A minimal robophysical model of quadriflagellate self-propulsion

Abstract

Locomotion at the microscale is remarkably sophisticated. Microorganisms have evolved diverse strategies to move within highly viscous environments, using deformable, propulsion-generating appendages such as cilia and flagella to drive helical or undulatory motion. In single-celled algae, these appendages can be arranged in different ways around an approximately 10μm cell body, and coordinated in distinct temporal patterns. Inspired by the observation that some quadriflagellates (bearing four flagella) have an outwardly similar morphology and flagellar beat pattern, yet swim at different speeds, this study seeks to determine whether variations in swimming performance could arise solely from differences in swimming gait. Robotics approaches are particularly suited to such investigations, where the phase relationships between appendages can be readily manipulated. Here, we developed autonomous, algae-inspired robophysical models that can self-propel in a viscous fluid. These macroscopic robots (length and width = 8.5 cm, height = 2 cm) have four independently actuated `flagella' that oscillate back and forth under low-Reynolds number conditions (Re=0.1-0.5). We tested the swimming performance of these robot models with appendages arranged in one of two distinct configurations, and coordinated in one of three distinct gaits. The gaits, namely the pronk, the trot, and the gallop, correspond to gaits adopted by distinct microalgal species. When the appendages are inserted perpendicularly around a central `body', the robot achieved a net performance of 0.15-0.63 body lengths per cycle, with the trot gait being the fastest. Robotic swimming performance was found to be comparable to that of the algal microswimmers across all gaits, with parallel appendage placement consistently leading to slower propulsion. By creating a minimal robot that can successfully reproduce cilia-inspired drag-based swimmging, our work paves the way for the design of next-generation devices that have the capacity to autonomously navigate aqueous environments.

Distinct gaits of self-propelled quadriflagellate microswimmers

“…These gait-dependent linear swimming speeds are consistent with the available data, in which the trot gait proceeds at 408 µ m/s, much faster than the pronk at 126 µ m/s, and gallop at 127 µ m/s [10], and several times faster than that of CR at ∼ 90 µ m/s [40, 41]. Due to technical limitations in visualising the free-swimming trajectories in 3D, experimental estimates of the axial rotation speeds of the quadriflagellate species are not yet available.…”

“…The answer deviates significantly from our intuitions associated with macroscopic vertebrate locomotion [9]. For instance, Pyramimonas parkeae swims using a ‘trot’ gait, achieving an average speed of up to 400 µ m /s , several times faster than its sister species Pyramimonas tetrarhynchus , which largely swims using the ‘pronk’ gait [7, 10]. In terms of cell size and shape, both species comprise obovate or oblong cells of approximately 20 µ m in length, 10 µ m in width, and four equal-length, front-mounted flagella (10 − 15 µ m), arranged in a cruciate pattern (Fig.…”

“…For simplicity, we shall neglect gait-switching dynamics here and focus only on the consequences of a sustained, deterministic gait. We will also discuss our results in light of available biological data, as well as measurements from a recent macroscopic (𝒪 (10)cm) robophysical model ([10]) of quadriflagellate algae.…”

“…1A). Despite their near-identical body and flagella morphology, different quadriflagellate swimmers nonetheless exhibit distinct motility characteristics [10]. Therefore, we ask if and how gait alone can influence swimming dynamics.…”

“…Different species of these algae assume distinct swimming gaits including the “pronk”, “gallop”, and “trot”. (b) A macroscopic robot modelled on these algae can achieve different rates of self-propulsion at low-Reynolds number, depending on gait (image modified from [10]). (c) Here, we model a quadriflagellate microswimmer using a system of 5-beads, and systematically evaluate the swimming performance of each gait.…”