Tuned muscle and spring properties increase elastic energy storage

Abstract

Elastic recoil drives some of the fastest and most powerful biological movements. For effective use of elastic recoil, the tuning of muscle and spring force capacity is essential. Although studies of invertebrate organisms that use elastic recoil show evidence of increased force capacity in their energy loading muscle, changes in the fundamental properties of such muscles have yet to be documented in vertebrates. Here, we used three species of frogs (Cuban tree frogs, bullfrogs and cane toads) that differ in jumping power to investigate functional shifts in muscle-spring tuning in systems using latch-mediated spring actuation (LaMSA). We hypothesized that variation in jumping performance would result from increased force capacity in muscles and relatively stiffer elastic structures, resulting in greater energy storage. To test this, we characterized the force-length property of the plantaris longus muscle-tendon unit (MTU), and quantified the maximal amount of energy stored in elastic structures for each species. We found that the plantaris longus MTU of Cuban tree frogs produced higher mass-specific energy and mass-specific forces than the other two species. Moreover, we found that the plantaris longus MTU of Cuban tree frogs had higher pennation angles than the other species, suggesting that muscle architecture was modified to increase force capacity through packing of more muscle fibers. Finally, we found that the elastic structures were relatively stiffer in Cuban tree frogs. These results provide a mechanistic link between the tuned properties of LaMSA components, energy storage capacity and whole-system performance.

Keywords: Elastic recoil; Frogs; LaMSA; Power amplification.

Fig. 1.

Conceptual figures showing how the relative properties of muscles and springs can affect the amount of elastic energy storage. A series of contractions are shown which all begin at a length of 1.3L_o and shorten against the stretch of a tendon until the contraction reaches a point on the isometric force–length relationship. The slope of the dashed lines indicate spring stiffness, and the area underneath the dashed lines corresponds to the energy stored. (A) A muscle that contracts against relatively stiff elastic structures (right) could store approximately 27% of the maximal energy it could store with tuned springs. A muscle that contracts against relatively compliant elastic structures (left) would store approximately 72% of the maximal energy. Thus, tuning spring stiffness to muscle force capacity should maximize energy storage. (B) The force–length relationship shifted upward for a muscle modified for increased force capacity. With a higher force capacity, a relatively stiffer spring should maximize energy storage.

Fig. 2.

Sample time series of fixed end contractions showing fascicle length, force and work in three frog species. (A) Cane toad, (B) bullfrog and (C) Cuban tree frog.

Fig. 3.

Representative force–length curves for three frog species. (A) Cane toad, (B) bullfrog and (C) Cuban tree frog. One representative contraction that produced the highest work is shown for each species. The muscles start on the descending limb of the force–length curve and shorten onto the plateau against the stretch of the tendon. The shaded triangles represent the work (or energy) that was stored into the elastic elements.

Fig. 4.

Summary data plots for cane toads, bullfrogs and Cuban tree frogs. (A) Mass-specific elastic energy, (B) muscle stress, (C) mass-specific force, (D) pennation angle and (E) normalized stiffness. Mass-specific energy was significantly different between Cuban tree frogs and cane toads (P<0.05). Stress did not significantly differ across species. Mass-specific force was significantly different between Cuban tree frogs and cane toads (P<0.001) and between Cuban tree frogs and bullfrogs (P<0.001), but was not significantly different between cane toads and bullfrogs (indicated by lowercase letters). Pennation angle was significantly different between Cuban tree frogs and cane toads (P<0.05). Normalized stiffness was significantly different between Cuban tree frogs and cane toads (P<0.05) and between Cuban tree frogs and bullfrogs (P<0.05), but was not significantly different between cane toads and bullfrogs.