A theory of physiological similarity in muscle-driven motion.

Muscle contraction is the primary source of all animal movement. I show that the maximum mechanical output of such contractions is determined by a characteristic dimensionless number, the "effective inertia," Γ, defined by a small set of mechanical, physiological, and anatomical properties of the interrogated musculoskeletal complex. Different musculoskeletal systems with equal Γ may be considered physiologically similar, in the sense that maximum performance involves equal fractions of the muscle's maximum strain rate, strain capacity, work, and power density. It can be demonstrated that there exists a unique, "optimal" musculoskeletal anatomy which enables a unit volume of muscle to deliver maximum work and power simultaneously, corresponding to Γ close to unity. External forces truncate the mechanical performance space accessible to muscle by introducing parasitic losses, and subtly alter how musculoskeletal anatomy modulates muscle performance, challenging canonical notions of skeletal force-velocity trade-offs. Γ varies systematically under isogeometric transformations of musculoskeletal systems, a result which provides fundamental insights into the key determinants of animal locomotor performance across scales.

Developmental biomechanics and age polyethism in leaf-cutter ants.

Many social insects display age polyethism: young workers stay inside the nest, and only older workers forage. This behavioural transition is accompanied by genetic and physiological changes, but the mechanistic origin of it remains unclear. To investigate if the mechanical demands on the musculoskeletal system effectively prevent young workers from foraging, we studied the biomechanical development of the bite apparatus in Atta vollenweideri leaf-cutter ants. Fully matured foragers generated peak in vivo bite forces of around 100 mN, more than one order of magnitude in excess of those measured for freshly eclosed callows of the same size. This change in bite force was accompanied by a sixfold increase in the volume of the mandible closer muscle, and by a substantial increase of the flexural rigidity of the head capsule, driven by a significant increase in both average thickness and indentation modulus of the head capsule cuticle. Consequently, callows lack the muscle force capacity required for leaf-cutting, and their head capsule is so compliant that large muscle forces would be likely to cause damaging deformations. On the basis of these results, we speculate that continued biomechanical development post eclosion may be a key factor underlying age polyethism, wherever foraging is associated with substantial mechanical demands.

Strong positive allometry of bite force in leaf-cutter ants increases the range of cuttable plant tissues.

Atta leaf-cutter ants are the prime herbivore in the Neotropics: differently sized foragers harvest plant material to grow a fungus as a crop. Efficient foraging involves complex interactions between worker size, task preferences and plant-fungus suitability; it is, however, ultimately constrained by the ability of differently sized workers to generate forces large enough to cut vegetation. In order to quantify this ability, we measured bite forces of Atta vollenweideri leaf-cutter ants spanning more than one order of magnitude in body mass. Maximum bite force scaled almost in direct proportion to mass; the largest workers generated peak bite forces 2.5 times higher than expected from isometry. This remarkable positive allometry can be explained via a biomechanical model that links bite forces with substantial size-specific changes in the morphology of the musculoskeletal bite apparatus. In addition to these morphological changes, we show that bite forces of smaller ants peak at larger mandibular opening angles, suggesting a size-dependent physiological adaptation, probably reflecting the need to cut leaves with a thickness that corresponds to a larger fraction of the maximum possible gape. Via direct comparison of maximum bite forces with leaf mechanical properties, we demonstrate (i) that bite forces in leaf-cutter ants need to be exceptionally large compared with body mass to enable them to cut leaves; and (ii), that the positive allometry enables colonies to forage on a wider range of plant species without the need for extreme investment in even larger workers. Our results thus provide strong quantitative arguments for the adaptive value of a positively allometric bite force.

Shear-sensitive adhesion enables size-independent adhesive performance in stick insects.

The ability to climb with adhesive pads conveys significant advantages and is widespread in the animal kingdom. The physics of adhesion predict that attachment is more challenging for large animals, whereas detachment is harder for small animals, due to the difference in surface-to-volume ratios. Here, we use stick insects to show that this problem is solved at both ends of the scale by linking adhesion to the applied shear force. Adhesive forces of individual insect pads, measured with perpendicular pull-offs, increased approximately in proportion to a linear pad dimension across instars. In sharp contrast, whole-body force measurements suggested area scaling of adhesion. This discrepancy is explained by the presence of shear forces during whole-body measurements, as confirmed in experiments with pads sheared prior to detachment. When we applied shear forces proportional to either pad area or body weight, pad adhesion also scaled approximately with area or mass, respectively, providing a mechanism that can compensate for the size-related loss of adhesive performance predicted by isometry. We demonstrate that the adhesion-enhancing effect of shear forces is linked to pad sliding, which increased the maximum adhesive force per area sustainable by the pads. As shear forces in natural conditions are expected to scale with mass, sliding is more frequent and extensive in large animals, thus ensuring that large animals can attach safely, while small animals can still detach their pads effortlessly. Our results therefore help to explain how nature's climbers maintain a dynamic attachment performance across seven orders of magnitude in body weight.

Extreme positive allometry of animal adhesive pads and the size limits of adhesion-based climbing.

Organismal functions are size-dependent whenever body surfaces supply body volumes. Larger organisms can develop strongly folded internal surfaces for enhanced diffusion, but in many cases areas cannot be folded so that their enlargement is constrained by anatomy, presenting a problem for larger animals. Here, we study the allometry of adhesive pad area in 225 climbing animal species, covering more than seven orders of magnitude in weight. Across all taxa, adhesive pad area showed extreme positive allometry and scaled with weight, implying a 200-fold increase of relative pad area from mites to geckos. However, allometric scaling coefficients for pad area systematically decreased with taxonomic level and were close to isometry when evolutionary history was accounted for, indicating that the substantial anatomical changes required to achieve this increase in relative pad area are limited by phylogenetic constraints. Using a comparative phylogenetic approach, we found that the departure from isometry is almost exclusively caused by large differences in size-corrected pad area between arthropods and vertebrates. To mitigate the expected decrease of weight-specific adhesion within closely related taxa where pad area scaled close to isometry, data for several taxa suggest that the pads' adhesive strength increased for larger animals. The combination of adjustments in relative pad area for distantly related taxa and changes in adhesive strength for closely related groups helps explain how climbing with adhesive pads has evolved in animals varying over seven orders of magnitude in body weight. Our results illustrate the size limits of adhesion-based climbing, with profound implications for large-scale bio-inspired adhesives.

Scaling of claw sharpness: mechanical constraints reduce attachment performance in larger insects.

Claws are the most widespread attachment devices in animals, but comparatively little is known about the mechanics of claw attachment. A key morphological parameter in determining attachment ability is claw sharpness; however, there is a conflict between sharpness and fracture resistance. Sharper claws can interlock on more surfaces but are more likely to break. Body size interacts with this conflict such that larger animals should have much blunter claws and consequently poorer attachment ability than smaller animals. This expected size-induced reduction in attachment performance has not previously been investigated, and it is unclear how animals deal with this effect, and whether it indeed exists. We explored the scaling of claw sharpness with body size using four insect species (Nauphoeta cinerea, Gromphadorhina portentosa, Atta cephalotes and Carausius morosus) each covering a large size range. The scaling of claw sharpness varied significantly between species, suggesting that they face different pressures regarding claw function. Attachment forces were measured for A. cephalotes and G. portentosa (which had different scaling of claw sharpness) on several rough surfaces using a centrifuge setup. As expected, attachment performance was poorer in larger animals. Firstly, larger animals were more likely to slip, although this effect depended on the scaling of claw sharpness. Secondly, when they gripped, they attached with smaller forces relative to their weight. This size-induced reduction in attachment performance has significant implications for the attachment ability of larger animals on rough surfaces.

Rate-dependence of 'wet' biological adhesives and the function of the pad secretion in insects.

Many insects use soft adhesive footpads for climbing. The surface contact of these organs is mediated by small volumes of a liquid secretion, which forms thin films in the contact zone. Here, we investigate the role of viscous dissipation by this secretion and the 'bulk' pad cuticle by quantifying the rate-dependence of the adhesive force of individual pads. Adhesion increased with retraction speed, but this effect was independent of the amount of pad secretion present in the contact zone, suggesting that the secretion's viscosity did not play a significant role. Instead, the rate-dependence can be explained by relating the strain energy release rate to the speed of crack propagation, using an established empirical power law. The 'wet' pads' behaviour was akin to that of 'dry' elastomers, with an equilibrium energy release rate close to that of dry van-der-Waals contacts. We suggest that the secretion mainly serves as a 'release layer', minimising viscous dissipation and thereby reducing the time- and 'loading-history'-dependence of the adhesive pads. In contrast to many commercial adhesives which derive much of their strength from viscous dissipation, we show that the major modulator of adhesive strength in 'wet' biological adhesive pads is friction, exhibiting a much larger effect than retraction speed. A comparison between 'wet' and 'dry' biological adhesives, using both results from this study and the literature, revealed a striking lack of differences in attachment performance under varying experimental conditions. Together, these results suggest that 'wet' and 'dry' biological adhesives may be more similar than previously thought.

Optimal Gearing of Musculoskeletal Systems.

Movement is integral to animal life, and most animal movement is actuated by the same engine: striated muscle. Muscle input is typically mediated by skeletal elements, resulting in musculoskeletal systems that are geared: at any instant, the muscle force and velocity are related to the output force and velocity only via a proportionality constant G, the "mechanical advantage". The functional analysis of such "simple machines" has traditionally centred around this instantaneous interpretation, such that a small vs large G is thought to reflect a fast vs forceful system, respectively. But evidence is mounting that a comprehensive analysis ought to also consider the mechanical energy output of a complete contraction. Here, we approach this task systematically, and deploy the theory of physiological similarity to study how gearing affects the flow of mechanical energy in a minimalist model of a musculoskeletal system. Gearing influences the flow of mechanical energy in two key ways: it can curtail muscle work output, because it determines the ratio between the characteristic muscle kinetic energy and work capacity; and it defines how each unit of muscle work is partitioned into different system energies, i.e., into kinetic vs. "parasitic" energy such as heat. As a consequence of both effects, delivering maximum work in minimum time and with maximum output speed generally requires a mechanical advantage of intermediate magnitude. This optimality condition can be expressed in terms of two dimensionless numbers that reflect the key geometric, physiological, and physical properties of the interrogated musculoskeletal system, and the environment in which the contraction takes place. Illustrative application to exemplar musculoskeletal systems predicts plausible mechanical advantages in disparate biomechanical scenarios; yields a speculative explanation for why gearing is typically used to attenuate the instantaneous force output (Gopt < 1); and predicts how G needs to vary systematically with animal size to optimise the delivery of mechanical energy, in superficial agreement with empirical observations. A many-to-one-mapping from musculoskeletal geometry to mechanical performance is identified, such that differences in G alone do not provide a reliable indicator for specialisation for force vs speed-neither instantaneously, nor in terms of mechanical energy output. The energy framework presented here can be used to estimate an optimal mechanical advantage across variable muscle physiology, anatomy, mechanical environment and animal size, and so facilitates investigation of the extent to which selection has made efficient use of gearing as degree of freedom in musculoskeletal "design".

The effect of muscle ultrastructure on the force, displacement and work capacity of skeletal muscle.

Skeletal muscle powers animal movement through interactions between the contractile proteins, actin and myosin. Structural variation contributes greatly to the variation in mechanical performance observed across muscles. In vertebrates, gross structural variation occurs in the form of changes in the muscle cross-sectional area : fibre length ratio. This results in a trade-off between force and displacement capacity, leaving work capacity unaltered. Consequently, the maximum work per unit volume-the work density-is considered constant. Invertebrate muscle also varies in muscle ultrastructure, i.e. actin and myosin filament lengths. Increasing actin and myosin filament lengths increases force capacity, but the effect on muscle fibre displacement, and thus work, capacity is unclear. We use a sliding-filament muscle model to predict the effect of actin and myosin filament lengths on these mechanical parameters for both idealized sarcomeres with fixed actin : myosin length ratios, and for real sarcomeres with known filament lengths. Increasing actin and myosin filament lengths increases stress without reducing strain capacity. A muscle with longer actin and myosin filaments can generate larger force over the same displacement and has a higher work density, so seemingly bypassing an established trade-off. However, real sarcomeres deviate from the idealized length ratio suggesting unidentified constraints or selective pressures.

Understanding trophic interactions in a warming world by bridging foraging ecology and biomechanics with network science.

Climate change will disrupt biological processes at every scale. Ecosystem functions and services vital to ecological resilience are set to shift, with consequences for how we manage land, natural resources, and food systems. Increasing temperatures cause morphological shifts, with concomitant implications for biomechanical performance metrics crucial to trophic interactions. Biomechanical performance, such as maximum bite force or running speed, determines the breadth of resources accessible to consumers, the outcome of interspecific interactions, and thus the structure of ecological networks. Climate change-induced impacts to ecosystem services and resilience are therefore on the horizon, mediated by disruption of biomechanical performance and, consequently, trophic interactions across whole ecosystems. Here, we argue that there is an urgent need to investigate the complex interactions between climate change, biomechanical traits and foraging ecology to help predict changes to ecological networks and ecosystem functioning. We discuss how these seemingly disparate disciplines can be connected through network science. Using an ant-plant network as an example, we illustrate how different data types could be integrated to investigate the interaction between warming, bite force and trophic interactions, and discuss what such an integration will achieve. It is our hope that this integrative framework will help to identify a viable means to elucidate previously intractable impacts of climate change, with effective predictive potential to guide management and mitigation.

Large deformation diffeomorphic mapping of 3D shape variation reveals two distinct mandible and head capsule morphs in Atta vollenweideri leaf-cutter worker ants.

Ants are crucial ecosystem engineers, and their ecological success is facilitated by a division of labour among sterile "workers". In some ant lineages, workers have undergone further morphological differentiation, resulting in differences in body size, shape, or both. Distinguishing between changes in size and shape is not trivial. Traditional approaches based on allometry reduce complex 3D shapes into simple linear, areal, or volume metrics; modern approaches using geometric morphometrics typically rely on landmarks, introducing observer bias and a trade-off between effort and accuracy. Here, we use a landmark-free method based on large deformation diffeomorphic metric mapping (LDDMM) to assess the co-variation of size and 3D shape in the mandibles and head capsules of Atta vollenweideri leaf-cutter ants, a species exhibiting extreme worker size-variation. Body mass varied by more than two orders of magnitude, but a shape atlas created via LDDMM on µ-CT-derived 3D mesh files revealed only two distinct head capsule and mandibles shapes-one for the minims (body mass < 1 mg) and one for all other workers. We discuss the functional significance of the identified 3D shape variation, and its implications for the evolution of extreme polymorphism in Atta.

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.

Iron-coated Komodo dragon teeth and the complex dental enamel of carnivorous reptiles.

Komodo dragons (Varanus komodoensis) are the largest extant predatory lizards and their ziphodont (serrated, curved and blade-shaped) teeth make them valuable analogues for studying tooth structure, function and comparing with extinct ziphodont taxa, such as theropod dinosaurs. Like other ziphodont reptiles, V. komodoensis teeth possess only a thin coating of enamel that is nevertheless able to cope with the demands of their puncture-pull feeding. Using advanced chemical and structural imaging, we reveal that V. komodoensis teeth possess a unique adaptation for maintaining their cutting edges: orange, iron-enriched coatings on their tooth serrations and tips. Comparisons with other extant varanids and crocodylians revealed that iron sequestration is probably widespread in reptile enamels but it is most striking in V. komodoensis and closely related ziphodont species, suggesting a crucial role in supporting serrated teeth. Unfortunately, fossilization confounds our ability to consistently detect similar iron coatings in fossil teeth, including those of ziphodont dinosaurs. However, unlike V. komodoensis, some theropods possessed specialized enamel along their tooth serrations, resembling the wavy enamel found in herbivorous hadrosaurid dinosaurs. These discoveries illustrate unexpected and disparate specializations for maintaining ziphodont teeth in predatory reptiles.

A biomechanical model for the relation between bite force and mandibular opening angle in arthropods.

Bite forces play a key role in animal ecology: they affect mating behaviour, fighting success, and the ability to feed. Although feeding habits of arthropods have a significant ecological and economical impact, we lack fundamental knowledge on how the morphology and physiology of their bite apparatus controls bite performance, and its variation with mandible gape. To address this gap, we derived a biomechanical model that characterizes the relationship between bite force and mandibular opening angle from first principles. We validate this model by comparing its geometric predictions with morphological measurements on the muscoloskeletal bite apparatus of Atta cephalotes leaf-cutter ants, using computed tomography (CT) scans obtained at different mandible opening angles. We then demonstrate its deductive and inductive utility with three examplary use cases: Firstly, we extract the physiological properties of the leaf-cutter ant mandible closer muscle from in vivo bite force measurements. Secondly, we show that leaf-cutter ants are specialized to generate extraordinarily large bite forces, equivalent to about 2600 times their body weight. Thirdly, we discuss the relative importance of morphology and physiology in determining the magnitude and variation of bite force. We hope that a more detailed quantitative understanding of the link between morphology, physiology, and bite performance will facilitate future comparative studies on the insect bite apparatus, and help to advance our knowledge of the behaviour, ecology and evolution of arthropods.

Three-dimensional kinematics of leaf-cutter ant mandibles: not all dicondylic joints are simple hinges.

Insects use their mandibles for a variety of tasks, including food processing, material transport, nest building, brood care, and fighting. Despite this functional diversity, mandible motion is typically thought to be constrained to rotation about a single fixed axis. Here, we conduct a direct quantitative test of this 'hinge joint hypothesis' in a species that uses its mandibles for a wide range of tasks: Atta vollenweideri leaf-cutter ants. Mandible movements from live restrained ants were reconstructed in three dimensions using a multi-camera rig. Rigid body kinematic analyses revealed strong evidence that mandible movement occupies a kinematic space that requires more than one rotational degree of freedom: at large opening angles, mandible motion is dominated by yaw. But at small opening angles, mandibles both yaw and pitch. The combination of yaw and pitch allows mandibles to 'criss-cross': either mandible can be on top when mandibles are closed. We observed criss-crossing in freely cutting ants, suggesting that it is functionally important. Combined with recent reports on the diversity of joint articulations in other insects, our results show that insect mandible kinematics are more diverse than traditionally assumed, and thus worthy of further detailed investigation. This article is part of the theme issue 'Food processing and nutritional assimilation in animals'.

Biomechanics of cutting: sharpness, wear sensitivity and the scaling of cutting forces in leaf-cutter ant mandibles.

Herbivores large and small need to mechanically process plant tissue. Their ability to do so is determined by two forces: the maximum force they can generate, and the minimum force required to fracture the plant tissue. The ratio of these forces determines the relative mechanical effort; how this ratio varies with animal size is challenging to predict. We measured the forces required to cut thin polymer sheets with mandibles from leaf-cutter ant workers which vary by more than one order of magnitude in body mass. Cutting forces were independent of mandible size, but differed by a factor of two between pristine and worn mandibles. Mandibular wear is thus likely a more important determinant of cutting force than mandible size. We rationalize this finding with a biomechanical analysis, which suggests that pristine mandibles are ideally 'sharp'-cutting forces are close to a theoretical minimum, which is independent of tool size and shape, and instead solely depends on the geometric and mechanical properties of the cut tissue. The increase of cutting force due to mandibular wear may be particularly problematic for small ants, which generate lower absolute bite forces, and thus require a larger fraction of their maximum bite force to cut the same plant. This article is part of the theme issue 'Food processing and nutritional assimilation in animals'.

Multilevel dynamic adjustments of geckos (Hemidactylus frenatus) climbing vertically: head-up versus head-down.

Many climbing animals use direction-dependent adhesives to attach to vertical or inclined surfaces. These structures adhere when activated via a pull but detach when pushed. Therefore, a challenge arises when a change in climbing direction causes external forces such as gravity to change its acting orientation upon the lizard. To investigate how specialized climbers adjust, we studied kinematics and dynamics of six Hemidactylus frenatus geckos climbing head-up and head-down a vertical racetrack. We found that limbs functionally swap their adhesive role: feet above the centre of mass (COM) generated adhesive forces, feet below the COM compressive forces, both equal in magnitude across directions. To investigate how lizards perform this swap, despite the constraint of their direction-dependent adhesives, we analysed kinematic adjustments across multiple smaller levels of hierarchy: limbs, feet and toes. All levels contributed: the hindfoot angle was reoriented realigning the adhesive structure, the hindlimb centre range of motion was further protracted and the hindfoot toe spreading was reduced. Notably, all three variables were adjustments of hindlimbs, suggesting that they make a more flexible contribution in upward versus downward climbing, while forelimbs may be anatomically or functionally constrained. The relevance of multilevel dynamic adjustments might inform the development of performant gaits for legged climbing robots.

replicAnt: a pipeline for generating annotated images of animals in complex environments using Unreal Engine.

Deep learning-based computer vision methods are transforming animal behavioural research. Transfer learning has enabled work in non-model species, but still requires hand-annotation of example footage, and is only performant in well-defined conditions. To help overcome these limitations, we developed replicAnt, a configurable pipeline implemented in Unreal Engine 5 and Python, designed to generate large and variable training datasets on consumer-grade hardware. replicAnt places 3D animal models into complex, procedurally generated environments, from which automatically annotated images can be exported. We demonstrate that synthetic data generated with replicAnt can significantly reduce the hand-annotation required to achieve benchmark performance in common applications such as animal detection, tracking, pose-estimation, and semantic segmentation. We also show that it increases the subject-specificity and domain-invariance of the trained networks, thereby conferring robustness. In some applications, replicAnt may even remove the need for hand-annotation altogether. It thus represents a significant step towards porting deep learning-based computer vision tools to the field.

Elastic energy storage and the efficiency of movement.

Movement is an integral part of animal biology. It enables organisms to escape from danger, acquire food, and perform courtship displays. Changing the speed or vertical position of a body requires mechanical energy. This energy is typically provided by the biological motor, striated muscle. Striated muscle uses chemical (metabolic) energy to produce force, to move this force over a distance to do work, and to do this work within some time to generate power. The metabolic energy consumed in producing these mechanical outputs is a major component of an organism's energy budget, particularly during repetitive, cyclical movements. This energy could otherwise be used for maintenance, growth, and reproduction. Hence, fitness may be enhanced by improving locomotor efficiency - the ratio between work done and metabolic energy consumed. This may be achieved by reducing the need for muscle to do work, and by increasing the efficiency with which muscle does work.