Article | Published:

Swimming Euglena respond to confinement with a behavioural change enabling effective crawling

Nature Physics (2019) | Download Citation

Abstract

Some euglenids, a family of aquatic unicellular organisms, can develop highly concerted, large-amplitude peristaltic body deformations. This remarkable behaviour has been known for centuries. Yet, its function remains controversial, and is even viewed as a functionless ancestral vestige. Here, by examining swimming Euglenagracilis in environments of controlled crowding and geometry, we show that this behaviour is triggered by confinement. Under these conditions, it allows cells to switch from unviable flagellar swimming to a new and highly robust mode of fast crawling, which can deal with extreme geometric confinement and turn both frictional and hydraulic resistance into propulsive forces. To understand how a single cell can control such an adaptable and robust mode of locomotion, we developed a computational model of the motile apparatus of Euglena cells consisting of an active striated cell envelope. Our modelling shows that gait adaptability does not require specific mechanosensitive feedback but instead can be explained by the mechanical self-regulation of an elastic and extended motor system. Our study thus identifies a locomotory function and the operating principles of the adaptable peristaltic body deformation of Euglena cells.

Main

Euglenids are a diversified family of unicellular flagellated protists abundant in a variety of aquatic ecosystems. Many species of euglenids are capable of performing large-amplitude, elegantly coordinated cell body deformations. This behaviour is referred to as the euglenoid movement or metaboly1,2,3. Depending on the species and within a species, metaboly can range from rounding and gentle bending or twisting to periodic highly concerted peristaltic waves travelling along the cell body. Observations of metaboly date back to the first microscopists4, and have fascinated researchers across disciplines ever since. It is known that an active striated cell envelope, called pellicle, controls cell shape1,5,6,7. However, the precise mechanism by which this cortical complex performs metaboly, including the molecular motors involved, is not known. More strikingly, the function of this behaviour remains elusive.

Metaboly has been interpreted as a mode of locomotion in a fluid environment8. In fact, the peristaltic version of metaboly has inspired prototypical models for low Reynolds number swimming9, and theoretical studies have shown that, thanks to its non-reciprocal nature, it is a competent swimming strategy7. Yet, since euglenids exhibiting metaboly are also capable of flagellar locomotion10, which allows them to move in a fluid about 50 times faster, swimming is not a compelling function justifying metaboly, a behaviour requiring an extended and intricate cellular machinery1,2,3. In euglenids feeding on large eukaryotic cells, it is accepted that metaboly enables the large cell deformations required for phagocytosis. Since eukaryovorous ancestors have evolved into osmotrophic and autotrophic euglenids, which do not engulf large particles but still exhibit metaboly, it has been argued that metaboly in these species may be an ancestral vestige without a specific function11,12,13. It has also been speculated that metaboly may be useful to break the protective cyst that some species can secrete and exit from it, to move in confined environments when some species penetrate dead animals or eggs to feed, or when other species lacking emergent flagella crawl in granular media1,14. These hypotheses, however, have not been systematically examined.

Confinement triggers metaboly

To investigate the role of confinement in the behaviour of euglenids and their motility, we examined cultures of E.gracilis, a prototypical photosynthetic species exhibiting metaboly, at various degrees of crowding (Fig. 1a and Supplementary Video 1). In dilute cultures, cells exhibited fast swimming in the posterior-to-anterior direction powered by an anterior flagellum, cruising at ~68 μm s–1. During flagellar swimming, cells maintained a fixed cigar shape ~50 μm long and with a maximum diameter of ~9 μm. Cells performed sharp turns as previously described15. In crowded cultures, presumably triggered by mechanosensation at the cell envelope and/or at the flagella1, cells exhibited a variety of behaviours in addition to fast swimming, including rounding, bulging and large-amplitude periodic cell deformations. Rounding was often associated with cell spinning, whereas metaboly did not seem to have a significant effect in locomotion.

Fig. 1: Confinement triggers changes in cell behaviour and metaboly.
Fig. 1

a, Euglena cells in dilute cultures (i) exhibited fast flagellar swimming without cell shape changes, at typical speeds of 68.2 ± 1.13 μm s–1 (standard error of the mean (s.e.m.), n = 50) or 1.31 ± 0.03 body lengths per second (s.e.m., n = 50). In crowded cultures (ii) cells displayed a variety of behaviours, including fast flagellar swimming (yellow arrow), cell rounding and spinning (red arrow) and large-amplitude cyclic cell body deformations—metaboly (purple ellipse) (Supplementary Video 1). b, When confined between glass plates, cells systematically developed metaboly. Observation using bright-field reflected light microscopy revealed the reconfigurations of the striated cell envelope (pellicle) concomitant with cell deformations in the plane of the glass plate (n = 5 cells) (Supplementary Videos 2 and 3). c, Schematic representation of the pellicle, the strip separation w and the local mechanism of active deformation of the pellicle, according to which the relative sliding between strips produces a shear strain γ along the direction of the strips. On application of a shear strain γ, an initially square pellicle region of width W transforms into a parallelogram where the total displacement along strips is γW. During the shape dynamics in b, w remained nearly constant (559 ± 0.003 nm, s.e.m., n = 100). d, According to a mathematical model for the kinematics of the pellicle (Supplementary Note 1), the rate of change of γ with arc length s along a strip (measured from the anterior end) is given by the curvature of the strip κ. e, By selecting strips in b emanating from the pole, where sliding is geometrically constrained, we could quantify the sliding displacement between adjacent strips γW required to bend an initially straight strip, where the colour-coding matches the strips highlighted in b. f, Cells swimming into tapered capillaries transitioned from fast flagellar swimming (i) to developing large-amplitude shape excursions (ii), including rounding (iii) and the prototypical highly orchestrated peristaltic cell deformations of metaboly (iv) (Supplementary Video 4). This transition between (i) and (ii) occurred at a ratio between capillary and cell diameter of about 2.1 ± 0.05 (s.e.m., n = 10).

We also triggered metaboly by confining cells between two glass plates separated along one side by a spacer to produce a wedge-shaped fluid chamber. Cells in the narrower regions of the chamber (with a typical gap of ~5 μm) systematically developed large-amplitude periodic shape changes. Using bright-field reflected light microscopy (Supplementary Methods), we were able to record simultaneously and continuously in time the shape changes and the reconfigurations of the pellicle envelope in the plane of the glass plate (Fig. 1b and Supplementary Videos 2 and 3). The pellicle is composed of interlocking narrow and long proteinaceous strips, often arranged helically and spanning from the anterior to the posterior ends of the cell. These strips lie beneath the plasma membrane and are subtended by systems of microtubules2. Previous observations in another species (Euglenafusca) showed that cell deformations were accompanied by sliding between adjacent pellicular strips, which kept their length and width constant1,5,16, similarly to how flagellar shape depends on microtubule sliding in the axoneme17. Interstrip active sliding results in local deformation of the cell envelope, a simple shear along the direction of the strips (Fig. 1c), which when coordinated in space and time can explain the shape dynamics during metaboly7,18.

Our continuous observations were consistent with this sliding model; strip width remained nearly constant (~560 nm), and in agreement with a simple shear local deformation of the pellicle, the total cell area remained nearly constant during shape transformations (Supplementary Methods). To further examine the shape-morphing mechanism, we developed a theoretical model linking strip curvature on a planar surface, as in Fig. 1b, and differential sliding along this strip, Fig. 1d and Supplementary Note 1. It allowed us to quantify over time the sliding displacement along selected strips (Fig. 1e), finding net sliding interstrip displacements of about 1 μm during the shape excursion in Fig. 1b. By comparing sliding displacements at different instants, we estimated sliding velocities of up to ~1 μm s–1, compatible with those of molecular motors along microtubules19. Besides confirming the pellicle strip sliding model, these observations showed that cell volume was nearly constant during metaboly (Supplementary Methods). Interestingly, cells performing metaboly confined between two parallel plates exhibited directed motion in the anterior-to-posterior direction at speeds ranging between 0.08 and 0.2 body lengths per cycle (Supplementary Videos 2 and 3).

To mimic the more realistic situation of multidimensional confinement while having a high degree of experimental control, we drove swimming cells towards tapered glass capillaries with diameters ranging between 300 μm and 6 μm with slopes always smaller than 0.006 in the region of interest (Fig. 1f and Supplementary Fig. 2). When the diameter of the capillary was significantly larger than the cell diameter, cells exhibited fast swimming. As cells moved towards the narrow end of the capillary, they collided with the wall and started developing the behaviours described in the crowded cultures, including bulging and rounding (Supplementary Video 4). By rounding, some cells were able to switch their orientation in the capillary (Supplementary Videos 4 and 5). Most cells eventually developed characteristic highly coordinated and periodic peristaltic body deformations consisting of a bulge moving in the posterior-to-anterior direction followed by a recovery phase during which the bulge at the posterior end reappears at the expense of that at the anterior end (Fig. 1f(iv) and Supplementary Video 4). Thus, similarly to culture crowding, confinement provided by the capillary triggered changes in cell behaviour, which now seemed to acquire a function: cell rounding to turn and metaboly to crawl.

Metaboly is an effective crawling strategy

Close examination of cells performing metaboly in the capillary showed that during their gait, the bulge moving in the posterior-to-anterior direction transiently contacted the capillary wall propelling the cell in the anterior-to-posterior direction, opposite to that of flagellar swimming (Fig. 2a(i) and Supplementary Video 6). The kinematics of the gait were highly non-reciprocal, and thus in principle compatible with self-propulsion in the non-inertial limit of our experiments20. Since cells could switch direction in the capillary, we observed cells crawling by metaboly away from and towards its narrower end. As a result, we were able to examine the features of this mode of locomotion at varying degrees of confinement. To ease understanding of pellicle kinematics, we arranged images in the figures and videos so that cells crawl from left to right. At higher confinement, cells adapted their gait by developing a broader bulge, which remained in contact with the wall during a larger fraction of the gait (Fig. 2a(ii) and Supplementary Video 6). However, the essential features of the crawling mechanism remained the same.

Fig. 2: Metaboly is an effective crawling mode of locomotion under confinement.
Fig. 2

a, At low confinement, the bulge travelling backwards along the cell body transiently contacted the capillary walls, producing a net forward motion (i). At higher confinement, cells adapted the gait, with a larger contact area of the bulge and smaller amplitude of cell deformations. However, the crawling mechanism remained the same (ii). b, Kymographs of crawling E.gracilis under increasing confinement show the regularity of the gait, the backward bulge motion and the forward cell motion. Crawling by metaboly was effective up to very large degrees of confinement (insets and Supplementary Video 6). dcap, capillary diameter; dcell, cell diameter. c,d, The normalized velocity expressed in cell body lengths per period was maximum at an intermediate capillary diameter (c), whereas the period of the gait was largely insensitive to confinement (d). The blue dashed lines in c and d are guides to the eye. The capillary diameter dcap was normalized by the cell diameter dcell as the cell was free-swimming with a fixed cigar shape in the wider part of the capillary (dcell 9 μm). The error bars in c and d refer to the s.e.m. and the size of samples is indicated. Here, one sample is a complete period, and data were gathered from 16 cells.

Kymographs of cells crawling showed the high regularity of the gait and its adaptation to increasing confinement (Fig. 2b). They also revealed that the net cell displacement was the result of a power phase, when the bulge travels towards the anterior end, and a recovery phase with backward cell motion. Remarkably, cells were able to crawl up to very high degrees of confinement, despite the little space available for shape transformations. Cells crawled fastest, at about 2.5 μm s–1 (0.4 body lengths per cycle), at intermediate degrees of confinement, where the bulge established sustained contact with the capillary walls and there was sufficient space for significant shape excursions (Fig. 2c). The period of the gait, however, was largely independent of confinement (Fig. 2d). Interestingly, the very small crawling velocities we recorded for weakly confined cells (Fig. 2a and largest diameter in Fig. 2c), which represent a transition between crawling and swimming, are in agreement with a theoretical study examining the complementary situation of swimmers undergoing large shape changes near walls under weaker capillary confinement21.

We then wondered if flagellar locomotion of fixed-shape cells would be effective in this situation. Confined cells propelled by flagella would have to overcome a frictional force against the capillary walls and a hydraulic resistance. We theoretically estimated that such cells would move 10 to 20 times slower than those crawling by metaboly (Supplementary Note 3). These estimations were consistent with observations of stuck cells beating their flagella (Supplementary Video 8). Thus, by developing metaboly under confinement, cells switched from ineffective flagellar propulsion to a highly robust crawling mode of locomotion.

Mechanism for locomotion during metaboly

To propel their body forward during migration in a low Reynolds number limit, Euglena cells must exert self-equilibrated forces on their environment, here, the walls and the fluid within the capillary. To experimentally characterize the physical interaction between cells and their environment, we drove cells not exhibiting deformations into narrow sections of capillaries by applying a known pressure difference while recording cell velocity, contact area and motion of suspended beads (Supplementary Video 7). These observations established that confined cells acted as hydraulic plugs and characterized the friction between cells and the wall as viscous and confinement-dependent (Supplementary Note 2).

We attempted to understand force transmission during crawling by metaboly in the light of a prevalent model of animal cells crawling in narrow spaces. According to this model, non-adherent confined cells generate propulsive forces through retrograde actin flows and unspecific friction with the confining wall. This propulsive force is balanced by a resistive hydrodynamic force required to displace the water column in the capillary22,23,24,25,26, unless water transport is sufficiently fast across the cell27. This framework has explained why a large hydraulic resistance relative to the wall friction stalls cell motion and results in fast retrograde flow, whereas vanishing hydraulic resistance leads to fast cell motion and minimal sliding between the polarized actin cytoskeleton and the wall. Transposing this model to Euglena cells crawling by metaboly, the backward motion of the pellicle bulge would be the analogue of retrograde actin flow of animal cells (Fig. 3a).

Fig. 3: Mechanism of locomotion during metaboly.
Fig. 3

a, Canonical model of propulsion of non-adherent polarized animal cells under confinement: frictional forces induced by actin retrograde flow propel the cell forward against resistive hydraulic forces required to displace the water column in the capillary (i). In Euglena cells crawling by metaboly, the backward-moving pellicle bulge is analogous to actin retrograde flow in animal polarized cells (ii). b, Kinematics of the theoretical model for the power phase of metaboly. Transformation of an idealized cylindrical pellicle by a uniform shear γ along the strips (i). By propagating a pellicle shear profile \(\bar \gamma (s)\) along the cell body following \(\gamma (s,t) = \bar \gamma (s - ct)\), we model a moving localized bulge, which, with our sign convention, moves leftwards at speed c < 0 in the frame of the cell (ii). c, In the limit of infinite frictional coupling relative to hydraulic resistance (i), cell velocity is determined by the no-slip condition in the contact region. As indicated by the blue control volume, metaboly then results in net water pumping in the direction opposite to cell motion. The average fluid velocity vf is defined as the flow rate Q divided by the cross-sectional area of the capillary. In the limit of zero frictional coupling relative to hydraulic resistance (iii), cell velocity is determined by the no water pumping condition, cells are fastest and the pellicle slides in the contact region, as indicated by the red arrows. In intermediate cases (ii), hydraulic forces (propulsive) and frictional forces (resistive) compete, there is some degree of sliding and pumping, and the cell velocity is intermediate. d, Kymograph of an immobile cell next to another cell crawling by metaboly (Supplementary Video 10). e, Quantification of fluid flow around crawling cells tracking suspended beads. Red (green) lines show representative trajectories over 25 s of beads close to (far away from) a cell. Error bars refer to the s.e.m. and sample size is indicated (a sampling point is the instantaneous velocity of a bead between two frames, data from 2 cells and 21 bead trajectories). f, Kymograph made from images intermittently focused at the capillary wall to visualize the pellicle and at the capillary axis to visualize cell shape. The trajectories of pellicle features (yellow curve) reveal sliding between the pellicle and the capillary wall in the contact region.

To test this analogy, we developed an idealized theoretical model of the power phase of the gait consistent with the shape-morphing principle of the pellicle of euglenids7,18 (Fig. 3b). In this model, a bulge establishes contact with a capillary of radius r over a length \(\ell _{\mathrm{c}}\), and moves backwards at speed c < 0 in the reference frame of the cell, which otherwise is a cylinder of radius r0. The strips in the contact region form an angle θ* with the cell axis satisfying cosθ* = r0/r. To weigh the relative importance of hydraulic and frictional resistance, we introduced the non-dimensional quantity \(\xi = \mu _{{\mathrm{wall}}}\ell _{\mathrm{c}}{\mathrm{/}}(\alpha r)\), where μwall is the wall–cell friction coefficient and α is a hydraulic resistance coefficient (Supplementary Note 4).

We first considered the limit of vanishing hydrodynamic resistance relative to wall friction, expressed as ξ → +∞. In this situation, the cell velocity v = −(1 − cosθ*)c was obtained from the kinematics of the propagating bulge by requiring no slippage between the pellicle and the wall (Fig. 3c(i) and Supplementary Video 9). This expression is consistent with the very small cell velocities at extreme confinement, where r ≈ r0 or cosθ* ≈ 1 (Fig. 2c). To examine the effect of cell motion on the fluid inside the capillary in this no-slip scenario, we evaluated with our model the induced water flow rate Q on either side of the bulge, which we assumed to act as a hydraulic plug. Strikingly, we found that as cells crawl without sliding in a given direction, they pump water in the opposite direction at a flow rate given by Q = πr2(1 − cosθ*)cosθ*c. This counterintuitive hydraulic behaviour results from the peristaltic shape changes of metaboly, and fundamentally differs from that of non-adherent polarized animal cells, which move like piston-like fixed-shape ‘squirmers’24,28. We then reasoned that, if crawling Euglena cells in this limit were pumping fluid backwards, then hydraulic resistance could in fact act as a propulsive force.

To theoretically test this idea, we considered the opposite limit of vanishing wall friction relative to hydraulic resistance, ξ → 0, and computed cell velocity by requiring zero induced flow rate as the bulge moved backwards. We found that in this scenario the pellicle slides relative to the wall. Furthermore, instead of stalling under high hydraulic resistance like polarized animal cells24, peristaltic Euglena cells actually move at a faster speed \(v = - \left( {1 - {\mathrm{cos}}^2\theta ^ \ast } \right){\kern 1pt} c\) (Fig. 3c(iii) and Supplementary Video 9). In an intermediate regime, in which propulsion is governed by the balance of finite wall friction and hydrodynamic resistance, our model predicted that cells are propelled by hydraulic resistance and dragged by wall friction, opposite to polarized animal cells (Supplementary Note 4). In summary, despite seeming similarities between the crawling modes of Euglena cells and of non-adherent polarized animal cells, our model highlighted fundamental differences associated with the large shape modulations of the former, and portrayed metaboly as a highly robust and adaptable mode of locomotion capable of using both frictional and hydraulic forces for propulsion depending on the mechanical nature of confinement. Furthermore, the fastest crawling cells in our experiments moved about 20 times faster than the fastest reported non-adherent polarized animal cells26.

One of the most striking predictions of this model is that confined Euglena cells, which act as hydraulic plugs, can move in a capillary without inducing any flow rate thanks to the shape deformations of metaboly. Supporting this prediction, we observed crawling cells accomplishing significant displacements next to stuck immobile cells (Fig. 3d and Supplementary Video 10). In the absence of stuck cells, we visualized the flow generated by crawling cells tracking the motion of suspended micrometre-sized beads (Fig. 3e and Supplementary Video 11). We found that beads in the vicinity of cells underwent rapid motions, revealing local flows induced by shape changes and flagellar beating. These bead velocities, however, exhibited rapid decay away from the cell body, where they were consistent with Brownian motion in a quiescent fluid. Thus, in the light of our model, cells in our capillary experiments were close to the limit of high hydraulic resistance, which acted as the propulsive force. In agreement with this notion, we observed significant pellicle sliding in cells crawling and turning in a capillary (Fig. 3f and Supplementary Videos 5 and 12). By contrast and showing the robustness of metaboly, our model suggests that cells between glass plates, where hydraulic confinement is very low, crawled by exploiting frictional propulsion (Fig. 1b and Supplementary Videos 2 and 3).

Computational model

Our previous observations have established that Euglena cells develop highly concerted shape deformations to crawl under confinement, and that cells can adapt their gait to varying degrees of confinement between plates or in a capillary. We then tried to understand whether this complex adaptive behaviour necessarily required a dedicated mechanosensing and mechanotransduction machinery or if, instead, the active pellicle could mechanically self-adapt its dynamics to a changing environment. To test this second possibility, we developed a theoretical and computational model of crawling in confinement by metaboly, which included the biological activity leading to strip sliding, the pellicle mechanics and the interaction with the environment (Supplementary Note 5).

Despite similarities, the actuation mechanism and molecular players involved in metaboly are far less understood than those behind the much faster flagellar beating17. On the basis of calcium precipitation assays and reactivation of metaboly in detergent-extracted cell models, interstrip sliding is thought to depend on molecular motors distinct from flagellar dyneins and associated to microtubules positioned along pellicular strips, which are locally and dynamically activated by the release/sequestration of cytoplasmic calcium from narrow subpellicular channels of endoplasmic reticulum6,29. In our model, we assumed that the space–time activation pattern driving cell deformations was unaffected by varying confinement, consistent with the confinement-independent period of metaboly (Fig. 2d). We modelled the pellicle as an extended motor system, and its activation as a space–time modulation of the sliding velocity between adjacent strips in the absence of force, \(v_{{\mathrm{motor}}}^0(s,t)\), where s is arc length along the strips and t is time (Fig. 4a(i,ii)). Forces between adjacent strips in the sliding direction can affect the velocity of the motor system. We considered an affine relation between the force experienced by the motor system, τ, and the actual sliding velocity, vmotor (Fig. 4a(iii))30,31. To determine the a priori unknown force distribution τ(s, t) acting on the extended motor system, we accounted for the pellicle elasticity and for its mechanical interaction with the environment, that is, the cellular pressure to maintain constant cell volume, hydraulic forces required to push the water column and contact/frictional forces against the capillary (Fig. 4a(iv)). We designed the activity pattern (Fig. 4a(ii)) to match the typical shape dynamics of metaboly at low confinement7. To solve the highly nonlinear equations governing the active mechanics of the deformable pellicle under confinement, we developed a spline-based finite-element computational method.

Fig. 4: Computational modelling of crawling in confinement by metaboly.
Fig. 4

a, Model ingredients. (i) The pellicle is viewed as an elastic and extended motor system, modelled by an axisymmetric continuum surface with a field of material orientations converging towards two poles and accounting for the configuration of strips. The activation of this motor system in space (along the arc length of strips, s) and time, t, is modulated to drive shape changes. Activation is modelled by the sliding velocity between adjacent strips in the absence of force, \(v_{{\mathrm{motor}}}^0(s,t)\). (ii) Time-periodic pattern of the activation \(v_{{\mathrm{motor}}}^0(s,t)\) during two gaits, in units of strip separation w per period T. (iii) The actual sliding velocity vmotor is modified by distributed forces along adjacent strips in the sliding direction, τ. We model the force-dependent velocity of the motor system with an affine relation characterized by the time- and space-dependent \(v_{{\mathrm{motor}}}^0\) and by a stall force τstall of fixed magnitude (see Supplementary Note 5 for a discussion). (iv) The distributed force acting on the motor system, τ(s,t), is determined by the mechanical interactions of the pellicle with its environment (cellular pressure; contact, frictional and hydraulic forces) and by the pellicle mechanics, which include bending elasticity and stretching elastic forces that penalize deviations between the actual pellicle shear-rate and that imposed by the motion of motors, vmotor(s, t)/w. b, Selected snapshots during the gait at four degrees of confinement. c, Kymographs obtained from simulations in the high fluid resistance (i) and the high wall friction (ii) limits at the same four degrees of confinement. The contact region is coloured in orange and the lines represent trajectories of material particles on the pellicle surface, showing sliding in the hydraulic-dominated case and no sliding in the friction-dominated case. Induced flow rate, normalized by the maximum cell velocity times the capillary cross-sectional area, is represented by grey curves in the case of high friction; it is zero in the limit of high hydraulic resistance. d, Normalized cell velocity in body lengths per period as a function of normalized capillary diameter predicted by the simulations.

In the absence of confinement, this model rapidly reached a limit cycle (or gait) within a few periods, exhibiting the characteristic peristaltic cell deformations of metaboly (Supplementary Video 13). As confinement incrementally constrained the shape excursions, we observed that the model self-adapted by developing a new limit cycle consistent with the imposed confinement (Fig. 4b), which led to cell migration in the presence of frictional wall coupling and/or hydraulic resistance (see Fig. 4c,d for the limits of high hydraulic resistance and high friction). Remarkably, the computational model reproduced all the features of confined crawling by metaboly reported in Fig. 2, including the kinematics of the gait under confinement (Fig. 4b,c) and the non-monotonic relation between capillary diameter and cell velocity (Fig. 4d), which we attributed to a trade-off between the ability to develop large shape excursions at low confinement and the sustained contact of the bulge running along a longer cell at high confinement. In agreement with the theoretical model in Fig. 3c, the computational model also predicted faster motion in the limit of high fluid resistance, in which the maximum velocity agreed quantitatively with our experiments. Taken together, these results support a view of the pellicle of euglenids as an elastic and extended motor system that, once biologically activated, can mechanically self-adjust to the degree of confinement to produce an effective gait.

Outlook

We have thus established that, in analogy with the mesenchymal-to-amoeboid transition of animal cells26 or the amoeboid-to-flagellar transition of Naegleriagruberi32, E.gracilis develop a transition between flagellar and metaboly modes of locomotion triggered by confinement. Biophysically, the peristaltic movement of Euglena during metaboly provides a new and remarkably robust mechanism of fast cell crawling. It is unclear, however, whether Euglena take advantage of this capability in natural conditions, where they predominantly swim in the water column. How and why E. gracilis cells retained an active pellicle, a vestige of a phagotrophic ancestry, and developed the ability to operate this machine in a non-reciprocal manner compatible with effective crawling is intriguing, as further emphasized by our examination of confined metaboly in a primary osmotrophic and a phagotrophic species of euglenids (Supplementary Note 6). From an engineering point of view, the ability of the pellicle to mechanically self-adapt and maintain the locomotory function under different geometric and mechanical conditions represents a remarkable instance of mechanical or embodied intelligence33,34, a design principle in bioinspired robotics by which part of the burden involved in controlling complex behaviours is outsourced to the mechanical compliance of the materials and mechanisms that build the device.

Methods

Culture of cells

Strain SAG 1224-5/27 of E.gracilis obtained from the SAG Culture Collection of Algae at the University of Göttingen (Germany) was maintained axenic in liquid culture medium Eg. Cultures were transferred weekly. Heterotrophic Distigmaproteus and Peranematrichophorum were obtained from Sciento (https://www.sciento.co.uk). Subcultures of P. trichophorum were established in Eau Volvic with Chlorogoniumcapillatum (SAG 12-2b) as food source. All cells were kept in sterile 16 ml polystyrene test tubes in an incubator IPP 110 plus from Memmert at 15 °C and at a light:dark cycle of 12:12 h under cold white LED illumination with an irradiance of about 50 μmol m–2 s–1.

Imaging of cells and preparation of tapered capillaries

An Olympus BX 61 upright microscope with motorized stage was employed in all experiments. These were performed at the Sensing and Moving Bioinspired Artifacts Laboratory of SISSA. Typically, the microscope was equipped with a LCAch 40× Ph2 objective (numerical aperture (NA) 0.55) for the imaging of the cells’ behaviour in capillaries using transmitted bright-field illumination. A Plan N 10× objective (NA = 0.25) was employed to image cells and 1-μm-diameter polystyrene beads by combining bright-field and fluorescence microscopy (Supplementary Note 1 and Supplementary Videos 7 and 11). The visualization of pellicle strips between microscope slides and in glass capillaries was achieved by exploiting bright-field reflected light microscopy and using a UPlanFL N 100× objective (NA 1.30 Oil). Micrographs were recorded with a CMOS digital camera from Basler (model acA2000-50gm) at a frame rate of either 20 f.p.s. or 40 f.p.s. The higher acquisition rate of 40 f.p.s. was employed to time-resolve the dynamics of pellicle strips’ reconfigurations and for the study of wall friction as reported in Supplementary Note 2. Tracking of fluorescence beads was performed using Particle Tracker 2D/3D of the MosaicSuite for ImageJ35. Tapered capillaries of circular cross-section were obtained from borosilicate glass tubes (Sutter Instrument, model B100-30-7.5HP) by employing a micropipette puller (Sutter Instrument, model P-97). A typical profile of such a capillary measured from micrographs is represented in Supplementary Fig. 2b. At each trial, a glass capillary was filled with a diluted solution of cells in culture medium Eg and fixed to the microscope stage by means of a custom-made, 3D-printed holder. To avoid optical aberrations that could arise from the curvature of the external surface of the capillary, it was positioned between two 0.17 mm coverslips and covered with microscopy immersion oil.

Estimation of cell area and volume

To estimate the area and volume of cells sandwiched between microscope glass slides separated by a distance H, we measured the surface area S and perimeter P of the part of the cell surface in contact with the glass slides by focusing the microscope on these planes. We approximated the surface area of the cell envelope as Scell = 2S + πHP/2 and its volume by Vcell = SH + πH2P/8, which assume that cross-sections of the part of the cell surface not in contact with the plates are half circles. Using 15 frames from Supplementary Video 3, where H = 4.3 μm, we estimated using this method Scell ≈ 1,887 μm2 ± 2% and Vcell ≈ 3,283 μm3 ± 1%.

Reporting Summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Code availability

Mathematica (version 11.3.0.0) custom algorithms were developed and used to analyse the theoretical model in Fig. 3 and Supplementary Note 4. Matlab (R2017b) custom algorithms were developed and used to compute sliding displacements from strip curvature (Fig. 1e and Supplementary Note 1) and to implement the computational model in Fig. 4 and Supplementary Note 5. These computer codes are available from the corresponding authors upon reasonable request.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon request.

Additional information

Journal peer review information: Nature Physics thanks Andrew Callan-Jones and other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Acknowledgements

G.N. and A.D.S. acknowledge the support of the European Research Council (AdG-340685-MicroMotility). M.A. acknowledges the support of the European Research Council (CoG-681434), the Generalitat de Catalunya (2017-SGR-1278 and ICREA Academia prize for excellence in research). We thank S. Guido for helpful discussions in the early stages of this study.

Author information

Affiliations

  1. SISSA–International School for Advanced Studies, Trieste, Italy

    • Giovanni Noselli
    •  & Antonio DeSimone
  2. OGS–Istituto Nazionale di Oceanografia e di Geofisica Sperimentale, Trieste, Italy

    • Alfred Beran
  3. Universitat Politècnica de Catalunya-BarcelonaTech, Barcelona, Spain

    • Marino Arroyo
  4. Institute for Bioengineering of Catalonia (IBEC), The Barcelona Institute of Science and Technology, Barcelona, Spain

    • Marino Arroyo
  5. The BioRobotics Institute, Scuola Superiore Sant’Anna, Pisa, Italy

    • Antonio DeSimone

Authors

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Contributions

G.N., M.A. and A.D.S. conceived the study. A.B. provided cells and culture expertise. G.N. performed the experiments. G.N., M.A. and A.D.S. analysed the data, performed theoretical analysis and wrote the paper.

Competing interests

The authors declare no competing interests.

Corresponding authors

Correspondence to Marino Arroyo or Antonio DeSimone.

Supplementary information

  1. Supplementary Information

    Supplementary Notes 1–6, Supplementary Figures 1–5 and Supplementary References 36–42.

  2. Reporting Summary

  3. Supplementary Video 1

    Video recordings of Euglena gracilis between glass slides separated by a spacer of thickness 80 µm. In dilute cultures (left), cells exhibit flagellar swimming without cell shape changes. In crowded cultures (right), cells display a variety of behaviours, including flagellar swimming, cell rounding and spinning, and large-amplitude periodic cell body deformations typical of metaboly.

  4. Supplementary Video 2

    Euglena gracilis cells exhibiting metaboly and directed motion in the anterior-to-posterior direction while confined between glass slides. Observation using bright-field reflected light microscopy reveals the reconfigurations of the striated cell envelope concomitant with cell body deformations in the plane of the glass slide. The separation between the slides is 6 µm.

  5. Supplementary Video 3

    Euglena gracilis cells exhibiting metaboly and directed motion in the anterior-to-posterior direction while confined between glass slides. Observation using bright-field reflected light microscopy reveals the reconfigurations of the striated cell envelope concomitant with cell body deformations in the plane of the glass slide. The separation between the slides is 4 µm.

  6. Supplementary Video 4

    Video recordings of Euglena gracilis in tapered capillaries. Cells swimming into tapered capillaries transition from flagellar swimming (top left) to developing large-amplitude shape excursions (top right), including rounding (bottom left). When confined in capillary diameters smaller than about twice the free-swimming cell diameter, most cells develop the prototypical peristaltic cell body deformations of metaboly (bottom right).

  7. Supplementary Video 5

    Euglena gracilis cell confined in a glass capillary and imaged using bright-field reflected light microscopy. Rounding of the cell body, as determined by the reconfigurations of the pellicle strips, allows the cell to switch its orientation. The microscope was intermittently focused at the pellicle/capillary interface to visualize the pellicle and at the capillary axis to visualize cell shape.

  8. Supplementary Video 6

    Video recordings of Euglena gracilis exhibiting metaboly and directed motion in tapered capillaries under increasing confinement, as quantified by the ratio of dcap/dcell, along with kymographs relative to the capillary axis. The movie shows that crawling by metaboly is effective up to very large degree of confinement.

  9. Supplementary Video 7

    Video recordings of Euglena gracilis not exhibiting body deformations and acting as hydraulic plugs driven by a known pressure difference, pin, of increasing magnitude between the capillary extremities. Data from these experiments allowed us to quantify a viscous and confinement-dependent friction between cells and the capillary walls.

  10. Supplementary Video 8

    Video recordings of Euglena cells stuck in a glass capillary and beating their anterior flagellum.

  11. Supplementary Video 9

    Results from the idealized model for the power phase of metaboly in the limit of infinite wall friction relative to hydraulic resistance (top), in the limit of zero wall friction relative to hydraulic resistance (bottom), and for an intermediate case where hydraulic propulsive forces and frictional resistive forces compete (middle). The blue arrows report the average fluid velocity induced by the cell, defined as the flow rate divided by the cross-sectional area of the capillary. The surface of the idealized model is decorated along slip lines by material particles to highlight their motion relative to the capillary walls in the contact region.

  12. Supplementary Video 10

    Video recordings of an Euglena cell effectively crawling by metaboly (right) in the presence of an immobile cell, stuck in the capillary and acting as a hydraulic plug (left).

  13. Supplementary Video 11

    Video recordings of Euglena gracilis performing metaboly in a capillary and of suspended polystyrene beads by combining bright-field and fluorescence microscopy. Data from these experiments allowed us to quantify the fluid flow around crawling cells by tracking the fluorescent beads. Only beads in the vicinity of the cell undergo rapid motions due to local flows induced by shape changes and flagellar beating.

  14. Supplementary Video 12

    Euglena gracilis crawling by metaboly while confined into a glass capillary. Observation using bright-field reflected light microscopy allows for the visualization of the pellicle strips in contact with the capillary wall. The microscope was intermittently focused at the pellicle/capillary interface to visualize the pellicle and at the capillary axis to visualize cell shape. The movie also reports the kymograph relative to the capillary axis. The trajectories of pellicle features reveal sliding between the pellicle and the capillary wall in the contact region.

  15. Supplementary Video 13

    Computational results from the theoretical model of crawling by metaboly under confinement. Results are shown for increasing confinement, as quantified by the ratio of dcap/dcell = {0.875, 1.0, 1.375, 1.8}, in the limit of high hydraulic resistance, and during three cycles. The cell motion is reported by black and white features fixed in the frame of the capillary. Notice that the model self-adapts to imposed confinement by developing a limit cycle (gait), which is consistent with the experimental observations on Euglena cells. The four gaits at different degrees of confinement are the result on the same activation pattern, represented as a space–time colour map (left).

  16. Supplementary Video 14

    Video recordings of Distigma proteus between glass slides separated on one side by a spacer of thickness 80 µm in order to realize a wedge-shaped fluid chamber. In the absence of confinement (gap between plates 36 µm), cells exhibit flagellar swimming. Significant confinement between the two plates (gap 5 µm) triggers non-reciprocal peristaltic cell deformations, which allow Distigma cells to crawl.

  17. Supplementary Video 15

    Video recordings of Peranema trichophorum between glass slides separated on one side by a spacer of thickness 80 µm in order to realize a wedge-shaped fluid chamber. In the absence of confinement (gap between plates 52–43 µm), cells glide on the substrate thanks to the movement of their flagellum. During gliding, cells occasionally bend their body, and this shape change is associated with sharp turns of the cell trajectory. Under high confinement between the glass plates (gap 7 µm), cells are not able to glide and develop periodic, largely reciprocal shape changes.

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DOI

https://doi.org/10.1038/s41567-019-0425-8