Force per cross-sectional area from molecules to muscles: a general property of biological motors

The force-calcium relationship is not affected by the cross-sectional area of skinned muscle fibres from rat soleus

Proportionality between force and muscle cross-sectional area (CSA) is a foundational principle in muscle mechanics. However, CSA-normalized force (known as specific force) is often lower in fibres with large CSAs compared to fibres with small CSAs from the same sample population. Many physiological mechanisms proposed to account for CSA-dependence of specific force converge on the requirement for fibre CSA to impact the relationship between force and the concentration of force-activating calcium. To determine if features of the force-calcium relationship exhibited CSA-dependence in mammalian skinned muscle fibres, force-calcium relationships were generated for 85 skinned slow soleus fibres of male Sprague-Dawley rats (n = 54 rats, 1-5 fibres per rat, age = 24 weeks, experimental temperature = 18 °C) and fit using the Hill equation. Fibres were separated into quartiles based on their CSA and then compared. Despite specific force being 46 % higher (P < 0.01) in the smallest (160 ± 51 mN∙mm-2; CSA = 3649 ± 708 μm2) compared to the largest (110 ± 20 mN∙mm-2; CSA = 8671 ± 1319 μm2) quartile, neither the calcium-sensitivity of force production (pCa50; P = 0.47; F(dFn = 3,DFd = 81) = 0.86) nor the Hill coefficient (nH; P = 0.38; F(dFn = 3,DFd = 81) = 1.03) differed significantly between quartiles (smallest quartile: pCa50 = 6.015 ± 0.097, nH = 1.80 ± 0.69; largest quartile: pCa50 = 6.062 ± 0.097, nH = 1.63 ± 0.32). Force plateaus were observed at higher calcium concentrations in all fibres indicating that calcium was adequate for full activation. These findings add to the body of evidence suggesting that CSA-dependence of specific force in mammalian skinned fibres is an artifact attributable to the considerable imprecision associated with the assessment of fibre CSA, and not a physiological phenomenon which would require consideration when modeling muscle force output.

The force has limits: Molecular motors in robotics

Molecular motors generate force to individually power molecular machines or collectively drive macroscopic actuators. The force output of molecular and macroscale motors appears to be constrained by the same scaling law relating motor force and mass. Here, potential origins of these universal performance characteristics are discussed and the implications examined.

Beyond power limits: the kinetic energy capacity of skeletal muscle

Muscle is the universal agent of animal movement, and limits to muscle performance are therefore an integral aspect of animal behaviour, ecology and evolution. A mechanical perspective on movement makes it amenable to analysis from first principles, and so brings the seeming certitude of simple physical laws to the challenging comparative study of complex biological systems. Early contributions on movement biomechanics considered muscle energy output to be limited by muscle work capacity, Wmax; triggered by seminal work in the late 1960s, it is now held broadly that a complete analysis of muscle energy output must also consider muscle power capacity, for no unit of work can be delivered in arbitrarily brief time. Here, we adopt a critical stance towards this paradigmatic notion of a power limit, and argue that the alternative constraint to muscle energy output is imposed instead by a characteristic kinetic energy capacity, Kmax, dictated by the maximum speed with which the actuating muscle can shorten. The two critical energies can now be directly compared, and define the physiological similarity index, Γ=Kmax/Wmax. It is the explanatory power of this comparison that lends weight to a shift in perspective from muscle power to kinetic energy capacity, as is argued through a series of illustrative examples. Γ emerges as an important dimensionless number in musculoskeletal dynamics, and sparks novel hypotheses on functional adaptations in musculoskeletal 'design' that depart from the parsimonious evolutionary null hypothesis of geometric similarity.

Reconsidering assumptions in the analysis of muscle fibre cross-sectional area

Cross-sectional area (CSA) is a fundamental variable in characterizing muscle mechanical properties. Typically, the CSA of a single muscle fibre is assessed by measuring either one or two diameters, and assuming the cross-section is either circular or elliptical in shape. However, fibre cross-sections have irregular shapes. The accuracy and precision of CSAs determined using circular and elliptical shape assumptions are unclear for mammalian skinned muscle fibres. Second harmonic generation imaging of skinned rabbit soleus fibres revealed that the circular assumption overstated real CSA by 5.3±25.9% whereas the elliptical assumption overstated real CSA by 2.8±6.9%. A preferred rotational alignment can bias the circular assumption, as real CSA was overstated by 22.1±24.8% when using the larger fibre diameter and understated by 11.4±13% when using the smaller fibre diameter. With 73% lower variable error and reduced bias, the elliptical assumption is superior to the circular assumption when assessing the CSA of skinned mammalian fibres.

Morphology and Mechanics of the Fin Whale Esophagus: The Key to Fast Processing of Large Food Volumes by Rorquals

Lunge feeding rorqual whales feed by engulfing a volume of prey laden water that can be as large as their own body. Multiple feeding lunges occur during a single foraging dive and the time between each lunge can be as short as 30 s (Goldbogen et al. 2013). During this short inter-lunge time, water is filtered out through baleen to concentrate prey in the oral cavity, and then the prey is swallowed prior to initiating the next lunge. Prey density in the ocean varies greatly, and despite the potential of swallowing a massive volume of concentrated prey as a slurry, the esophagus of rorqual whales has been anecdotally described as unexpectedly narrow with a limited capacity to expand. How rorquals swallow large quantities of food down a narrow esophagus during a limited inter-lunge time remains unknown. Here, we show that the small diameter muscular esophagus in the fin whale is optimized to transport a slurry of food to the stomach. A thick wall of striated muscle occurs at the pharyngeal end of the esophagus which, together with the muscular wall of the pharynx, may generate a pressure head for transporting the food down the esophagus to the stomach as a continuous stream rather than separating the food into individual boluses swallowed separately. This simple model is consistent with estimates of prey density and stomach capacity. Rorquals may be the only animals that capture a volume of food too large to swallow as a single intact bolus without oral processing, so the adaptations of the esophagus are imperative for transporting these large volumes of concentrated food to the stomach during a time-limited dive involving multiple lunges.

Elastic energy-recycling actuators for efficient robots

Electric motors are widely used in robots but waste energy in many applications. We introduce an elastic energy-recycling actuator that maintains the versatility of motors while improving energy efficiency in cyclic tasks. The actuator comprises a motor in parallel with an array of springs that can be individually engaged and disengaged, while retaining stored energy, by pairs of low-power electroadhesive clutches. We developed a prototype actuator and tested it in five repetitive tasks with features common in robotic applications but difficult to perform efficiently. The actuator reduced power consumption by at least 50% in all cases and by 97% in the best case. Elastic energy recovery, controlled by low-power clutches, can improve the efficiency of mobile robots, assistive devices, and other engineered systems.

Dynamic similarity and the peculiar allometry of maximum running speed

Animal performance fundamentally influences behaviour, ecology, and evolution. It typically varies monotonously with size. A notable exception is maximum running speed; the fastest animals are of intermediate size. Here we show that this peculiar allometry results from the competition between two musculoskeletal constraints: the kinetic energy capacity, which dominates in small animals, and the work capacity, which reigns supreme in large animals. The ratio of both capacities defines the physiological similarity index Γ, a dimensionless number akin to the Reynolds number in fluid mechanics. The scaling of Γ indicates a transition from a dominance of muscle forces to a dominance of inertial forces as animals grow in size; its magnitude defines conditions of "dynamic similarity" that enable comparison and estimates of locomotor performance across extant and extinct animals; and the physical parameters that define it highlight opportunities for adaptations in musculoskeletal "design" that depart from the eternal null hypothesis of geometric similarity. The physiological similarity index challenges the Froude number as prevailing dynamic similarity condition, reveals that the differential growth of muscle and weight forces central to classic scaling theory is of secondary importance for the majority of terrestrial animals, and suggests avenues for comparative analyses of locomotor systems.

Probiotics Attenuate Myopathic Changes in Aging Rats via Activation of the Myogenic Stellate Cells

Aging represents a complex biological process associated with decline in skeletal muscle functions. Aging impairs satellite cells that serve as muscle progenitor cells. Probiotic supplementation may have many beneficial effects via various mechanisms. We examined the possible effects of probiotics in stimulating the proliferation of myogenic stellate cells in aging rats. Twenty-four male albino Sprague-Dawley rats were classified equally into four groups: adult control, old control, adult + probiotics, and old + probiotics. Probiotics (Lactobacillus LB) were administered gavage at a dose of 1 ml (1 × 109 CFU/ml/day) for 4 weeks. A significant increase in the relative gastrocnemius weight ratio and improvement of contractile parameters was detected in the old + probiotics group (0.6 ± 0.01) compared to the old control group (0.47 ± 0.01; P < 0.001). Probiotics significantly upregulated the activities of GSH, while NO and MDA were markedly decreased compared to control groups (P ≤ 0.001). Also, probiotics increased the mRNA and protein expressions of myogenin and CD34 (P < 0.05) as determined by real-time PCR and immunohistochemistry. Moreover, the old + probiotics group showed apparent restoration of the connective tissue spaces, reflecting the all-beneficial effects of probiotics. Our findings indicated that probiotics attenuated myopathic changes in aging rats probably through activation of the myogenic stellate cells. Probiotics improved the muscle weight, function, antioxidant activity, and myogenic transcription factors of the skeletal muscle.

Assumptions about the cross-sectional shape of skinned muscle fibers can distort the relationship between muscle force and cross-sectional area

Comparisons of muscle force output are often performed after normalization to muscle physiological cross-sectional area (CSA). Differences in force per CSA (i.e., specific force) suggest the presence of physiological differences in contractile function. Permeabilized mammalian skeletal muscle fibers frequently exhibit substantial declines in specific force with increasing CSA, suggesting that smaller fibers are intrinsically stronger than larger fibers of the same group. However, the potential for CSA assessment error to account for CSA-dependent differences in specific force has not received adequate attention. Assessment of fiber CSA typically involves measurement of fiber width and perhaps also height, and CSA is calculated by assuming the cross sections are either circular or elliptical with major and minor axes aligned with the optical measurement system. Differences between the assumed and real cross-sectional shapes would cause variability in the ratio of assessed CSA (aCSA) to real CSA (rCSA). This variability can insidiously bias aCSA such that large aCSAs typically overstate rCSAs of the fibers they represent, and small aCSAs typically understate the rCSAs of the fibers they represent. As aCSA is the denominator for the specific force calculation, scatterplots of specific force versus aCSA would be expected to show declines in specific force as aCSA increases without a corresponding effect in a scatterplot of specific force versus rCSA. When comparing active and passive muscle forces between data subsets defined by aCSA, the impact of CSA assessment error should be considered before exploring other physiological mechanisms.

What Is the Force-per-Molecule Inside a Biomaterial Having Randomly Oriented Units?

Both synthetic and natural protein-based materials are made of randomly oriented cross-linked molecules. Here we introduce a coarse-grained approach to estimate the average force-per-molecule for materials made from globular proteins. Our approach has three steps: placement of molecules inside a unit volume, cross-linking, and trimming to remove the protein domains that do not participate to the force response. Following this procedure, we estimate the number of active domains per cross-section area, that allows for a direct calculation of the force-per-domain. Among the variables considered, we found that concentration was the most sensitive parameter. We then synthesized protein hydrogels made from BSA and polyprotein L and measured the stresses that these materials can withstand. We found that forces-per-molecules of up to 17 pN per domain can be obtained experimentally using protein hydrogels. Our approach represents an important step toward understanding the scaling of tension in biomaterials.

A Tunable, Simplified Model for Biological Latch Mediated Spring Actuated Systems

We develop a model of latch-mediated spring actuated (LaMSA) systems relevant to comparative biomechanics and bioinspired design. The model contains five components: two motors (muscles), a spring, a latch, and a load mass. One motor loads the spring to store elastic energy and the second motor subsequently removes the latch, which releases the spring and causes movement of the load mass. We develop freely available software to accompany the model, which provides an extensible framework for simulating LaMSA systems. Output from the simulation includes information from the loading and release phases of motion, which can be used to calculate kinematic performance metrics that are important for biomechanical function. In parallel, we simulate a comparable, directly actuated system that uses the same motor and mass combinations as the LaMSA simulations. By rapidly iterating through biologically relevant input parameters to the model, simulated kinematic performance differences between LaMSA and directly actuated systems can be used to explore the evolutionary dynamics of biological LaMSA systems and uncover design principles for bioinspired LaMSA systems. As proof of principle of this concept, we compare a LaMSA simulation to a directly actuated simulation that includes either a Hill-type force-velocity trade-off or muscle activation dynamics, or both. For the biologically-relevant range of parameters explored, we find that the muscle force-velocity trade-off and muscle activation have similar effects on directly actuated performance. Including both of these dynamic muscle properties increases the accelerated mass range where a LaMSA system outperforms a directly actuated one.

Hamstring muscle activation strategies during eccentric contractions are related to the distribution of muscle damage

Large inter‐individual variability of activation strategies is observed during hamstring strengthening exercises but their consequences remain unexplored. The objective of this study was to determine whether individual activation strategies are related to the distribution of damage across the hamstring muscle heads semimembranosus (SM), semitendinosus (ST), and biceps femoris (BF) after eccentric contractions. 24 participants performed 5 sets of 15 maximal eccentric contractions of knee flexors on a dynamometer, while activation of each muscle head was assessed using surface electromyography. Knee flexion maximal isometric strength was assessed before exercise and 48 h afterward. Shear modulus was measured using shear wave elastography before exercise and 30 min afterward to quantify the distribution of damage across the hamstring muscle heads. At 48 h, maximal knee flexion torque had decreased by 15.9% ± 16.9% (p < 0.001). Although no differences between activation ratios of each muscle were found during the eccentric exercise (all p > 0.364), we reported a heterogeneous distribution of damage, with a larger change in shear modulus of ST/Hams than SM/Hams (+70.8%, p < 0.001) or BF/Hams (+50.3%, p < 0.001). A large correlation was found between the distribution of activation and the distribution of damage for ST/Hams (r = 0.69; p < 001). This study provides evidence that the distribution of activation during maximal eccentric contractions has mechanical consequences for synergist muscles. Further studies are needed to understand whether individual activation strategies influence the distribution of structural adaptations after a training program.

A pH-powered mechanochemical engine regulates the buoyancy of Chaoborus midge larvae

The freshwater aquatic larvae of the Chaoborus midge are the world's only truly planktonic insects, regulating their buoyancy using two pairs of internal air-filled sacs, one in the thorax and the other in the seventh abdominal segment. In 1911, August Krogh demonstrated the larvae's ability to control their buoyancy by exposing them to an increase in hydrostatic pressure.¹ However, how these insects control the volume of their air-sacs has remained a mystery. Gas is not secreted into the air-sacs, as the luminal gas composition is always the same as that dissolved in the surrounding water.^1,2 Instead, the air-sac wall was thought to play some role.^3-6 Here we reveal that bands of resilin in the air-sac's wall are responsible for the changes in volume. These bands expand and contract in response to changes in pH generated by an endothelium that envelops the air-sac. Vacuolar type H⁺ V-ATPase (VHA) in the endothelium acidifies and shrinks the air-sac, while alkalinization and expansion are regulated by the cyclic adenosine monophosphate signal transduction pathway. Thus, Chaoborus air-sacs function as mechanochemical engines, transforming pH changes into mechanical work against hydrostatic pressure. As the resilin bands interlaminate with bands of cuticle, changes in resilin volume are constrained to a single direction along the air-sac's longitudinal axis. This makes the air-sac functionally equivalent to a cross-striated pH muscle and demonstrates a unique biological role for resilin as an active structural element.

Materials for Smart Soft Actuator Systems

In contrast to conventional hard actuators, soft actuators offer many vivid advantages, such as improved flexibility, adaptability, and reconfigurability, which are intrinsic to living systems. These properties make them particularly promising for different applications, including soft electronics, surgery, drug delivery, artificial organs, or prosthesis. The additional degree of freedom for soft actuatoric devices can be provided through the use of intelligent materials, which are able to change their structure, macroscopic properties, and shape under the influence of external signals. The use of such intelligent materials allows a substantial reduction of a device's size, which enables a number of applications that cannot be realized by externally powered systems. This review aims to provide an overview of the properties of intelligent synthetic and living/natural materials used for the fabrication of soft robotic devices. We discuss basic physical/chemical properties of the main kinds of materials (elastomers, gels, shape memory polymers and gels, liquid crystalline elastomers, semicrystalline ferroelectric polymers, gels and hydrogels, other swelling polymers, materials with volume change during melting/crystallization, materials with tunable mechanical properties, and living and naturally derived materials), how they are related to actuation and soft robotic application, and effects of micro/macro structures on shape transformation, fabrication methods, and we highlight selected applications.

Plasticity of the gastrocnemius elastic system in response to decreased work and power demand during growth

Elastic energy storage and release can enhance performance that would otherwise be limited by the force-velocity constraints of muscle. Although functional influence of a biological spring depends on tuning between components of an elastic system (the muscle, spring-driven mass and lever system), we do not know whether elastic systems systematically adapt to functional demand. To test whether altering work and power generation during maturation alters the morphology of an elastic system, we prevented growing guinea fowl (Numida meleagris) from jumping. We compared the jump performance of our treatment group at maturity with that of controls and measured the morphology of the gastrocnemius elastic system. We found that restricted birds jumped with lower jump power and work, yet there were no significant between-group differences in the components of the elastic system. Further, subject-specific models revealed no difference in energy storage capacity between groups, though energy storage was most sensitive to variations in muscle properties (most significantly operating length and least dependent on tendon stiffness). We conclude that the gastrocnemius elastic system in the guinea fowl displays little to no plastic response to decreased demand during growth and hypothesize that neural plasticity may explain performance variation.

The ultrafast snap of a finger is mediated by skin friction

The snap of a finger has been used as a form of communication and music for millennia across human cultures. However, a systematic analysis of the dynamics of this rapid motion has not yet been performed. Using high-speed imaging and force sensors, we analyse the dynamics of the finger snap. We discover that the finger snap achieves peak angular accelerations of 1.6 × 10⁶° s^-2 in 7 ms, making it one of the fastest recorded angular accelerations the human body produces (exceeding professional baseball pitches). Our analysis reveals the central role of skin friction in mediating the snap dynamics by acting as a latch to control the resulting high velocities and accelerations. We evaluate the role of this frictional latch experimentally, by covering the thumb and middle finger with different materials to produce different friction coefficients and varying compressibility. In doing so, we reveal that the compressible, frictional latch of the finger pads likely operates in a regime optimally tuned for both friction and compression. We also develop a soft, compressible friction-based latch-mediated spring actuated model to further elucidate the key role of friction and how it interacts with a compressible latch. Our mathematical model reveals that friction plays a dual role in the finger snap, both aiding in force loading and energy storage while hindering energy release. Our work reveals how friction between surfaces can be harnessed as a tunable latch system and provides design insight towards the frictional complexity in many robotic and ultra-fast energy-release structures.

Intramuscular injection of skeletal muscle derived extracellular matrix mitigates denervation atrophy after sciatic nerve transection

Peripheral nerve injury and the associated muscle atrophy has an estimated annual healthcare burden of $150 billion dollars in the United States. When considering the total annual health-related spending of $3.5 trillion, these pathologies alone occupy about 4.3%. The prevalence of these ailments is rooted, at least in part, in the lack of specific preventative therapies that can be administered to muscle while it remains in the denervated state. To address this, skeletal muscle-derived ECM (skECM) was injected directly in denervated muscle with postoperative analysis performed at 20 weeks, including gait analysis, force production, cytokine quantification, and histological analysis. skECM was shown to be superior against non-injected muscle controls showing no difference in contraction force to uninjured muscle at 20 weeks. Cytokines IL-1β, IL-18, and IFNγ appeared to mediate regeneration with statistical regression implicating these cytokines as strong predictors of muscle contraction, showing significant linear correlation.

Transtibial limb loss does not increase metabolic cost in three-dimensional computer simulations of human walking

Loss of a lower limb below the knee, i.e., transtibial limb loss, and subsequently walking with a prosthesis, is generally thought to increase the metabolic cost of walking vs. able-bodied controls. However, high-functioning individuals with limb loss such as military service members often walk with the same metabolic cost as controls. Here we used a 3-D computer model and optimal control simulation approach to test the hypothesis that transtibial limb loss in and of itself causes an increase in metabolic cost of walking. We first generated N = 36 simulations of walking at 1.45 m/s using a “pre-limb loss” model, with two intact biological legs, that minimized deviations from able-bodied experimental walking mechanics with minimum muscular effort. We then repeated these simulations using a “post-limb loss” model, with the right leg’s ankle muscles and joints replaced with a simple model of a passive transtibial prosthesis. No other changes were made to the post-limb loss model’s remaining muscles or musculoskeletal parameters compared to the pre-limb loss case. Post-limb loss, the gait deviations on average increased by only 0.17 standard deviations from the experimental means, and metabolic cost did not increase (3.58 ± 0.10 J/m/kg pre-limb loss vs. 3.59 ± 0.12 J/m/kg post-limb loss, p = 0.65). The results suggest that transtibial limb loss does not directly lead to an increase in metabolic cost, even when deviations from able-bodied gait mechanics are minimized. High metabolic costs observed in individuals with transtibial limb loss may be due to secondary changes in strength or general fitness after limb loss, modifiable prosthesis issues, or to prioritization of factors that affect locomotor control other than gait deviations and muscular effort.

The cibarial pump of the xylem-feeding froghopper Philaenus spumarius produces negative pressures exceeding 1 MPa

The xylem sap of vascular plants is an unlikely source of nutrition, being both nutrient poor and held under tensions (negative pressures) that can exceed 1 MPa. But some insects feed on xylem sap exclusively, extracting copious quantities using a muscular cibarial pump. However, neither the strength of the insect's suction, nor the direct energetic cost of xylem ingestion, have ever been quantified. Philaenus spumarius froghoppers were used to address these gaps in our knowledge. Micro-CT scans of its cibarium and measurements of cibarial muscle sarcomere length revealed that P. spumarius can generate a maximum tension of 1.3 ± 0.2 MPa within its cibarium. The energetic cost of xylem extraction was quantified using respirometry to measure the metabolic rate (MR) of P. spumarius while they fed on hydroponically grown legumes, while xylem sap excretion rate and cibarial pumping frequency were simultaneously recorded. Increasing the plants' xylem tensions up to 1.1 MPa by exposing their roots to polyethylene glycol did not reduce the insects' rate of xylem excretion, but significantly increased both MR and pumping frequency. We conclude that P. spumarius can gain energy feeding on xylem sap containing previously reported energy densities and at xylem tensions up to their maximum suction capacity.

The evolutionary biomechanics of locomotor function in giant land animals

Giant land vertebrates have evolved more than 30 times, notably in dinosaurs and mammals. The evolutionary and biomechanical perspectives considered here unify data from extant and extinct species, assessing current theory regarding how the locomotor biomechanics of giants has evolved. In terrestrial tetrapods, isometric and allometric scaling patterns of bones are evident throughout evolutionary history, reflecting general trends and lineage-specific divergences as animals evolve giant size. Added to data on the scaling of other supportive tissues and neuromuscular control, these patterns illuminate how lineages of giant tetrapods each evolved into robust forms adapted to the constraints of gigantism, but with some morphological variation. Insights from scaling of the leverage of limbs and trends in maximal speed reinforce the idea that, beyond 100-300 kg of body mass, tetrapods reduce their locomotor abilities, and eventually may lose entire behaviours such as galloping or even running. Compared with prehistory, extant megafaunas are depauperate in diversity and morphological disparity; therefore, turning to the fossil record can tell us more about the evolutionary biomechanics of giant tetrapods. Interspecific variation and uncertainty about unknown aspects of form and function in living and extinct taxa still render it impossible to use first principles of theoretical biomechanics to tightly bound the limits of gigantism. Yet sauropod dinosaurs demonstrate that >50 tonne masses repeatedly evolved, with body plans quite different from those of mammalian giants. Considering the largest bipedal dinosaurs, and the disparity in locomotor function of modern megafauna, this shows that even in terrestrial giants there is flexibility allowing divergent locomotor specialisations.

Jump takeoff in a small jumping spider

Jumping in animals presents an interesting locomotory strategy as it requires the generation of large forces and accurate timing. Jumping in arachnids is further complicated by their semi-hydraulic locomotion system. Among arachnids, jumping spiders (Family Salticidae) are agile and dexterous jumpers. However, less is known about jumping in small salticid species. Here we used Habronattus conjunctus, a small jumping spider (body length ~ 4.5 mm) to examine its jumping performance and compare it to that of other jumping spiders and insects. We also explored how legs are used during the takeoff phase of jumps. Jumps were staged between two raised platforms. We analyzed jumping videos with DeepLabCut to track 21 points on the cephalothorax, abdomen, and legs. By analyzing leg liftoff and extension patterns, we found evidence that H. conjunctus primarily uses the third legs to power jumps. We also found that H. conjunctus jumps achieve lower takeoff speeds and accelerations than most other jumping arthropods, including other jumping spiders. Habronattus conjunctus takeoff time was similar to other jumping arthropods of the same body mass. We discuss the mechanical benefits and drawbacks of a semi-hydraulic system of locomotion and consider how small spiders may extract dexterous jumps from this locomotor system.

How fast do mobile organisms respond to stimuli? Response times from bacteria to elephants and whales

Quick responses to fast changes in the environment are crucial in animal behaviour and survival, for example to seize prey, escape predators, or negotiate obstacles. Here, we study the 'simple response time' that is the time elapsed between receptor stimulation and motor activation as typically shown in escape responses, for mobile organisms of various taxa ranging from bacteria to large vertebrates. We show that 95% of these simple response times lie within one order of magnitude of the overall geometric mean of about 25 ms, which is similar to that of a well-studied sensory time scale, the inverse of the critical flicker fusion frequency in vision, also lying within close bounds for all the organisms studied. We find that this time scale is a few times smaller than the minimum time to move by one body length, which is known to lie also within a relatively narrow range for all moving organisms. The remarkably small 10²-fold range of the simple response time among so disparate life forms varying over 10²⁰-fold in body mass suggests that it is determined by basic physicochemical constraints, independently on the structure and scale of the organism. We thus propose first-principle estimates of the simple response and sensory time scales in terms of physical constants and a few basic biological properties common to mobile organisms and constraining their responses.

Reverse-engineering and modeling the 3D passive and active responses of skeletal muscle using a data-driven, non-parametric, spline-based procedure

In this work we present a non-parametric data-driven approach to reverse-engineer and model the 3D passive and active responses of skeletal muscle, applied to tibialis anterior muscle of Wistar rats. We assume a Hill-type additive relation for the stored energy into passive and active contributions. The terms of the stored energy have no upfront assumed shape, nor material parameters. These terms are determined directly from experimental data in spline form solving numerically the functional equations of the tests from which experimental data is available. To characterize typical longitudinal-to-transverse behavior in rodent's muscle, experiments from Morrow et al. (J. Mech. Beh. Biomed. Mater. 2010; 3: 124-129) are employed. Then, the passive and active behaviors of Wistar rats are determined from the experiments of Calvo et al. (J. Bomech. 2010; 43:318-325) and Ramirez et al. (J. Theor. Biol. 2010; 267:546-553). The twitch shape is not assumed, but reverse-engineered from experimental data. The influence of the strain and the stimulus voltage and frequency in the active response, are also modeled. A convenient stimulus power-related variable is proposed to comprise both voltage and frequency dependencies in the active response. Then, the behavior of the resulting muscle model depends only on the muscle strain maintained during isometric tests in the muscle and the stimulus power variable, along the time from initiation of the tetanus state.

Estimation of the force-velocity properties of individual muscles from measurement of the combined plantarflexor properties

The force-velocity (F-V) properties of isolated muscles or muscle fibers have been well studied in humans and other animals. However, determining properties of individual muscles in vivo remains a challenge because muscles usually function within a synergistic group. Modeling has been used to estimate the properties of an individual muscle from the experimental measurement of the muscle group properties. While this approach can be valuable, the models and the associated predictions are difficult to validate. In this study, we measured the in situ F-V properties of the maximally activated kangaroo rat plantarflexor group and used two different assumptions and associated models to estimate the properties of the individual plantarflexors. The first model (Mdl1) assumed that the percent contributions of individual muscles to group force and power were based upon the muscles' cross-sectional area and were constant across the different isotonic loads applied to the muscle group. The second model (Mdl2) assumed that the F-V properties of the fibers within each muscle were identical, but because of differences in muscle architecture, the muscles' contributions to the group properties changed with isotonic load. We compared the two model predictions with independent estimates of the muscles' contributions based upon sonomicrometry measurements of muscle length. We found that predictions from Mdl2 were not significantly different from sonomicrometry-based estimates while those from Mdl1 were significantly different. The results of this study show that incorporating appropriate fiber properties and muscle architecture is necessary to parse the individual muscles' contributions to the group F-V properties.

Quantal biomechanical effects in speech postures of the lips

The unique biomechanical and functional constraints on human speech make it a promising area for research investigating modular control of movement. The present article illustrates how a modular control approach to speech can provide insights relevant to understanding both motor control and observed variation across languages. We specifically explore the robust typological finding that languages produce different degrees of labial constriction using distinct muscle groupings and concomitantly distinct lip postures. Research has suggested that these lip postures exploit biomechanical regions of nonlinearity between neural activation and movement, also known as quantal regions, to allow movement goals to be realized despite variable activation signals. We present two sets of computer simulations showing that these labial postures can be generated under the assumption of modular control and that the corresponding modules are biomechanically robust: first to variation in the activation levels of participating muscles, and second to interference from surrounding muscles. These results provide support for the hypothesis that biomechanical robustness is an important factor in selecting the muscle groupings used for speech movements and provide insight into the neurological control of speech movements and how biomechanical and functional constraints govern the emergence of speech motor modules. We anticipate that future experimental work guided by biomechanical simulation results will provide new insights into the neural organization of speech movements.NEW & NOTEWORTHY This article provides additional evidence that speech motor control is organized in a modular fashion and that biomechanics constrain the kinds of motor modules that may emerge. It also suggests that speech can be a fruitful domain for the study of modularity and that a better understanding of speech motor modules will be useful for speech research. Finally, it suggests that biomechanical modeling can serve as a useful complement to experimental work when studying modularity.

Does protein unfolding play a functional role in vivo?

Unfolding and refolding of multidomain proteins under force have yet to be recognized as a major mechanism of function for proteins in vivo. In this review, we discuss the inherent properties of multidomain proteins under a force vector from a structural and functional perspective. We then characterize three main systems where multidomain proteins could play major roles through mechanical unfolding: muscular contraction, cellular mechanotransduction, and bacterial adhesion. We analyze how key multidomain proteins for each system can produce a gain-of-function from the perspective of a fine-tuned quantized response, a molecular battery, delivery of mechanical work through refolding, elasticity tuning, protection and exposure of cryptic sites, and binding-induced mechanical changes. Understanding how mechanical unfolding and refolding affect function will have important implications in designing mechano-active drugs against conditions such as muscular dystrophy, cancer, or novel antibiotics.

The ovipositor actuation mechanism of a parasitic wasp and its functional implications

Parasitic wasps use specialized needle‐like structures, ovipositors, to drill into substrates to reach hidden hosts. The external ovipositor (terebra) consists of three interconnected, sliding elements (valvulae), which are moved reciprocally during insertion. This presumably reduces the required pushing force on the terebra and limits the risk of damage whilst probing. Although this is an important mechanism, it is still not completely understood how the actuation of the valvulae is achieved, and it has only been studied with the ovipositor in rest position. Additionally, very little is known about the magnitude of the forces generated during probing. We used synchrotron X‐ray microtomography to reconstruct the actuation mechanism of the parasitic wasp Diachasmimorpha longicaudata (Braconidae) in four distinct phases of the probing cycle. We show that only the paired first valvulae of the terebra move independently, while the second valvula moves with the metasoma (‘abdomen’). The first valvula movements are initiated by rotation of one chitin plate (first valvifer) with respect to another such plate (second valvifer). This is achieved indirectly by muscles connecting the non‐rotating second valvifer and the abdominal ninth tergite. Contrary to previous reports, we found muscle fibres running inside the terebra, although their function remains unclear. The estimated maximal forces that can be exerted by the first valvulae are small (protraction 1.19 mN and retraction 0.874 mN), which reduces the risk of buckling, but are sufficient for successful probing. The small net forces of the valvulae on the substrate may still lead to buckling of the terebra; we show that the sheaths surrounding the valvulae prevent this by effectively increasing the diameter and second moment of area of the terebra. Our findings improve the comprehension of hymenopteran probing mechanisms, the function of the associated muscles, and the forces and damage‐limiting mechanism that are involved in drilling a slender terebra into a substrate.

Scaling of inertial delays in terrestrial mammals

As part of its response to a perturbation, an animal often needs to reposition its body. Inertia acts to oppose the corrective motion, delaying the completion of the movement-we refer to this elapsed time as inertial delay. As animal size increases, muscle moment arms also increase, but muscles are proportionally weaker, and limb inertia is proportionally larger. Consequently, the scaling of inertial delays is complex. Our intent is to determine how quickly different sized animals can produce corrective movements when their muscles act at their force capacity, relative to the time within which those movements need to be performed. Here, we quantify inertial delay using two biomechanical models representing common scenarios in animal locomotion: a distributed mass pendulum approximating swing limb repositioning (swing task), and an inverted pendulum approximating whole body posture recovery (posture task). We parameterized the anatomical, muscular, and inertial properties of these models using literature scaling relationships, then determined inertial delay for each task across a large range of movement magnitudes and the full range of terrestrial mammal sizes. We found that inertial delays scaled with an average of M0.28 in the swing task and M0.35 in the posture task across movement magnitudes-larger animals require more absolute time to perform the same movement as small animals. The time available to complete a movement also increases with animal size, but less steeply. Consequently, inertial delays comprise a greater fraction of swing duration and other characteristic movement times in larger animals. We also compared inertial delays to the other component delays within the stimulus-response pathway. As movement magnitude increased, inertial delays exceeded these sensorimotor delays, and this occurred for smaller movements in larger animals. Inertial delays appear to be a challenge for motor control, particularly for bigger movements in larger animals.

The analgesic action of Aussie current in women with non-specific chronic lumbar pain

Background/aims

Despite electrostimulation being a common adjuvant therapy for non-specific low back pain, the use of Aussie current for muscle contraction is still underreported in the literature. The present study aimed to assess the use of Aussie current in the treatment of chronic, non-specific lumbar pain.

Methods

Twenty-four young women with chronic non-specific low back pain were randomly assigned to the Aussie current group or control group. Pain (visual analogue scale and McGill Pain Questionnaire), function (Oswestry Disability Index), trunk muscle resistance (the time the participant remained in a predefined static position) and multifidus muscle thickness (ultrasound images) were analysed bilaterally before, at the end of and 30 days after completing the treatment protocol. The treatment group received 12 sessions of Aussie current over a period of 4 weeks. The electrodes were arranged laterally and bilaterally to the spinous processes of the first and fifth lumbar vertebrae.

Results

There was a reduction in the pain profile for the Aussie group, as measured by a visual analogue scale and the McGill Pain Questionnaire. There was an increase in trunk muscle resistance and in muscle thickness in the Aussie group when compared to the control group. There were no changes in the Oswestry Disability Index in either group.

Conclusions

Aussie current resulted in significant improvements in pain, endurance and muscle thickness in women with chronic, non-specific low back pain.

Vorticella: A Protozoan for Bio-Inspired Engineering

In this review, we introduce Vorticella as a model biological micromachine for microscale engineering systems. Vorticella has two motile organelles: the oral cilia of the zooid and the contractile spasmoneme in the stalk. The oral cilia beat periodically, generating a water flow that translates food particles toward the animal at speeds in the order of 0.1–1 mm/s. The ciliary flow of Vorticella has been characterized by experimental measurement and theoretical modeling, and tested for flow control and mixing in microfluidic systems. The spasmoneme contracts in a few milliseconds, coiling the stalk and moving the zooid at 15–90 mm/s. Because the spasmoneme generates tension in the order of 10–100 nN, powered by calcium ion binding, it serves as a model system for biomimetic actuators in microscale engineering systems. The spasmonemal contraction of Vorticella has been characterized by experimental measurement of its dynamics and energetics, and both live and extracted Vorticellae have been tested for moving microscale objects. We describe past work to elucidate the contraction mechanism of the spasmoneme, recognizing that past and continuing efforts will increase the possibilities of using the spasmoneme as a microscale actuator as well as leading towards bioinspired actuators mimicking the spasmoneme.