Retrograde and Direct Wave Locomotion in a Photosensitive Self-Oscillating Gel

Crawling motion mediated by retrograde and direct waves, that is, in the opposite or the same direction, respectively, as the muscular wave that generates it, is a fundamental mode of biological locomotion, from which more complex and sophisticated locomotion modes involving outgrowths such as limbs and wings may have evolved. A detailed general description of muscular wave locomotion and its relationship with other modes of locomotion is a challenging task. We employ a model of a photosensitive self-oscillating gel, in which chemical pulse waves and a stimulus-responsive medium play roles analogous to nerve pulses and deformable muscles in an animal, to generate retrograde and direct waves under non-uniform illumination. Analysis reveals that the directional locomotion arises from a force asymmetry that results in unequal translation lengths in the push and pull regions associated with a pulse wave. This asymmetry can be modulated by the kinetic parameters of the photosensitive Belousov-Zhabotinsky reaction and the performance parameters of the gel, enabling a transition between retrograde and direct wave locomotion.