Fishing out collective memory of migratory schools

Animals form groups for many reasons, but there are costs and benefits associated with group formation. One of the benefits is collective memory. In groups on the move, social interactions play a crucial role in the cohesion and the ability to make consensus decisions. When migrating from spawning to feeding areas, fish schools need to retain a collective memory of the destination site over thousands of kilometres, and changes in group formation or individual preference can produce sudden changes in migration pathways. We propose a modelling framework, based on stochastic adaptive networks, that can reproduce this collective behaviour. We assume that three factors control group formation and school migration behaviour: the intensity of social interaction, the relative number of informed individuals and the strength of preference that informed individuals have for a particular migration area. We treat these factors independently and relate the individuals’ preferences to the experience and memory for certain migration sites. We demonstrate that removal of knowledgeable individuals or alteration of individual preference can produce rapid changes in group formation and collective behaviour. For example, intensive fishing targeting the migratory species and also their preferred prey can reduce both terms to a point at which migration to the destination sites is suddenly stopped. The conceptual approaches represented by our modelling framework may therefore be able to explain large-scale changes in fish migration and spatial distribution.     

Aggregation by depletion attraction in cultures of bacteria producing exopolysaccharide

In bacteria, the production of exopolysaccharides—polysaccharides secreted by the cells into their growth medium—is integral to the formation of aggregates and biofilms. These exopolysaccharides often form part of a matrix that holds the cells together. Investigating the bacterium Sinorhizobium meliloti, we found that a mutant that overproduces the exopolysaccharide succinoglycan showed enhanced aggregation, resulting in phase separation of the cultures. However, the aggregates did not appear to be covered in polysaccharides. Succinoglycan purified from cultures was applied to different concentrations of cells, and observation of the phase behaviour showed that the limiting polymer concentration for aggregation and phase separation to occur decreased with increasing cell concentration, suggesting a ‘crowding mechanism’ was occurring. We suggest that, as found in colloidal dispersions, the presence of a non-adsorbing polymer in the form of the exopolysaccharide succinoglycan drives aggregation of S. meliloti by depletion attraction. This force leads to self-organization of the bacteria into small clusters of laterally aligned cells, and, furthermore, leads to aggregates clustering into biofilm-like structures on a surface.     

The interplay between a self-organized process and an environmental template: corpse clustering under the influence of air currents in ants

Many spatial patterns observed in nature emerge from local processes and their interactions with the local environment. The clustering of objects by social insects represents such a pattern formation process that can be observed at both the individual and the collective level. In this paper, we study the interaction between air currents and clustering behaviour in order to address the coordinating mechanisms at the individual level that underlie the spatial pattern formation process in a heterogeneous environment. We choose the corpse clustering behaviour of the ant Messor sanctus as an experimental paradigm. In a specifically designed experimental set-up with a well-controlled laminar air flow (approx. 1 cm s-1), we first quantify the modulation of the individual corpse aggregation behaviour as a function of corpse density, air flow intensity and the ant's position with respect to corpse piles and air flow direction. We then explore by numerical simulation how the forming corpse piles modify the laminar air flow around them and link this result with the individual behaviour modulation. Finally, we demonstrate on the collective level that this laminar air flow leads to an elongation and a slow displacement of the formed corpse piles in the direction of the air current. Both the individual behaviour modulated by air flow and the air flow modulated by the forming corpse piles can explain the pile patterns observed on the collective level as a stigmergic process. We discuss the generality of this coordinating mechanism to explain the clustering phenomena in heterogeneous environments reported in the literature.     

Energy dissipation rate analysis of a low upper shelf data set

Stable and unstable tearing in metals is currently analysed by J integral theory. Test and analysis methods are fully standardised and the validity of the approach has been demonstrated by reference to laboratory and type testing. A central requirement of the J method is that the J_R curve remain invariant as size increases (specimen dimension to structure). A set of data from the literature which show the slope of the J_R curve decreasing with increasing specimen size are presented. This represents an unsafe trend in terms of predicting structural behaviour from small specimens tests. The observed behaviour is explained successfully with energy dissipation rate theory. At the same time energy dissipation rate theory can also explain the more normally observed behaviour of size invariant J_R curves. It is concluded that stable and unstable tearing in metals is best described by the energy dissipation rate approach.     

Modelling planar polarity of epithelia: the role of signal relay in collective cell polarization

Collective cell polarization is an important characteristic of tissues. Epithelia commonly display cellular structures that are polarized within the plane of the tissue. Establishment of this planar cell polarity requires mechanisms that locally align polarized structures between neighbouring cells, as well as cues that provide global information about alignment relative to an axis of a tissue. In the Drosophila ovary, the cadherin Fat2 is required to orient actin filaments located at the basal side of follicle cells perpendicular to the long axis of the egg chamber. The mechanisms directing this orientation of actin filaments, however, remain unknown. Here we show, using genetic mosaic analysis, that fat2 is not essential for the local alignment of actin filaments between neighbouring cells. Moreover, we provide evidence that Fat2 is involved in the propagation of a cue specifying the orientation of actin filaments relative to the tissue axis. Monte Carlo simulations of actin filament orientation resemble the results of the genetic mosaic analysis, if it is assumed that a polarity signal can propagate from a signal source only through a connected chain of wild-type cells. Our results suggest that Fat2 is required for propagating global polarity information within the follicle epithelium through direct cell–cell contact. Our computational model might be more generally applicable to study collective cell polarization in tissues.     

Fractal analysis of behaviour in a wild primate: behavioural complexity in health and disease

Parasitism and other stressors are ubiquitous in nature but their effects on animal behaviour can be difficult to identify. We investigated the effects of nematode parasitism and other indicators of physiological impairment on the sequential complexity of foraging and locomotion behaviour among wild Japanese macaques (Macaca fuscata yakui). We observed all sexually mature individuals (n = 28) in one macaque study group between October 2007 and August 2008, and collected two faecal samples/month/individual (n = 362) for parasitological examination. We used detrended fluctuation analysis (DFA) to investigate long-range autocorrelation in separate, binary sequences of foraging (n = 459) and locomotion (n = 446) behaviour collected via focal sampling. All behavioural sequences exhibited long-range autocorrelation, and linear mixed-effects models suggest that increasing infection with the nodular worm Oesophagostomum aculeatum, clinically impaired health, reproductive activity, ageing and low dominance status were associated with reductions in the complexity of locomotion, and to a lesser extent foraging, behaviour. Furthermore, the sequential complexity of behaviour increased with environmental complexity. We argue that a reduction in complexity in animal behaviour characterizes individuals in impaired or ‘stressed’ states, and may have consequences if animals cannot cope with heterogeneity in their natural habitats.     

The effect of sampling rate on observed statistics in a correlated random walk

Tracking the movement of individual cells or animals can provide important information about their motile behaviour, with key examples including migrating birds, foraging mammals and bacterial chemotaxis. In many experimental protocols, observations are recorded with a fixed sampling interval and the continuous underlying motion is approximated as a series of discrete steps. The size of the sampling interval significantly affects the tracking measurements, the statistics computed from observed trajectories, and the inferences drawn. Despite the widespread use of tracking data to investigate motile behaviour, many open questions remain about these effects. We use a correlated random walk model to study the variation with sampling interval of two key quantities of interest: apparent speed and angle change. Two variants of the model are considered, in which reorientations occur instantaneously and with a stationary pause, respectively. We employ stochastic simulations to study the effect of sampling on the distributions of apparent speeds and angle changes, and present novel mathematical analysis in the case of rapid sampling. Our investigation elucidates the complex nature of sampling effects for sampling intervals ranging over many orders of magnitude. Results show that inclusion of a stationary phase significantly alters the observed distributions of both quantities.     

Lag,lock, sync,slip: the many ‘phases’ of coupled flagella

In a multitude of life''s processes, cilia and flagella are found indispensable. Recently, the biflagellated chlorophyte alga Chlamydomonas has become a model organism for the study of ciliary motility and synchronization. Here, we use high-speed, high-resolution imaging of single pipette-held cells to quantify the rich dynamics exhibited by their flagella. Underlying this variability in behaviour are biological dissimilarities between the two flagella—termed cis and trans, with respect to a unique eyespot. With emphasis on the wild-type, we derive limit cycles and phase parametrizations for self-sustained flagellar oscillations from digitally tracked flagellar waveforms. Characterizing interflagellar phase synchrony via a simple model of coupled oscillators with noise, we find that during the canonical swimming breaststroke the cis flagellum is consistently phase-lagged relative to, while remaining robustly phase-locked with, the trans flagellum. Transient loss of synchrony, or phase slippage, may be triggered stochastically, in which the trans flagellum transitions to a second mode of beating with attenuated beat envelope and increased frequency. Further, exploiting this alga''s ability for flagellar regeneration, we mechanically induced removal of one or the other flagellum of the same cell to reveal a striking disparity between the beatings of the cis and trans flagella, in isolation. These results are evaluated in the context of the dynamic coordination of Chlamydomonas flagella.     

Determining asymptotically large population sizes in insect swarms

Social animals commonly form aggregates that exhibit emergent collective behaviour, with group dynamics that are distinct from the behaviour of individuals. Simple models can qualitatively reproduce such behaviour, but only with large numbers of individuals. But how rapidly do the collective properties of animal aggregations in nature emerge with group size? Here, we study swarms of Chironomus riparius midges and measure how their statistical properties change as a function of the number of participating individuals. Once the swarms contain order 10 individuals, we find that all statistics saturate and the swarms enter an asymptotic regime. The influence of environmental cues on the swarm morphology decays on a similar scale. Our results provide a strong constraint on how rapidly swarm models must produce collective states. But our findings support the feasibility of using swarms as a design template for multi-agent systems, because self-organized states are possible even with few agents.     

The entropic basis of collective behaviour

We identify a unique viewpoint on the collective behaviour of intelligent agents. We first develop a highly general abstract model for the possible future lives these agents may encounter as a result of their decisions. In the context of these possibilities, we show that the causal entropic principle, whereby agents follow behavioural rules that maximize their entropy over all paths through the future, predicts many of the observed features of social interactions among both human and animal groups. Our results indicate that agents are often able to maximize their future path entropy by remaining cohesive as a group and that this cohesion leads to collectively intelligent outcomes that depend strongly on the distribution of the number of possible future paths. We derive social interaction rules that are consistent with maximum entropy group behaviour for both discrete and continuous decision spaces. Our analysis further predicts that social interactions are likely to be fundamentally based on Weber''s law of response to proportional stimuli, supporting many studies that find a neurological basis for this stimulus–response mechanism and providing a novel basis for the common assumption of linearly additive ‘social forces’ in simulation studies of collective behaviour.     

Optical parameters of the tunable Bragg reflectors in squid

Cephalopods (e.g. octopus, squid and cuttlefish) dynamically tune the colour and brightness of their skin for camouflage and communication using specialized skin cells called iridocytes. We use high-resolution microspectrophotometry to investigate individual tunable Bragg structures (consisting of alternating reflectin protein-containing, high-refractive index lamellae and low-refractive index inter-lamellar spaces) in live and chemically fixed iridocytes of the California market squid, Doryteuthis opalescens. This subcellular, single-stack microspectrophotometry allows for spectral normalization, permitting use of a transfer-matrix model of Bragg reflectance to calculate all the parameters of the Bragg stack—the refractive indices, dimensions and numbers of the lamellae and inter-lamellar spaces. Results of the fitting analyses show that eight or nine pairs of low- and high-index layers typically contribute to the observed reflectivity in live cells, whereas six or seven pairs of low- and high-index layers typically contribute to the reflectivity in chemically fixed cells. The reflectin-containing, high-index lamellae of live cells have a refractive index proportional to the peak reflectivity, with an average of 1.405 ± 0.012 and a maximum around 1.44, while the reflectin-containing lamellae in fixed tissue have a refractive index of 1.413 ± 0.015 suggesting a slight increase of refractive index in the process of fixation. As expected, incremental changes in refractive index contribute to the greatest incremental changes in reflectivity for those Bragg stacks with the most layers. The excursions in dimensions required to tune the measured reflected wavelength from 675 (red) to 425 nm (blue) are a decrease from ca 150 to 80 nm for the high-index lamellae and from ca 120 to 50 nm for the low-index inter-lamellar spaces. Fixation-induced dimensional changes also are quantified, leading us to suggest that further microspectrophotometric analyses of this iridocyte system can be used as a model system to quantify the effects of various methods of tissue fixation. The microspectrophotometry technique described can be expected to provide deeper insights into the molecular and physical mechanisms governing other biophotonically active cells and structures.     

Limited interactions in flocks: relating model simulations to empirical data

The mechanism of self-organization resulting in coordinated collective motion has received wide attention from a range of scientists interested in both its technical and biological relevance. Models have been highly influential in highlighting how collective motion can be produced from purely local interactions between individuals. Typical models in this field are termed ‘metric’ because each individual only reacts to conspecifics within a fixed distance. A recent large-scale study has, however, provided evidence that interactions ruling collective behaviour occur between a fixed number of nearest neighbours (‘topological’ framework). Despite their importance in clarifying the nature of the mechanism underlying animal interactions, these findings have yet to be produced by either metric or topological models. Here, we present an original individual-based model of collective animal motion that reproduces the previous findings. Our approach bridges the current gap between previous model analysis and recent evidence, and presents a framework for further study.     

Maintenance of phenotypic diversity within a set of virulence encoding genes of the malaria parasite Plasmodium falciparum

Infection by the human malaria parasite Plasmodium falciparum results in a broad spectrum of clinical outcomes, ranging from severe and potentially life-threatening malaria to asymptomatic carriage. In a process of naturally acquired immunity, individuals living in malaria-endemic regions build up a level of clinical protection, which attenuates infection severity in an exposure-dependent manner. Underlying this shift in the immunoepidemiology as well as the observed range in malaria pathogenesis is the var multigene family and the phenotypic diversity embedded within. The var gene-encoded surface proteins Plasmodium falciparum erythrocyte membrane protein 1 mediate variant-specific binding of infected red blood cells to a diverse set of host receptors that has been linked to specific disease manifestations, including cerebral and pregnancy-associated malaria. Here, we show that cross-reactive immune responses, which minimize the within-host benefit of each additionally expressed gene during infection, can cause selection for maximum phenotypic diversity at the genome level. We further show that differential functional constraints on protein diversification stably maintain uneven ratios between phenotypic groups, in line with empirical observation. Our results thus suggest that the maintenance of phenotypic diversity within P. falciparum is driven by an evolutionary trade-off that optimizes between within-host parasite fitness and between-host selection pressure.     

The effect of remodelling and contractility of the actin cytoskeleton on the shear resistance of single cells: a computational and experimental investigation

The biomechanisms that govern the response of chondrocytes to mechanical stimuli are poorly understood. In this study, a series of in vitro tests are performed, in which single chondrocytes are subjected to shear deformation by a horizontally moving probe. Dramatically different probe force–indentation curves are obtained for untreated cells and for cells in which the actin cytoskeleton has been disrupted. Untreated cells exhibit a rapid increase in force upon probe contact followed by yielding behaviour. Cells in which the contractile actin cytoskeleton was removed exhibit a linear force–indentation response. In order to investigate the mechanisms underlying this behaviour, a three-dimensional active modelling framework incorporating stress fibre (SF) remodelling and contractility is used to simulate the in vitro tests. Simulations reveal that the characteristic force–indentation curve observed for untreated chondrocytes occurs as a result of two factors: (i) yielding of SFs due to stretching of the cytoplasm near the probe and (ii) dissociation of SFs due to reduced cytoplasm tension at the front of the cell. In contrast, a passive hyperelastic model predicts a linear force–indentation curve similar to that observed for cells in which the actin cytoskeleton has been disrupted. This combined modelling–experimental study offers a novel insight into the role of the active contractility and remodelling of the actin cytoskeleton in the response of chondrocytes to mechanical loading.     

Collective action and the collaborative brain

Humans are unique both in their cognitive abilities and in the extent of cooperation in large groups of unrelated individuals. How our species evolved high intelligence in spite of various costs of having a large brain is perplexing. Equally puzzling is how our ancestors managed to overcome the collective action problem and evolve strong innate preferences for cooperative behaviour. Here, I theoretically study the evolution of social-cognitive competencies as driven by selection emerging from the need to produce public goods in games against nature or in direct competition with other groups. I use collaborative ability in collective actions as a proxy for social-cognitive competencies. My results suggest that collaborative ability is more likely to evolve first by between-group conflicts and then later be utilized and improved in games against nature. If collaborative abilities remain low, the species is predicted to become genetically dimorphic with a small proportion of individuals contributing to public goods and the rest free-riding. Evolution of collaborative ability creates conditions for the subsequent evolution of collaborative communication and cultural learning.     

Stability in flux: community structure in dynamic networks

The structure of many biological, social and technological systems can usefully be described in terms of complex networks. Although often portrayed as fixed in time, such networks are inherently dynamic, as the edges that join nodes are cut and rewired, and nodes themselves update their states. Understanding the structure of these networks requires us to understand the dynamic processes that create, maintain and modify them. Here, we build upon existing models of coevolving networks to characterize how dynamic behaviour at the level of individual nodes generates stable aggregate behaviours. We focus particularly on the dynamics of groups of nodes formed endogenously by nodes that share similar properties (represented as node state) and demonstrate that, under certain conditions, network modularity based on state compares well with network modularity based on topology. We show that if nodes rewire their edges based on fixed node states, the network modularity reaches a stable equilibrium which we quantify analytically. Furthermore, if node state is not fixed, but can be adopted from neighbouring nodes, the distribution of group sizes reaches a dynamic equilibrium, which remains stable even as the composition and identity of the groups change. These results show that dynamic networks can maintain the stable community structure that has been observed in many social and biological systems.     

Fast,high-throughput measurement of collective behaviour in a bacterial population

Swimming bacteria explore their environment by performing a random walk, which is biased in response to, for example, chemical stimuli, resulting in a collective drift of bacterial populations towards ‘a better life’. This phenomenon, called chemotaxis, is one of the best known forms of collective behaviour in bacteria, crucial for bacterial survival and virulence. Both single-cell and macroscopic assays have investigated bacterial behaviours. However, theories that relate the two scales have previously been difficult to test directly. We present an image analysis method, inspired by light scattering, which measures the average collective motion of thousands of bacteria simultaneously. Using this method, a time-varying collective drift as small as 50 nm s⁻¹ can be measured. The method, validated using simulations, was applied to chemotactic Escherichia coli bacteria in linear gradients of the attractant α-methylaspartate. This enabled us to test a coarse-grained minimal model of chemotaxis. Our results clearly map the onset of receptor methylation, and the transition from linear to logarithmic sensing in the bacterial response to an external chemoeffector. Our method is broadly applicable to problems involving the measurement of collective drift with high time resolution, such as cell migration and fluid flows measurements, and enables fast screening of tactic behaviours.     

Automated,contour-based tracking and analysis of cell behaviour over long time scales in environments of varying complexity and cell density

Understanding single and collective cell motility in model environments is foundational to many current research efforts in biology and bioengineering. To elucidate subtle differences in cell behaviour despite cell-to-cell variability, we introduce an algorithm for tracking large numbers of cells for long time periods and present a set of physics-based metrics that quantify differences in cell trajectories. Our algorithm, termed automated contour-based tracking for in vitro environments (ACTIVE), was designed for adherent cell populations subject to nuclear staining or transfection. ACTIVE is distinct from existing tracking software because it accommodates both variability in image intensity and multi-cell interactions, such as divisions and occlusions. When applied to low-contrast images from live-cell experiments, ACTIVE reduced error in analysing cell occlusion events by as much as 43% compared with a benchmark-tracking program while simultaneously tracking cell divisions and resulting daughter–daughter cell relationships. The large dataset generated by ACTIVE allowed us to develop metrics that capture subtle differences between cell trajectories on different substrates. We present cell motility data for thousands of cells studied at varying densities on shape-memory-polymer-based nanotopographies and identify several quantitative differences, including an unanticipated difference between two ‘control’ substrates. We expect that ACTIVE will be immediately useful to researchers who require accurate, long-time-scale motility data for many cells.