Control of the mitotic cleavage plane by local epithelial topology.

For nearly 150 years, it has been recognized that cell shape strongly influences the orientation of the mitotic cleavage plane (e.g., Hofmeister, 1863). However, we still understand little about the complex interplay between cell shape and cleavage-plane orientation in epithelia, where polygonal cell geometries emerge from multiple factors, including cell packing, cell growth, and cell division itself. Here, using mechanical simulations, we show that the polygonal shapes of individual cells can systematically bias the long-axis orientations of their adjacent mitotic neighbors. Strikingly, analyses of both animal epithelia and plant epidermis confirm a robust and nearly identical correlation between local cell topology and cleavage-plane orientation in vivo. Using simple mathematics, we show that this effect derives from fundamental packing constraints. Our results suggest that local epithelial topology is a key determinant of cleavage-plane orientation, and that cleavage-plane bias may be a widespread property of polygonal cell sheets in plants and animals.

The extension of internal humidity levels beyond the soil surface facilitates mound expansion in Macrotermes.

Termites in the genus Macrotermes construct large-scale soil mounds above their nests. The classic explanation for how termites coordinate their labour to build the mound, based on a putative cement pheromone, has recently been called into question. Here, we present evidence for an alternate interpretation based on sensing humidity. The high humidity characteristic of the mound's internal environment extends a short distance into the low-humidity external world, in a 'bubble' that can be disrupted by external factors like wind. Termites transport more soil mass into on-mound reservoirs when shielded from water loss through evaporation, and into experimental arenas when relative humidity is held at a high value. These results suggest that the interface between internal and external conditions may serve as a template for mound expansion, with workers moving freely within a zone of high humidity and depositing soil at its edge. Such deposition of additional moist soil will increase local humidity, in a feedback loop allowing the 'interior' zone to progress further outward and lead to mound expansion.

Effects of load mass and size on cooperative transport in ants over multiple transport challenges.

Some ant species cooperatively transport a wide range of extremely large, heavy food objects of various shapes and materials. While previous studies have examined how object mass and size affect the recruitment of additional workers, less is understood about how these attributes affect the rest of the transport process. Using artificial baits with independently varying mass and size, we reveal their effects on cooperative transport in Paratrechina longicornis across two transport challenges: movement initiation and obstacle navigation. As expected, object mass was tightly correlated with number of porters as workers adjust group size to the task. Mass affected performance similarly across the two challenges, with groups carrying heavy objects having lower performance. Yet, object size had differing effects depending on the challenge. While larger objects led to reduced performance during movement initiation - groups took longer to start moving these objects and had lower velocities - there was no evidence for this during obstacle navigation, and the opposite pattern was weakly supported. If a group struggles to start moving an object, it does not necessarily predict difficulty navigating around obstacles; groups should persist in trying to move 'difficult' objects, which may be easier to transport later in the process. Additionally, groups hitting obstacles were not substantially disrupted, and started moving again sooner than at the start, despite the nest direction being blocked. Paratrechina longicornis transport groups never failed, performing well at both challenges while carrying widely varying objects, and even transported a bait weighing 1900 times the mass of an individual.

Differential construction response to humidity by related species of mound-building termites.

Macrotermes michaelseni and M. natalensis are two morphologically similar termite species occupying the same habitat across southern Africa. Both build large mounds and tend mutualistic fungal symbionts for nutrients, but despite these behavioural and physiological similarities, the mound superstructures they create differ markedly. The behavioural differences behind this discrepancy remain elusive, and are the subject of ongoing investigations. Here, we show that the two species demonstrate distinctive building activity in a laboratory-controlled environment consisting of still air with low ambient humidity. In these conditions, M. michaelseni transports less soil from a central reservoir, deposits this soil over a smaller area, and creates structures with a smaller volumetric envelope than M. natalensis In high humidity, no such systematic difference is observed. This result suggests a differential behavioural threshold or sensitivity to airborne moisture that may relate to the distinct macro-scale structures observed in the African bushland.

Costs of task allocation with local feedback: Effects of colony size and extra workers in social insects and other multi-agent systems.

Adaptive collective systems are common in biology and beyond. Typically, such systems require a task allocation algorithm: a mechanism or rule-set by which individuals select particular roles. Here we study the performance of such task allocation mechanisms measured in terms of the time for individuals to allocate to tasks. We ask: (1) Is task allocation fundamentally difficult, and thus costly? (2) Does the performance of task allocation mechanisms depend on the number of individuals? And (3) what other parameters may affect their efficiency? We use techniques from distributed computing theory to develop a model of a social insect colony, where workers have to be allocated to a set of tasks; however, our model is generalizable to other systems. We show, first, that the ability of workers to quickly assess demand for work in tasks they are not currently engaged in crucially affects whether task allocation is quickly achieved or not. This indicates that in social insect tasks such as thermoregulation, where temperature may provide a global and near instantaneous stimulus to measure the need for cooling, for example, it should be easy to match the number of workers to the need for work. In other tasks, such as nest repair, it may be impossible for workers not directly at the work site to know that this task needs more workers. We argue that this affects whether task allocation mechanisms are under strong selection. Second, we show that colony size does not affect task allocation performance under our assumptions. This implies that when effects of colony size are found, they are not inherent in the process of task allocation itself, but due to processes not modeled here, such as higher variation in task demand for smaller colonies, benefits of specialized workers, or constant overhead costs. Third, we show that the ratio of the number of available workers to the workload crucially affects performance. Thus, workers in excess of those needed to complete all tasks improve task allocation performance. This provides a potential explanation for the phenomenon that social insect colonies commonly contain inactive workers: these may be a 'surplus' set of workers that improves colony function by speeding up optimal allocation of workers to tasks. Overall our study shows how limitations at the individual level can affect group level outcomes, and suggests new hypotheses that can be explored empirically.

Excavation and aggregation as organizing factors in de novo construction by mound-building termites.

Termites construct complex mounds that are orders of magnitude larger than any individual and fulfil a variety of functional roles. Yet the processes through which these mounds are built, and by which the insects organize their efforts, remain poorly understood. The traditional understanding focuses on stigmergy, a form of indirect communication in which actions that change the environment provide cues that influence future work. Termite construction has long been thought to be organized via a putative 'cement pheromone': a chemical added to deposited soil that stimulates further deposition in the same area, thus creating a positive feedback loop whereby coherent structures are built up. To investigate the detailed mechanisms and behaviours through which termites self-organize the early stages of mound construction, we tracked the motion and behaviour of major workers from two Macrotermes species in experimental arenas. Rather than a construction process focused on accumulation of depositions, as models based on cement pheromone would suggest, our results indicated that the primary organizing mechanisms were based on excavation. Digging activity was focused on a small number of excavation sites, which in turn provided templates for soil deposition. This behaviour was mediated by a mechanism of aggregation, with termites being more likely to join in the work at an excavation site as the number of termites presently working at that site increased. Statistical analyses showed that this aggregation mechanism was a response to active digging, distinct from and unrelated to putative chemical cues that stimulate deposition. Agent-based simulations quantitatively supported the interpretation that the early stage of de novo construction is primarily organized by excavation and aggregation activity rather than by stigmergic deposition.

Collective strategy for obstacle navigation during cooperative transport by ants.

Group cohesion and consensus have primarily been studied in the context of discrete decisions, but some group tasks require making serial decisions that build on one another. We examine such collective problem solving by studying obstacle navigation during cooperative transport in ants. In cooperative transport, ants work together to move a large object back to their nest. We blocked cooperative transport groups of Paratrechina longicornis with obstacles of varying complexity, analyzing groups' trajectories to infer what kind of strategy the ants employed. Simple strategies require little information, but more challenging, robust strategies succeed with a wider range of obstacles. We found that transport groups use a stochastic strategy that leads to efficient navigation around simple obstacles, and still succeeds at difficult obstacles. While groups navigating obstacles preferentially move directly toward the nest, they change their behavior over time; the longer the ants are obstructed, the more likely they are to move away from the nest. This increases the chance of finding a path around the obstacle. Groups rapidly changed directions and rarely stalled during navigation, indicating that these ants maintain consensus even when the nest direction is blocked. Although some decisions were aided by the arrival of new ants, at many key points, direction changes were initiated within the group, with no apparent external cause. This ant species is highly effective at navigating complex environments, and implements a flexible strategy that works for both simple and more complex obstacles.

On the origins of the mitotic shift in proliferating cell layers.

BACKGROUND: During plant and animal development, monolayer cell sheets display a stereotyped distribution of polygonal cell shapes. In interphase cells these shapes range from quadrilaterals to decagons, with a robust average of six sides per cell. In contrast, the subset of cells in mitosis exhibits a distinct distribution with an average of seven sides. It remains unclear whether this 'mitotic shift' reflects a causal relationship between increased polygonal sidedness and increased division likelihood, or alternatively, a passive effect of local proliferation on cell shape. METHODS: We use a combination of probabilistic analysis and mathematical modeling to predict the geometry of mitotic polygonal cells in a proliferating cell layer. To test these predictions experimentally, we use Flp-Out stochastic labeling in the Drosophila wing disc to induce single cell clones, and confocal imaging to quantify the polygonal topologies of these clones as a function of cellular age. For a more generic test in an idealized cell layer, we model epithelial sheet proliferation in a finite element framework, which yields a computationally robust, emergent prediction of the mitotic cell shape distribution. RESULTS: Using both mathematical and experimental approaches, we show that the mitotic shift derives primarily from passive, non-autonomous effects of mitoses in neighboring cells on each cell's geometry over the course of the cell cycle. Computationally, we predict that interphase cells should passively gain sides over time, such that cells at more advanced stages of the cell cycle will tend to have a larger number of neighbors than those at earlier stages. Validating this prediction, experimental analysis of randomly labeled epithelial cells in the Drosophila wing disc demonstrates that labeled cells exhibit an age-dependent increase in polygonal sidedness. Reinforcing these data, finite element simulations of epithelial sheet proliferation demonstrate in a generic framework that passive side-gaining is sufficient to generate a mitotic shift. CONCLUSIONS: Taken together, our results strongly suggest that the mitotic shift reflects a time-dependent accumulation of shared cellular interfaces over the course of the cell cycle. These results uncover fundamental constraints on the relationship between cell shape and cell division that should be general in adherent, polarized cell layers.

The role of hydrodynamics in collective motions of fish schools and bioinspired underwater robots.

Collective behaviour defines the lives of many animal species on the Earth. Underwater swarms span several orders of magnitude in size, from coral larvae and krill to tunas and dolphins. Agent-based algorithms have modelled collective movements of animal groups by use of social forces, which approximate the behaviour of individual animals. But details of how swarming individuals interact with the fluid environment are often under-examined. How do fluid forces shape aquatic swarms? How do fish use their flow-sensing capabilities to coordinate with their schooling mates? We propose viewing underwater collective behaviour from the framework of fluid stigmergy, which considers both physical interactions and information transfer in fluid environments. Understanding the role of hydrodynamics in aquatic collectives requires multi-disciplinary efforts across fluid mechanics, biology and biomimetic robotics. To facilitate future collaborations, we synthesize key studies in these fields.

The emergence of geometric order in proliferating metazoan epithelia.

The predominantly hexagonal cell pattern of simple epithelia was noted in the earliest microscopic analyses of animal tissues, a topology commonly thought to reflect cell sorting into optimally packed honeycomb arrays. Here we use a discrete Markov model validated by time-lapse microscopy and clonal analysis to demonstrate that the distribution of polygonal cell types in epithelia is not a result of cell packing, but rather a direct mathematical consequence of cell proliferation. On the basis of in vivo analysis of mitotic cell junction dynamics in Drosophila imaginal discs, we mathematically predict the convergence of epithelial topology to a fixed equilibrium distribution of cellular polygons. This distribution is empirically confirmed in tissue samples from vertebrate, arthropod and cnidarian organisms, suggesting that a similar proliferation-dependent cell pattern underlies pattern formation and morphogenesis throughout the metazoa.

Hysteresis stabilizes dynamic control of self-assembled army ant constructions.

Biological systems must adjust to changing external conditions, and their resilience depends on their control mechanisms. How is dynamic control implemented in noisy, decentralized systems? Army ants' self-assembled bridges are built on unstable features, like leaves, which frequently move. Using field experiments and simulations, we characterize the bridges' response as the gaps they span change in size, identify the control mechanism, and explore how this emerges from individuals' decisions. For a given gap size, bridges were larger after the gap increased rather than decreased. This hysteresis was best explained by an accumulator model, in which individual decisions to join or leave a bridge depend on the difference between its current and equilibrium state. This produces robust collective structures that adjust to lasting perturbations while ignoring small, momentary shifts. Our field data support separate joining and leaving cues; joining is prompted by high bridge performance and leaving by an excess of ants. This leads to stabilizing hysteresis, an important feature of many biological and engineered systems.

Implicit coordination for 3D underwater collective behaviors in a fish-inspired robot swarm.

Many fish species gather by the thousands and swim in harmony with seemingly no effort. Large schools display a range of impressive collective behaviors, from simple shoaling to collective migration and from basic predator evasion to dynamic maneuvers such as bait balls and flash expansion. A wealth of experimental and theoretical work has shown that these complex three-dimensional (3D) behaviors can arise from visual observations of nearby neighbors, without explicit communication. By contrast, most underwater robot collectives rely on centralized, above-water, explicit communication and, as a result, exhibit limited coordination complexity. Here, we demonstrate 3D collective behaviors with a swarm of fish-inspired miniature underwater robots that use only implicit communication mediated through the production and sensing of blue light. We show that complex and dynamic 3D collective behaviors-synchrony, dispersion/aggregation, dynamic circle formation, and search-capture-can be achieved by sensing minimal, noisy impressions of neighbors, without any centralized intervention. Our results provide insights into the power of implicit coordination and are of interest for future underwater robots that display collective capabilities on par with fish schools for applications such as environmental monitoring and search in coral reefs and coastal environments.

Validating a Termite-Inspired Construction Coordination Mechanism Using an Autonomous Robot.

Many species of termites build large, structurally complex mounds, and the mechanisms behind this coordinated construction have been a longstanding topic of investigation. Recent work has suggested that humidity may play a key role in the mound expansion of savannah-dwelling Macrotermes species: termites preferentially deposit soil on the mound surface at the boundary of the high-humidity region characteristic of the mound interior, implying a coordination mechanism through environmental feedback where addition of wet soil influences the humidity profile and vice versa. Here we test this potential mechanism physically using a robotic system. Local humidity measurements provide a cue for material deposition. As the analogue of the termite's deposition of wet soil and corresponding local increase in humidity, the robot drips water onto an absorbent substrate as it moves. Results show that the robot extends a semi-enclosed area outward when air is undisturbed, but closes it off when air is disturbed by an external fan, consistent with termite building activity in still vs. windy conditions. This result demonstrates an example of adaptive construction patterns arising from the proposed coordination mechanism, and supports the hypothesis that such a mechanism operates in termites.

Hydrodynamic advantages of in-line schooling.

Fish benefit energetically when swimming in groups, which is reflected in lower tail-beat frequencies for maintaining a given speed. Recent studies further show that fish save the most energy when swimming behind their neighbor such that both the leader and the follower benefit. However, the mechanisms underlying such hydrodynamic advantages have thus far not been established conclusively. The long-standing drafting hypothesis-reduction of drag forces by judicious positioning in regions of reduced oncoming flow-fails to explain advantages of in-line schooling described in this work. We present an alternate hypothesis for the hydrodynamic benefits of in-line swimming based on enhancement of propulsive thrust. Specifically, we show that an idealized school consisting of in-line pitching foils gains hydrodynamic benefits via two mechanisms that are rooted in the undulatory jet leaving the leading foil and impinging on the trailing foil: (i) leading-edge suction on the trailer foil, and (ii) added-mass push on the leader foil. Our results demonstrate that the savings in power can reach as high as 70% for a school swimming in a compact arrangement. Informed by these findings, we designed a modification of the tail propulsor that yielded power savings of up to 56% in a self-propelled autonomous swimming robot. Our findings provide insights into hydrodynamic advantages of fish schooling, and also enable bioinspired designs for significantly more efficient propulsion systems that can harvest some of their energy left in the flow.

Modeling and inferring cleavage patterns in proliferating epithelia.

The regulation of cleavage plane orientation is one of the key mechanisms driving epithelial morphogenesis. Still, many aspects of the relationship between local cleavage patterns and tissue-level properties remain poorly understood. Here we develop a topological model that simulates the dynamics of a 2D proliferating epithelium from generation to generation, enabling the exploration of a wide variety of biologically plausible cleavage patterns. We investigate a spectrum of models that incorporate the spatial impact of neighboring cells and the temporal influence of parent cells on the choice of cleavage plane. Our findings show that cleavage patterns generate "signature" equilibrium distributions of polygonal cell shapes. These signatures enable the inference of local cleavage parameters such as neighbor impact, maternal influence, and division symmetry from global observations of the distribution of cell shape. Applying these insights to the proliferating epithelia of five diverse organisms, we find that strong division symmetry and moderate neighbor/maternal influence are required to reproduce the predominance of hexagonal cells and low variability in cell shape seen empirically. Furthermore, we present two distinct cleavage pattern models, one stochastic and one deterministic, that can reproduce the empirical distribution of cell shapes. Although the proliferating epithelia of the five diverse organisms show a highly conserved cell shape distribution, there are multiple plausible cleavage patterns that can generate this distribution, and experimental evidence suggests that indeed plants and fruitflies use distinct division mechanisms.

Epithelial topology.

It is universally accepted that genetic control over basic aspects of cell and molecular biology is the primary organizing principle in development and homeostasis of living systems. However, instances do exist where important aspects of biological order arise without explicit genetic instruction, emerging instead from simple physical principles, stochastic processes, or the complex self-organizing interaction between random and seemingly unrelated parts. Being mostly resistant to direct genetic dissection, the analysis of such emergent processes falls into a grey area between mathematics, physics and molecular cell biology and therefore remains very poorly understood. We recently proposed a mathematical model predicting the emergence of a specific non-Gaussian distribution of polygonal cell shapes from the stochastic cell division process in epithelial cell sheets; this cell shape distribution appears to be conserved across a diverse set of animals and plants.1 The use of such topological models to study the process of cellular morphogenesis has a long history, starting almost a century ago, and many insights from those original works influence current experimental studies. Here we review current and past literature on this topic while exploring some new ideas on the origins and implications of topological order in proliferating epithelia.

Surface curvature guides early construction activity in mound-building termites.

Termite colonies construct towering, complex mounds, in a classic example of distributed agents coordinating their activity via interaction with a shared environment. The traditional explanation for how this coordination occurs focuses on the idea of a 'cement pheromone', a chemical signal left with deposited soil that triggers further deposition. Recent research has called this idea into question, pointing to a more complicated behavioural response to cues perceived with multiple senses. In this work, we explored the role of topological cues in affecting early construction activity in Macrotermes. We created artificial surfaces with a known range of curvatures, coated them with nest soil, placed groups of major workers on them and evaluated soil displacement as a function of location at the end of 1 h. Each point on the surface has a given curvature, inclination and absolute height; to disambiguate these factors, we conducted experiments with the surface in different orientations. Soil displacement activity is consistently correlated with surface curvature, and not with inclination nor height. Early exploration activity is also correlated with curvature, to a lesser degree. Topographical cues provide a long-term physical memory of building activity in a manner that ephemeral pheromone labelling cannot. Elucidating the roles of these and other cues for group coordination may help provide organizing principles for swarm robotics and other artificial systems. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Fast, accurate, small-scale 3D scene capture using a low-cost depth sensor.

Commercially available depth sensing devices are primarily designed for domains that are either macroscopic, or static. We develop a solution for fast microscale 3D reconstruction, using off-the-shelf components. By the addition of lenses, precise calibration of camera internals and positioning, and development of bespoke software, we turn an infrared depth sensor designed for human-scale motion and object detection into a device with mm-level accuracy capable of recording at up to 30Hz.

Arrestant property of recently manipulated soil on Macrotermes michaelseni as determined through visual tracking and automatic labeling of individual termite behaviors.

The construction of termite nests has been suggested to be organized by a stigmergic process that makes use of putative cement pheromone found in saliva and recently manipulated soil ("nest material"), hypothesized to specifically induce material deposition by workers. Herein, we tracked 100 individuals placed in arenas filled with a substrate of half nest material, half clean soil, and used automatic labeling software to identify behavioral states. Our findings suggest that nest material acts to arrest termites; termites prefer to spend time on nest material when compared against clean soil. Residency time was significantly greater, and all construction behaviors occurred significantly more often on nest material. The arrestant function of nest material must be accounted for in experiments that seek semiochemical cues for the organization of labor. Future research will focus on the manner in which termites combine olfaction with tactile cues as well as other organizing factors during construction.