speeds for F. draycotensis and bending constants from other motile filamentous cyanobacteria [34, 35] to derive physiologically relevant parameters (Table S1-2), which we then used to simulate buckling and plectoneme formation. These events occur when the leading end of the gliding filament either ‘de-coordinates’ to reverse independently of the trailing end or becomes pinned. The two ends of the filament then produce opposing forces and torques, translating and rotating towards each other (Figure 3A) [29]. For the chosen parameters, the model captures both buckling and plectoneme formation as observed experimentally (Figure 3B, C and Movie S7). The length and flexibility K of the filaments determine the type of instability, whilst adhesion and the ratio of twisting to bending modulus (G) also control the dynamics and buckled shape (see Figure S3 and Movie S8). We derived analytical expressions for the instability thresholds for buckling and twisting instabilities, allowing us to determine critical filament lengths for bending and plectoneme formation of around 120 µm and 320 µm respectively (see Methods and SI). Both thresholds align well with experimental observations (Figure 3D). The analytical length threshold for twisting instability is slightly lower than the shortest filaments we observed forming plectonemes, which could be due to some twisting instabilities not leading to full plectoneme formation.

Model simulations enable us to explore a wide range of parameters for gliding active filaments, resulting in a wide range of instability and deformation behaviours, including: absence of buckling/plectonemes; extensive buckling but no plectonemes; plectonemes; and multiple buckling/loops (see Figures Figure 3E, S3, and Movie S8). We found that there exists a limited region of the parameter space, relating to length and K, and to a lesser extentΓ (see Methods and SI), in which the experimentally observed single buckling and plectoneme formation occurs (Figures 3E and S3).

Given the observed filament entanglements around collected beads and also the formation of macrostructures in the liquid phase in gently shaken cultures (Figure S4D and Methods), we also simulated the interaction of two touching filaments, gliding on each other in the absence of a surface. Within the plectoneme-forming parameter region identified above, we found filaments to readily entangle and remain entangled when a de-coordinated reversal occurs, (Figure 3F.i and Movie S9). However, when the interacting filaments are too stiff or short to form plectonemes, then they do not entangle, and only glide past one another (Figure 3F.ii and Movie S9). These simulations qualitatively capture observed entanglement dynamics, and in particular the involvement of plectonemes in initiation of entanglement, which is seen experimentally (Movie S10-12). Taken together, these model-based results show that buckling and plectoneme formation, as well as the associated entanglement, are confined to a limited parameter space, requiring filaments with certain physical properties.

Shorter gliding filaments cannot collect particles nor form granule macrostructures

It is difficult to test all model predictions experimentally. However, filament length is one crucial parameter affecting buckling and plectoneme formation that can be explored. To do so, we took the F. draycotensis cultures through a homogenization and filtering protocol (see Methods) to create a ‘shortened’ and ‘lengthened’ population of filaments, with the mean lengths of 40 µm and 60 µm respectively (Figure 4A). We then quantified macrostructure formation in these two populations. The shortened 7 population showed gliding motility with similar characteristics to the lengthened population (Figure 4A), but they did not perform particle collection or macrostructure formation over the time window in which the longer population did (Figure 1A and Figure 4B, C).

Fig. 4.

To further test the role of length in particle collection, we quantified the motility and macrostructure formation in an additional species of filamentous cyanobacteria: Pseudanabaena sp., which is taxonomically divergent from F. draycotensis(see Methods and Figure S5), but shows gliding motility with slightly faster speeds than F. draycotensis and similar back-and-forth movement (Movie S13). However, they are considerably shorter than F. draycotensis, with a mean filament length of 20 µm (Figure 4A). They are therefore predicted by the physical model to be unable to form plectonemes, and indeed, we observed no such instabilities in timelapse videos of Pseudanabaena motility, taken over comparable timescales to F. draycotensis data in which plectonemes were observed (compare Movies S1 and S13). Using our macroscopic assay of filament behaviour, we observed no particle collection nor aggregate formation by the Pseudanabaena filaments (Figure 4D). Multiple days of culture growth under static conditions produced biofilm structures instead of granular macrostructures (Figure S6).

We conclude that, while motile filaments do generally form macrostructures, the nature of these structures depends on their physical properties. Noting that F. dray-cotensis and Pseudanabaena sp. are separated by two billion years of evolution [36] (Figure S5), such primarily physical characterisation may be more significant than other physiological variations in determining the observed diversity of macrostructures formed by different species of filamentous cyanobacteria.

Discussion

Here we presented and characterised a surprising, emergent behaviour in motile filamentous cyanobacteria: active collection of solid particles from the environment and incorporation of these into persistent macroscopic granular structures. In particular, our results show that the ability of filaments to buckle and form plectonemes promotes filament entanglement and particle collection, thereby leading to the construction of granular macrostructures. The capacity for buckling and plectoneme formation is unlikely to be confined to a single clade; rather, it should arise in any species whose filaments satisfy critical length and flexibility criteria derived here. This insight, as well as the presented modelling and experimental approaches and model systems, will allow development of a predictive framework for understanding the diversity of macrostructures observed in different natural and biotechnological settings and in different filamenteous (cyano)bacterial species.

While we described particle collection and macrostructure formation under laboratory conditions, the presented model systems will help us to study these processes under more specific environmental and biological scenarios, such as in the water column or under different flow regimes on surfaces. For example, the F. draycotensis cultures studied here are obtained from a freshwater reservoir, where granular aggregates are commonly observed in the water column, rock pools and on shore rocks (Figure S4). In the laboratory, we observed F. draycotensis macrostructure formation in the bulk liquid phase of gently shaken cultures (Figure S4). However, further systematic studies are needed to quantify granule formation in other settings, such as varied flow conditions or low filament densities. The presented findings and their future extensions will be useful in biotechnology, to help with bioengineering of cyanobacterial granules for water remediation applications [2, 5] using targeted, suitably long and flexible filamentous species and culturing conditions.

These results call for studies of macrostructure formation in conjunction with stronger emphasis on quantification of filament physical properties. Notably, the presented physical model predictions, regarding the filament length and stiffness required for plectoneme formation and particle collection, were sufficient to explain the difference in collection behaviour in species of two deeply divergent cyanobacterial orders, without invoking lineage-specific biochemistry. Filamentous multicellularity and gliding motility are ancestral traits broadly conserved across cyanobacteria [16, 27], suggesting that these biophysical principles may extend to other filamentous cyanobacteria found in environmental mats, biofilms, and stromatolites. Plectoneme formation and macrostructure formation may also be present in other filamentous prokaryotes, such as the sulfide-oxidising cable bacteria (Desulfobulbaceae), whose long and flexible filaments form dense sedimentary networks that affect local pH and mineral precipitation profiles [53]. This could affect local concentration of reactive mineral phases, with important consequences for sediment geochemistry.

It is notable that we first observed particle collection with iron-containing precipitates. Iron is a common limiting nutrient for cyanobacteria in many environments where it readily precipitates out of solution. Whilst we found particle collection to be a general capability, extending to any inert solid particle, it is plausible that micronsized particles that filaments encounter in nature would include mineral precipitates and nutrient-rich organic matter. Collection of these into macrostructures can be interlinked with embedding of, or subsequent colonisation by, other bacteria. Indeed, cyanobacterial macrostructures are repeatedly shown to be key habitats for the emergence of interlinked microbial metabolisms. Such microbial interactions and overall microbial diversity in granules is shown to be disrupted when macrostructure formation is inhibited in F. draycotensis communities [4]. Thus, particle collection and macrostructure formation can have significant downstream functional consequences.

We find that motility-driven macrostructure formation is a highly dynamic process, involving emergent particle collection. Not only is it driven by motile filaments, but the resulting macrostructures can also move, disassemble, and reassemble. These emergent dynamics result from the interaction of thousands of filaments: such population-level behaviours are widely studied in active matter physics. Such studies have found phase transitions in the patterning of certain filamentous cyanobacteria due to densitydependent nematic ordering [54]; and photoresponsive morphologies in multi-filament bundles [28]. The co-development of models and experiments in the readily-culturable filamentous species like F. draycotensis will enable further study of these dynamic, emergent complex behaviours in filamentous active matter.

Methods

Culturing of cyanobacterial community

All cyanobacterial cultures are established from a freshwater source (Draycote Reservoir, UK) and are maintained under stable laboratory conditions as described before [4]. Cultures are kept in the laboratory under regular serial sub-culturing in BG11+ medium (DSMZ medium reference number 1593), with additional vitamins [4]. Subculturing was done approximately monthly, with cultures grown under continuous 12 h/12 h light/dark cycles with white, fluorescent illumination of 14-20 µmol photons m⁻² s⁻¹ at room temperature under static conditions. For each passaging step, we performed a 1:50 dilution by transferring 150 µL of re-suspended filamentous culture into a final volume of 30 mL of BG11+.

Granule sectioning

Macrostructures of different ‘age’ and size were removed from cultures using a widebore pipette tip to avoid deformation. Structures were fixed using a glutaraldehydelysine fixation process, adapted from a method for preserving bacterial capsules [37]. Firstly, photogranules were placed in PBS for 5 minutes to remove amines. The granules were then transferred between a series of solutions, all prepared in PBS at room temperature: 50 mM lysine (10 minutes), then 50 mM lysine and 2.5% glutaraldehyde (10 minutes), then 2.5% glutaraldehyde (2 hours), finally followed with 3 transfers into PBS (5 minutes each). Photogranules are snap frozen within a PVP:HMPC hydrogel matrix (2.5% PVP and 7.5% HMPC, g/g) for cryosectioning, based on methods used in [38]. A Bright OTF7000 Cryostat was used to perform cryo-sectioning (chamber: − 20^°C, sample head: − 14^°C). Samples were sectioned to a thickness of 100µm, and collected onto cover glass slides for imaging.

Iron analysis of granule cores

A F. draycotensis culture was allowed to grow under normal growth conditions described above and regularly checked for visible yellow particles over two days. Emerging, visible particles are collected by pipette under sterile conditions and placed into 11 collection tubes containing high-purity water. These are centrifuged (10,000 × g, 10 minutes) to pellet the yellow material, the water is removed and the granules resuspended into 70% ethanol solution for 30 minutes to terminate cell growth. The collection tubes are centrifuged again, and washed three times with 70% ethanol. The material is then centrifuged, and resuspended again in ultra-pure water. The water wash step is repeated twice to remove ethanol. The sample is then placed into a vacuum condenser (Genevac) to remove the water.

X-ray Photoelectron Spectroscopy (XPS) of granule cores

XPS was performed by attaching a sample of the extracted granule core to electrically-conductive carbon tape, mounted onto a sample bar with a layer of filter paper between the samples and the sample bar to ensure electrical isolation and hence mitigate differential charging, before being loaded into a Kratos Axis Ultra DLD spectrometer which possesses a base pressure below 1 × 10⁻¹⁰ mbar. XPS measurements were performed in the main analysis chamber, with the sample being illuminated using a monochromated Al Kα x-ray source (hν = 1486.7 eV). The measurements were conducted at room temperature and at a take-off angle of 90° with respect to the surface parallel. The core level spectra were recorded using a pass energy of 20 eV (resolution approx. 0.4 eV), from an analysis area of 300 × 700 microns. The work function and binding energy scale of the spectrometer were calibrated using the Fermi edge and 3d5/2 peak recorded from a polycrystalline Ag sample prior to the commencement of the experiments. To prevent surface charging the surface was flooded with a beam of low-energy electrons from a charge neutraliser throughout the experiment and this necessitated recalibration of the binding energy scale. To achieve this, the C-C/C-H component of the C 1s spectrum was referenced to 285.0 eV. The data were analysed in the CasaXPS package using Shirley backgrounds and mixed Gaussian-Lorentzian (Voigt) lineshapes. For compositional analysis, the analyser transmission function has been determined using clean metallic foils to determine the detection efficiency across the full binding energy range.

Inductively coupled plasma mass spectrometry (ICP-MS) analysis of granule cores

Cultures were fractioned into supernatant, cell pellet and yellow granular core, as explained above. Samples of BG11+ media was also included for analysis, to serve as a media reference. All sample fractions were placed in the Genevac and dried until total dryness was achieved. Dried sample was then dissolved in 70% high-purity nitric acid, diluted into water (1:20) and then filtered through 0.22µm PES filters, and analysed on the ICP-MS. A SPS4 auto-sampler Agilent 7900 was used for ICP-MS. The following equipment conditions were set: spray chamber temperature: 15^°C, plasma gas flow rate: 15 L min-1, carrier gas flow rate: 0.9 L min⁻¹, nebuliser gas flow rate: 1.05 L min⁻¹, auxiliary gas flow rate: 0.9 L min-1, and helium mode gas flow rate: 4.0 mL min⁻¹. The forward power was 1550 watts, with a flow rate of 0.1 rps. Detector analog HV 2152V, pulse HV 956V, with a discriminator voltage of 5 mV and a 4.3 mL helium gas flow rate. Prior to the sequence, the instrument was auto-tuned, and during the analysis, the P/A was modified using calibration standards.

Shaken cultures

For the ‘swirling’ flask shown in Figure S4D, cultures were photographed after 16 days of growth. The culture was grown in an Algem 1.4 (ALGae Environment Modelling lab scale photobioreactor), by Algenuity, at a rotation rate of 80 rpm. The flask was illuminated from beneath with LEDs at ≈ 60 µmol photons m⁻² s⁻¹, on a 12hr/12hr light/dark cycle. The culture was set up using a 1:50 dilution (8ml culture in total 400 ml BG11+ media).

Macroscopic aggregate formation experiments

The process of aggregate formation was recorded on a macroscopic scale in 50mL glass beakers of approximately 37 mm diameter. The beakers were inoculated with 0.4 mL of a mature culture sample, aged between 35 and 70 days, and diluted 1 in 50 into 19.6 mL of fresh BG11+ media to give a total fluid volume of 20 mL. As the microbial communities found in culture flasks of this age have usually formed persistent, cohesive granules, we homogenise the inoculant to break up these structures before setting up the beaker experiments. We do this by pipetting approximately 1 mL of sample up and down in an Eppendorf tube. We then dilute the homogenised inoculant to an optical density of 0.4 compared to a media blank (absorbance at 750 nm, measured using a SPECTRONIC 200 Spectrophotometer, Thermo Fisher Scientific).

The experiment is set up by placing the beakers containing only the fresh media under a DSLR camera (Nikon) held on a post at sufficient distance to allow the entire base of the beaker to be focused in the imaging plane. The beakers are lit from below using a sheet of LED lights, diffused through multiple layers of white diffusion paper (Lee Filters, 216 White Diffusion Lighting Gel) to give a brightness of 36µmol photons m⁻² s⁻¹ at the base of the beakers. The camera is focused by hand at the beginning of the experiment, with adjustments made during the imaging time as necessary. Once the initial focus is set, the sample is added to the media in the beaker, and the beaker is covered with a plastic petri dish lid to reduce evaporation. Images are then taken once every minute for up to 2000 minutes (33.3 hours).

The macroscopic collection assay in Figure S2 was performed in the same glass beakers as all other ‘macroscopic aggregate formation’ experiments. For Figure S2A, we used higher initial densities of culture, and rotated the beakers gently at 150rpm (using a Heidolph Unimax 1010 rotary shaker) to physically concentrate any solids to the centre of the beaker via fluid flow. This allowed easy visibility of either active collection (in the case of the motile culture) or precipitation (for the other two cases) after 5 hours. Additional agitation was then performed by manually swirling and tapping the beaker. For Figure S2B, we used a derived bacterial community lacking F. draycotensis, grown on BG11+ with added 0.8% (≈ 44mM) glucose. As this ‘no-cyanobacteria’ community soon becomes optically dense, black polystyrene beads (Thermo Scientific Black ChromoSpheres Polymer Microspheres, 284µm diameter) are added to the beakers to allow particle collection to be easily visualised.

Macroscopic aggregate formation image analysis

Images of macroscopic aggregate formation within glass beakers are segmented and analysed to measure particle size and speed. Segmentation is performed on the blue channel of the RGB images, which has the largest contrast between the background and the aggregates. The images are automatically thresholded to segment the particles from the background, then particle positions and areas are measured using the Analyze Particles function in ImageJ. The particles are then tracked using the Trackpy module in Python. This code is available at https://github.com/OSS-Lab/Cyanobacteria_particle_collation.

Microscopy imaging of filaments and beads

Particle collection at the microscale was imaged using an Olympus IX83 inverted microscope with a Photometrics CoolSnap-HQ2 camera. Time-lapse videos were taken in brightfield and fluorescence imaging. Chlorophyll autofluorescence of the filaments was imaged using a CoolLED pE-300 illumination system and a Chroma HcRed1 filter cube (Excitation filter: ≈ 550-600 nm, Dichroic mirror: Q610lp, Emission filter: HQ640/50m, ≈ 615-665 nm). We used time intervals of 10s-60s and an exposure time of 100ms. Exampler timelapse images are available at https://zenodo.org/uploads/18680430.

Experiments were performed in a 6 cm glass petri dish base, with a plastic petri dish used as a lid. 12mL of BG11+ media was added to the dish, along with a small quantity of 48µm diameter black polystyrene microspheres (ChromoSphere Dry Dyed Polymer Particles, Black, BK050). Between 0.2-0.4 mL of homogenised mature sample of the cyanobacteria was then added and imaging was initiated immediately afterwards.

Lectin staining

Following one of microscale collection experiments described above, we stained the sample with a fluorescein-tagged lectin stain (RCA-120, Vectorlabs.) This lectin agglutinates sugars including galactose [30], which is known to be a major component of the EPS produced by F. draycotensis [4]. Images of the stained sample were taken using a Zeiss 880 confocal microscope. The RCA-120 lectin was imaged using a 488 nm argon laser, with a PMT emission range of 510-550 nm (green channel), whilst the autofluorescence from the filaments and beads was imaged using a 633 nm HeNe and an emission range on the PMT of 638-700 nm. Imaging was performed with a pinhole diameter of 45.96µm, and a MBD 488/561/633 beamsplitter was used to allow imaging across both channels simultaneously

Creation of shortened F. draycotensis populations

Populations of F. draycotensis with shortened filaments were created by homogenising ≈ 1.5 mL mature culture, then allowing it to settle for ≈ 30 minutes in a 2 mL Eppendorf tube, resulting in a loose aggregate. The ‘supernatant’ of this aggregate is extracted and filtered through a 40µm mesh (Greiner Bio-One EASYstrainer Cell Strainer, Small) to give the ‘short population’. The loosely aggregated filaments are resuspended and homogenised by pipetting up and down in order to give the ‘long’ population. The densities of the two populations are matched by optical density measurements, and the length distribution and motility of both of the populations are confirmed by microscopy.

Length and speed distributions of filament populations

We used time-lapse microscopy images of filaments gliding on a glass surface to measure length and speed distributions of various populations of filaments. Time-lapse images are available at https://zenodo.org/uploads/18680430. Samples were prepared on glass slides with an imaging spacer (Thermo Fisher 25µL Gene frame) and sealed with a plastic cover slip, and imaged on an Olympus IX83 inverted microscope in the HcRed fluorescence channel. The filament density was sufficiently high that any frame of the video contains a significant fraction of filaments that overlap with one another. We therefore implemented an automated segmentation routine to extract the filaments, based on the method outlined in [39]. This code is available at https://github.com/OSS-Lab/Cyanobacteria_particle_collation. The filament trajectories were then linked in Python using the Trackpy module in order to calculate filament speeds.

Phylogenomic analysis

A phylogenomic tree was constructed from 29 cyanobacterial genomes spanning six orders (Gloeobacterales, Synechococcales, Pseudanabaenales, Cyanobacteriales, Phormidesmiales PCC-6307, Leptolyngbyales, and Elainellales). Reference genomes were obtained from NCBI, preferentially selecting RefSeq assemblies where available (see Table S3). Additional genomes were derived from metagenomic analysis of cyanobacterial enrichment cultures from a recent study [40]. Six ribosomal protein markers (Ribosomal L1, L2, L3, L4, L5, and L6) were identified from each genome using Hidden Markov Model (HMM) profiles from the Bacteria71 single-copy core gene collection in anvi’o [41]. For each genome, the best-scoring hit per marker was retained, and amino acid sequences were extracted and concatenated, yielding an alignment of 1,472 positions. Poorly aligned regions were removed using trimAl v1.4 [42] with a gap threshold of 0.5, retaining columns in which at least 50 of sequences contained a residue, resulting in a trimmed alignment of 1,322 positions. Maximum-likelihood phylogeny was inferred using FastTree v2.2.0 [43] with the JTTCAT substitution model and 20 rate categories. Branch support was assessed using Shimodaira–Hasegawa-like approximate likelihood ratio test values computed from 1,000 resamples as recommended [44]. The tree was rooted on Gloeobacter spp., which represents the earliest-diverging cyanobacterial lineage [36]. Morphological traits (filamentous or unicellular) and habitat information (freshwater, terrestrial, marine, or symbiont) were assigned to each strain based on published literature. The tree was visualised and annotated using TreeViewer [45].

Filament modelling and simulation methods

Filament model

We developed a 3D physical model of slender, elastic filaments undergoing active motion to describe the gliding motility, buckling, and plectoneme formation of the filamentous cyanobacteria. The model code is available at https://github.com/OSS-Lab/Cyanobacteria_particle_collation. This model builds on an existing framework that combines the classical equilibrium theory for passive elastic filaments—formulated through Kirchhoff rod models for systems such as DNA [31–33]— with immersed-boundary methods for describing filament dynamics in a viscous fluid [46–49]. We extend this approach to include the local active forces generated by gliding motility, and interactions with the external environment. We approximate the medium in which the cyanobacteria move as a viscous fluid above a solid surface, which causes friction and sets the dynamics of filament motion. Within this formalism, any filament deviating from its relaxed, straight configuration experiences elastic forces and torques that oppose bending and twisting, and these are transmitted to the viscous fluid as hydrodynamic singularities. The filament then moves and reorients according to the local active flow field [46–49].

Filament description

The configuration of the filament can be described by the centreline position X(s) of the filament at a given point s and its local orientation, given by the local material frame, an orthonormal director basis [d₁(s), d₂(s), d₃(s)]. In the classical Kirchhoff framework, d₃(s) is the tangent to the curve X(s), and d₁ and d₂ point normal to the curve X(s). The twist vector κ(s) is then defined from the derivatives of the director basis with respect to the arclength, ∂_sd_i = κ × d_i, where κ = κ₁d₁ + κ₂d₂ + Ωd₃. The elements of the twist vector are known as filament curvatures, and the curvature in the third direction Ω is referred to as the twist density. In our dynamic simulations, because the filament moves with the local flow, as in [47], we allow the material frame to deviate from the tangent and normal vector triad as it rotates with the flow. We also allow for some weak extension of the filament, but impose a large stretch modulus b₃ and shear force constants b₁ and b₂.

Bending and twisting forces and moments

With these formulations in place, we can write down the equation of state describing the elastic forces (F) and torques (i.e., moments, M) on a point s on the filament at time t for a given filament configuration as;

where we introduced the twist coefficient, K_t, and the bending coefficient, K_b, describing the resistance of the filament to twisting and bending, respectively, and b₃ and b₁, b₂ describe its resistance to stretch and shear, with b_i > K_b, K_t.

To characterise the filament mechanics, we introduce the relative bending stiffness K = K_b/K_B,0 relative to the mean experimental value from several cyanobacteria filaments K_B,0 [34, 35], and the ratio of twist-to-bending moduli,Γ = K_t/K_b.

Active gliding

To model active gliding motility, we incorporate the active forces and torques from each cell of the filament. While the exact underlying mechanism for the gliding is not well understood, we know that - in F. draycotensis filaments - each cell translates and rotates as it moves [29]. As a minimal model for gliding, we consider that at each point, the filament experiences local forces and moments along the local tangent vector, with densities f_glide and n_glide, respectively. We impose that the gliding only occurs when the filament is in contact with a solid surface, which can be another filament.

Surface interaction

We also impose a steric repulsion between the surface and the filament. The steric interactions are active where the centreline of the filament is touching the surface, x < 0, are directed normal to the surface, and increase linearly with x,

Finally, we consider adhesion between the surface and the filament, with a typical strength c_adh, the effect of which we explore in simulations. It is active on portions of the filament that are in the adhesion region x ∈ [δ_adh/2, δ_adh], with , so that the force is oriented perpendicular to the surface, cancels at the bounds of the adhesion layer, and reaches a maximum c_adh in the middle of the filament.

Force balance

With the above definitions in place, we can write the force balance on a point s on the filament at time t. To do so, we use a coupled system of equations where the elastic forces and torques generated by the bending and twisting of the filament are transmitted to the viscous fluid. The rod experiences the elastic forces and torques from eq. (1), active force and torque densities f_glide, n_glide from gliding, viscous forces and torques from the fluid f_v, n_v, and steric interactions with the surface f_ste. The force and moment balance is;

Surrounding fluid

Our simulations for the elastic rod in a viscous fluid relies on the immersed boundary method for a slender filament [46–49], which describes the interaction between the active elastic filaments and the surrounding viscous fluid. In this setup, the elastic and gliding forces and torques are directly transmitted to the fluid according to eq. (2), and they generate an active flow around the filament. The filament in turn moves and deforms with the local fluid velocity.

The surrounding viscous fluid verifies the incompressible Stokes equations for the fluid velocity u and pressure p,

with g denoting the distribution of forces per unit volume imposed on the fluid.

As the propulsion, elastic, and adhesion forces on the filament are all transmitted to the fluid as point forces and torques, they generate a local force per unit volume distribution, g(x, t). To avoid singularities in the flow velocity, we use a regularisation kernel ψ_ϵ such that the forces are not applied on singular points of the filament but over an area of typical size ϵ.

With . We then compute the local velocity of the fluid given this distribution of local forces according to eq. (3) as the sum of regularised Stokeslet (left integral) and rotlet (right integral) singularities.

In addition, we enforce the no-slip boundary condition at the solid surface u ((− δ, y, z), t) = 0 by using regularised image singularities for the Stokeslets and rotlets [50–52]. That is, we ensure that the fluid at the solid surface has zero velocity by adding an adequate combination of local flow singularities at the mirror points from the active filament, with their exact expression given in [52].

Filament dynamics

The filament then moves and rotates with the local fluid velocity, as

with the local flow vorticity.

The numerical implementation for the resulting system follows [47]. We discretise the filament in sections of size ds. To compute the derivatives of the forces and moments along the arclength, we compute them at midpoints of the filament and use auxiliary reference frames at these midpoints. We then use a forward Euler algorithm to solve the coupled system of equations. In all our simulations, we use parameter values from the literature on filamentous bacteria when available [29, 34, 35], and infer physically consistent values for the other parameters. The parameters used in the simulations are given in Table S1 for physical properties and in Table S2 for numerical implementation, and their influence on simulation outcomes are discussed in the SI.

Two filament interactions

We extended these simulations to explore the buckling and twisting dynamics of two filaments moving against each other. In the two filament system, gliding along the filament direction occurs for points that are within the contact region of the other filament (instead of the surface) and generate an equal and opposite force on the other filament. We also account for steric interactions between the filaments. We study in particular their entanglement when a reversal occurs in the middle of one of the filaments, as seen experimentally. We find that plectoneme formation regime (long, flexible filaments) in the two-filament system leads to entanglement, as depicted in Figure 3F.ii. Shorter filaments, which wouldn’t form plectonemes on the surface, instead tend to glide past one another and separate even when a reversal occurs (Movie S9).

Simulation parameters

In all our simulations, we use parameter values from the literature on filamentous bacteria when available [29, 34, 35], and infer physically consistent values for the other parameters (see Table S1).

For the motility, we use the experimentally measured gliding force density f_glide = 1 nN.µm⁻¹ [35]. We assume that bacteria glide over a film of thickness of 1µm above the solid surface, and set the medium viscosity µ to match the experimental gliding speed of the filament v_glide ≈ 1µm.s⁻¹ for a 200µm filament based on F.draycotensis filament speeds measured here and previously [29]. We then chose a torque density so that the rotation rate matches its measured experimental value ω_glide/v_glide ≈ 0.87µm⁻¹ [29].

The bending of filamentous cyanobacteria has been studied experimentally [34, 35], but we couldn’t find in the literature values for the twisting modulus of filamentous bacteria, and assumed a unit twist-to-bend ratioΓ, but also explored other values in simulations. We take the adhesion force to be stronger than the gliding forces, c_adh = f_glide. For smaller values of this coefficient, buckling leads to a detachment from the surface, contradicting experimental observations (see Figure 3E and S3). The numerical parameters are chosen for the simulations to be stable, relying on previous implementations of elasto-hydrodynamic simulations [49].

Data availability

This work generated computational models and microscopy timelapse images, as datasets. These are available at GitHub (https://github.com/OSS-Lab/Cyanobacteria) and a dedicated Zenodo repository (https://doi.org/10.5281/zenodo.18680429).

Acknowledgements

We acknowledge Lijiang Song in the Mass Spectrometry Facility, Department of Chemistry at University of Warwick (UoW) for the use of facilities and assistance with ICP-MS, and Marc Walker and Christopher Waldron at the UoW Photoemission Research Technology Platform for their help with the XPS analyses. We thank current and past Soyer group members for discussions and Ben Martynoga, Marco Polin, Roman Stocker, Mohamed Abou Donia, and Emanuele Locatelli for their comments on this work.

Additional information

Author contributions

RP, AT, and OSS conceptualised and developed the methodology of the study. RP, MC, KC, and AS performed experiments and analyses, while AT developed models and ran simulations. RP, AT, and OSS performed formal analysis and visualisation of the data. RP, AT, and OSS wrote the manuscript and all authors contributed to its review and editing. OSS obtained funding for the study, and OSS and MC were responsible for project administration.

Funding

Gordon and Betty Moore Foundation (GBMF)

https://doi.org/10.37807/GBMF9200

• Orkun S Soyer

Additional files

Supplementary Text

Supplementary Movie S1

Supplementary Movie S2

Supplementary Movie S3

Supplementary Movie S4

Supplementary Movie S5

Supplementary Movie S6

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