Common mechanics of mode switching in locomotion of limbless and legged animals

Abstract

Crawling using muscular waves is observed in many species, including planaria, leeches, nemertea, aplysia, snails, chitons, earthworms and maggots. Contraction or extension waves propagate along the antero-posterior axis of the body as the crawler pushes the ground substratum backward. However, the observation that locomotory waves can be directed forward or backward has attracted much attention over the past hundred years. Legged organisms such as centipedes and millipedes exhibit parallel phenomena; leg tips form density waves that propagate backward or forward. Mechanical considerations reveal that leg-density waves play a similar role to locomotory waves in limbless species, and that locomotory waves are used by a mechanism common to both legged and limbless species to achieve crawling. Here, we report that both mode switching of the wave direction and friction control were achieved when backward motion was induced in the laboratory. We show that the many variations of switching in different animals can essentially be classified in two types according to mechanical considerations. We propose that during their evolution, limbless crawlers first moved in a manner similar to walking before legs were obtained. Therefore, legged crawlers might have learned the mechanical mode of movement involved in walking long before obtaining legs.

Dynamic gait transition in theScolopendromorpha scolopocryptops rubiginosus L. Kochcentipede

“…Therefore, the waves were retrograde waves, which propagate opposite to the direction of motion. The dense parts of retrograde waves consist of the legs that are nearly stationary with respect to the ground during power strokes, while the sparse parts consist of the legs that move forward with respect to the ground during recovery strokes [9]. A tentative motion before retraction in the 16th leg (the period between the black arrowheads) and lengthened protraction period in the 17th to 20th legs were observed.…”

“…One of the most remarkable differences between the retrograde waves and direct waves is in timing when the distance between the leg-tips of successive legs become smallest [9]. Because the dense part in the retrograde waves appears during the retraction period, the centipede may stumble if the trajectory intersects the leg-crossing region.…”

“…These waves are referred to as locomotory waves in this paper. Although the propulsive machinery is very different among these crawlers, it has been shown that the locomotory waves are kinematically similar to each other [8] and play the common mechanical role of pushing the body forward [9, 10].…”

“…In natural circumstances, crawlers migrate under various conditions, and should therefore possess some ability to adapt their gait. Laboratory observations about gait-modulation of crawlers have been made [9, 12–15]. Manton [8]showed that the gait patterns of many-legged organisms are characterised by wavenumber (the phase difference between successive legs), rotation frequency (the multiplicative inverse of the duration of a cycle of a leg movement), duty factor (the relative duration of the recovery and power strokes by the legs), span (the moving distance during a power stroke of a leg), and stride (the moving distance during a cycle of a leg movement, i.e.…”

Active Poroelastic Two-Phase Model for the Motion of Physarum Microplasmodia

“…Different modes of motion driven by periodic deformation waves are not restricted to 31 Physarum MP, but are also found in rather general mathematical models [25] and in the 32 locomotion of a wide variety of limbless and legged animals [26]. More recently, different 33 modes have also been found in the Belousov-Zhabotinsky reaction in a light-driven 34 photosensitive gel [27-30]; Epstein and coworkers have classified the modes using the 35 terms retrograde and direct wave locomotion [28] and also report on a form of oscillatory 36 migration without net displacement of the average position [29].…”