Many biological microswimmers can modulate their swimming gait to achieve directional control of motility, especially when performing steering towards specific directional cues. This can be achieved without the need for obvious morphological or structural asymmetries in the form of the organism, or in the number or organisation of propulsion-generating appendages such as cilia. In this work, we identify and validate a core principle of asymmetric turning in biflagellate microswimmers: propulsive forces interact constructively to drive translation whilst interacting destructively to drive rotation. We explore the ramifications of this tunable biflagellar swimming mechanism across a range of systems, from a simple, back-of-the-envelope model to a detailed computational representation of an exemplar swimmer. This leads to a markedly general quantitative relation between key drivers of asymmetry, such as ciliary beat frequency, and the curvature of emergent trajectories. We discuss how the model green alga Chlamydomonas reinhardtii, which actuates its two cilia in a symmetric breaststroke for forward swimming, may exploit this feature for phototaxis. Finally, we validate our predictions in a Chlamydomonas-inspired robophysical model, implementing closed-loop control to achieve phototactic turning.
Achieving directional control of motility is a fundamental challenge of swimming at low-Reynolds number [1,2]. For small prokaryotic organisms of characteristic size 1-2 µm, swimming trajectories are easily overwhelmed by rotational diffusion; consequently, few such organisms have evolved the capacity to steer [3]. In contrast, larger eukaryotic cells perform more elaborate strategies for controlling their heading in a stimulus-dependent manner, often involving the coordinated movement of multiple cilia (also known as eukaryotic flagella). Despite the diversity of naturally occurring motility and navigation mechanisms, actively migrating cells (such as algae, diatoms, amoeba, immune cells and cancer cells) universally assume complex trajectories with time-varying curvatures. This suggests that the ability to adjust motility in response to internal or external cues is a fundamental phenomenon across species [4][5][6].
In many cases, the swimmer itself exhibits some persistent geometrical asymmetry, which gives rise to symmetry breaking. Uniflagellates including spermatozoa rely on beat waveform modulation to reorient themselves [7], whereas biflagellate zoospores with heterodynamic flagella undergo rapid turning events by alternating the activity of the anterior and posterior flagella [8]. A similar process occurs in cirri-bearing hypotrich ciliates, which undergo specialised manoeuvres for turning (called sidestepping reactions) [9,10]. Other cells have no apparent morphological asymmetries, such as the biflagellate green alga Chlamydomonas shown in Fig. 1, but can nonetheless fine tune the actuation of their two symmetrically positioned, equal-length flagella. While individual studies have attempted to explore the coupling between swimmer arXiv:2602.17521v1 [physics.bio-ph] 19 Feb 2026 geometry, actuation and motility trajectories [11][12][13], investigation of how asymmetric drivers of motility relate to the asymmetry or curvature of the resulting trajectories is lacking. Comprehensive theoretical understanding of how asymmetries in propulsion are propagated has important consequences not only for decoding the hidden biochemical processes regulating cell motility, but also for the design of novel synthetic swimmers.
Owing to the marked complexity of microscale swimming, the most faithful theoretical models of cell-scale swimmers require intricate descriptions of the geometry of the swimmer and high resolution hydrodynamics to capture interactions with the fluid environment. This model specificity can afford significant advantages, such as enabling more precise prediction of swimmer behaviours that accounts for various confounding factors, such as the presence of fluid boundaries or other swimmers [14][15][16]. On the other hand, simple models are often better suited to generalisation, with proven potential to generate broad insight into fundamental principles of cellular swimming [17][18][19]. It is worth highlighting that, whilst the simplicity and often wide-reaching applicability of minimal models can be beguiling, their use is predicated on appropriate, model-specific caveats and acknowledgement of the constraints on their validity.
In this study, we establish a general, quantitative relationship between cell-scale asymmetries in propulsion and the resulting swimming trajectories. To this end, we analyse simple models of a biflagellate swimmer that comprise a body with two periodically driven appendages, abstracting away the details of ciliary waveforms and, to some extent, swimmer geometry. We develop and investigate a sequence of theoretical models of increasing complexity: a minimal toy model that accounts for essential features of our exemplar swimmer; an improved model that better captures relevant physics; and a geometrically faithful computational model. In each case, we focus on the impact of measurable physical parameters (such as beat amplitude, frequency and phase difference) on the resulting dynamics, and establish conditions for the validity of our predictions. We complement these theoretical insights by realising a robophysical model of biflagellar swimming that, in contrast, requires no specific assumptions on the detailed nature of the fluid-structure interactions involved. Finally, we implement proof-of-concept closed-loop phototaxis in our robotic model, motivated by living organisms’ routine leveraging of tunable asymmetries in motility to produce deterministic steering in response to environmental cues [20][21][22][23]. These robophysical explorations validate the predictions of our theoretical modelling in practice.
We first pose a general, toy model for planar ciliadriven motion. We focus on what will prove to be a defining feature of the dynamics: the constructive in-teraction of two cilia-like appendages when generating propulsion and their contrastingly destructive interactions when generating rotation. In other words, we explore the consequences of the simple observation
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