Functional morphology of gliding motility in benthic diatoms

Significance

Gliding is a major form of cellular movement in prokaryotes and eukaryotes. Despite having no appendages and a rigid cell body, photosynthetic algae called diatoms can glide, harnessing a slit in the cell wall called the raphe. Gliding motility is a conserved trait in this ecologically important group, yet its mechanism remains elusive. Motility allows diatoms to migrate toward nutrients and pheromones, and to regulate light exposure for photosynthesis. Here, we combine quantitative behavioral experiments in 2D and 3D, biophysical characterization, and stochastic simulations to reveal a surprising diversity in the motility patterns of different biofilm-forming diatoms. This natural diversity highlights the functional morphology of the raphe as a potential driver of niche occupation within complex ecosystems such as biofilms.

Abstract

Diatoms, a highly successful group of photosynthetic algae, contribute to a quarter of global primary production. Many species are motile, despite having no appendages and a completely rigid cell body. Cells move to seek out nutrients, locate mating partners, and undergo vertical migration. To explore the natural diversity of diatom motility, we perform a comparative study across five common biofilm-forming species. Combining morphological measurements with high-resolution cell tracking, we establish how gliding movements relate to the morphology of the raphe—a specialized slit in the cell wall responsible for motility generation. Our detailed analyses reveal that cells exhibit a rich but species-dependent phenotype, switching stochastically between four stereotyped motility states. We model this behavior and use stochastic simulations to predict how heterogeneity in microscale navigation patterns leads to differences in long-time diffusivity and dispersal. In a representative species, we extend these findings to quantify diatom gliding in complex, naturalistic 3D environments, suggesting that cells may exploit these distinct motility signatures to achieve niche segregation in nature.

From the smallest bacterium to the largest animals, locomotion is a conserved trait that allows organisms to thrive and diversify in new habitats (1–3). Microscopic organisms display an overwhelming array of movement mechanisms for navigating in 2D and 3D, yet, the same mechanism can also be used by different organisms due to convergent evolution (4). Gliding motility, where cells move actively while adhering to substrates, is present in diverse phylogenetically unrelated species, including myxobacteria, mollicutes, cyanobacteria, and apicomplexans (4–7). Many benthic diatoms modulate their gliding motility in response to environmental changes (8–15), yet the cells have no appendages and cannot change shape due to their completely rigid silica cell walls. This unusual motility is in contrast to other motile organisms that use specialized appendages such as cilia, flagella, and pili (16, 17) or temporary protrusions in the case of amoeboid movement (18).

Diatom gliding represents a unique and mechanistically interesting system for understanding cell migration on surfaces without shape changes. Gliding involves the secretion of mucus-like extracellular polymeric substances through a raphe—a specialized slit in the cell wall (Fig. 1A), though the exact molecular mechanism remains disputed (19, 20). Movement is likely driven by an actomyosin system (21–24), where myosin translocation coincides with cell movement in the opposite direction (Fig. 1B). In contrast to gliding in most other eukaryotic cells where actin filaments are remodeled (25–27), here actin bundles are fixed (running parallel to the raphe), again emphasizing a possible functional role of the raphe.

Fig. 1.

Diatom morphology and gliding motility assay. (A) Schematic of a diatom. The raphe (red solid and dotted lines), a specialized slit in the cell wall implicated in cell movement, runs along the whole length of the valve either continuously or interrupted by the central nodule. The raphe is present on both the Top and Bottom valves of the cell. (B) Hypothesized mechanism of diatom gliding. Secreted adhesive strands are connected via transmembrane components to the actin–myosin complex underlying the raphe. The cell moves in the opposite direction of the force supplied by myosin motors acting along the actin cables [modified image from Molino and Wetherbee (22)]. (C) Experimental setup. Diatoms cultured on a glass-bottomed dish (35 mm) were imaged using an inverted light microscope. (D) A sample gliding trajectory of the diatom Seminavis robusta, color-coded by instantaneous glide speed (arrows show the direction of motion).

As a major constituent of benthic ecosystems, diatom communities play a key role in global carbon fixation and nutrient cycling (28–30). They actively choose surfaces for attachment and gliding, and exploit fine-scale spatial and temporal heterogeneity in the environment such as light, dissolved nutrients, and mating pheromones (8–10, 14). Some species also exhibit vertical diel migration through the photic zone (∼500 μm—3 mm), an efficient process consuming only 0.03 pcal (or 0.0001% glucose consumption) for a cell moving upward or downward over a distance of 400 μm (31–33). Despite the significance of active motility in influencing species dispersal and ecosystem functioning, our knowledge of individual cell behaviors at the microscopic scale is limited (20, 21, 34, 35). Previous studies have focused on resolving the migration and composition of diatom communities (28, 36, 37).

To address this knowledge gap, we present a comprehensive multispecies analysis of diatom motility revealing an unprecedented diversity in motility patterns which we hypothesize may be attributed to differences in body and raphe morphology of our chosen study species. Through quantitative single-cell imaging and tracking experiments (Fig. 1 C and D), we show that diatoms exhibit a basic set of reproducible behaviors, or stereotyped states, but diverse gliding trajectories can be generated by changing the associated transition rates between states. This allows us to construct a generic model of diatom motility that effectively captures the detailed microscopic features of cell movement and predicts their long-time dispersal. To establish whether these features of diatom motility persist within complex, naturalistic environments, we also perform 3D motility tracking in a representative diatom—the first experiment of this kind. Our results emphasize the functional morphology of the raphe as a driver of divergent diatom gliding behaviors exhibited by distinct genera.

Results

Diatom Raphe Morphology Influences Gliding Motility.

We study five representative diatoms commonly found in benthic biofilms: Cylindrotheca closterium (hereafter Cylindrotheca), Halamphora sp. (hereafter Halamphora), Nitzschia ovalis (hereafter Nitzschia), Pleurosigma sp. (hereafter Pleurosigma), and Seminavis robusta (hereafter Seminavis). See Materials and Methods and SI Appendix, Table S1 for details of the experimental protocols. The species were chosen for their distinctive and divergent body/raphe morphologies which we hypothesize to influence motility. Cells vary greatly in length from 5 to 85 μm. We prepared samples for scanning electron microscopy (SEM) to visualize raphe shape and estimate raphe curvature κ_r by manual tracing (Fig. 2 and SI Appendix, Fig. S2 and Materials and Methods).

Fig. 2.

Raphe morphology and track patterns of five biofilm-forming diatoms. From Left to Right: scanning electron microscopy (SEM) of each diatom with raphe highlighted (color overlay denotes the raphe curvature κ_r), sample brightfield image of a moving cell (the Inset shows a schematic on the motion), and maximum intensity projection of a diatom population for (A) Cylindrotheca closterium, (B) Halamphora sp., (C) Nitzschia ovalis, (D) Pleurosigma sp., and (E) Seminavis robusta.

All five diatoms are biraphid pennates with two raphe systems on both valves, but they differ significantly in body shape and raphe placement (38) (Fig. 2). Biraphids may be symmetric (Pleurosigma) or asymmetric (Seminavis, Halamphora), depending on whether the valves are positioned symmetrically relative to the transapical axis of the diatom. More unusual raphe morphologies are found in Cylindrotheca and Nitzschia, both nitzschoid diatoms. Cylindrotheca has a 3D helical raphe spiraling along a needle-shaped cell body (35), which has higher curvature compared to the other diatoms (Fig. 1A). The raphe canal also has a nonsmooth undulating surface. The raphe of Nitzschia lies inside a keel or canal with pores leading to the surface (38) (Fig. 1C). Both Halamphora and Seminavis have relatively straight raphes running from the central nodule to both ends (Fig. 2 B and E). The distal raphe of Seminavis is slightly deflected to one side of the valve. In Pleurosigma the raphe follows the distinctive sigmoidal shape of the valves, with the distal raphe ends deflected toward opposite sides of the mantle (Fig. 2D).

The shape of the raphe, which is physically constrained by the cell body, is reflected in the trajectories (Fig. 2, columns 2 and 3). We explore this quantitatively by performing high-resolution single-cell tracking experiments (n = 4,121 across 5 species). Diatoms were cultured on glass-bottomed plastic microwells and allowed to establish an early biofilm to ensure surface conditions are primed for motility assays. Only a subset of the diatoms are motile (SI Appendix, Fig. S1). Various gliding patterns were observed (Movies S1–S5). Most cells followed straight or slightly curved tracks with frequent changes in direction (Fig. 2, second column). We measured the diatom’s centroid position $\mathbf{r}(t)=[x(t),y(t)]$ (spot tracking) and body orientation $\theta (t)$ (ellipse fitting of the segmented diatom image) simultaneously (Fig. 3A). From this, we calculated its translational velocity $\mathbf{v}(t)$, resolved into components $v_{\Vert }(t)$ and $v_{\perp }(t)$ parallel and perpendicular to the cell body, and rotational velocity $\omega (t)$ (Materials and Methods and Fig. 3B). Cell orientation angles were corrected for jump discontinuities.

Fig. 3.

Gliding characteristics of diatoms. (A) Spot/centroid tracking and ellipse tracking were used to obtain the cell’s coordinate position, $\mathbf{r}(t)=[x(t),y(t)]$, and the orientation, θ, respectively. (B) From this, tangential velocity, $v_{\Vert }(t)$, and angular velocity, $\omega (t)$ were calculated. (C) Violin plot showing the distribution of tangential speed, $|v_{\Vert }|$, of each diatom species. (D–H) Track characterization. From Left to Right: (i) Representative trajectories colored by time; (ii) Temporal dynamics of sample tracks highlighting the relationship between tangential velocity, $v_{\Vert }(t)$, cell orientation, $\theta (t)$, and direction of movement, ${\theta }_v(t)$; (iii) Bivariate histogram of the per-glide curvature $〈{log}_{10}\kappa 〉$ and $〈|\mathbf{v}|〉$; (iv) Histograms of track curvature κ and raphe κ_r for the “average” diatom (see main text). The full distributions are shown in SI Appendix, Fig. S5.

Diatom gliding is slow and jerky (<20 μm s⁻¹) compared to many other motile microbes (Fig. 3C). Representative trajectories are plotted in Fig. 3D–H, i, and color-coded by time. Halamphora and Seminavis which have straight raphes predominantly form straight tracks with occasional turns and reverses. Meanwhile, Cylindrotheca glides with very frequent reversals (Movies S1, S2, and S5). This intermittent behavior may result from its twisted raphe since only a subsection can adhere to the surface at any given time. The largest diatom Pleurosigma does not reverse sharply but instead makes wider, hairpin-like reverses due to the sigmoidal raphe ends. Finally, Nitzschia forms either clockwise or counterclockwise circular trajectories. Comparing body orientation $\theta (t)$ with velocity direction ${\theta }_v(t)$ reveals that straight glides, either forward or backward, coincide with near-perfect alignment of the diatom body with the track (Fig. 3D–H, ii). Instead, reversals are polarity switches where a gliding cell comes to rest ($v(t)$ crosses zero) and immediately moves off in the opposite direction. These appear as $\pm \pi$ jumps in ${\theta }_v(t)$ but the cell-fixed orientation $\theta (t)$ remains continuous.

Gliding, which corresponds to relatively straight paths, can be isolated from nonglides using a curvature threshold (SI Appendix, Fig. S3). For each glide event, the mean curvature $⟨\kappa ⟩$ (Materials and Methods and SI Appendix, Fig. S4) and mean glide speed $⟨|v(t)|⟩$ of individual glides are inversely related (Fig. 3D–H, iii), meaning that straight path segments coincide with fast movement, whereas higher curvature segments correspond to slower movement and transitions (see next section).

Next, we compare the histograms of κ (from track segments during glides) and κ_r (from SEM images) for each species (Fig. 3D–H, iv). We consider glide segments whose mean speed lies between the 45th and 55th percentiles (Materials and Methods and SI Appendix, Fig. S4), to select for diatoms of average size, which is most likely to be represented in the smaller SEM dataset. To see why average speed correlates with diatom length, we note that within the same species longer diatoms should have straighter raphes, and raphe curvature correlates negatively with speed (Fig. 3D–H, iii). Remarkably, the distributions match for all species, suggesting that diatoms glide on paths whose local curvature is determined by their raphes. For Nitzschia, which performs circular loops, the preferred glide curvature is most prominent. The agreement is less good for Cylindrotheca, partly because we cannot accurately trace 3D raphes from 2D projections in the SEM images. For this diatom, κ_r is generally higher than κ, likely because only some parts of its helical raphe are aligned with the substrate.

Overall, these findings reveal that raphe morphology directly influences characteristics of the gliding paths of diatoms.

Classification of Diatom Motility Phenotypes.

Despite major differences in trajectory morphology across the five species, we observed that the diatoms undergo just four stereotyped behaviors, namely Glide, Reverse, Pivot, and Stop (Fig. 4A). Discretizing motility patterns into low-dimensional gaits/states and studying transitions between these states allows us to quantify how behavior changes over time, and make comparisons across species (5, 39, 40). Glides are associated with persistent movement in a certain direction, involving motion along the body-axis direction (as discussed above). The circular motion of Nitzschia is also considered gliding in this interpretation. A reversal is a sudden event during which the diatom switches to gliding with its trailing end, which becomes the new leading end. Pivots occur when a diatom that is only partially adhered to a surface rotates about using the trailing end. Finally, a stop corresponds to cessation of movement.

Fig. 4.

Four-state Markov model of diatom motility. (A) Definition of the four possible states. (B) Example of trajectory segmentation into motility states: the Left panels—sample trajectories for Halamphora (Top) and Pleurosigma (Bottom), color-coded based on the motility state (ellipses indicate the average size of each diatom), Right panels—respective time evolution of $S(t)$ (arrows highlight the reversals). (C) The four states visualized in the $\{|v_{||}(t)|,|\omega (t)|\}$ parameter space. The region delineating each state is constructed from the bivariate histogram (logarithmic scale) (shifted by 0.01 for better visualization of small values) after applying a smoothing filter and calculating the convex hull (97.5-percentile). (D) Distinct transition networks for each diatom species. Circles represent the states, and arrows the transitions between states. The size of each circle scales with the mean dwell time per state, while the thickness of each arrow scales with the pair-wise transition probability between states (transitions with probability ≤0.2 have been pruned for ease of visualization). (E) Distributions of gliding duration with fit to exponential distributions (Cylindrotheca, Halamphora, Nitzschia, and Seminavis) or lognormal distribution (Pleurosigma).

We classified the state of a diatom at every time frame (Materials and Methods). The output is illustrated with two example tracks in Fig. 4B, where the trajectories are colored by state and plotted alongside the corresponding cumulative tangential velocity defined by $S(t)=\sum _{t^{\prime }=0}^t{v}_{\Vert }(t^{\prime })\mathrm{\Delta }t$. More example tracks can be found in SI Appendix, Fig. S6. Halamphora glides at a very stable speed ($S(t)$ has almost constant positive or negative slope). Glides are interspersed with random reversals (arrowheads), after which the preferred glide speed is quickly reestablished. Similar behavior is observed for Seminavis and Nitzschia (although with chiral motion) and, to a certain extent, also for Cylindrotheca, whose movements are more irregular. Pleurosigma exhibits quasi-periodic interruptions to movement, accelerating/decelerating more gradually resulting in very constrained tracks.

Across all species, the four states are well differentiated by the diatoms’ tangential speed $v_{||}(t)$ and rotational speed $\omega (t)$. The four states occupy similar regions of the $\{|v_{||}(t)|,|\omega (t)|\}$-parameter space (Fig. 4C), despite differences in absolute values across species. A greater overlap is observed for Cylindrotheca, due to its low and erratic speed.

We used a four-state Markov chain to estimate the statistics of state transitions, where all nonself transitions are assumed possible except those leaving the Reverse state toward any other state than Glide, since a reversal implies the reestablishment of persistent, directed motion. We estimated mean dwell times and pairwise transition probabilities from the data and represent these as transition networks (Fig. 4D) (Materials and Methods and SI Appendix, Tables S2–S11). All diatoms are found predominantly in the Glide state, often accounting for 55 to 75% of the time, the rest is spent in the Stop, Pivot, and Reverse states, in descending order (SI Appendix, Fig. S7). For all diatoms, transitions between Glide and Reverse, or between Glide and Stop, are highly likely. The characteristic transition probabilities and mean dwelling times vary greatly across species, especially for Glide. While Glide durations are strongly exponentially distributed for most diatoms (Fig. 4E), Pleurosigma exhibits frequent and periodic reversals which we fit instead to a lognormal distribution. Pleurosigma is the only species showing oscillatory behavior, with a periodicity of approximately 23 s (SI Appendix, Table S10).

We showed that different diatoms exhibit distinct but stereotyped gliding behaviors that are fully captured by stochastic transitions between just four underlying states. These states may be a conserved feature of all raphe-based motility systems, while the main difference between species is that they can access distinct motility patterns by uniquely combining these gaits according to different transition rates.

Stochastic Model of Diatom Gliding.

Next, we develop simulations of diatom gliding motility, with physical parameters calibrated directly using trajectories from each species. The stochasticity of diatom movement is captured using Stochastic Differential Equations for the evolution of the 2D position $\mathbf{r}(t)=[x(t),y(t)]$ and the orientation $\theta (t)$:

$$\begin{array}{cc}\hfill \text{d}\mathbf{r}(t)& =f(\theta (t),s(t),t)\text{d}t+{\mathbf{u}}_{||}(t)v_{||\sigma }\text{d}{W}_{\text{tra}}(t),\hfill \end{array}$$ [1a]

$$\begin{array}{cc}\hfill \text{d}\theta (t)& =g(s(t),t)\text{d}t+{\omega }_{\sigma }\text{d}{W}_{\text{rot}}(t),\hfill \end{array}$$ [1b]

where ${\mathbf{u}}_{||}=[cos\theta (t),sin\theta (t)]$, $W_{\text{tra}}$ and $W_{\text{rot}}$ are two uncorrelated Wiener processes so that $\mathbb{E}[\text{d}{W}_i(t)\text{d}{W}_j(t^{\prime })]={\delta }_{\mathit{ij}}\delta (t-t^{\prime })$, where i and j are indices for the labels “tra” and “rot,” $\delta (t)$ is the Dirac delta-function and δ_ij the Kronecker delta. The parameters $v_{||\sigma }$ and ω_σ then represent the magnitude of such stochastic fluctuations, with the translational and rotational diffusion constants are denoted by $D_{\text{tra}}=v_{||\sigma }^2/2$ and $D_{\text{rot}}={\omega }_{\sigma }^2/2$ respectively. Finally, the functions $f(\theta (t),s(t),t)$ and $g(s(t),t)$ are set separately accordingly to the diatom’s motility state. Note that the evolution of position is coupled to that of orientation, as $f(\theta (t),s(t),t)$ is a function of $\theta (t)$. Moreover, both functions depend on the diatom’s “polarity” $s(t)\in \{-1,+1\}$, an indicator representing whether the diatom is moving forward or backward (this is an arbitrary choice since diatoms have no identifiable “front” or “back”) that switches its value with every reversal.

In the Glide state $f(\theta (t),s(t),t)=s(t){\mathbf{u}}_{||}(t)v_{||\mu }$ and $g(s(t),t)=s(t){\omega }_{\mu }$, where $v_{||\mu }$ is the mean gliding speed and ω_μ the mean rotational speed. The diatom moves forward (or backward, depending on $s(t)$) with additive Gaussian white noise, and rotates with similar dynamics. For simplicity, we assume translational motion is only in the tangential direction (aligned with the cell’s long axis), consistent with the data.

In the Pivot state $f(\theta (t),s(t),t)=s(t)\frac{\overline{L}}{2}\text{d}{\mathbf{u}}_{||}(t)$, where $\overline{L}$ is the mean diatom length of each species, and $g(s(t),t)=s(t){\omega }_{\mu }$: the orientation changes according to a mean rotational velocity and Gaussian white noise, while the tangential displacement results from rotation about either end of the cell, determined by $s(t)$.

Finally, in theStop the Reverse states $f(\theta (t),s(t),t)=0$ and $g(s(t),t)=0$, leaving only the stochastic terms with zero expected net displacement/rotation. The polarity $s(t)$ switches sign at the transition to Reverse, forcing the subsequent Glide to occur in the opposite direction. Here, Reverse is instantaneous, which is an approximation of the actual reversal dynamics.

The values of $v_{||\mu }$, $v_{||\sigma }$, ω_μ and ω_σ depend on the motility state as well as the species, and must be calibrated to the experimental data. We further assume, denoting the associated state by superscripts, that $v_{||\sigma }^{\text{S}}=v_{||\sigma }^{\text{P}}=v_{||\sigma }^{\text{R}}$ and ${\omega }_{\sigma }^{\text{S}}={\omega }_{\sigma }^{\text{R}}$, i.e. translational fluctuations have the same magnitude in Stop, Pivot and Reverse, while rotational fluctuations have the same magnitude in Stop and Reverse. We are then left with a total of 8 parameters to calibrate for each species: $v_{||\mu }^{\text{G}}$, $v_{||\sigma }^{\text{G}}$, ${\omega }_{\mu }^{\text{G}}$, ${\omega }_{\sigma }^{\text{G}}$, $v_{||\sigma }^{\text{S}}$, ${\omega }_{\sigma }^{\text{S}}$, ${\omega }_{\mu }^{\text{P}}$, and ${\omega }_{\sigma }^{\text{P}}$.

Model Calibration.

We calibrated the model separately on each species. For Glide, we estimated $v_{||}(t)$ and $\omega (t)$ from all tracks, discarding frames not classified as Glide. Since each sequence of consecutive Glide frames has a slightly different mean speed across the different tracks, we perform a velocity scaling on $v_{||}(t)$ to better capture velocity fluctuations during glides (Materials and Methods). The same scaling is applied to $\omega (t)$.

Since diatoms have no discernible “front” or “back,” reversals lead to a double-peaked distribution for $v_{||}(t)$. Therefore, a generic model should not be biased toward a specific tangential direction (forward vs. backward) nor a specific rotational direction (clockwise vs. counterclockwise), so we count both $\pm v_{||}(t)$ and $\pm \omega (t)$ to construct distributions that are symmetric about the y-axis (e.g. Fig. 5A for Seminavis, results for other species can be found in SI Appendix, Fig. S8).

Fig. 5.

Model calibration and simulation. (A) Calibration of Glide parameters for diatom species Seminavis. (i) the sum of two normal distributions is fitted to the probability distribution of $v_{||}$ to estimate $v_{||\mu }^{\text{G}}$ and $v_{||\sigma }^{\text{G}}$. (ii) a normal distribution is fitted to the probability distribution of ω to estimate ${\omega }_{\mu }^{\text{G}}$ and ${\omega }_{\sigma }^{\text{G}}$. (B) Summary of workflow from experiment to simulation. (C) Examples of simulated trajectories. (D) MSD obtained from simulations (red line) plotted on Top of the experimental MSD (black), with the gray area around it representing the 10-to-90 percentile range of the square displacement. Additional simulations with Glide as the only possible state (cyan).

We improved the fit accuracy with a coarse-graining approach to reduce the influence of measurement noise, using a moving window of $5$ frames (Materials and Methods). $v_{\mu }^{\text{G}}$ and $v_{\sigma }^{\text{G}}$ are then fitted to the sum of two Normal distributions $\mathcal{N}(\mu ,\sigma )$ and $\mathcal{N}(-\mu ,\sigma )$ (Fig. 5A, i):

$$\begin{array}{c}\hfill \begin{array}{cc}\hfill p(v_{||})& \approx \frac{1}{2(v_{||\sigma }^{\text{G}}/\sqrt{5})\sqrt{2\pi }}exp\left(-\frac{1}{2}{\left(\frac{v_{||}-v_{||\mu }^{\text{G}}}{(v_{||\sigma }^{\text{G}}/\sqrt{5})}\right)}^2\right)\hfill \\ \hfill & +exp\left(-\frac{1}{2}{\left(\frac{v_{||}+v_{||\mu }^{\text{G}}}{(v_{||\sigma }^{\text{G}}/\sqrt{5})}\right)}^2\right),\hfill \end{array}\end{array}$$ [2]

where the factor $1/\sqrt{5}$ rises from the coarse-graining. For all diatom types except Nitzschia, ${\omega }_{\mu }^{\text{G}}=0$, and ${\omega }_{\sigma }^{\text{G}}$ is estimated by fitting to $\mathcal{N}(0,\sigma )$ (Fig. 4A, ii)

$$\begin{array}{c}\hfill p(\omega )\approx \frac{1}{({\omega }_{\sigma }^{\text{G}}/\sqrt{5})\sqrt{2\pi }}exp\left(-\frac{1}{2}{\left(\frac{\omega }{({\omega }_{\sigma }^{\text{G}}/\sqrt{5})}\right)}^2\right).\end{array}$$ [3]

Since Nitzschia exhibits chiral motion, ${\omega }_{\mu }^{\text{G}}$ and ${\omega }_{\sigma }^{\text{G}}$ are fitted to the sum of two Normal distributions, analogously to the calibration of $v_{\mu }^{\text{G}}$ and $v_{\sigma }^{\text{G}}$. The Stop and Pivot parameters are calibrated analogously (Materials and Methods).

The complete procedure is summarized in Fig. 5B, with distributions of $v_{||}$ and ω for all diatom species and states, provided in SI Appendix, Figs. S8–S10.

Long-Time Dynamics and Dispersal.

Next, we investigate how the microscale strategy affects macroscale dispersal in both experiments and simulations. Diatom movement was simulated using a hybrid Gillespie-Langevin algorithm that captures both the discrete-time stochastic switching of the motility state and the continuous-time dynamics of the state itself. The simulated and experimental trajectories qualitatively match (Figs. 2 and 5C), with good quantitative agreement between the Mean Squared Displacement $\text{MSD}(\tau )=⟨\Vert \mathbf{r}(t_i+\tau )-\mathbf{r}(t_i){\Vert }^2⟩$ (Fig. 5D).

The MSD analysis shows that all diatoms are ballistic at short times, but diffusive at longer times. Cylindrotheca transitions to diffusive motion after ∼100 s, while Halamphora and Seminavis transition after a longer time, with observations limited by the maximum recording duration (600 s). To understand whether the ballistic to diffusive transition is due to rotational fluctuations or motility state switching, we performed simulations which do not allow diatoms to leave the Glide state (Fig. 5D). The resulting MSD curves are approximately ballistic up to timescales that are much longer than the maximum duration of the experimental trajectories, showing that the transition to diffusive behavior can be attributed to reversals and pivots. Since glides are exponentially distributed in Cylindrotheca, Halamphora, and Seminavis (Fig. 4E), reversals cause these diatoms to perform a 1D random walk. In contrast, Pleurosigma and Nitzschia do not transition from ballistic to diffusive behavior directly. Rather, these species exhibit an intermediate timescale at which the MSD grows sublinearly due to oscillations: loops in the case of Nitzschia and periodic reversals in the case of Pleurosigma (Fig. 4E). The period of both loops (∼41 s, see SI Appendix, Fig. S11) and reversals (∼23 s, see Fig. 4E) is shorter than the timescale for randomization of direction by rotational diffusion, causing these diatoms to revisit recently explored areas. At even longer timescales, diffusive behavior is recovered (Fig. 6A). Note the discrepancy observed in some diatoms between experimental and simulated MSDs at the highest values of τ is due to experimental tracks with large displacement being interrupted when a cell leaves the field of view; the surviving tracks are therefore biased toward smaller displacements. Alternative MSD plots are provided in SI Appendix, Fig. S12 where only tracks that reached the full 600 s are considered.

Fig. 6.

Long-time dispersal and vertical migration. (A) MSDs of all species over timescales of up to ${10}^4$ s, predicted from the fully calibrated simulations. The velocity autocorrelation function (Materials and Methods) for the same simulations is shown in SI Appendix, Fig. S13. (B) Schematic of diatoms’ vertical migration highlighting the different ecological niches they inhabit.

Finally, we predict the overall migration trend for each species with long-time simulations for τ up to ${10}^4$ s (Fig. 6A). Taken together, the results reveal how the distinct motility patterns of the diatoms lead to a natural segregation of their macroscopic diffusivities. These are 15.16 $\mathrm{\mu }{\text{m}}^2{\text{s}}^{-1}$ for Cylindrotheca, 54.62 $\mathrm{\mu }{\text{m}}^2{\text{s}}^{-1}$ for Halamphora, 0.70 $\mathrm{\mu }{\text{m}}^2{\text{s}}^{-1}$ for Nitzschia, 19.64 $\mathrm{\mu }{\text{m}}^2{\text{s}}^{-1}$ for Pleurosigma, and 100.06 $\mathrm{\mu }{\text{m}}^2{\text{s}}^{-1}$ for Seminavis, with Seminavis and Halamphora being the most diffusive, and Nitzschia the least diffusive. These are consistent with the putative dispersal trends of these species from available literature (Fig. 6B and Discussion).

3D Experiments and Simulation.

To bridge our findings on controlled 2D substrates with the more naturalistic settings inhabited by the organisms, we created a structured 3D environment (depth $\sim 2$ mm) using crushed cryolite, a material with a similar refractive index as seawater, enabling direct microscopic observation and 3D tracking (Fig. 7A and Materials and Methods). In this novel assay, cells navigated the interstices and across the surfaces of the cryolite particles, thereby recreating their movement patterns within natural 3D biofilms.

Fig. 7.

Diatom gliding motility in a complex 3D environment. (A) 3D environment design. Schematic of a 3D substrate (total depth: 2,000 to 2,500 μm) made up of cryolite (gray circles) which has a refractive index similar to seawater. The observation area was limited to 200 μm depth. Diatoms can occupy the interstices between and glide along the surfaces of the cryolite particles. Fluorescence image showing the distribution of cells (magenta) in the 3D environment (gray background). (Scale bar, 100 μm.) (B) Sample tracks of Seminavis gliding motility in 3D. (C) Seminavis exhibits the four behavioral states in 3D, each color represents a separate 10 μm z-slice. (D) Mean-squared displacement curves from the 3D experimental data and simulations.

We focus on Seminavis, chosen because it exhibited all four behavioral states with reasonable probability in our 2D experiments (Fig. 4D), and its larger size facilitates observation. Cells traversed the structure, migrating over vertical distances of ∼200 μm. Sample 3D tracks are shown in Fig. 7B. As in the 2D experiments, cells showed all four behavioral states of glide, reverse, pivot, and stop (Fig. 7C and Moive S6). Cells also used pivots and reversals to reorient themselves.

To quantify diatom dispersal in 3D, we again measured the MSD in the experiments (Fig. 7D) (n = 151). For Seminavis, the 3D MSD matched the 2D curve (Fig. 5D) at small times, but the cells transitioned more rapidly from ballistic to diffusive behavior in 3D, likely due to collisions with the cryolite particles. To verify this, we extend our simulations to 3D (Materials and Methods), using the same state transition parameters as before, and a new mean glide speed of ∼2.7 $\mathrm{\mu }\text{m}{\text{s}}^{-1}$ estimated from the 3D trajectories. To mimic collisions with the obstacles, we stochastically set an upper bound for the dwell time in the Glide state (Materials and Methods). A mean bound time of 37 s was chosen so that diatoms, gliding at an average speed of ∼2.7 $\mathrm{\mu }\text{m}{\text{s}}^{-1}$, approximately cover 100 $\mathrm{\mu }\text{m}$, the approximate size of the “free space” between particles (e.g., the white areas in the fluorescence image in Fig. 7A).

These results show that diatom movement through complex 3D environments is quantitatively well-captured by the key features measured in our controlled 2D assays, and suggest that such patterns are intrinsic to each diatom species and therefore a reliable predictor of macroscopic dispersal.

Discussion

In this contribution, we have studied the gliding motility of five representative biofilm-forming diatoms and revealed their distinctive single-cell motility patterns. Using long-time, high-resolution imaging we discretized their motion into four states based on mathematically well-defined movement characteristics. We developed stochastic simulations to fully capture all features of diatom movement to make predictions about their long-time dispersal. This was extended to 3D and validated against experimental measurements of cells navigating through realistic 3D environments using a representative diatom. Using emerging analytical and experimental techniques, we have uncovered the natural diversity in behavior across different motile taxa and presented a comprehensive framework that enables precise and quantitative comparisons.

The mysterious gliding motility of diatoms has fascinated researchers for centuries. Gliding has unique features that deviate from established behaviors of flagellated or ciliated microswimmers (5, 39, 41). The molecular mechanism of diatom motility is hypothesized to involve the raphe and raphe-associated actin bundles (21, 23, 24). Here, leveraging the distinct raphe morphologies of different diatoms, we have demonstrated that different motility patterns result from the intrinsic shape and curvature profile of the raphe slit. The dominant curvature of gliding trajectories coincides with the curvature of the raphe itself. We therefore expect morphological similarity to translate into similarity in terms of motility phenotype. Indeed, Halamphora and Seminavis both have simple straight raphes (38) and quantitatively most similar motility patterns. Thus, the functional morphology of the raphe holds essential clues about how motile diatoms diversified throughout evolution, complementing existing taxonomic or phylogenomic evidence.

Our results strongly support the emerging view that motility relies upon an actin–myosin “highway” that is closely aligned with the raphe slit geometry (21–23). This mechanism is distinct from those adopted by other gliding eukaryotic cells. In the diatom Craspedostauros australis, bidirectional movement of fluorescently tagged myosins correlates with body movement (24). Here, by simultaneously tracking cell position and body orientation, we showed that cells glide persistently only when the body is aligned with the trajectory heading. Misalignment is associated with reversals or pivots, likely due to changes in adhesion (15, 24). Out-of-plane tilting movements are most pronounced in diatoms with more complex raphes that cannot adhere fully to the substrate, such as Cylindrotheca and Nitzschia (42).

Within diatoms, evolution of the raphe and gliding motility was highly consequential for species diversification (43). Although the raphe places fundamental physical constraints on motility that presumably accounts for the four core behavioral states, we still measured very different diffusivities across species. This functional divergence suggests a possible link between diatom motility, morphology, and evolutionary adaptation to distinct ecological niches. Different motility patterns could lead to niche segregation, influencing the diversification and spatial distribution of organisms (44–48). Within mixed-species biofilms, different diatoms, both epipelic—motile cells that live primarily on muddy sediments, and epipsammic—nonmotile cells that live among sand grains, are known to occupy specific niches depending on their size, morphology, and growth preferences (Fig. 6B). Smaller epipelic diatoms like Halamphora or Seminavis exploit fast motility for diel migration, traversing the entire photic zone in 0.5 to 1 h. Larger cells like Pleurosigma may inhabit the subsurface where they do not traverse large distances but instead exploit their large body size by constantly reorienting or pivoting their body axis to regulate light exposure (49). Nitzschia ovalis is likely an epipsammic diatom found on the biofilm surface (50, 51) that contributes to overall biofilm cohesion and integrity, where again long-distance migration is not required, consistent with their low diffusivity.

We also obtained the first measurements and direct visualization of vertical movement in diatoms, revealing that the intrinsic behaviors of gliding diatoms in homogeneous, controlled 2D environments translate readily into complex 3D settings. In nature, distinct motility strategies enable cells to efficiently exploit critical resources, particularly light, while reducing competition from conspecifics (8, 52, 53). In the photic zone, which measures ∼500 μm in muddy or ∼3mm in sandy sediments (28, 54, 55), diatoms use both in-plane and vertical motility to reap the benefits of light for photosynthesis while avoiding light stress (8, 49, 52, 53, 56). In nature, steep vertical gradients in light intensity may further shape the motility patterns of the cells. Motility is also influenced by temperature, with ice-dwelling diatoms exhibiting specialized motility strategies to navigate extreme temperatures (15). More generally, physical constraints can also drive significant phenotypic diversity in other motile organisms (57, 58).

Together, our experiments, analysis, and simulations reveal how variability in motility strategy directly influences the macroscale dispersal of diatoms. Using experimentally calibrated simulations, we can confidently predict long-term trends in regimes that are inaccessible in experiments. Future work should explore how these trends may be influenced by environmental perturbations such as light, fluid flow, chemicals, pheromones (8, 11, 53). Ultimately, our findings should be framed against the scale and environment in which diatoms live to reveal the ecological significance of their motility.

Materials and Methods

Diatom Culturing and Experimental Setup.

We selected five representative taxa with different frustule shapes and raphe systems that might impact adhesion and motility (Fig. 2A). The diatom strains used are C. closterium (DCG 0980), Halamphora sp. (CCAP 1050/13), Nitzschia ovalis (CCAP 1052/12), Pleurosigma sp. (RCC 6814) and Seminavis robusta (DCG0096-0115). All diatoms were cultured in f/2 media supplemented with silicate (59) under a 14:10 light:dark cycle at 21 ^°C, with cool-white fluorescent lamps at 35 μmol m⁻² s⁻², with the exception of Pleurosigma, which was cultivated at 15 ^°C under 25 μmol m⁻² s⁻².

For 2D experiments, cultures were prepared by aliquoting stock cultures to an initial cell density of 10³ using fresh culture media (total volume per well: 1.5 mL) in μ-Slide 2 Well chambers (Ibidi GmbH). The biofilm is considered fully developed after 7 to 9 d (>5 × 10⁴ cells mL⁻¹), videos were recorded to capture baseline motility patterns for that species, in the absence of any other environmental perturbations. We used an inverted microscope (Leica DMi8) equipped with a Leica camera (DMC2900) to take 10 min videos at 1 fps of different observation regions in the well. A standard broad-spectrum white LED (see SI Appendix, Fig. S8 in ref. 39) with intensities ranging from 30 to 90 μmol m⁻² s⁻¹ served as the light source for all imaging experiments. The light settings were optimized to account for the significant variations in cell sizes across the different species (Fig. 2). Individual settings for each species can be found in SI Appendix, Table S12. The total number of videos for each diatom were Cylindrotheca (n = 39), Halamphora (n = 30), Nitzschia (n = 46), Pleurosigma (n = 31), and Seminavis (n = 30).

For 3D experiments, μ-Slide 8 Well (Ibidi GmbH) chambers were filled with crushed cryolite (400 mg) to mimic naturalistic 3D environments that are 2,000 to 2,500 μm in depth. The crystal has a similar refractive index as seawater ($n_{\text{seawater}}=1.34$, $n_{\text{cryolite}}=1.34$), allowing direct microscopic observation of cells in brightfield. To visualize the structure of the 3D environment formed by the powdered crystal (Fig. 7A), 1 μL of 1:1,000 fluorescein (Merck) was added to a well and incubated for 10 min before observation. Chlorophyll a (blue excitation: 450 nm) and fluorescein (green excitation: 550 nm) were consecutively imaged to differentiate between the environment and diatoms.

Live imaging was performed using Seminavis as a representative species. As before, cells were cultured in flasks (TC flasks, 25 cm², Corning) for 7 d reaching a density of >5 × 10⁴ cells mL⁻¹. For motility assays, 300 μL of this culture was transferred to each μ-Slide 8 Well. Cells were allowed to settle into the wells for a day prior to imaging. To reconstruct the 3D movement of diatoms, we imaged a ∼200 μm-thick region in the center of the substrate using a broad-spectrum white LED [CoolLED pT-100 light description (https://www.coolled.com/products/pt-100/)] with a light intensity of 30 μmol m⁻² s⁻¹. We obtained a high-resolution z-stack at 2.2 fps (with 20 slices, stepsize 10 μm) using an inverted microscope (Olympus IX83) coupled to a Kinetix camera (01-Kinetix-M-C, Teledyne).

Scanning Electron Microscopy and Raphe Tracing.

For SEM, the samples were initially fixed in a solution comprising 2% glutaraldehyde and 2% paraformaldehyde in 0.1M PIPES buffer at pH 7.2 at room temperature for 1 h. Following fixation, the cells underwent three washes in the same buffer, each for 5 min, and were subsequently transferred onto poly-L-lysine-coated coverslips. Postfixation was carried out in 1% aqueous osmium tetroxide for 1 h. This was followed by another series of three 5-min washes in deionized water. The cells were then subjected to a graded ethanol dehydration series, involving sequential immersions in 30%, 50%, 70%, 80%, 90%, and 95% ethanol for 5 min each, followed by two 10-min immersions in 100% ethanol. Complete dehydration was achieved using hexamethyldisilazane (HMDS, Merck, Gillingham, UK) for 3 min, after which the samples were air-dried. The dried samples were mounted onto aluminum stubs using carbon adhesive tabs and subsequently coated with a 10 nm layer of gold/palladium (80/20) using a Q150TES sputter coater (Quorum Technologies Ltd., Laughton, UK). To enhance conductivity, silver paint was applied to the sides of the coverslips. The specimens were then imaged using a Zeiss GeminiSEM 500 scanning electron microscope (Carl Zeiss Ltd., Cambridge, UK) operated at 1.5 kV.

From SEM images, manual raphe shape tracing was done by creating several point selections (n= 50 to 150) along the raphe using the open-source software Fiji (60). This gives a series of x and y coordinates for each raphe that were used to calculate the raphe curvature (κ_r) (Curvature Calculation), Fig. 2A and SI Appendix, Fig. S2).

Video Processing and Tracking.

We wrote custom Jython scripts in the open-source software Fiji (60) for preprocessing raw videos and tracking. For 2D experiments, cells were detected and tracked as ellipses using the Kalman tracker algorithm in Trackmate (61, 62), the settings of which were optimized for each video. Only extremely motile cells, those that moved at least 15 times their body length, were considered for the analysis (SI Appendix, Fig. S1). The total number of tracks for each diatom were 110 for Cylindrotheca, 605 for Halamphora, 122 for Nitzschia, 450 for Pleurosigma, and 834 for Seminavis.

For 3D experiments, tracking is more challenging, as cells change shape as they go in and out of focus, and can only be detected in Trackmate as spherical spots and could not be fitted to ellipses to obtain cell orientation (62). We performed spot-tracking using Kalman tracker with similar settings for all videos, to obtain coordinates for the diatom’s position. The resulting tracks were manually inspected to ensure correctly segmented tracks were connected and spurious connections were deleted. We tracked 3 videos resulting in 151 tracks.

To investigate whether diatoms exhibit the same four behavioral states during 3D exploration, we processed the videos by color-coding each slice or depth (10 μm). Maximum intensity projections were then performed to condense the data into a 2D representation (Movie S6 and Fig. 7C).

Calculation of Track Parameters.

For every recorded trajectory, we obtained the time series of the diatoms’ position, with a time interval of $\mathrm{\Delta }t=1\mathrm{s}$ between consecutive frames. The position consists of the two Cartesian coordinates $\mathbf{r}(t)=[x(t),y(t)]$ for the center of the diatom, as well as the diatom’s orientation $\theta (t)$, relative to the x-axis taken from the fitted ellipse (Fig. 3A). Due to the symmetry of the ellipse, two possible (opposite) orientations can be identified at each frame. We correct frame-to-frame inconsistencies by assigning $\theta (t)\Rightarrow (\theta (t)+\pi )\text{mod}2\pi$ when $|\theta (t)-\theta (t-1)|>\pi /2$ (i.e., the smallest rotation is assumed to be the most likely).

At each time frame, the translational velocity was extracted as $\mathbf{v}(t)=(\mathbf{r}(t+\mathrm{\Delta }t)-\mathbf{r}(t))/\mathrm{\Delta }t$, and the angular velocity as $\omega (t)=(\theta (t+\mathrm{\Delta }t)-\theta (t))/\mathrm{\Delta }t$. The velocity $\mathbf{v}(t)$ is decomposed into a tangential (i.e., in the direction of $\theta (t)$) and a normal (i.e., orthogonal to $\theta (t)$) components. Consider the unit vectors ${\mathbf{u}}_{||}((t)=[cos(\theta (t)),sin(\theta (t))]$ and ${\mathbf{u}}_{\perp }(t)=[-sin(\theta (t)),cos(\theta (t))]$, representing the diatom’s tangential and normal directions, respectively. The velocity is then divided (Fig. 3B) into a tangential contribution

$$\begin{array}{c}\hfill v_{||}(t)=\mathbf{v}(t)·{\mathbf{u}}_{||}((t),\end{array}$$ [4]

with · the dot product, and a normal contribution

$$\begin{array}{c}\hfill v_{\perp }(t)=\mathbf{v}(t)·{\mathbf{u}}_{\perp }(t).\end{array}$$ [5]

Curvature Calculation.

The curvatures κ and ${\kappa }_{\text{r}}$ of the diatoms’ tracks and raphes, respectively, are obtained by fitting a circle to three points at different positions along the raphes/tracks, and taking the inverse of the circle’s radius. The raw data were first resampled in order to have the same spatial resolution across raphes and tracks of the same diatom species. Then, the curvature values were calculated by applying a moving window along the raphe/track, using three points for the circle fitting—the start, the middle, and the end of the window. The spatial resolution, which in turn determines the size of the window, is different for each diatom species, thus producing measurements of curvature that are relative to diatoms’ average body length. A more detailed description and visualization of both the resampling and curvature estimation procedures can be found in SI Appendix, Fig. S4.

Motility State Designation.

The automation of the motility state designation requires a preliminary processing of the time sequences of tangential velocity, which is described in SI Appendix, Fig. S14 and produces an alternative velocity ${\tilde{v}}_{||}(t)$. This quantity, alongside $\omega (t)$, is sufficient to reliably automate the state designation via a process that is described in SI Appendix.

Estimation of Transition Probabilities.

We implemented a continuous Markov model to describe the cell’s switching between discrete states, designated as Glide, Stop, Pivot, and Reverse as outlined above. A transition probability matrix which contains information on when cells move from state i to j was constructed from the entire dataset. From this, we calculated the pair-wise transition rates between states and the mean dwelling or sojourn time (i.e., the time spent in a state) using the R package msm (63).

Additional Details on Model Calibration.

To account for the highly variable speed of gliding, we perform a velocity rescaling. $v_{||}(t)$ is rescaled by the mean glide speed for that glide multiplied by the mean glide speed across all recorded tracks for that species (considering only frames classified as Glide). Doing so, all glides acquire the same mean speed, but the original ratio of their mean to the SD of $v_{||}(t)$ is preserved.

We also perform a coarse-graining approach to reduce measurement noise. Velocities $v_{||}(t)$ and $\omega (t)$ were first randomized to remove temporal correlations and then averaged over a moving window of $5$ frames. The dynamics are thus approximated by an effective noise process that ignores all short-timescale variations while producing, on average, equivalent long-timescale random displacements.

For the calibration of the Stop state, $v_{||\sigma }^{\text{S}}$ and ${\omega }_{\sigma }^{\text{S}}$, are estimated by fitting to a Normal distribution with zero mean, as there is no mean displacement/rotation in this state. Instead, ${\omega }_{\mu }^{\text{P}}$ and ${\omega }_{\sigma }^{\text{P}}$ are estimated by fitting the distribution to the sum of two Normal distributions with the same SD and means of equal magnitude and opposite sign, as both clockwise and counterclockwise pivots can occur.

Model Extension to 3D.

In the 3D model, the state of the diatom is represented by the position $\mathbf{r}(t)=[x(t),y(t),z(t)]$, the moving frame $E(t)=[E_{\text{yaw}}(t),E_{\text{pitch}}(t),E_{\text{roll}}(t)]$, where $E_i(t)$ are orthogonal bases, and the polarity $s(t)$.

In the Glide motility state, the orientation of the diatom evolves according to

$$\begin{array}{c}\hfill E_{\text{yaw}}(t+\mathrm{\Delta }t)=Y({\omega }_{\mu }^{\text{G}}s(t)\mathrm{\Delta }t+{\omega }_{\sigma }^{\text{G}}{\eta }_{\text{yaw}}(t)\sqrt{\mathrm{\Delta }t})E_{\text{yaw}}(t),\end{array}$$ [6]

$$\begin{array}{c}\hfill E_{\text{pitch}}(t+\mathrm{\Delta }t)=P({\omega }_{\sigma }^{\text{G}}{\eta }_{\text{pitch}}(t)\sqrt{\mathrm{\Delta }t})E_{\text{pitch}}(t),\end{array}$$ [7]

$$\begin{array}{c}\hfill E_{\text{roll}}(t+\mathrm{\Delta }t)=R({\omega }_{\sigma }^{\text{G}}{\eta }_{\text{roll}}(t)\sqrt{\mathrm{\Delta }t})E_{\text{roll}}(t),\end{array}$$ [8]

where ${\eta }_i(t)$ are independent sources of Gaussian white noise and $Y(\alpha )$, $P(\beta )$ and $R(\gamma )$ are the rotation matrices for the diatom’s yaw, pitch, and roll, respectively. Yaw, pitch, and roll all involve diffusion, with the assumption that the magnitude of the fluctuations, ${\omega }_{\sigma }^{\text{G}}$, is the same for all rotations. Additionally, yaw involves chiral motion, which we assume only occurs around the normal axis (the axis running from the top to the bottom of the diatom). The position is then updated:

$$\begin{array}{c}\hfill \mathbf{r}(t+\mathrm{\Delta }t)=E_{\text{roll}}(t)s(t)v_{||\mu }^{\text{G}}\mathrm{\Delta }t+E_{\text{roll}}(t)v_{||\sigma }^{\text{G}}{\eta }_{\text{tra}}(t)\sqrt{\mathrm{\Delta }t},\end{array}$$ [9]

which includes self-propulsion in the direction faced by the diatom, given by $E_{\text{roll}}(t)s(t)$, as well as diffusion along the same axis (${\eta }_{\text{tra}}$ being the source of Gaussian white noise for translation).

As for the 2D case, Stop and Reverse only involve diffusion, with $s(t)$ switching sign at the start of a reversal. Pivoting occurs on the diatom’s trailing end and is assumed to be a combination of yaw and pitch. Like the other states, it also included a diffusion component.

To mimic the presence of obstacles in the 3D environment, we set an upper bound on the dwell time in the simulations. After drawing the dwell time from an exponential distribution, another time is also drawn from a Normal distribution with mean 37 s (and SD 7.4 s), and the final dwelling time is set as the minimum of the two.

Supplementary Material

Appendix 01 (PDF)

Movie S1.

Sample video of Cylindrotheca closterium cell motility. Individual cells exhibit a glide-reverse movement. The movie was accelerated 50X.

Movie S2.

Sample video of Halamphora sp. cell motility. Individual cells exhibit continuous gliding coupled with occasional reverses followed by reorientations. The movie was accelerated 50X.

Movie S3.

Sample video of Nitzschia ovalis cell motility. Individual cells exhibit continuous gliding and often form circular tracks. The movie was accelerated 50X.

Movie S4.

Sample video of Pleurosigma sp. cell motility. Individual cells exhibit short gliding periods with frequent pivoting behaviours. The movie was accelerated 50X.

Movie S5.

Sample video of Seminavis robusta cell motility. Individual cells exhibit continuous gliding coupled with occasional reverses followed by reorientations. The movie was accelerated 50X.

Movie S6.

Sample video of Seminavis robusta cell motility in an artificial 3D environment. Z-stacks were taken at 2.2fps (20 slices, 10μm apart). Individual cells exhibit continuous gliding coupled with occasional reverses followed by reorientations. The movie was accelerated 50X. Close-up video was accelerated 20X.

Data, Materials, and Software Availability

All raw and processed tracking data from the 2D and 3D experiments, and SEM images of the raphes have been deposited in Zenodo (https://doi.org/10.5281/zenodo.14751417) (64).