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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'.

Mucociliary clearance (MCC) is one of the most important defence mechanisms of the human respiratory system. Its failure is implicated in many chronic and debilitating airway diseases. However, due to the complexity of lung organization, we currently lack full understanding on the relationship between these regional differences in anatomy and biology and MCC functioning. For example, it is unknown whether the regional variability of airway geometry, cell biology and ciliary mechanics play a functional role in MCC. It therefore remains unclear whether the regional preference seen in some airway diseases could originate from local MCC dysfunction. Though great insights have been gained into the genetic basis of cilia ultrastructural defects in airway ciliopathies, the scaling to regional MCC function and subsequent clinical phenotype remains unpredictable. Understanding the multiscale mechanics of MCC would help elucidate genotype-phenotype relationships and enable better diagnostic tools and treatment options. Here, we review the hierarchical and variable organization of ciliated airway epithelium in human lungs and discuss how this organization relates to MCC function. We then discuss the relevancy of these structure-function relationships to current topics in lung disease research. Finally, we examine how state-of-the-art computational approaches can help address existing open questions. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.

The oral surface of sea stars is lined with arrays of tube feet that enable them to achieve highly controlled locomotion on various terrains. The activity of the tube feet is orchestrated by a nervous system that is distributed throughout the body without a central brain. How such a distributed nervous system produces a coordinated locomotion is yet to be understood. We develop mathematical models of the biomechanics of the tube feet and the sea star body. In the model, the feet are coupled mechanically through their structural connection to a rigid body. We formulate hierarchical control laws that capture salient features of the sea star nervous system. Namely, at the tube foot level, the power and recovery strokes follow a state-dependent feedback controller. At the system level, a directionality command is communicated through the nervous system to all tube feet. We study the locomotion gaits afforded by this hierarchical control model. We find that these minimally coupled tube feet coordinate to generate robust forward locomotion, reminiscent of the crawling motion of sea stars, on various terrains and for heterogeneous tube feet parameters and initial conditions. Our model also predicts a transition from crawling to bouncing consistently with recent experiments. We conclude by commenting on the implications of these findings for understanding the neuromechanics of sea stars and their potential application to autonomous robotic systems.

The interactions of microtubules with motor proteins are ubiquitous in cellular and sub-cellular processes that involve motility and cargo transport. In vitro motility assays have demonstrated that motor-driven microtubules exhibit rich dynamical behaviors from straight to curved configurations. Here, we theoretically investigate the dynamic instabilities of elastic filaments, with free-ends, driven by single follower forces that emulate the action of molecular motors. Using the resistive force theory at low Reynolds number, and a combination of numerical techniques with linear stability analysis, we show the existence of four distinct regimes of filament behavior, including a novel buckled state with locked curvature. These successive instabilities recapitulate the full range of experimentally-observed microtubule behavior, implying that neither structural nor actuation asymmetry are needed to elicit this rich repertoire of motion.

Phoretic particles self-propel using self-generated physico-chemical gradients at their surface. Within a suspension, they interact hydrodynamically by setting the fluid around them into motion and chemically by modifying the chemical background seen by their neighbours. While most phoretic systems evolve in confined environments due to buoyancy effects, most models focus on their interactions in unbounded flows. Here, we propose a first model for the interaction of phoretic particles in Hele-Shaw confinement and show that in this limit, hydrodynamic and phoretic interactions share not only the same scaling but also the same form, albeit in opposite directions. In essence, we show that phoretic interactions effectively reverse the sign of the interactions that would be obtained for swimmers interacting purely hydrodynamically. Yet, hydrodynamic interactions cannot be neglected as they significantly impact the magnitude of the interactions. This model is then used to analyse the behavior of a suspension. The suspension exhibits swirling and clustering collective modes dictated by the orientational interactions between particles, similar to hydrodynamic swimmers, but here governed by the surface properties of the phoretic particle; the reversal in the sign of the interaction tends to slow down the swimming motion of the particles.

Cilia and flagella are highly conserved slender organelles that exhibit a variety of rhythmic beating patterns from non-planar cone-like motions to planar wave-like deformations. Although their internal structure, composed of a microtubule-based axoneme driven by dynein motors, is known, the mechanism responsible for these beating patterns remains elusive. Existing theories suggest that the dynein activity is dynamically regulated, via a geometric feedback from the cilium's mechanical deformation to the dynein force. An alternative, open-loop mechanism based on a 'flutter' instability was recently proven to lead to planar oscillations of elastic filaments under follower forces. Here, we show that an elastic filament in viscous fluid, clamped at one end and acted on by an external distribution of compressive axial forces, exhibits a Hopf bifurcation that leads to non-planar spinning of the buckled filament at a locked curvature. We also show the existence of a second bifurcation, at larger force values, that induces a transition from non-planar spinning to planar wave-like oscillations. We elucidate the nature of these instabilities using a combination of nonlinear numerical analysis, linear stability theory and low-order bead-spring models. Our results show that, away from the transition thresholds, these beating patterns are robust to perturbations in the distribution of axial forces and in the filament configuration. These findings support the theory that an open-loop, instability-driven mechanism could explain both the sustained oscillations and the wide variety of periodic beating patterns observed in cilia and flagella.

We consider the inverse problem of classifying flow patterns from local sensory measurements. This problem is inspired by the ability of various aquatic organisms to respond to ambient flow signals, and is relevant for translating these abilities to underwater robotic vehicles. In Colvert, Alsalman and Kanso, B&B (2018), we trained neural networks to classify vortical flows by relying on a single flow sensor that measures a 'time history' of the local vorticity. Here, we systematically investigate the effects of distinct types of sensors on the accuracy of flow classification. We consider four types of sensors-vorticity, flow velocities parallel and transverse to the direction of flow propagation, and flow speed-and show that the networks trained using transverse velocity outperform other networks, even when subjected to aggressive data corruption. We then train the network to classify flow patterns instantaneously, using a spatially-distributed array of sensors and a single 'one time' sensory measurement. The network, based on a handful of spatially-distributed sensors, exhibits remarkable accuracy in flow classification. These results lay the groundwork for developing learning algorithms for the dynamic deployment of sensory arrays in unsteady flows.

Fish schooling is often modeled with self-propelled particles subject to phenomenological behavioral rules. Although fish are known to sense and exploit flow features, these models usually neglect hydrodynamics. Here, we propose a novel model that couples behavioral rules with far-field hydrodynamic interactions. We show that (1) a new "collective turning" phase emerges, (2) on average, individuals swim faster thanks to the fluid, and (3) the flow enhances behavioral noise. The results of this model suggest that hydrodynamic effects should be considered to fully understand the collective dynamics of fish.

Unsteady flows contain information about the objects creating them. Aquatic organisms offer intriguing paradigms for extracting flow information using local sensory measurements. In contrast, classical methods for flow analysis require global knowledge of the flow field. Here, we train neural networks to classify flow patterns using local vorticity measurements. Specifically, we consider vortex wakes behind an oscillating airfoil and we evaluate the accuracy of the network in distinguishing between three wake types, 2S, 2P  +  2S and 2P  +  4S. The network uncovers the salient features of each wake type.

One-dimensional crystals of passively-driven particles in microfluidic channels exhibit collective vibrational modes reminiscent of acoustic 'phonons'. These phonons are induced by the long-range hydrodynamic interactions among the particles and are neutrally stable at the linear level. Here, we analyze the effect of particle activity - self-propulsion - on the emergence and stability of these phonons. We show that the direction of wave propagation in active crystals is sensitive to the intensity of the background flow. We also show that activity couples, at the linear level, transverse waves to the particles' rotational motion, inducing a new mode of instability that persists in the limit of large background flow, or, equivalently, vanishingly small activity. We then report a new phenomenon of phonons switching back and forth between two adjacent crystals in both passively-driven and active systems, similar in nature to the wave switching observed in quantum mechanics, optical communication, and density stratified fluids. These findings could have implications for the design of commercial microfluidic systems and the self-assembly of passive and active micro-particles into one-dimensional structures.

We show that mucociliary membranes of animal epithelia can create fluid-mechanical microenvironments for the active recruitment of the specific microbiome of the host. In terrestrial vertebrates, these tissues are typically colonized by complex consortia and are inaccessible to observation. Such tissues can be directly examined in aquatic animals, providing valuable opportunities for the analysis of mucociliary activity in relation to bacteria recruitment. Using the squid-vibrio model system, we provide a characterization of the initial engagement of microbial symbionts along ciliated tissues. Specifically, we developed an empirical and theoretical framework to conduct a census of ciliated cell types, create structural maps, and resolve the spatiotemporal flow dynamics. Our multiscale analyses revealed two distinct, highly organized populations of cilia on the host tissues. An array of long cilia ([Formula: see text]25 [Formula: see text]m) with metachronal beat creates a flow that focuses bacteria-sized particles, at the exclusion of larger particles, into sheltered zones; there, a field of randomly beating short cilia ([Formula: see text]10 [Formula: see text]m) mixes the local fluid environment, which contains host biochemical signals known to prime symbionts for colonization. This cilia-mediated process represents a previously unrecognized mechanism for symbiont recruitment. Each mucociliary surface that recruits a microbiome such as the case described here is likely to have system-specific features. However, all mucociliary surfaces are subject to the same physical and biological constraints that are imposed by the fluid environment and the evolutionary conserved structure of cilia. As such, our study promises to provide insight into universal mechanisms that drive the recruitment of symbiotic partners., Competing Interests: Conflict of interest statement: Coauthor E.A.C.H.-H. and reviewer M.A.R.K. are both affiliated with the University of California, Berkeley, but in different departments.

Human movement patterns have been shown to be particularly variable if many combinations of activity in different muscles all achieve the same task goal (i.e., are goal-equivalent). The nervous system appears to automatically vary its output among goal-equivalent combinations of muscle activity to minimize muscle fatigue or distribute tissue loading, but the neural mechanism of this "good" variation is unknown. Here we use a bimanual finger task, electroencephalography (EEG), and machine learning to determine if cortical signals can predict goal-equivalent variation in finger force output. 18 healthy participants applied left and right index finger forces to repeatedly perform a task that involved matching a total (sum of right and left) finger force. As in previous studies, we observed significantly more variability in goal-equivalent muscle activity across task repetitions compared to variability in muscle activity that would not achieve the goal: participants achieved the task in some repetitions with more right finger force and less left finger force (right > left) and in other repetitions with less right finger force and more left finger force (left > right). We found that EEG signals from the 500 milliseconds (ms) prior to each task repetition could make a significant prediction of which repetitions would have right > left and which would have left > right. We also found that cortical maps of sites contributing to the prediction contain both motor and pre-motor representation in the appropriate hemisphere. Thus, goal-equivalent variation in motor output may be implemented at a cortical level.

Fluid-based locomotion at low Reynolds number is subject to the constraints of Purcell's scallop theorem: reciprocal shape kinematics identical under a time-reversal symmetry cannot cause locomotion. In particular, a single degree-of-freedom scallop undergoing opening and closing motions cannot swim. Most strategies for symmetry breaking and locomotion rely on direct control of the swimmer's shape kinematics. Less is known about indirect control via actuation of the fluid medium. To address how such indirect actuation strategies can lead to locomotion, we analyze a Λ-shaped model system analogous to Purcell's scallop but able to deform passively in oscillatory flows. Neutrally buoyant scallops undergo no net locomotion. We show that dense, elastic scallops can exhibit passive locomotion in zero-mean oscillatory flows. We examine the efficiency of swimming parallel to the background flow and analyze the stability of these motions. We observe transitions from stable to unstable swimming, including ordered transitions from fluttering to chaoticlike motions and tumbling. Our results demonstrate that flow oscillations can be used to passively actuate and control the motion of microswimmers, which may be relevant to applications such as surgical robots and cell sorting and manipulation in microfluidic devices.

Motile cilia are used by many eukaryotic cells to transport flow. Cilia-driven flows are important to many physiological functions, yet a deep understanding of the interplay between the mechanical structure of cilia and their physiological functions in healthy and diseased conditions remains elusive. To develop such an understanding, one needs a quantitative framework to assess cilia performance and robustness when subject to perturbations in the cilia apparatus. Here we link cilia design (beating patterns) to function (flow transport) in the context of experimentally and theoretically derived cilia models. We particularly examine the optimality and robustness of cilia design. Optimality refers to efficiency of flow transport, while robustness is defined as low sensitivity to variations in the design parameters. We find that suboptimal designs can be more robust than optimal ones. That is, designing for the most efficient cilium does not guarantee robustness. These findings have significant implications on the understanding of cilia design in artificial and biological systems.

Motile and driven particles confined in microfluidic channels exhibit interesting emergent behavior, from propagating density bands to density shock waves. A deeper understanding of the physical mechanisms responsible for these emergent structures is relevant to a number of physical and biomedical applications. Here, we study the formation of density shock waves in the context of an idealized model of microswimmers confined in a narrow channel and subject to a uniform external flow. Interestingly, these density shock waves exhibit a transition from "subsonic" with compression at the back to "supersonic" with compression at the front of the population as the intensity of the external flow increases. This behavior is the result of a nontrivial interplay between hydrodynamic interactions and geometric confinement, and it is confirmed by a novel quasilinear wave model that properly captures the dependence of the shock formation on the external flow. These findings can be used to guide the development of novel mechanisms for controlling the emergent density distribution and the average population speed, with potentially profound implications on various processes in industry and biotechnology, such as the transport and sorting of cells in flow channels.

Geometric confinement plays an important role in the dynamics of natural and synthetic microswimmers from bacterial cells to self-propelled particles in high-throughput microfluidic devices. However, little is known about the effects of geometric confinement on the emergent global patterns in such self-propelled systems. Recent experiments on bacterial cells report that, depending on the cell concentration, cells either spontaneously organize into vortical motion in thin cylindrical and spherical droplets or aggregate at the inner boundary of the droplets. Our goal in this paper is to investigate, in the context of an idealized physical model, the interplay between geometric confinement and level of flagellar activity on the emergent collective patterns. We show that decreasing flagellar activity induces a hydrodynamically triggered transition in confined microswimmers from swirling to global circulation (vortex) to boundary aggregation and clustering. These results highlight that the complex interplay between confinement, flagellar activity, and hydrodynamic flows in concentrated suspensions of microswimmers could lead to a plethora of global patterns that are difficult to predict from geometric consideration alone.