Run stop shock, run shock run: Spontaneous and stimulated gait-switching in a unicellular octo agellate

In unicellular agellates, growing evidence suggests control over a complex repertoire of swimming gaits is conferred intracellularly by ultrastructural components, resulting in motion that depends on agella number and con guration. We report the discovery of a novel, tripartite motility in an octo agellate alga, comprising a forward gait (run), a fast knee-jerk response with dramatic reversals in beat waveform (shock), and, remarkably, long quiescent periods (stop) within which the agella quiver. In a reaction graph representation, transition probabilities show that gait switching is only weakly reversible. Shocks occur spontaneously but are also triggered by direct mechanical contact. In this primitive alga, the capability for a millisecond stop-start switch from rest to full speed implicates an early evolution of excitable signal transduction to and from peripheral appendages.

In unicellular agellates, growing evidence suggests control over a complex repertoire of swimming gaits is conferred intracellularly by ultrastructural components, resulting in motion that depends on agella number and conguration. We report the discovery of a novel, tripartite motility in an octoagellate alga, comprising a forward gait (run ), a fast knee-jerk response with dramatic reversals in beat waveform (shock ), and, remarkably, long quiescent periods (stop) within which the agella quiver. In a reaction graph representation, transition probabilities show that gait switching is only weakly reversible. Shocks occur spontaneously but are also triggered by direct mechanical contact.
In this primitive alga, the capability for a millisecond stop-start switch from rest to full speed implicates an early evolution of excitable signal transduction to and from peripheral appendages.
In his De Incessu Animalium Aristotle had thus described the walk of a horse [1]: the back legs move diagonally in relation to the front legs, for after the right fore leg animals move the left hind leg, and then the left foreleg, and nally the right hind leg. The control mechanism of leg activation was unknown to Aristotle, but is now understood to arise from`central pattern generators' [2,3], which produce electrophysiological signals (action potentials) that drive limbs in a range of spatiotemporal symmetries. While microorganisms achieve motility through microscale analogues of limbs called cilia and agella, absent a nervous system the mechanism of control must be quite dierent. Nevertheless, species of unicellular algae are capable of executing patterns of agellar beating akin to the trot and gallop of quadrupeds [4]. In these cases, the extent of intracellular control of appendages is becoming increasingly evident [47].
Here, we detail the discovery of a surprising motility in the octoagellate marine alga Pyramimonas octopus ( Fig. 1). Swimming requires coordination of eight agella in a pseudo-breaststroke, in which diametrically opposed pairs beat largely in synchrony. We nd that this forward run gait can be interrupted by abrupt episodes involving dramatic changes in agella beating hereafter termed shocks, which occur spontaneously but can also be induced by external stimuli. Cells also display a distinctive stop gait which can be prolonged, where cell body movement is stalled but yet the agella quiver with minute oscillations. P. octopus belongs to a fascinating group of unicellular algae bearing 2 k agella, which substantiates a delicate interplay between passive uid mechanics and active intracellular control in the coordination of multiple agella [4]. Compared to bacteria, the larger size of these algae facilitates visualization, allowing us to demonstrate how agellar beating leads directly to gait-switching and trajectory reorientation, and to expose the excitable nature of the eukaryotic agellum.
Cell cultures were obtained from the Scandanavian Collection of Algae and Protozoa (SCCAP K-0001, P. stop gaits (Fig. 2a) are coincident with the three major modes of beating, respectively (ciliary, agellar, and quiescent) [9]. Changes in agellar activity produce gait transitions. However, unlike their bacterial counterparts, eukaryotic agellar beating is not due to basal rotors but rather a coordinated action of dyneins distributed throughout the axoneme [10]. Forward swimming in P. octopus arises from ciliary beating (`puller'), but during shocks all eight agella are thrown abruptly in front of the cell where they undulate in sperm-like fashion (`pusher'). Signicant hydrodynamic interactions synchronize the agella during shocks. These`knee-jerk' reactions last only 20 − 30 ms, and are related to the escape response of Chlamydomonas and Spermatozopsis. The latter is triggered by intense photo- [11,12] or mechanical stimuli [13], but last much longer (0.2 − 1.0 s) and do not occur spontaneously. The stop gait has no equivalent in the repertoire of green algae studied so far.
We focus on the stereotypical sequence stop shock run: a cell initiates a run from rest via a shock (Fig.   2b). Dening the instantaneous alignment D =v ·ê R between the swimming directionv and the cell body axiŝ e R , the puller-like run (D = 1) may be distinguished from the pusher-like shock (D = −1). Averaged over 10 cells, the translational speed rises rapidly from zero to a maximum of 1, 712 ± 392 µm/s, but relaxation to a mean run speed of 428 ± 64 µm/s takes ∼ 0.05 s. To separate the agellar motion from body orientation, we track two dynamically morphing boundaries that are delineated by image intensity: an inner one for the cell body, and an outer one exterior to the agella (SM). The lengthscale λ(t) = x∈B\A x/|B \A|− x∈A x/|A| , measures the physical separation between the agella and the cell body proper, where || · || is the Euclidean norm, | · | the cardinality of a set, and A, B are pixels interior of the inner and outer boundaries respectively. Naturally, cells at rest exhibit minimal shape uctuations. In Fig. 2c, the three states (realized at instants t = t 1 , t 2 , and t 3 ), localize to specic regions of phase-space. Averaging over multiple events, bifurcations from stops to runs via shocks appear as loops with two distinct branches, one involving rapid changes in speed, and the second in shape (Fig. 2c).
To estimate the transition probabilities between gaits, we implemented a continuous time Markov model, where the instantaneous speed v was discretized to automate a three-state classication from the empirical tracking data (Fig. 3a). The state variable X(t) takes the values {0 = stop, 1 = run, 2 = shock}. The transition rate matrix Q = {q ij }, dened by q ij = lim ∆t→0 P(X(∆t) = j|X(0) = i)/∆t for i = j (a time-homogeneous Markov process), and q ii = − j =i q ij , was estimated to be:  The process admits an embedded Markov chain for discrete jump times, with entries {k ij , i = j} analogous to chemical reaction rates, which represent the probability of transitioning from i → j conditioned on a transition occurring ( j k ij = 1, ∀i). Here k ii = 0 (no self-transitions), and k 01 = 0.0582, k 02 = 0.9418, k 10 = 0.2112, k 12 = 0.7888, k 20 = 0 and k 21 = 1.0000 (Fig. 3b).
Every state is positive recurrent and the process is irreducible. While run shock bifurcations occur readily, the direct reaction shock stop is not possible. The network is weakly reversible, not reversible [14], and detailed balance is clearly violated (as is the Kolmogorov ux criterion: k 01 k 12 k 20 = k 02 k 21 k 10 ). The model predicts an equilibrium distribution π(stop, run, shock) = (0.6666, 0.3126, 0.0208). From a histogram of speeds (for a larger dataset which also includes tracks with no transitions), we estimated the relative dwell times in each state: (68.6%, 30.8%, 0.6%), according to cut-os of 0 ∼ 40, 40 ∼ 500, > 500 µm/s (Fig. 3c), which is similar to {π i }: with discrepancies arising due to subjectivity in choice of cut-o, and prevalence of short-duration tracks.
Gait-switching can greatly aect free-swimming trajectories. Fig. 3d-f zooms in on three primary sequences permitted by Fig. 3b: run shock run, stop shock run, and run stop. Typically for photosynthetic unicells, forward swimming is helical with a variable pitch superimposed onto self-rotation. Tracks comprise lowcurvature portions due to runs, and sharp turns due to rapid conversion of agellar beating and transient reversal during shocks (Fig. 2d). Canonical runs decelerate from ∼ 400 µm/s to full-stop, by sequentially deactivating subsets of agella (SM), the ensuing torque imbalance gradually increases track asymmetry and curvature (Fig. 3f ). Gait-switching requires two very disparate timescales (Fig. 3g): an ultrafast, millisecond, timescale for bifurcations to and from shocks, but a much slower one for entry into stop states. The former is reminiscent of neuronal spiking while the latter is akin to decay of leakage currents. For the rst two sequences, the mean is well-t to a sharply peaked Gaussian (σ = 8.6 ms, 11.6 ms respectively), whereas run to stop conversions follow The stopped state can be maintained for up to minutes, before the next restart (Fig. 4) [15]. Emergence of global limit-cycle oscillations in the agella is Hopf-like.
In addition to eecting directional reorientation and sensing [16], the shock gait serves another key phys- upon direct mechanical contact. Compared to Chlamydomonas, whose agella display a certain load-response [6,13,18,19], P. octopus possess a much heightened mechanosensitivity, where the same downstream pathways leading to spontaneous shocks can be activated by touch, to produce stimulated shocks that are identical in morphology and dynamics to those described earlier (Fig. 2,3). with bending rigidity EI = 840 pNµm 2 [17] we estimate the contact force F = 3EI · δ/L 3 from the measured tip deection in the two cases: fail: ∼ 3.0 pN, success: ∼ 6.6 pN. Signal tranduction from the distal point of contact must have occurred within milliseconds.
The unusual motility of P. octopus is a signicant departure from known classical strategies. Peritrichous enteric bacteria rotate rigid agellar helices one way or another to cause runs and tumbles, producing a twostate, paradigmatic strategy for prokaryotic chemotaxis and gradient sensing based on stochastic switching between directed swimming and random reorientation [20].
The freshwater alga C. reinhardtii displays a eukaryotic version of this, swimming an in-phase breaststroke [21 23] but turning sharply when biagellar synchrony is lost (`phase drift') [24]. Other bacteria species adopt alternative strategies [2527], e.g. the monotrichous V. cholerae undergoes a run-reverse-ick motion where agellar hook elasticity is key. Contrastingly, the mechanism of enslavement of P. octopus swimming to its agellar dynamics is neither due to motor reversal at the base of the agellum (as in E. coli) nor to loss of biagellar synchronization (as in C. reinhardtii), but rather to a total conversion of beating waveform along the agellum axoneme proper.
These algae oer rare insight into the bifurcations between dierent modes of beating in the same organelle.
Identifying principal modes of beating (ciliary, agellar, or quiescent) with (run, shock or stop) states, we adopted a natural framework that is liberated from assumptions of specic prototypical gaits (breaststroke, trot, etc). Patterns of agellar actuation even during`run' phases are diverse and species-specic [4], and environmental stimuli can elicit further changes [18,30]. The P. octopus shock, while identiable with the stimulus-induced (light, mechanical) avoidance reaction of C. reinhardtii and S. similis, is importantly only one component of a tripartite repetoire, is more than an order of magnitude shorter in duration, and occurs spontaneously. Our three-state classication therefore does not purport to incorporate the totality of gaits but rather sheds new light on the physiology of gait control. By exploring the statistics of gait transitions, we demonstrated that the gait-switching process, and not just agellar beating itself [31], operates far from equilibrium thereby providing a route to enhanced biological sensitivity [32].
The discoveries that agellar activity in P. octopus exhibits rapid activation but slow deactivation, and that apparently quiescent agella undergo small-amplitude oscillations, have great implications for beat emergence and motor coordination in eukaryotic agella [2830].
The millisecond shock timescale facilitates rapid removal from predators or obstacles, analogously to the escape response of ciliates [11]. More generally, depending on the species, agella type, and number, the ways of achieving motion, no motion, or change of motion are diverse.
The purple bacterium B. photometrium has a sudden light-induced reaction (the Schreckbewegung reaction, or fright movement') [33], whereas sensory inputs that inhibit/enhance the ring rate of a`twiddle generator' [34] can alter the directionality of bacterial agellar motors.
The cilia of a more advanced phyllum ctenophores rely on neurons to switch between oscillatory/non-oscillatory states [35]. As important sensory appendages in animals [13,36], rapid transduction of signal must likewise be an essential attribute of mammalian cilia. Thus, in a very primitive unicellular alga, we may have found an evolutionary precedent for the kind of rapid signalling from a distance that, billions of years hence, would come to characterize the key physiological functions of mammalian cilia.