The weak link: do muscle properties determine locomotor performance in frogs?

Impact of hindlimb length variation on jumping dynamics in the Longshanks mouse

Distantly related mammals (e.g. jerboa, tarsiers, kangaroos) have convergently evolved elongated hindlimbs relative to body size. Limb elongation is hypothesized to make these species more effective jumpers by increasing their kinetic energy output (through greater forces or acceleration distances), thereby increasing take-off velocity and jump distance. This hypothesis, however, has rarely been tested at the population level, where natural selection operates. We examined the relationship between limb length, muscular traits and dynamics using Longshanks mice, which were selectively bred over 22 generations for longer tibiae. Longshanks mice have approximately 15% longer tibiae and 10% longer femora compared with random-bred Control mice from the same genetic background. We collected in vivo measures of locomotor kinematics and force production, in combination with behavioral data and muscle morphology, to examine how changes in bone and muscle structure observed in Longshanks mice affect their hindlimb dynamics during jumping and clambering. Longshanks mice achieved higher mean and maximum lunge-jump heights than Control mice. When jumping to a standardized height (14 cm), Longshanks mice had lower maximum ground reaction forces, prolonged contact times and greater impulses, without significant differences in average force, power or whole-body velocity. While Longshanks mice have longer plantarflexor muscle bodies and tendons than Control mice, there were no consistent differences in muscular cross-sectional area or overall muscle volume; improved lunge-jumping performance in Longshanks mice is not accomplished by simply possessing larger muscles. Independent of other morphological or behavioral changes, our results point to the benefit of longer hindlimbs for performing dynamic 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.

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.

Muscle-tendon unit design and tuning for power enhancement, power attenuation, and reduction of metabolic cost

The contractile elements in skeletal muscle fibers operate in series with elastic elements, tendons and potentially aponeuroses, in muscle-tendon units (MTUs). Elastic strain energy (ESE), arising from either work done by muscle fibers or the energy of the body, can be stored in these series elastic elements (SEEs). MTUs vary considerably in their design in terms of the relative lengths and stiffnesses of the muscle fibers and SEEs, and the force and work generating capacities of the muscle fibers. However, within an MTU it is thought that contractile and series elastic elements can be matched or tuned to maximize ESE storage. The use of ESE is thought to improve locomotor performance by enhancing contractile element power during activities such as jumping, attenuating contractile element power during activities such as landing, and reducing the metabolic cost of movement during steady-state activities such as walking and running. The effectiveness of MTUs in these potential roles is contingent on factors such as the source of mechanical energy, the control of the flow of energy, and characteristics of SEE recoil. Hence, we suggest that MTUs specialized for ESE storage may vary considerably in the structural, mechanical, and physiological properties of their components depending on their functional role and required versatility.

A power amplification dyad in seahorses

Throughout evolution, organisms repeatedly developed elastic elements to power explosive body motions, overcoming ubiquitous limits on the power capacity of fast-contracting muscles. Seahorses evolved such a latch-mediated spring-actuated (LaMSA) mechanism; however, it is unclear how this mechanism powers the two complementary functions necessary for feeding: rapidly swinging the head towards the prey, and sucking water into the mouth to entrain it. Here, we combine flow visualization and hydrodynamic modelling to estimate the net power required for accelerating the suction feeding flows in 13 fish species. We show that the mass-specific power of suction feeding in seahorses is approximately three times higher than the maximum recorded from any vertebrate muscle, resulting in suction flows that are approximately eight times faster than similar-sized fishes. Using material testing, we reveal that the rapid contraction of the sternohyoideus tendons can release approximately 72% of the power needed to accelerate the water into the mouth. We conclude that the LaMSA system in seahorses is powered by two elastic elements, the sternohyoideus and epaxial tendons. These elements jointly actuate the coordinated acceleration of the head and the fluid in front of the mouth. These findings extend the known function, capacity and design of LaMSA systems.

Muscle preactivation and the limits of muscle power output during jumping in the Cuban tree frog Osteopilus septentrionalis

Previous studies of jumping in frogs have found power outputs in excess of what is possible from direct application of muscle power and concluded that jumping requires the storage and release of elastic strain energy. Of course, the muscles must produce the work required and their power output should be consistent with known muscle properties if the total duration of muscle activity is known. Using the Cuban tree frog, Osteopilus septentrionalis, I measured jumping performance from kinematics and used EMG measurements of three major jumping muscles to determine the duration of muscle activity. Using the total mass of all the hindlimb muscles, muscle mass-specific work output up to 60 J kg-1 was recorded. Distributed over the duration of the jump, both average and peak muscle mass-specific power output increased approximately linearly with the work done, reaching values of over 750 and 2000 W kg-1, respectively. However, the muscles were activated before the jump started. Both preactivation duration and EMG amplitude increased with increasing amounts of work performed. Assuming the muscles could produce work from EMG onset until toe-off, the average muscle mass-specific power over this longer interval also increased with work done, but only up to a work output of 36 J kg-1. The mean power above this value of work was 281 W kg-1, which is approximately 65% of the estimated maximum isotonic power. Several reasons are put forward for suggesting this power output, although within the known properties of the muscles, is nevertheless an impressive achievement.

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.

Elastic recoil action amplifies jaw closing speed in an aquatic feeding salamander

Tendon springs often influence locomotion by amplifying the speed and power of limb joint rotation. However, less is known about elastic recoil action in feeding systems, particularly for small aquatic animals. Here, we ask if elastic recoil amplifies the speed of gape closing during aquatic food processing in the Axolotl (Ambystoma mexicanum). We measure activation of the adductor mandibulae externus via electromyography and strain of the jaw adductor muscle-tendon unit (MTU), and gape kinematics via fluoromicrometry. The muscle is pre-activated coincident with gape opening, which causes MTU stretch. Activation lasts significantly shorter for fish than cricket processing, and muscle shortening during MTU lengthening yields significantly greater elastic strain for cricket processing. The speed of MTU shortening, which dictates the speed of gape closing is 2.5-4.4 times greater than the speed of the initial shortening of the muscle fascicles for fish and cricket gape cycles, respectively. These data demonstrate a clear role for elastic recoil, which may be unexpected for a MTU in a feeding system of a small, aquatic animal. Amplification of jaw-closing speed resulting from elastic recoil likely confers ecological advantages in reducing prey escape risks during food processing in a dense and viscous fluid environment.

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 integration of sensory feedback in the modulation of anuran landing preparation

Controlled landing requires preparation. Mammals and bipedal birds vary how they prepare for landing by predicting the timing and magnitude of impact from the integration of visual and non-visual information. Here, we explore how the cane toad Rhinella marina - an animal that moves primarily through hopping - integrates sensory information to modulate landing preparation. Earlier work suggests that toads may modulate landing preparation using predictions of impact timing and/or magnitude based on non-visual sensory feedback during takeoff rather than visual cues about the landing itself. We disentangled takeoff and landing conditions by hopping toads off platforms of different heights while measuring electromyographic (EMG) activity of an elbow extensor (m. anconeus) and capturing high-speed images to quantify whole body and forelimb kinematics. This enabled us to test how toads integrate visual and non-visual information in landing preparation. We asked two questions: (1) when they conflict, do toads correlate landing preparation with takeoff or landing conditions? And (2) for hops with the same takeoff conditions, does visual information alter the timing of landing preparation? We found that takeoff conditions are a better predictor of the onset of landing preparation than landing conditions, but that visual information is not ignored. When hopping off higher platforms, toads start to prepare for landing later when takeoff conditions are invariant. This suggests that, unlike mammals, toads prioritize non-visual sensory feedback about takeoff conditions to coordinate landing, but that they do integrate visual information to fine-tune landing preparation.

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.

A Dynamic Simulation of Musculoskeletal Function in the Mouse Hindlimb During Trotting Locomotion

Mice are often used as animal models of various human neuromuscular diseases, and analysis of these models often requires detailed gait analysis. However, little is known of the dynamics of the mouse musculoskeletal system during locomotion. In this study, we used computer optimization procedures to create a simulation of trotting in a mouse, using a previously developed mouse hindlimb musculoskeletal model in conjunction with new experimental data, allowing muscle forces, activation patterns, and levels of mechanical work to be estimated. Analyzing musculotendon unit (MTU) mechanical work throughout the stride allowed a deeper understanding of their respective functions, with the rectus femoris MTU dominating the generation of positive and negative mechanical work during the swing and stance phases. This analysis also tested previous functional inferences of the mouse hindlimb made from anatomical data alone, such as the existence of a proximo-distal gradient of muscle function, thought to reflect adaptations for energy-efficient locomotion. The results do not strongly support the presence of this gradient within the mouse musculoskeletal system, particularly given relatively high negative net work output from the ankle plantarflexor MTUs, although more detailed simulations could test this further. This modeling analysis lays a foundation for future studies of the control of vertebrate movement through the development of neuromechanical simulations.

Effect of a prehop on the muscle-tendon interaction during vertical jumps

Many movements use stretch-shortening cycles of a muscle-tendon unit (MTU) for storing and releasing elastic energy. The required stretching of medial gastrocnemius (MG) tendinous tissue during jumps, however, requires large length changes of the muscle fascicles because of the lack of MTU length changes. This has a negative impact on the force-generating capacity of the muscle fascicles. The purpose of this study was to induce a MG MTU stretch before shortening by adding a prehop to the squat jump. Eleven well-trained athletes specialized in jumping performed a prehop squat jump (PHSJ) and a standard squat jump (SSJ). Kinematic data were collected using a 3D motion capture system and were used in a musculoskeletal model to calculate MTU lengths. B-mode ultrasonography of the MG was used to measure fascicle length and pennation angle during the jumps. By combining the muscle-tendon unit lengths, fascicle lengths, and pennation angles, the stretch and recoil of the series elastic element of MG were calculated using a simple geometric muscle-tendon model. Our results show less length changes of the muscle fascicles during the upward motion and lower maximal shortening velocities, increasing the moment-generating capacity of the plantar flexors, reflected in the higher ankle joint moment in the PHSJ compared with the SSJ. Although muscle-tendon interaction during the PHSJ was more optimal, athletes were not able to increase their jump height compared with the SSJ. NEW & NOTEWORTHY This is the first study that aimed to improve the muscle-tendon interaction in squat jumping. We effectively introduced a stretch to the medial gastrocnemius muscle-tendon unit resulting in lower maximal shortening velocities and thus an increase in the plantar flexor force-generating capacity, reflected in the higher ankle joint moment in the prehop squat jump compared with the standard squat jump. Here, we demonstrate an effective method for mechanical optimization of the muscle-tendon interaction in the medial gastrocnemius during squat jumping.

Frog tendon structure and its relationship with locomotor modes

Tendon collagen fibrils are the basic force-transmitting units of the tendon. Yet, surprisingly little is known about the diversity in tendon anatomy and ultrastructure, and the possible relationships between this diversity and locomotor modes utilized. Our main objectives were to investigate: (a) the ultra-structural anatomy of the tendons in the digits of frogs; (b) the diversity of collagen fibril diameters across frogs with different locomotor modes; (c) the relationship between morphology, as expressed by the morphology of collagen fibrils and tendons, and locomotor modes. To assess the relationship between morphology and the locomotor modes of the sampled taxa we performed a principal component analysis considering body length, fibrillar cross sectional area (CSA) and tendon CSA. A MANOVA showed that differences between species with different locomotor modes were significant with collagen fibril diameter being the discriminating factor. Overall, our data related the greatest collagen fibril diameter to the most demanding locomotor modes, conversely, the smallest collagen fibril CSA and the highest tendon CSA were observed in animals showing a hopping locomotion requiring likely little absorption of landing forces given the short jump distances.

Phylogenetic patterns and correlation of key structures for jumping: bone crests and cross-sectional areas of muscles in Leptodactylus (Anura, Leptodactylidae)

Anurans are characterized by their saltatory mode of locomotion, which is associated with a specific morphology. The coordinated action of the muscles and bones of the pelvic girdle is key to the transmission of the force of the hindlimbs to the axial skeleton during jumping. Two features are critical for optimal locomotory performance: the cross-sectional area of muscle and the bone crest attachment sites. The first character is a proxy of the force exerted by the muscle, whereas the crests are muscle attachments sites related to muscle force. The provisory relationship between these features has previously been identified and bone crest size can be used to infer the magnitude and, therefore, muscle force in fossils records. In this work, we explore the correlation between the cross-sectional area of essential muscles to the jumping mechanism (longissimus dorsi, extensor iliotibialis B, tenuissimus, puboischiofemoralis internus B, coccygeo-sacralis and coccygeo-iliacus) and the bone crests where these muscles are inserted (dorsal tubercle, dorsal crest and urostylar crest) in species of the genus Leptodactylus. This genus, along with other leptodactylids, exhibits a diversity of locomotor modes, including jumping, hopping, swimming and burrowing. We therefore analyzed the morphometric variation in the two features, cross-sectional area and bone crest area, expecting a correlation with different locomotor types. Our results showed: (i) a correlation between the urostylar crest and the cross-sectional area of the related muscles; (ii) that the bone crest surface area of urostyle and ilium and the cross-sectional area of the corresponding muscles can be utilized to infer locomotor faculties in leptodactylid frogs; and (iii) that the evolution of both characters demonstrates a general tendency from lower values in leptodactylid ancestors to higher values in the Leptodactylus genus. The results attest to the importance of the comparison of current ecological and phylogenetic analogues as they allow us to infer functionality and behavior in fossil and extant groups based on skeletal evidence. Phylogenetic patterns in character evolution and their correlation with locomotory types could imply that functional restrictions are also inherited in leptodactylid.

Scaling of work and power in a locomotor muscle of a frog

Muscle work and power are important determinants of movement performance in animals. How these muscle properties scale determines, in part, the scaling of performance during movements, such as jump height or distance. Muscle-mass-specific work is predicted to remain constant across a range of scales, assuming geometric similarity, while muscle-mass-specific power is expected to decrease with increasing scale. We tested these predictions by examining muscle morphology and contractile properties of plantaris muscles from frogs ranging in mass from 1.28 to 20.60 g. Scaling of muscle work and power was examined using both linear regression on log₁₀-transformed data (LR) and non-linear regressions on untransformed data (NLR). Results depended on the method of regression not because of large changes in scaling slopes, but because of changing levels of statistical significance using corrections for multiple tests, demonstrating the importance of careful consideration of statistical methods when analyzing patterns of scaling. In LR, muscle-mass-specific work decreased with increasing scale, but an accompanying positive allometry of muscle mass predicts constant movement performance at all scales. These relationships were non-significant in NLR, though scaling with geometric similarity also predicts constant jump performance across scales, because of proportional increases in available muscle energy and body mass. Both intrinsic shortening velocity and muscle-mass-specific power were positively allometric in both types of analysis. Nonetheless, scale accounts for little variation in contractile properties overall over the range examined, indicating that other sources of intraspecific variation may be more important in determining muscle performance and its effects on movement.

Dynamic Musculoskeletal Functional Morphology: Integrating diceCT and XROMM

The tradeoff between force and velocity in skeletal muscle is a fundamental constraint on vertebrate musculoskeletal design (form:function relationships). Understanding how and why different lineages address this biomechanical problem is an important goal of vertebrate musculoskeletal functional morphology. Our ability to answer questions about the different solutions to this tradeoff has been significantly improved by recent advances in techniques for quantifying musculoskeletal morphology and movement. Herein, we have three objectives: (1) review the morphological and physiological parameters that affect muscle function and how these parameters interact; (2) discuss the necessity of integrating morphological and physiological lines of evidence to understand muscle function and the new, high resolution imaging technologies that do so; and (3) present a method that integrates high spatiotemporal resolution motion capture (XROMM, including its corollary fluoromicrometry), high resolution soft tissue imaging (diceCT), and electromyography to study musculoskeletal dynamics in vivo. The method is demonstrated using a case study of in vivo primate hyolingual biomechanics during chewing and swallowing. A sensitivity analysis demonstrates that small deviations in reconstructed hyoid muscle attachment site location introduce an average error of 13.2% to in vivo muscle kinematics. The observed hyoid and muscle kinematics suggest that hyoid elevation is produced by multiple muscles and that fascicle rotation and tendon strain decouple fascicle strain from hyoid movement and whole muscle length. Lastly, we highlight current limitations of these techniques, some of which will likely soon be overcome through methodological improvements, and some of which are inherent. Anat Rec, 301:378-406, 2018. © 2018 Wiley Periodicals, Inc.

Enhancement of muscle and locomotor performance by a series compliance: A mechanistic simulation study

The objective was to better understand how a series compliance alters contraction kinetics and power output of muscle to enhance the work done on a load. A mathematical model was created in which a gravitational point load was connected via a linear spring to a muscle (based on the contractile properties of the sartorius of leopard frogs, Rana pipiens). The model explored the effects of load mass, tendon compliance, and delay between onset of contraction and release of the load (catch) on lift height and power output as measures of performance. Series compliance resulted in increased lift height over a relatively narrow range of compliances, and the effect was quite modest without an imposed catch mechanism unless the load was unrealistically small. Peak power of the muscle-tendon complex could be augmented up to four times that produced with a muscle alone, however, lift height was not predicted by peak power. Rather, lift height was improved as a result of the compliance synchronizing the time courses of muscle force and shortening velocity, in particular by stabilizing shortening velocity such that muscle power was sustained rather than rising and immediately falling. With a catch mechanism, enhanced performance resulted largely from energy storage in the compliance during the period of catch, rather than increased time for muscle activation before movement commenced. However, series compliance introduced a trade-off between work done before versus after release of the catch. Thus, the ability of tendons to enhance locomotor performance (i.e. increase the work done by muscle) appears dependent not only on their established role in storing energy and increasing power, but also on their ability to modulate the kinetics of muscle contraction such that power is sustained over more of the contraction, and maximizing the balance of work done before versus after release of a catch.

The diversity and evolution of locomotor muscle properties in anurans

Anuran jumping is a model system for linking muscle physiology to organismal performance. However, anuran species display substantial diversity in their locomotion, with some species performing powerful leaps from riverbanks or tree branches, while other species move predominantly via swimming, short hops or even diagonal-sequence gaits. Furthermore, many anurans with similar locomotion and morphology are actually convergent (e.g. multiple independent evolutions of 'tree frogs'), while closely related species may differ drastically, as with the walking toad (Melanophryniscus stelzneri) and bullfrog-like river toad (Phrynoides aspera) compared with other Bufonid toads. These multiple independent evolutionary changes in locomotion allow us to test the hypothesis that evolutionary increases in locomotor performance will be linked to the evolution of faster, high-power muscles. I tested the jumping, swimming and walking (when applicable) performance of 14 species of anurans and one salamander, followed by measurement of the contractile properties of the semimembranosus and plantaris longus muscles and anatomical measurements, using phylogenetic comparative methods. I found that increased jumping performance correlated to muscle contractile properties associated with muscle speed (e.g. time to peak tetanus, maximum shortening speed, peak isotonic power), and was tightly linked to relevant anatomical traits (e.g. leg length, muscle mass). Swimming performance was not correlated to jumping, and was correlated with fewer anatomical and muscular variables. Thus, muscle properties evolve along with changes in anatomy to produce differences in overall locomotor performance.

Network architecture associated with the highly specialized hindlimb of frogs

Network analyses have been increasingly used in the context of comparative vertebrate morphology. The structural units of the vertebrate body are treated as discrete elements (nodes) of a network, whose interactions at their physical contacts (links) determine the phenotypic modules. Here, we use the network approach to study the organization of the locomotor system underlying the hindlimb of frogs. Nodes correspond to fibrous knots, skeletal and muscular units. Edges encode the ligamentous and monoaxial tendinous connections in addition to joints. Our main hypotheses are that: (1) the higher centrality scores (measured as betweenness) are recorded for fibrous elements belonging to the connective system, (2) the organization of the musculoskeletal network belongs to a non-trivial modular architecture and (3) the modules in the hindlimb reflect functional and/or developmental constraints. We confirm all our hypotheses except for the first one, since bones overpass the fibrous knots in terms of centrality. Functionally, there is a correlation between the proximal-to-distal succession of modules and the progressive recruitment of elements involved with the motion of joints during jumping. From a developmental perspective, there is a correspondence between the order of the betweenness scores and the ontogenetic chronology of hindlimbs in tetrapods. Modular architecture seems to be a successful organization, providing of the building blocks on which evolution forges the many different functional specializations that organisms exploit.

Effects of temperature and force requirements on muscle work and power output

Performance of muscle-powered movements depends on temperature through its effects on muscle contractile properties. In vitro stimulation of Cuban treefrog (Osteopilus septentrionalis) plantaris muscles reveals that interactions between force and temperature affect the mechanical work of muscle. At low temperatures (9-17°C), muscle work depends on temperature when shortening at any force, and temperature effects are greater at higher forces. At warmer temperatures (13-21°C), muscle work depends on temperature when shortening with intermediate and high forces (≥30% peak isometric tetanic force). Shortening velocity is most strongly affected by temperature at low temperatures and high forces. Power is also most strongly affected at low temperature intervals, but this effect is minimized at intermediate forces. Effects of temperature on muscle force explain these interactions; force production decreases at lower temperatures, increasing the challenge of moving a constant force relative to the muscle's capacity. These results suggest that animal performance that requires muscles to do work with low forces relative to a muscle's maximum force production will be robust to temperature changes, and this effect should be true whether muscle acts directly or through elastic-recoil mechanisms and whether force is prescribed (i.e. internal) or variable (i.e. external). Conversely, performance requiring muscles to shorten with relatively large forces is expected to be more sensitive to temperature changes.

Inverse dynamic modelling of jumping in the red-legged running frog, Kassina maculata

Although the red-legged running frog, Kassina maculata, is secondarily a walker/runner, it retains the capacity for multiple locomotor modes, including jumping at a wide range of angles (nearly 70 deg). Using simultaneous hind limb kinematics and single-foot ground reaction forces, we performed inverse dynamics analyses to calculate moment arms and torques about the hind limb joints during jumping at different angles in K. maculata. We show that forward thrust is generated primarily at the hip and ankle, while body elevation is primarily driven by the ankle. Steeper jumps are achieved by increased thrust at the hip and ankle and greater downward rotation of the distal limb segments. Because of its proximity to the GRF vector, knee posture appears to be important in controlling torque directions about this joint and, potentially, torque magnitudes at more distal joints. Other factors correlated with higher jump angles include increased body angle in the preparatory phase, faster joint openings and increased joint excursion, higher ventrally directed force, and greater acceleration and velocity. Finally, we demonstrate that jumping performance in K. maculata does not appear to be compromised by presumed adaptation to walking/running. Our results provide new insights into how frogs engage in a wide range of locomotor behaviours and the multi-functionality of anuran limbs.

Movements of vastly different performance have similar underlying muscle physiology

Many animals use elastic-recoil mechanisms to power extreme movements, achieving levels of performance that would not be possible using muscle power alone. Contractile performance of vertebrate muscle depends strongly on temperature, but the release of energy from elastic structures is far less thermally dependent, thus elastic recoil confers thermal robustness to whole-animal performance. Here we explore the role that muscle contractile properties play in the differences in performance and thermal robustness between elastic and non-elastic systems by examining muscle from two species of plethodontid salamanders that use elastically powered tongue projection to capture prey and one that uses non-elastic tongue projection. In species with elastic mechanisms, tongue projection is characterized by higher mechanical power output and thermal robustness compared with tongue projection of closely related genera with non-elastic mechanisms. In vitro and in situ muscle experiments reveal that species differ in their muscle contractile properties, but these patterns do not predict the performance differences between elastic and non-elastic tongue projection. Overall, salamander tongue muscles are similar to other vertebrate muscles in contractile performance and thermal sensitivity. We conclude that changes in the tongue-projection mechanism, specifically the elaboration of elastic structures, are responsible for high performance and thermal robustness in species with elastic tongue projection. This suggests that the evolution of high-performance and thermally robust elastic-recoil mechanisms can occur via relatively simple changes to morphology, while muscle contractile properties remain relatively unchanged.

Geographical variation in limb muscle mass of the Andrew’s toad (Bufo andrewsi)

Muscles are vital for the process of movement, mating and escape of predators in amphibians. During evolution, the morphological and genetic characteristics as well as the size of muscles in species will change to adapt different environments. Theory predicts that low male-male competition in high-altitude/latitude selects for small limb muscles. Here, we used the Andrew’s toad (Bufo andrewsi) as a model animal to test this prediction by analyzing geographical variation in the mass of limb muscles across nine populations from the Hengduan Mountains in China. Inconsistent with the prediction, we found that latitude and altitude did not affect the relative mass of total combined limb muscles and mass of combined hindlimb muscles among populations. Meanwhile, the relative mass of combined forelimb muscles, the two forelimb muscles (flexor carpi radialis and extensor carpi radialis) and the four hindlimb muscles (e.g. biceps femoris, semimebranous, semitendinosus and peroneus) was lowest in middle latitude and largest in low latitude whereas gracilis minor was largest in high latitudes. However, we did not find any correlations between the two forelimb muscles and the four hindlimb muscles and altitude. Our findings suggest that combined forelimb muscles, flexor carpi radialis, extensor carpi radialis, biceps femoris, semimebranous, semitendinosus and peroneus are largest in low latitudes due to pressures of mate competition.

Robust jumping performance and elastic energy recovery from compliant perches in tree frogs

Arboreal animals often move on compliant branches, which may deform substantially under loads, absorbing energy. Energy stored in a compliant substrate may be returned to the animal or it may be lost. In all cases studied so far, animals jumping from a static start lose all of the energy imparted to compliant substrates and performance is reduced. Cuban tree frogs (Osteopilus septentrionalis) are particularly capable arboreal jumpers, and we hypothesized that these animals would be able to recover energy from perches of varying compliance. In spite of large deflections of the perches and consequent substantial energy absorption, frogs were able to regain some of the energy lost to the perch during the recoil. Takeoff velocity was robust to changes in compliance, but was lower than when jumping from flat surfaces. This highlights the ability of animals to minimize energy loss and maintain dependable performance on challenging substrates via behavioral changes.

Power amplification in an isolated muscle-tendon unit is load dependent

During rapid movements, tendons can act like springs, temporarily storing work done by muscles and then releasing it to power body movements. For some activities, such as frog jumping, energy is released from tendon much more rapidly than it is stored, thus amplifying muscle power output. The period during which energy is loaded into a tendon by muscle work may be aided by a catch mechanism that restricts motion, but theoretical studies indicate that power can be amplified in a muscle-tendon load system even in the absence of a catch. To explore the limits of power amplification with and without a catch, we studied the bullfrog plantaris muscle-tendon during in vitro contractions. A novel servomotor controller allowed us to measure muscle-tendon unit (MTU) mechanical behavior during contractions against a variety of simulated inertial-gravitational loads, ranging from zero to 1× the peak isometric force of the muscle. Power output of the MTU system was load dependent and power amplification occurred only at intermediate loads, reaching ∼1.3× the peak isotonic power output of the muscle. With a simulated anatomical catch mechanism in place, the highest power amplification occurred at the lowest loads, with a maximum amplification of more than 4× peak isotonic muscle power. At higher loads, the benefits of a catch for MTU performance diminished sharply, suggesting that power amplification >2.5× may come at the expense of net mechanical work delivered to the load.

The mechanics of elastic loading and recoil in anuran jumping

Many animals use catapult mechanisms to produce extremely rapid movements for escape or prey capture, resulting in power outputs far beyond the limits of muscle. In these catapults, muscle contraction loads elastic structures, which then recoil to release the stored energy extremely rapidly. Many arthropods employ anatomical ‘catch mechanisms’ to lock the joint in place during the loading period, which can then be released to allow joint motion via elastic recoil. Jumping vertebrates lack a clear anatomical catch, yet face the same requirement to load the elastic structure prior to movement. There are several potential mechanisms to allow loading of vertebrate elastic structures, including the gravitational load of the body, a variable mechanical advantage, and moments generated by the musculature of proximal joints. To test these hypothesized mechanisms, we collected simultaneous 3D kinematics via X-ray Reconstruction of Moving Morphology (XROMM) and single-foot forces during the jumps of three Rana pipiens. We calculated joint mechanical advantage, moment and power using inverse dynamics at the ankle, knee, hip and ilio-sacral joints. We found that the increasing proximal joint moments early in the jump allowed for high ankle muscle forces and elastic pre-loading, and the subsequent reduction in these moments allowed the ankle to extend using elastic recoil. Mechanical advantage also changed throughout the jump, with the muscle contracting against a poor mechanical advantage early in the jump during loading and a higher mechanical advantage late in the jump during recoil. These ‘dynamic catch mechanisms’ serve to resist joint motion during elastic loading, then allow it during elastic recoil, functioning as a catch mechanism based on the balance and orientation of forces throughout the limb rather than an anatomical catch.

Mechanical output in jumps of marmosets (Callithrix jacchus)

In this study we determined the mechanical output of common marmosets (Callithrix jacchus) during jumping. Vertical ground reaction forces were measured in 18 animals while they jumped from an instrumented crossbar to a crossbar located 70 cm higher. From the vertical force time histories, we calculated the rate of change of mechanical energy of the centre of mass (dE/dt). The mean value of dE/dt during the push-off amounted to 51.8±6.2 W kg(-1) body mass, and the peak value to 116.4±17.6 W kg(-1) body mass. We used these values in combination with masses of leg muscles, determined in two specimens, to estimate mean and peak values of dE/dt of 430 and 970 W kg(-1) muscle, respectively. These values are higher than values reported in the literature for jumps of humans and bonobos, but smaller than those of jumps of bushbabies. Surprisingly, the mean value of dE/dt of 430 W kg(-1) muscle was close to the maximal power output of 516 W kg(-1) muscle reported in the literature for isokinetic contractions of rat medial gastrocnemius, one of the fastest mammalian muscles. Further study of the force-velocity relationship of muscle tissue of small primates is indicated.

Phylogenetic patterns of skeletal morphometrics and pelvic traits in relation to locomotor mode in frogs

Frogs are one of the most speciose groups of vertebrate tetrapods (> 6200sp) with a diverse array of locomotor behaviours. Despite the impressive diversity in frog locomotor behaviours, there remains a paucity of information on the relationship between skeletal variation and locomotor mode in frogs and the evolutionary patterns in which these relationships are framed across the frog phylogeny. Our current understanding of the evolution of frog locomotion shows that hopping transitioned into jumping within the Neobatrachia where a variety of pelvic/hindlimb length patterns and locomotor niches have appeared, but this has yet to be studied over a broad taxonomic sample of frogs. Although limb length remains as the primary predictor of leaping performance, pelvic and sacral morphometrics have not been quantified in relation to limb proportions, body size and locomotor mode and previous studies have not sampled more than 24 families. We present a large-scale phylogenetic comparison of skeletal morphometrics in relation to locomotor mode in 188 genera from 37 families. Osteological variation in limb/pelvic girdle morphometrics and pelvic traits that are posited to be associated with locomotor mode were analysed to identify which aspects of the frog skeleton are the best descriptors of locomotor mode. Our results, contrary to previous work, reveal that the greatest axis of variation in frogs is represented by the shape of the sacrum with two pelvic morphologies evident in qualitative and quantitative ancestral trait reconstructions. Limb morphology was not significantly different across most locomotor modes, but we identified several outliers in hindlimb phylomorphospace. Patterns of sacral evolution together with hindlimb length outliers reveal how the general bauplan of this successful group of vertebrate tetrapods is constrained, has radiated and has converged on certain phenotypes to fill an array of locomotor modes.

Evidence for a vertebrate catapult: elastic energy storage in the plantaris tendon during frog jumping

Anuran jumping is one of the most powerful accelerations in vertebrate locomotion. Several species are hypothesized to use a catapult-like mechanism to store and rapidly release elastic energy, producing power outputs far beyond the capability of muscle. Most evidence for this mechanism comes from measurements of whole-body power output; the decoupling of joint motion and muscle shortening expected in a catapult-like mechanism has not been demonstrated. We used high-speed marker-based biplanar X-ray cinefluoroscopy to quantify plantaris muscle fascicle strain and ankle joint motion in frogs in order to test for two hallmarks of a catapult mechanism: (i) shortening of fascicles prior to joint movement (during tendon stretch), and (ii) rapid joint movement during the jump without rapid muscle-shortening (during tendon recoil). During all jumps, muscle fascicles shortened by an average of 7.8 per cent (54% of total strain) prior to joint movement, stretching the tendon. The subsequent period of initial joint movement and high joint angular acceleration occurred with minimal muscle fascicle length change, consistent with the recoil of the elastic tendon. These data support the plantaris longus tendon as a site of elastic energy storage during frog jumping, and demonstrate that catapult mechanisms may be employed even in sub-maximal jumps.

Evidence for a vertebrate catapult: elastic energy storage in the plantaris tendon during frog jumping

Anuran jumping is one of the most powerful accelerations in vertebrate locomotion. Several species are hypothesized to use a catapult-like mechanism to store and rapidly release elastic energy, producing power outputs far beyond the capability of muscle. Most evidence for this mechanism comes from measurements of whole-body power output; the decoupling of joint motion and muscle shortening expected in a catapult-like mechanism has not been demonstrated. We used high-speed marker-based biplanar X-ray cinefluoroscopy to quantify plantaris muscle fascicle strain and ankle joint motion in frogs in order to test for two hallmarks of a catapult mechanism: (i) shortening of fascicles prior to joint movement (during tendon stretch), and (ii) rapid joint movement during the jump without rapid muscle-shortening (during tendon recoil). During all jumps, muscle fascicles shortened by an average of 7.8 per cent (54% of total strain) prior to joint movement, stretching the tendon. The subsequent period of initial joint movement and high joint angular acceleration occurred with minimal muscle fascicle length change, consistent with the recoil of the elastic tendon. These data support the plantaris longus tendon as a site of elastic energy storage during frog jumping, and demonstrate that catapult mechanisms may be employed even in sub-maximal jumps.

Muscle power attenuation by tendon during energy dissipation

An important function of skeletal muscle is deceleration via active muscle fascicle lengthening, which dissipates movement energy. The mechanical interplay between muscle contraction and tendon elasticity is critical when muscles produce energy. However, the role of tendon elasticity during muscular energy dissipation remains unknown. We tested the hypothesis that tendon elasticity functions as a mechanical buffer, preventing high (and probably damaging) velocities and powers during active muscle fascicle lengthening. We directly measured lateral gastrocnemius muscle force and length in wild turkeys during controlled landings requiring rapid energy dissipation. Muscle-tendon unit (MTU) strain was measured via video kinematics, independent of muscle fascicle strain (measured via sonomicrometry). We found that rapid MTU lengthening immediately following impact involved little or no muscle fascicle lengthening. Therefore, joint flexion had to be accommodated by tendon stretch. After the early contact period, muscle fascicles lengthened and absorbed energy. This late lengthening occurred after most of the joint flexion, and was thus mainly driven by tendon recoil. Temporary tendon energy storage led to a significant reduction in muscle fascicle lengthening velocity and the rate of energy absorption. We conclude that tendons function as power attenuators that probably protect muscles against damage from rapid and forceful lengthening during energy dissipation.

Network reconfiguration and neuronal plasticity in rhythm-generating networks

Neuronal networks are highly plastic and reconfigure in a state-dependent manner. The plasticity at the network level emerges through multiple intrinsic and synaptic membrane properties that imbue neurons and their interactions with numerous nonlinear properties. These properties are continuously regulated by neuromodulators and homeostatic mechanisms that are critical to maintain not only network stability and also adapt networks in a short- and long-term manner to changes in behavioral, developmental, metabolic, and environmental conditions. This review provides concrete examples from neuronal networks in invertebrates and vertebrates, and illustrates that the concepts and rules that govern neuronal networks and behaviors are universal.

Mechanics, modulation and modelling: how muscles actuate and control movement

Animal movement is often complex, unsteady and variable. The critical role of muscles in animal movement has captivated scientists for over 300 years. Despite this, emerging techniques and ideas are still shaping and advancing the field. For example, sonomicrometry and ultrasound techniques have enhanced our ability to quantify muscle length changes under in vivo conditions. Robotics and musculoskeletal models have benefited from improved computational tools and have enhanced our ability to understand muscle function in relation to movement by allowing one to simulate muscle-tendon dynamics under realistic conditions. The past decade, in particular, has seen a rapid advancement in technology and shifts in paradigms related to muscle function. In addition, there has been an increased focus on muscle function in relation to the complex locomotor behaviours, rather than relatively simple (and steady) behaviours. Thus, this Theme Issue will explore integrative aspects of muscle function in relation to diverse locomotor behaviours such as swimming, jumping, hopping, running, flying, moving over obstacles and transitioning between environments. Studies of walking and running have particular relevance to clinical aspects of human movement and sport. This Theme Issue includes contributions from scientists working on diverse taxa, ranging from humans to insects. In addition to contributions addressing locomotion in various taxa, several manuscripts will focus on recent advances in neuromuscular control and modulation during complex behaviours. Finally, some of the contributions address recent advances in biomechanical modelling and powered prostheses. We hope that our comprehensive and integrative Theme Issue will form the foundation for future work in the fields of neuromuscular mechanics and locomotion.