The interaction of in vivo muscle operating lengths and passive stiffness in rat hindlimbs.

The operating length of a muscle is a key determinant of its ability to produce force in vivo. Muscles that operate near the peak of their force-length relationship will generate higher forces whereas muscle operating at relatively short length may be safe from sudden lengthening perturbations and subsequent damage. At longer lengths, passive mechanical properties have the potential to contribute to force or constrain operating length with stiffer muscle-tendon units theoretically being restricted to shorter lengths. Connective tissues typically increase in density during aging, thus increasing passive muscle stiffness and potentially limiting the operating lengths of muscle during locomotion. Here, we compare in vivo and in situ muscle strain from the medial gastrocnemius in young (7 months old) and aged (30-32 months old) rats presumed to have varying passive tissue stiffness to test the hypothesis that stiffer muscles operate at shorter lengths relative to their force-length relationship. We measured in vivo muscle operating length during voluntary locomotion on inclines and flat trackways and characterized the muscle force-length relationship of the medial gastrocnemius using fluoromicrometry. Although no age-related results were evident, rats of both age groups demonstrated a clear relationship between passive stiffness and in vivo operating length, such that shorter operating lengths were significantly correlated with greater passive stiffness. Our results suggest that increased passive stiffness may restrict muscles to operating lengths shorter than optimal lengths, potentially limiting force capacity during locomotion.

Viscoelastic materials are most energy efficient when loaded and unloaded at equal rates.

Biological springs can be used in nature for energy conservation and ultra-fast motion. The loading and unloading rates of elastic materials can play an important role in determining how the properties of these springs affect movements. We investigate the mechanical energy efficiency of biological springs (American bullfrog plantaris tendons and guinea fowl lateral gastrocnemius tendons) and synthetic elastomers. We measure these materials under symmetric rates (equal loading and unloading durations) and asymmetric rates (unequal loading and unloading durations) using novel dynamic mechanical analysis measurements. We find that mechanical efficiency is highest at symmetric rates and significantly decreases with a larger degree of asymmetry. A generalized one-dimensional Maxwell model with no fitting parameters captures the experimental results based on the independently characterized linear viscoelastic properties of the materials. The model further shows that a broader viscoelastic relaxation spectrum enhances the effect of rate-asymmetry on efficiency. Overall, our study provides valuable insights into the interplay between material properties and unloading dynamics in both biological and synthetic elastic systems.

Architectural gear ratio depends on actuator spacing in a physical model of pennate muscle.

Pennate muscles are defined by the architectural arrangement of their muscle fibers, which run at an angle to the primary axis of muscle shortening. Pennation angles can vary dynamically over the course of individual contractions, influencing the speed and distance of muscle shortening. Despite their relevance to muscle performance, the physical mechanisms that drive dynamic changes in pennation angle remain poorly understood. Muscle fibers bulge radially as they shorten, a consequence of maintaining a constant internal fluid volume, and we hypothesized that radial interactions between tightly packed muscle fibers are essential to dynamic pennation angle changes. To explore this, we built physical models of pennate muscles in which the radial distance between fiber-like actuators could be experimentally altered. Models were built from pennate arrays of McKibben actuators, a type of pneumatic actuator that forcefully shortens and bulges radially when inflated with compressed air. Consistent with past studies of biological muscle and engineered pennate actuators, we found that the magnitude of pennation angle change during contraction varied with load. Importantly, however, we found that pennation angle changes were also strongly influenced by the radial distance between neighboring McKibben actuators. Increasing the radial distance between neighboring actuators reduced pennation angle change during contraction and effectively eliminated variable responses to load. Radial interactions between muscle fibers are rarely considered in theoretical and experimental analyses of pennate muscle; however, these findings suggest that radial interactions between fibers drive pennation angle changes and influence pennate muscle performance. Our results provide insight into the fundamental mechanism underlying dynamic pennation angle changes in biological muscle and highlight design considerations that can inform the development of engineered pennate arrays.

Modulation of limb mechanics in alligators moving across varying grades.

Graded substrates require legged animals to modulate their limb mechanics to meet locomotor demands. Previous work has elucidated strategies used by cursorial animals with upright limb posture, but it remains unclear how sprawling species such as alligators transition between grades. We measured individual limb forces and 3D kinematics as alligators walked steadily across level, 15 deg incline and 15 deg decline conditions. We compared our results with the literature to determine how limb posture alters strategies for managing the energetic variation that accompanies shifts in grade. We found that juvenile alligators maintain spatiotemporal characteristics of gait and locomotor speed while selectively modulating craniocaudal impulses (relative to level) when transitioning between grades. Alligators seem to accomplish this using a variety of kinematic strategies, but consistently sprawl both limb pairs outside of the parasagittal plane during decline walking. This latter result suggests alligators and other sprawling species may use movements outside of the parasagittal plane as an axis of variation to modulate limb mechanics when transitioning between graded substrates. We conclude that limb mechanics during graded locomotion are fairly predictable across quadrupedal species, regardless of body plan and limb posture, with hindlimbs playing a more propulsive role and forelimbs functioning to dissipate energy. Future work will elucidate how shifts in muscle properties or function underlie such shifts in limb kinematics.

The effects of temperature on elastic energy storage and release in a system with a dynamic mechanical advantage latch.

Changes in temperature alter muscle kinetics and in turn affect whole-organism performance. Some organisms use the elastic recoil of biological springs, structures which are far less temperature sensitive, to power thermally robust movements. For jumping frogs, the use of elastic energy in tendons is facilitated through a geometric latching mechanism that operates through dynamic changes in the mechanical advantage (MA) of the hindlimb. Despite the well-documented use of elastic energy storage, frog jumping is a locomotor behavior that is significantly affected by changes in temperature. Here, we used an in vitro muscle preparation interacting in real time with an in silico model of a legged jumper to understand how changes in temperature affect the flow of energy in a system using a MA latch. We used the plantaris longus muscle-tendon unit (MTU) to power a virtual limb with changing MA and a mass being accelerated through a real-time feedback controller. We quantified the amount of energy stored in and recovered from elastic structures and the additional contribution of direct muscle work after unlatching. We found that temperature altered the duration of the energy loading and recovery phase of the in vitro/in silico experiments. We found that the early phase of loading was insensitive to changes in temperature. However, an increase in temperature did increase the rate of force development, which in turn allowed for increased energy storage in the second phase of loading. We also found that the contribution of direct muscle work after unlatching was substantial and increased significantly with temperature. Our results show that the thermal robustness achieved by an elastic mechanism depends strongly on the nature of the latch that mediates energy flow, and that the relative contribution of elastic and direct muscle energy likely shapes the thermal sensitivity of locomotor systems.

Adapting small jumping robots to compliant environments.

Jumping animals launch themselves from surfaces that vary widely in compliance from grasses and shrubs to tree branches. However, studies of robotic jumpers have been largely limited to those jumping from rigid substrates. In this paper, we leverage recent work describing how latches in jumping systems can mediate the transition from stored potential energy to kinetic energy. By including a description of the latch in our system model of both the jumper and compliant substrate, we can describe conditions in which a jumper can either lose energy to the substrate or recover energy from the substrate resulting in an improved jump performance. Using our mathematical model, we illustrate how the latch plays a role in the ability of a system to adapt its jump performance to a wide range of substrates that vary in their compliance. Our modelling results are validated using a 4 g jumper with a range of latch designs jumping from substrates with varying mass and compliance. Finally, we demonstrate the jumper recovering energy from a tree branch during take-off, extending these mechanistic findings to robots interacting with a more natural environment.

Hindlimb muscle spindles inform preparatory forelimb coordination prior to landing in toads.

Animals move across a wide range of surface conditions in real-world environments to acquire resources and avoid predation. To effectively navigate a variety of surfaces, animals rely on several mechanisms including intrinsic mechanical responses, spinal-level central pattern generators, and neural commands that require sensory feedback. Muscle spindle Ia afferents play a critical role in providing sensory feedback and informing motor control strategies across legged vertebrate locomotion, which is apparent in cases where this sensory input is compromised. Here, we tested the hypothesis that spindle Ia afferents from hindlimb muscles are important for coordinating forelimb landing behavior in the cane toad. We performed bilateral sciatic nerve reinnervations to ablate the stretch reflex from distal hindlimb muscles while allowing for motor neuron recovery. We found that toads significantly delayed the onset and reduced the activation duration of their elbow extensor muscle following spindle Ia afferent ablation in the hindlimbs. However, reinnervated toads achieved similar elbow extension at touchdown to that of their pre-surgery state. Our results suggest that while toads likely tuned the activation timing of forelimb muscles in response to losing Ia afferent sensation from the hindlimbs they were likely able to employ compensatory strategies that allowed them to continue landing effectively with reduced sensory information during take-off. These findings indicate muscle spindle Ia afferents may contribute to tuning complex movements involving multiple limbs.

Tuned muscle and spring properties increase elastic energy storage.

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.

Fatigue resistant jaw muscles facilitate long-lasting courtship behaviour in the southern alligator lizard (Elgaria multicarinata).

The southern alligator lizard (Elgaria multicarinata) exhibits a courtship behaviour during which the male firmly grips the female's head in his jaws for many hours at a time. This extreme behaviour counters the conventional wisdom that reptilian muscle is incapable of powering high-endurance behaviours. We conducted in situ experiments in which the jaw-adductor muscles of lizards were stimulated directly while bite force was measured simultaneously. Fatigue tests were performed by stimulating the muscles with a series of tetanic trains. Our results show that a substantial sustained force gradually develops during the fatigue test. This sustained force persists after peak tetanic forces have declined to a fraction of their initial magnitude. The observed sustained force during in situ fatigue tests is consistent with the courtship behaviour of these lizards and probably reflects physiological specialization. The results of molecular analysis reveal that the jaw muscles contain masticatory and tonic myosin fibres. We propose that the presence of tonic fibres may explain the unusual sustained force properties during mate-holding behaviour. The characterization of muscle properties that facilitate extreme performance during specialized behaviours may reveal general mechanisms of muscle function, especially when done in light of convergently evolved systems exhibiting similar performance characteristics.

The Multi-Scale, Three-Dimensional Nature of Skeletal Muscle Contraction.

Muscle contraction is a three-dimensional process, as anyone who has observed a bulging muscle knows. Recent studies suggest that the three-dimensional nature of muscle contraction influences its mechanical output. Shape changes and radial forces appear to be important across scales of organization. Muscle architectural gearing is an emerging example of this process.

Why do Large Animals Never Actuate Their Jumps with Latch-Mediated Springs? Because They can Jump Higher Without Them.

As animals get smaller, their ability to generate usable work from muscle contraction is decreased by the muscle's force-velocity properties, thereby reducing their effective jump height. Very small animals use a spring-actuated system, which prevents velocity effects from reducing available energy. Since force-velocity properties reduce the usable work in even larger animals, why don't larger animals use spring-actuated jumping systems as well? We will show that muscle length-tension properties limit spring-actuated systems to generating a maximum one-third of the possible work that a muscle could produce-greatly restricting the jumping height of spring-actuated jumpers. Thus a spring-actuated jumping animal has a jumping height that is one-third of the maximum possible jump height achievable were 100% of the possible muscle work available. Larger animals, which could theoretically use all of the available muscle energy, have a maximum jumping height that asymptotically approaches a value that is about three times higher than that of spring-actuated jumpers. Furthermore, a size related "crossover point" is evident for these two jumping mechanisms: animals smaller than this point can jump higher with a spring-actuated mechanism, while animals larger than this point can jump higher with a muscle-actuated mechanism. We demonstrate how this limit on energy storage is a consequence of the interaction between length-tension properties of muscles and spring stiffness. We indicate where this crossover point occurs based on modeling and then use jumping data from the literature to validate that larger jumping animals generate greater jump heights with muscle-actuated systems than spring-actuated systems.

Modeling the Determinants of Mechanical Advantage During Jumping: Consequences for Spring- and Muscle-Driven Movement.

Systems powered by elastic recoil need a latch to prevent motion while a spring is loaded but allow motion during spring recoil. Some jumping animals that rely on elastic recoil use the increasing mechanical advantage of limb extensor muscles to accomplish latching. We examined the ways in which limb morphology affects latching and the resulting performance of an elastic-recoil mechanism. Additionally, because increasing mechanical advantage is a consequence of limb extension that may be found in many systems, we examined the mechanical consequences for muscle in the absence of elastic elements. By simulating muscle contractions against a simplified model of an extending limb, we found that increasing mechanical advantage can limit the work done by muscle by accelerating muscle shortening during limb extension. The inclusion of a series elastic element dramatically improves mechanical output by allowing for additional muscle work that is stored and released from the spring. This suggests that elastic recoil may be beneficial for more animals than expected when assuming peak isotonic power output from muscle during jumping. The mechanical output of elastic recoil depends on limb morphology; long limbs moving small loads maximize total work, but it is done at a low power, whereas shorter limbs moving larger loads do less work at a higher power. This work-power trade-off of limb morphology is true with or without an elastic element. Systems with relatively short limbs may have performance that is robust to variable conditions such as body mass or muscle activation, while long-limbed systems risk complete failure with relatively minor perturbations. Finally, a changing mechanical advantage latch allows for muscle work to be done simultaneously with spring recoil, changing the predictions for spring mechanical properties. Overall, the design constraints revealed by considering the mechanics of this particular latch will inform our understanding of the evolution of elastic-recoil mechanisms and our attempts to engineer similar systems.

The high speed radular prey strike of a fish-hunting cone snail.

Cone snails are venomous marine gastropods that hydraulically propel a hollow, chitinous radular harpoon into prey [1,2]. This radular harpoon serves both as projectile and conduit for venom delivery. In the fish-hunting cone snail Conus catus, the radular harpoon is also utilized to tether the snail to its prey, rapidly paralyzed by neuroexcitatory peptides [2,3]. Effective prey capture in C. catus requires both fast-acting neurotoxins and a delivery system quick enough to exceed the prey fish's rapid escape responses [4]. We report here that the cone snail's prey strike is one of the fastest in the animal kingdom. A unique cellular latch mechanism prevents harpoon release until sufficient pressure builds and overcomes the forces of the latch, resulting in rapid acceleration into prey [2]. The radular harpoon then rapidly decelerates as its bulbous base reaches the end of the proboscis, a distensible hydrostatic skeleton extended toward the prey [2], with little slowing during prey impalement. The velocities achieved are the fastest movements of any mollusk and exceed previous estimates by over an order of magnitude [1].

Compliant Substrates Disrupt Elastic Energy Storage in Jumping Tree Frogs.

Arboreal frogs navigate complex environments and face diverse mechanical properties within their physical environment. Such frogs may encounter substrates that are damped and absorb energy or are elastic and can store and release energy as the animal pushes off during take-off. When dealing with a compliant substrate, a well-coordinated jump would allow for the recovery of elastic energy stored in the substrate to amplify mechanical power, effectively adding an in-series spring to the hindlimbs. We tested the hypothesis that effective use of compliant substrates requires active changes to muscle activation and limb kinematics to recover energy from the substrate. We designed an actuated force platform, modulated with a real-time feedback controller to vary the stiffness of the substrate. We quantified the kinetics and kinematics of Cuban tree frogs (Osteopilus septentrionalis) jumping off platforms at four different stiffness conditions. In addition, we used electromyography to examine the relationship between muscle activation patterns and substrate compliance during take-off in a knee extensor (m. cruralis) and an ankle extensor (m. plantaris). We find O. septentrionalis do not modulate motor patterns in response to substrate compliance. Although not actively modulated, changes in the rate of limb extension suggest a trade-off between power amplification and energy recovery from the substrate. Our results suggest that compliant substrates disrupt the inertial catch mechanism that allows tree frogs to store elastic energy in the tendon, thereby slowing the rate of limb extension and increasing the duration of take-off. However, the slower rate of limb extension does provide additional time to recover more energy from the substrate. This work serves to broaden our understanding of how the intrinsic mechanical properties of a system may broaden an organism's capacity to maintain performance when facing environmental perturbations.

Structural Determinants of Muscle Gearing During Dynamic Contractions.

In skeletal muscle, interactions between contractile and connective tissue elements at multiple scales result in emergent properties that determine mechanical performance. One of these phenomena is architectural gearing, which is quantified as the ratio of muscle velocity to muscle fiber velocity. Many pennate muscles operate with a gear ratio greater than one because muscles shorten through a combination of muscle fiber shortening and fiber rotation. Within a muscle, gearing is variable across contractions. During low force contractions, muscles operate at high gear while muscles operate at low gear during high force contractions. This variable gearing has a significant impact on muscle performance as muscle architectural changes favor muscle speed during fast contractions and muscle force during slow, high force contractions. We hypothesize that gearing in any given contraction is determined by the dynamic interaction of fiber-generated forces, fluid force transmission, and the elastic behavior of intramuscular connective tissues. Because muscle is isovolumetric, muscle fibers must bulge radially when they shorten. Radial bulging and fiber-generated forces off-axis from the muscle line of action exert forces that load connective tissues that ensheath fibers, fascicles, and the whole muscle. The way in which fluid pressures and fiber forces interact to load connective tissues in three-dimensions remains poorly understood because of the complex and multiscale nature of these interactions. Here we review evidence for variable gearing in pennate muscles, present a conceptual model that describes the fundamental interactions that determine gearing, and discuss where gaps remain in our understanding of the determinants and consequences of muscle shape change and variable gearing.

Morphological and kinematic specializations of walking frogs.

The anuran body plan is defined by morphological features associated with saltatory locomotion, but these specializations may have functional consequences for other modes of locomotion. Several frog species use a quadrupedal walking gait as their primary mode of locomotion, characterized by limbs that move in diagonal pairs. Here, we examine how walking species may deviate from the ancestral body plan and how the kinematics of a quadrupedal gait are modified to accommodate the anuran body plan. We use a comparative analysis of limb lengths to test the hypothesis that quadrupedal anurans shift away from the standard anuran condition defined by short forelimbs and long hindlimbs. We also use three-dimensional high-speed videography in four anuran species (Kassina senegalensis, Melanophryniscus stelzneri, Phrynomantis bifasciatus, and Phyllomedusa hypochondrialis) to characterize footfall patterns and body posture during quadrupedal locomotion, measuring the angle and timing of joint excursions in the fore- and hindlimb during walking to compare kinematics between limbs of disparate lengths. Our results show frogs specialized for walking tend to have less disparity in the lengths of their fore- and hindlimbs compared with other anurans. We find quadrupedal walking species use a vertically retracted hindlimb posture to accommodate their relatively longer hindlimbs and minimize body pitch angle during a stride. Overall, this novel quadrupedal gait can be accommodated by changes in limb posture during locomotion and changes in the relative limb lengths of walking specialists.

The principles of cascading power limits in small, fast biological and engineered systems.

Mechanical power limitations emerge from the physical trade-off between force and velocity. Many biological systems incorporate power-enhancing mechanisms enabling extraordinary accelerations at small sizes. We establish how power enhancement emerges through the dynamic coupling of motors, springs, and latches and reveal how each displays its own force-velocity behavior. We mathematically demonstrate a tunable performance space for spring-actuated movement that is applicable to biological and synthetic systems. Incorporating nonideal spring behavior and parameterizing latch dynamics allows the identification of critical transitions in mass and trade-offs in spring scaling, both of which offer explanations for long-observed scaling patterns in biological systems. This analysis defines the cascading challenges of power enhancement, explores their emergent effects in biological and engineered systems, and charts a pathway for higher-level analysis and synthesis of power-amplified systems.

Lowering metabolic rate mitigates muscle atrophy in western fence lizards.

Extended periods of skeletal muscle disuse can cause a significant loss of contractile proteins, which compromises the ability to generate force, mechanical work or power, thus compromising locomotor performance. Several hibernating organisms can resist muscle atrophy despite months of inactivity. This resistance has been attributed to a reduction in body temperature and metabolic rate and activation of physiological pathways that counteract pathways of protein degradation. However, in these systems, such strategies are not mutually exclusive and the effects of these mechanisms can be difficult to separate. In this study, we used the western fence lizard, Sceloporus occidentalis, as an ectothermic model to determine whether a reduction in metabolic rate is sufficient to resist muscle atrophy. We induced atrophy through sciatic denervation of the gastrocnemius muscle and housed lizards at either 15 or 30°C for 6-7 weeks. Following treatment, we used muscle ergometry to measure maximum isometric force, the force-velocity relationship and contractile dynamics in the gastrocnemius. This approach allowed us to relate changes in the size and morphology to functional metrics of contractile performance. A subset of samples was used to histologically determine muscle fiber types. At 30°C, denervated muscles had a larger reduction in muscle mass, physiological cross-sectional area and maximum isometric force than at 15°C. Maximum shortening velocity of the muscle decreased slightly in animals housed at 30°C but did not change in those housed at 15°C. Our results suggest that metabolic rate alone can influence the rate of muscle atrophy and that ectothermic vertebrates may have an intrinsic mechanism to resist muscle atrophy during seasonal periods of inactivity.

Modeling age-related changes in muscle-tendon dynamics during cyclical contractions in the rat gastrocnemius.

Efficient muscle-tendon performance during cyclical tasks is dependent on both active and passive mechanical tissue properties. Here we examine whether age-related changes in the properties of muscle-tendon units (MTUs) compromise their ability to do work and utilize elastic energy storage. We empirically quantified passive and active properties of the medial gastrocnemius muscle and material properties of the Achilles tendon in young (∼6 mo) and old (∼32 mo) rats. We then used these properties in computer simulations of a Hill-type muscle model operating in series with a Hookean spring. The modeled MTU was driven through sinusoidal length changes and activated at a phase that optimized muscle-tendon tuning to assess the relative contributions of active and passive elements to the force and work in each cycle. In physiologically realistic simulations where young and old MTUs started at similar passive forces and developed similar active forces, the capacity of old MTUs to store elastic energy and produce positive work was compromised. These results suggest that the observed increase in the metabolic cost of locomotion with aging may be in part due to the recruitment of additional muscles to compensate for the reduced work at the primary MTU. Furthermore, the age-related increases in passive stiffness coupled with a reduced active force capacity in the muscle can lead to shifts in the force-length and force-velocity operating range that may significantly impact mechanical and metabolic performance. Our study emphasizes the importance of the interplay between muscle and tendon mechanical properties in shaping MTU performance during cyclical contractions.