Fig 1.
Morphology of the ctenophore Bolinopsis vitrea.
Fig 2.
Kinematic tracking experimental arena.
(A) Schematic of the 3D recording system showing the three orthogonal camera views. The three tracked points (apical organ (red) and tentacular bulbs (blue and green)), are shown in each camera view. (B) An example of a reconstructed trajectory; black line is the swimming trajectory, which we define to be the path of the midpoint of the line segment connecting the tentacular bulbs. Green and red triangles show the initial and final position of the animal.
Fig 3.
Morphology and ctene row kinematics of a typical Bolinopsis vitrea.
(A) Top view showing the eight ctene rows, the ctene row position angle ε, and the sagittal and tentacular planes (dB = 7.6mm); the “sagittal rows” are the rows adjacent to the sagittal plane, while the “tentacular rows” are adjacent to the tentacular plane. (B) Side view showing the ctene rows along the body (LB = 7.4mm), and κ, the angle for the most aboral ctene. (C) Stylized example timeseries of ctene tip speed for one ctene over one beat cycle, where tp is the power stroke duration and tr the recovery stroke duration. (D) Ctene row close side view, showing a tracked ctene tip trajectory (Ae, solid white line), and the estimated ctene reachable space (Ao, red dashed ellipsoid inscribed in black half circle of radius l; shown elsewhere on the ctene row for clarity). Stroke amplitude (Φ) and the direction of the power stroke are also marked.
Table 1.
Ctenophore morphometric and kinematic parameters.
Table 2.
Morphometric measurements of included B. vitrea (mean ± one standard deviation).
Fig 4.
Schematic of a ctenophore’s simplified geometry moving in 3D space.
The unit vectors , and
define the global (fixed) coordinate system while
, and
correspond to the moving coordinate system attached to the spheroidal body.
Table 3.
Reduced-order swimming model parameters.
Vector quantities are expressed in the global frame unless marked with a prime (as in ).
Fig 5.
Ctenophore reduced-order modeling.
(A) Lateral view of a ctenophore; red dots mark the position of the ctenes that circumscribe its body in eight rows. (B) Real ctene tip trajectory from a tracked time series of ctene kinematics (gray lines, spaced equally in time). (C) Ctenophore modeled as a spheroidal body; red dots indicate the application point for each modeled (time-varying) ctene propulsion force. (D) Simplified elliptical trajectory for a modeled ctene, which is a flat plate with time-varying length. The plate oscillates parallel to a plane tangent to the curved surface of the modeled body (kλ, tangential angle to the body surface). The time-varying tip position (xA, yA) is prescribed as a function of the five ctene beating control parameters: f, Φ, l, Sa, and Ta (see S1 Video).
Fig 6.
Ctenophores are capable of several different swimming control strategies based on the activation of their ctene rows, which are controlled in pairs (such that each body quadrant receives one frequency input).
While each quadrant can operate at an independent frequency, we typically observe only two frequencies during turns, such that there is a single frequency differential (fout>fin). The above images schematically show (A) turning mode 1, (B) turning mode 2, (C) turning mode 3, and (D) straight swimming (mode 4).
Table 4.
Appendage control strategies observed in freely swimming B. vitrea (27 total trajectories).
Fig 7.
Maneuverability-Agility Plot (MAP).
Experimental measurements of freely swimming B. vitrea (red dots) and for all simulated cases of modes 1, 2, and 3 (blue dots). Lower values of indicate sharp turns (more maneuverable); higher values of
indicate faster swimming (more agile). Values in the upper left (low
, high
) are straightforwardly achievable with straight swimming (mode 4) or with Δf<2Hz; these points were not simulated. Simulating mode 4 mathematically would result in
, since the eight rows beat at the same frequency. However, mode 3 will approach the behavior of mode 4 as Δf = fout−fin approaches zero. Here, the minimum value is Δf = 2Hz, so the upper-left corner of the MAP is not occupied. Simulations were halted after the timestep in which
exceeded 10, resulting in some trials with
slightly greater than 10.
Table 5.
Range and resolution of the frequencies used in the analytical simulations.
Fig 8.
MAPs for the different turning modes, along with beat frequency differential (Δf = fout−fin).
(A) Turning mode 1 (2 vs. 2 ctene rows). (B) Turning mode 2 (4 vs. 4 ctene rows) with consecutive sagittal rows at different frequencies. (C) Turning mode 2 (4 vs. 4 ctene rows) with consecutive tentacular rows at different frequencies. (D) Turning mode 3 (6 vs. 2 ctene rows).
Fig 9.
Motor volume (MV) constructed from the 27 tracked swimming trajectories of B. vitrea.
Black lines show swimming trajectories (midpoint between tentacular bulbs) and volume swept by animals’ bodies (gray cloud) during each maneuver. Animal volume is estimated as a prolate spheroid based on morphological measurements (Table 2). The yellow sketches indicate the initial position of the ctenophore; the motor volume is elongated in X because all trajectories were considered from the same starting orientation, and because our dataset contains only animals with a nonzero initial velocity (since animals freely swam through the field of view). (A) Side view and (B) front view of the tracked swimming trajectories and motor volume show that B. vitrea can turn over a large range of angles.
Table 6.
Experimental recordings (mean ± one standard deviation).
Fig 10.
Computationally simulated MV for the 3 ctenophore row control strategies, with a variable number of rows beating at 30 Hz, swimming either forward or backward, for a simulated time of one second.
The darker gray ellipsoid placed on the origin illustrates the animals’ initial position. Turning mode 1 is shown in blue, mode 2 in black and mode 3 in red. (A) Side view displaying the backward (-x) and forward (+x) swimming trajectories. Asymmetry arises from the distribution of ctenes along the body. (B) Front view of the swimming trajectories, showing the wide range of turning directions.
Table 7.
Maneuverability and agility measurements for the simulated motor volume of a lobate ctenophore.
Fig 11.
Computationally simulated MV for 255 ctene row control strategies, with 1≤ncr≤8 rows beating at 30 Hz, swimming either forward or backward for a simulated time of one second.
(A) Side view displaying the backward (-x) and forward (+x) swimming trajectories. (B) Front view of the swimming trajectories, showing the wide range of turning directions. Across all simulated trajectories, the minimum achieved is 0.22 (backward swimming) and 0.20 (forward swimming); the maximum achieved
is 1.79BL/s (equal for forward and backward swimming).