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We examine the stability of the ‘coast’ motion of fish, that is to say, the motion of a neutrally buoyant fish at constant speed in a straight line. The forces and moments acting on the fish body are thus perfectly balanced. The fish motion is said to be unstable if a perturbation in the conditions surrounding the fish results in forces and moments that tend to increase the perturbation, and it is stable if these emerging forces tend to reduce the perturbation and return the fish to its original state. Stability may be achieved actively or passively. Active stabilization requires neurological control that activates musculo-skeletal components to compensate for the external perturbations acting against stability. Passive stabilization on the other hand requires no energy input by the fish and is dependent upon the fish morphology, i.e. geometry and elastic properties. In this paper, we use a deformable body consisting of an articulated body equipped with torsional springs at its hinge joints and submerged in an unbounded perfect fluid as a simple model to study passive stability as a function of the body geometry and spring stiffness. We show that for given body dimensions, the spring elasticity, when properly chosen, leads to passive stabilization of the (otherwise unstable) coast motion. [ABSTRACT FROM PUBLISHER]

The collective patterns that emerge in schooling fish are often analyzed using models of self-propelled particles in unbounded domains. However, while schooling fish in both field and laboratory settings interact with domain boundaries, these effects are typically ignored. Here, we propose a model that incorporates geometric confinement, by accounting for both flow and wall interactions, into existing data-driven behavioral rules. We show that new collective phases emerge where the school of fish "follows the tank wall" or "double mills." Importantly, confinement induces repeated switching between two collective states, schooling and milling. We describe the group dynamics probabilistically, uncovering bistable collective states along with unintuitive bifurcations driving phase transitions. Our findings support the hypothesis that collective transitions in fish schools could occur spontaneously, with no adjustment at the individual level, and opens venues to control and engineer emergent collective patterns in biological and synthetic systems that operate far from equilibrium., Competing Interests: Competing interests statement:The authors declare no competing interest.

It is unclear how animals with radial symmetry control locomotion without a brain. Using a combination of experiments, mathematical modeling, and robotics, we tested the extent to which this control emerges in sea stars (Protoreaster nodosus) from the local control of their hundreds of feet and their mechanical interactions with the body. We discovered that these animals compensate for an experimental increase in their submerged weight by recruiting more feet that synchronize in the power stroke of the locomotor cycle during their bouncing gait. Mathematical modeling of the mechanics of a sea star replicated this response to loading without a central controller. A robotic sea star was found to similarly recruit more actuators under higher loads through purely decentralized control. These results suggest that an array of biological or engineered actuators are capable of cooperative transport where the actuators are dynamically recruited by the mechanics of the body. In particular, the body's vertical oscillations serve to recruit feet in greater numbers to overcome the weight to propel the body forward. This form of distributed control contrasts the conventional view of animal locomotion as governed by the central nervous system and offers inspiration for the design of engineered devices with arrays of actuators., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 Elsevier Inc. All rights reserved.)

A hydrostatic skeleton allows a soft body to transmit muscular force via internal pressure. A human's tongue, an octopus' arm and a nematode's body illustrate the pervasive presence of hydrostatic skeletons among animals, which has inspired the design of soft engineered actuators. However, there is a need for a theoretical basis for understanding how hydrostatic skeletons apply mechanical work. We therefore modeled the shape change and mechanics of natural and engineered hydrostatic skeletons to determine their mechanical advantage (MA) and displacement advantage (DA). These models apply to a variety of biological structures, but we explicitly consider the tube feet of a sea star and the body segments of an earthworm, and contrast them with a hydraulic press and a McKibben actuator. A helical winding of stiff, elastic fibers around these soft actuators plays a critical role in their mechanics by maintaining a cylindrical shape, distributing forces throughout the structure and storing elastic energy. In contrast to a single-joint lever system, soft hydrostats exhibit variable gearing with changes in MA generated by deformation in the skeleton. We found that this gearing is affected by the transmission efficiency of mechanical work (MA×DA) or, equivalently, the ratio of output to input work. The transmission efficiency changes with the capacity to store elastic energy within helically wrapped fibers or associated musculature. This modeling offers a conceptual basis for understanding the relationship between the morphology of hydrostatic skeletons and their mechanical performance., Competing Interests: Competing interests The authors declare no competing or financial interests., (© 2024. Published by The Company of Biologists Ltd.)

Scyphomedusae are widespread in the oceans and their swimming has provided valuable insights into the hydrodynamics of animal propulsion. Most of this research has focused on symmetrical, linear swimming. However, in nature, medusae typically swim circuitous, nonlinear paths involving frequent turns. Here we describe swimming turns by the scyphomedusa Aurelia aurita during which asymmetric bell margin motions produce rotation around a linearly translating body center. These jellyfish 'skid' through turns and the degree of asynchrony between opposite bell margins is an approximate predictor of turn magnitude during a pulsation cycle. The underlying neuromechanical organization of bell contraction contributes substantially to asynchronous bell motions and inserts a stochastic rotational component into the directionality of scyphomedusan swimming. These mechanics are important for natural populations because asynchronous bell contraction patterns are common in situ and result in frequent turns by naturally swimming medusae., (© 2024 IOP Publishing Ltd.)

The freshwater polyp Hydra is a popular biological model system; however, we still do not understand one of its most salient behaviors, the generation of spontaneous body wall contractions. Here, by applying experimental fluid dynamics analysis and mathematical modeling, we provide functional evidence that spontaneous contractions of body walls enhance the transport of chemical compounds from and to the tissue surface where symbiotic bacteria reside. Experimentally, a reduction in the frequency of spontaneous body wall contractions is associated with a changed composition of the colonizing microbiota. Together, our findings suggest that spontaneous body wall contractions create an important fluid transport mechanism that (1) may shape and stabilize specific host-microbe associations and (2) create fluid microhabitats that may modulate the spatial distribution of the colonizing microbes. This mechanism may be more broadly applicable to animal-microbe interactions since research has shown that rhythmic spontaneous contractions in the gastrointestinal tracts are essential for maintaining normal microbiota., Competing Interests: JN, CG, AK, EK, TB No competing interests declared, (© 2023, Nawroth, Giez et al.)

The type VI secretion system (T6SS) is a broadly distributed interbacterial weapon that can be used to eliminate competing bacterial populations. Although unarmed target populations are typically used to study T6SS function in vitro, bacteria most likely encounter other T6SS-armed competitors in nature. However, the connection between subcellular details of the T6SS and the outcomes of such mutually lethal battles is not well understood. Here, we incorporate biological data derived from natural competitors of Vibrio fischeri light organ symbionts to build a biochemical model for T6SS at the single-cell level, which we then integrate into an agent-based model (ABM). Using the ABM, we isolate and experiment with strain-specific physiological differences between competitors in ways not possible with biological samples to identify winning strategies for T6SS-armed populations. Through in vitro experiments, we discover that strain-specific differences exist in T6SS activation speed. ABM simulations corroborate that faster activation is dominant in determining survival during competition. Once competitors are fully activated, the energy required for T6SS creates a tipping point where increased weapon building and firing becomes too costly to be advantageous. Through ABM simulations, we identify the threshold where this transition occurs in the T6SS parameter space. We also find that competitive outcomes depend on the geometry of the battlefield: unarmed target cells survive at the edges of a range expansion where unlimited territory can be claimed. Alternatively, competitions within a confined space, much like the light organ crypts where natural V. fischeri compete, result in the rapid elimination of the unarmed population., (© The Author(s) 2023. Published by Oxford University Press on behalf of National Academy of Sciences.)

Many elastic structures exhibit rapid shape transitions between two possible equilibrium states: umbrellas become inverted in strong wind and hopper popper toys jump when turned inside out. This snap through is a general motif for the storage and rapid release of elastic energy, and it is exploited by many biological and engineered systems from the Venus flytrap to mechanical metamaterials. Shape transitions are known to be related to the type of bifurcation the system undergoes, however, to date, there is no general understanding of the mechanisms that select these bifurcations. Here we analyze numerically and analytically two systems proposed in recent literature in which an elastic strip, initially in a buckled state, is driven through shape transitions by either rotating or translating its boundaries. We show that the two systems are mathematically equivalent, and identify three cases that illustrate the entire range of transitions described by previous authors. Importantly, using reduction order methods, we establish the nature of the underlying bifurcations and explain how these bifurcations can be predicted from geometric symmetries and symmetry-breaking mechanisms, thus providing universal design rules for elastic shape transitions.

Elastic strips provide a general motif for studying shape transitions. When actuated through rotation of its boundaries, a buckled strip exhibits, depending on the direction of rotation, three types of shape transitions: buckling, algebraic snap-through, or exponential snap-through. The transition dynamics is linked to the character of the bifurcation, which, in turn, is disclosed by the normal form of the system, but deriving normal forms is challenging. Recent work has used asymptotic methods to obtain this form for algebraic snap-through, but, to date, there is no methodology for extending this analysis to other transitions. Here we introduce a method to analyze the dynamic characteristics of an elastic strip near a transition and extend, in a straightforward manner, the previously proposed asymptotic analysis to exponential snap-through and buckling transitions. Importantly, we show that these normal forms dictate all the dynamic characteristics of the elastic strip near a shape transition. Our analysis provides reliable tools to diagnose and anticipate elastic shape transitions.

An effective evasion strategy allows prey to survive encounters with predators. Prey are generally thought to escape in a direction that is either random or serves to maximize the minimum distance from the predator. Here, we introduce a comprehensive approach to determine the most likely evasion strategy among multiple hypotheses and the role of biomechanical constraints on the escape response of prey fish. Through a consideration of six strategies with sensorimotor noise and previous kinematic measurements, our analysis shows that zebrafish larvae generally escape in a direction orthogonal to the predator's heading. By sensing only the predator's heading, this orthogonal strategy maximizes the distance from fast-moving predators, and, when operating within the biomechanical constraints of the escape response, it provides the best predictions of prey behavior among all alternatives. This work demonstrates a framework for resolving the strategic basis of evasion in predator-prey interactions, which could be applied to a broad diversity of animals.

Ciliated tissues, such as in the mammalian lungs, brains, and reproductive tracts, are specialized to pump fluid. They generate flows by the collective activity of hundreds of thousands of individual cilia that beat in a striking metachronal wave pattern. Despite progress in analyzing cilia coordination, a general theory that links coordination and fluid pumping in the limit of large arrays of cilia remains lacking. Here, we conduct in silico experiments with thousands of hydrodynamically interacting cilia, and we develop a continuum theory in the limit of infinitely many independently beating cilia by combining tools from active matter and classical Stokes flow. We find, in both simulations and theory, that isotropic and synchronized ciliary states are unstable. Traveling waves emerge regardless of initial conditions, but the characteristics of the wave and net flows depend on cilia and tissue properties. That is, metachronal phase coordination is a stable global attractor in large ciliary carpets, even under finite perturbations to cilia and tissue properties. These results support the notion that functional specificity of ciliated tissues is interlaced with the tissue architecture and cilia beat kinematics and open up the prospect of establishing structure to function maps from cilium-level beat to tissue-level coordination and fluid pumping.

The Hawaiian bobtail squid, Euprymna scolopes , harvests its luminous symbiont, Vibrio fischeri , from the surrounding seawater within hours of hatching. During embryogenesis, the host animal develops a nascent light organ with ciliated fields on each lateral surface. We hypothesized that these fields function to increase the efficiency of symbiont colonization of host tissues. Within minutes of hatching from the egg, the host's ciliated fields shed copious amounts of mucus in a non-specific response to bacterial surface molecules, specifically peptidoglycan (PGN), from the bacterioplankton in the surrounding seawater. Experimental manipulation of the system provided evidence that nitric oxide in the mucus drives an increase in ciliary beat frequency (CBF), and exposure to even small numbers of V. fischeri cells for short periods resulted in an additional increase in CBF. These results indicate that the light-organ ciliated fields respond specifically, sensitively, and rapidly, to the presence of nonspecific PGN as well as symbiont cells in the ambient seawater. Notably, the study provides the first evidence that this induction of an increase in CBF occurs as part of a thus far undiscovered initial phase in colonization of the squid host by its symbiont, i.e., host recognition of V. fischeri cues in the environment within minutes. Using a biophysics-based mathematical analysis, we showed that this rapid induction of increased CBF, while accelerating bacterial advection, is unlikely to be signaled by V. fischeri cells interacting directly with the organ surface. These overall changes in CBF were shown to significantly impact the efficiency of V. fischeri colonization of the host organ. Further, once V. fischeri has fully colonized the host tissues, i.e., about 12-24 h after initial host-symbiont interactions, the symbionts drove an attenuation of mucus shedding from the ciliated fields, concomitant with an attenuation of the CBF. Taken together, these findings offer a window into the very first interactions of ciliated surfaces with their coevolved microbial partners., Competing Interests: JN was employed by Helmholtz Zentrum München. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Gundlach, Nawroth, Kanso, Nasrin, Ruby and McFall-Ngai.)

Metachronal motion is used across a wide range of organisms for a diverse set of functions. However, despite its ubiquity, analysis of this behavior has been difficult to generalize across systems. Here we provide an overview of known commonalities and differences between systems that use metachrony to generate fluid flow. We also discuss strategies for standardizing terminology and defining future investigative directions that are analogous to other established subfields of biomechanics. Finally, we outline key challenges that are common to many metachronal systems, opportunities that have arisen due to the advent of new technology (both experimental and computational), and next steps for community development and collaboration across the nascent network of metachronal researchers., (© The Author(s) 2021. Published by Oxford University Press on behalf of the Society for Integrative and Comparative Biology. All rights reserved. For permissions please email: journals.permissions@oup.com.)

Beating flagella exhibit a variety of synchronization modes. This synchrony has long been attributed to hydrodynamic coupling between the flagella. However, recent work with flagellated algae indicates that a mechanism internal to the cell, through the contractile fibres connecting the flagella basal bodies, must be at play to actively modulate flagellar synchrony. Exactly how basal coupling mediates flagellar coordination remains unclear. Here, we examine the role of basal coupling in the synchronization of the model biflagellate Chlamydomonas reinhardtii using a series of mathematical models of decreasing levels of complexity. We report that basal coupling is sufficient to achieve inphase, antiphase and bistable synchrony, even in the absence of hydrodynamic coupling and flagellar compliance. These modes can be reached by modulating the activity level of the individual flagella or the strength of the basal coupling. We observe a slip mode when allowing for differential flagellar activity, just as in experiments with live cells. We introduce a dimensionless ratio of flagellar activity to basal coupling that is predictive of the mode of synchrony. This ratio allows us to query biological parameters which are not yet directly measurable experimentally. Our work shows a concrete route for cells to actively control the synchronization of their flagella.

Biological microfilaments exhibit a variety of synchronization modes. Recent experiments observed that a pair of isolated eukaryotic flagella, coupled solely via the fluid medium, display synchrony at nontrivial phase lags in addition to in-phase and antiphase synchrony. Using an elastohydrodynamic filament model in conjunction with numerical simulations and a Floquet-type theoretical analysis, we demonstrate that it is possible to reach multiple synchronization states by varying the intrinsic activity of the filament and the strength of hydrodynamic coupling between the two filaments. Then, we derive an evolution equation for the phase difference between the two filaments at weak coupling, and use a Kuramoto-style phase sensitivity analysis to reveal the nature of the bifurcations underlying the transitions between these different synchronized states.

Cilia, or eukaryotic flagella, are microscopic active filaments expressed on the surface of many eukaryotic cells, from single-celled protozoa to mammalian epithelial surfaces. Cilia are characterized by a highly conserved and intricate internal structure in which molecular motors exert forces on microtubule doublets causing cilia oscillations. The spatial and temporal regulations of this molecular machinery are not well understood. Several theories suggest that geometric feedback control from cilium deformations to molecular activity is needed. Here, we implement a recent sliding control model, where the unbinding of molecular motors is dictated by the sliding motion between microtubule doublets. We investigate the waveforms exhibited by the model cilium, as well as the associated molecular motor dynamics, for hinged and clamped boundary conditions. Hinged filaments exhibit base-to-tip oscillations while clamped filaments exhibit both base-to-tip and tip-to-base oscillations. We report the change in oscillation frequencies and amplitudes as a function of motor activity and sperm number, and we discuss the validity of these results in the context of experimental observations of cilia behaviour. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.