Self-organization of collective escape in pigeon flocks

Bird flocks under predation demonstrate complex patterns of collective escape. These patterns may emerge by self-organization from local interactions among group-members. Computational models have been shown to be valuable for identifying what behavioral rules may govern such interactions among individuals during collective motion. However, our knowledge of such rules for collective escape is limited by the lack of quantitative data on bird flocks under predation in the field. In the present study, we analyze the first GPS trajectories of pigeons in airborne flocks attacked by a robotic falcon in order to build a species-specific model of collective escape. We use our model to examine a recently identified distance-dependent pattern of collective behavior: the closer the prey is to the predator, the higher the frequency with which flock members turn away from it. We first extract from the empirical data of pigeon flocks the characteristics of their shape and internal structure (bearing angle and distance to nearest neighbors). Combining these with information on their coordination from the literature, we build an agent-based model adjusted to pigeons’ collective escape. We show that the pattern of turning away from the predator with increased frequency when the predator is closer arises without prey prioritizing escape when the predator is near. Instead, it emerges through self-organization from a behavioral rule to avoid the predator independently of their distance to it. During this self-organization process, we show how flock members increase their consensus over which direction to escape and turn collectively as the predator gets closer. Our results suggest that coordination among flock members, combined with simple escape rules, reduces the cognitive costs of tracking the predator while flocking. Such escape rules that are independent of the distance to the predator can now be investigated in other species. Our study showcases the important role of computational models in the interpretation of empirical findings of collective behavior.     

Evidence that pigeons orient to geomagnetic intensity during homing

The influence of the Earth's magnetic field on locomotory orientation has been studied in many taxa but is best understood for homing pigeons (Columba livia). Effects of experimentally induced and naturally occurring perturbations in the geomagnetic field suggest that pigeons are sensitive to changes in geomagnetic parameters. However, whether pigeons use the Earth's magnetic field for position determination remains unknown. Here we report an apparent orientation to the intensity gradient of the geomagnetic field observed in pigeons homing from sites in and around a magnetic anomaly. From flight trajectories recorded by GPS-based tracking devices, we noted that many pigeons released at unfamiliar sites initially flew, in some cases up to several kilometres, in directions parallel and/or perpendicular to the bearing of the local intensity field. This behaviour occurred irrespective of the homeward direction and significantly more often than what was expected by random chance. Our study describes a novel behaviour which provides strong evidence that pigeons when homing detect and respond to spatial variation in the Earth's magnetic field--information of potential use for navigation.     

Pineal Body and Magnetic Sensitivity: Homing in Pinealectomized Pigeons under Overcast Skies

Since birds use the earth's magnetic field for compass orientation when astronomical cues are lacking and it has recently been suggested that the pineal body is part of their magnetic compass, test releases have been performed in overcast conditions with pigeons deprived of the pineal body. On the whole, both experimental and control birds were capable of homeward orientation, though the bearings of experimental were rather more scattered. No differences in homing speed or success were recorded. Thus, the pineal body does not appear to play an important role in the homing of pigeons.     

Thermal unfolding simulations of apo-calmodulin using leap-dynamics

The simulation method leap-dynamics (LD) has been applied to protein thermal unfolding simulations to investigate domain-specific unfolding behavior. Thermal unfolding simulations of the 148-residue protein apo-calmodulin with implicit solvent were performed at temperatures 290 K, 325 K, and 360 K and compared with the corresponding molecular dynamics trajectories in terms of a number of calculated conformational parameters. The main experimental results of unfolding are reproduced in showing the lower stability of the C-domain: at 290 K, both the N- and C-domains are essentially stable; at 325 K, the C-domain unfolds, whereas the N-domain remains folded; and at 360 K, both domains unfold extensively. This behavior could not be reproduced by molecular dynamics simulations alone under the same conditions. These results show an encouraging degree of convergence between experiment and LD simulation. The simulations are able to describe the overall plasticity of the apo-calmodulin structure and to reveal details such as reversible folding/unfolding events within single helices. The results show that by using the combined application of a fast and efficient sampling routine with a detailed molecular dynamics force field, unfolding simulations of proteins at atomic resolution are within the scope of current computational power.     

The Orientational Consequences of Flocking Behaviour in Homing Pigeons,Columba livia

Two experiments are described which investigate the orientational consequences of flocking in homing pigeons Columba livia. Previous experiments have shown that homing pigeons placed inside a clear-sided release box for 5 min before release from a familiar site have enhanced ground homing speed compared with those placed in an opaque-sided box. It is assumed that previewing the surrounding landscape allows for faster homing since a bird denied this information must accumulate the knowledge on release. In experiment 1, using the same technique developed in these experiments but releasing the birds in pairs we showed that within familiar areas, homing pigeons can exploit a partner that has acquired more information, allowing them to home more quickly. In experiment 2 we attempted to test three potential strategies which may occur during homing flights. The results do not conclusively distinguish between these three mechanisms but suggest that orientation of the pairs of birds is most likely to have resulted from a compromise of individual tendencies, or from following the best homer, but not from following a ‘governing leader’. The consequence of these mechanisms is discussed.     

Collision rates for rare cell capture in periodic obstacle arrays strongly depend on density of cell suspension

Recently, computational modelling has been successfully used for determination of collision rates for rare cell capture in periodic obstacle arrays. The models were based on particle advection simulations where the cells were advected according to velocity field computed from two dimensional Navier–Stokes equations. This approach may be used under the assumption of very dilute cell suspensions where no mutual cell collisions occur. We use the object-in-fluid framework to demonstrate that even with low cell-to-fluid ratio, the optimal geometry of the obstacle array significantly changes. We show computational simulations for ratios of 3.5, 6.9 and 10.4% determining the optimal geometry of the periodic obstacle arrays. It was already previously demonstrated that cells in periodic obstacle arrays follow trajectories in two modes: the colliding mode and the zig–zag mode. The colliding mode maximizes the cell-obstacle collision frequency. Our simulations reveal that for dilute suspensions and for suspensions with cell-to-fluid ratio 3.5%, there is a range of column shifts for which the cells follow colliding trajectories. However we showed, that for 6.9 and 10.4%, the cells never follow colliding trajectories.     

Virtual trajectory and stiffness ellipse during multijoint arm movement predicted by neural inverse models

We predict the virtual trajectories and stiffness ellipses during multijoint arm movements by computer simulations. A two-link manipulator with four single-joint muscles and two double-joint muscles is used as a model of the human arm. Physical parameters of the model are derived from several experimental data. Among them, special emphasis is put on low values of the dynamic hand stiffness recently measured during single joint and multijoint movements. The feedback-error-learning scheme to acquire the inverse dynamics model and the inverse statics model is utilized for this prediction. The virtual trajectories are much more complex than the actual trajectories. This indicates that planning the virtual trajectory is as difficult as solving the inverse dynamics problem for medium and fast movements, and simply falsifies the advocated computational advantage of the virtual trajectory control hypothesis. Thus, we conclude that learning inverse models is essential even in the virtual trajectory control framework. Finally, we propose a new computational model to learn the complicated shape of the virtual trajectories by integrating the virtual trajectory control and the feedback-error-learning scheme.     

Constant electric field simulations of the membrane potential illustrated with simple systems

Advances in modern computational methods and technology make it possible to carry out extensive molecular dynamics simulations of complex membrane proteins based on detailed atomic models. The ultimate goal of such detailed simulations is to produce trajectories in which the behavior of the system is as realistic as possible. A critical aspect that requires consideration in the case of biological membrane systems is the existence of a net electric potential difference across the membrane. For meaningful computations, it is important to have well validated methodologies for incorporating the latter in molecular dynamics simulations. A widely used treatment of the membrane potential in molecular dynamics consists of applying an external uniform electric field E perpendicular to the membrane. The field acts on all charged particles throughout the simulated system, and the resulting applied membrane potential V is equal to the applied electric field times the length of the periodic cell in the direction perpendicular to the membrane. A series of test simulations based on simple membrane-slab models are carried out to clarify the consequences of the applied field. These illustrative tests demonstrate that the constant-field method is a simple and valid approach for accounting for the membrane potential in molecular dynamics studies of biomolecular systems. This article is part of a Special Issue entitled: Membrane protein structure and function.     

Stepping and Crowding of Molecular Motors: Statistical Kinetics from an Exclusion Process Perspective

Motor enzymes are remarkable molecular machines that use the energy derived from the hydrolysis of a nucleoside triphosphate to generate mechanical movement, achieved through different steps that constitute their kinetic cycle. These macromolecules, nowadays investigated with advanced experimental techniques to unveil their molecular mechanisms and the properties of their kinetic cycles, are implicated in many biological processes, ranging from biopolymerization (e.g., RNA polymerases and ribosomes) to intracellular transport (motor proteins such as kinesins or dyneins). Although the kinetics of individual motors is well studied on both theoretical and experimental grounds, the repercussions of their stepping cycle on the collective dynamics still remains unclear. Advances in this direction will improve our comprehension of transport process in the natural intracellular medium, where processive motor enzymes might operate in crowded conditions. In this work, we therefore extend contemporary statistical kinetic analysis to study collective transport phenomena of motors in terms of lattice gas models belonging to the exclusion process class. Via numerical simulations, we show how to interpret and use the randomness calculated from single particle trajectories in crowded conditions. Importantly, we also show that time fluctuations and non-Poissonian behavior are intrinsically related to spatial correlations and the emergence of large, but finite, clusters of comoving motors. The properties unveiled by our analysis have important biological implications on the collective transport characteristics of processive motor enzymes in crowded conditions.     

Stepping and Crowding of Molecular Motors: Statistical Kinetics from an Exclusion Process Perspective

Motor enzymes are remarkable molecular machines that use the energy derived from the hydrolysis of a nucleoside triphosphate to generate mechanical movement, achieved through different steps that constitute their kinetic cycle. These macromolecules, nowadays investigated with advanced experimental techniques to unveil their molecular mechanisms and the properties of their kinetic cycles, are implicated in many biological processes, ranging from biopolymerization (e.g., RNA polymerases and ribosomes) to intracellular transport (motor proteins such as kinesins or dyneins). Although the kinetics of individual motors is well studied on both theoretical and experimental grounds, the repercussions of their stepping cycle on the collective dynamics still remains unclear. Advances in this direction will improve our comprehension of transport process in the natural intracellular medium, where processive motor enzymes might operate in crowded conditions. In this work, we therefore extend contemporary statistical kinetic analysis to study collective transport phenomena of motors in terms of lattice gas models belonging to the exclusion process class. Via numerical simulations, we show how to interpret and use the randomness calculated from single particle trajectories in crowded conditions. Importantly, we also show that time fluctuations and non-Poissonian behavior are intrinsically related to spatial correlations and the emergence of large, but finite, clusters of comoving motors. The properties unveiled by our analysis have important biological implications on the collective transport characteristics of processive motor enzymes in crowded conditions.     

Group decisions and individual differences: route fidelity predicts flight leadership in homing pigeons (Columba livia)

How social-living animals make collective decisions is currently the subject of intense scientific interest, with increasing focus on the role of individual variation within the group. Previously, we demonstrated that during paired flight in homing pigeons, a fully transitive leadership hierarchy emerges as birds are forced to choose between their own and their partner''s habitual routes. This stable hierarchy suggests a role for individual differences mediating leadership decisions within homing pigeon pairs. What these differences are, however, has remained elusive. Using novel quantitative techniques to analyse habitual route structure, we show here that leadership can be predicted from prior route-following fidelity. Birds that are more faithful to their own route when homing alone are more likely to emerge as leaders when homing socially. We discuss how this fidelity may relate to the leadership phenomenon, and propose that leadership may emerge from the interplay between individual route confidence and the dynamics of paired flight.     

A Multi-Paradigm Modeling Framework to Simulate Dynamic Reciprocity in a Bioreactor

Despite numerous technology advances, bioreactors are still mostly utilized as functional black-boxes where trial and error eventually leads to the desirable cellular outcome. Investigators have applied various computational approaches to understand the impact the internal dynamics of such devices has on overall cell growth, but such models cannot provide a comprehensive perspective regarding the system dynamics, due to limitations inherent to the underlying approaches. In this study, a novel multi-paradigm modeling platform capable of simulating the dynamic bidirectional relationship between cells and their microenvironment is presented. Designing the modeling platform entailed combining and coupling fully an agent-based modeling platform with a transport phenomena computational modeling framework. To demonstrate capability, the platform was used to study the impact of bioreactor parameters on the overall cell population behavior and vice versa. In order to achieve this, virtual bioreactors were constructed and seeded. The virtual cells, guided by a set of rules involving the simulated mass transport inside the bioreactor, as well as cell-related probabilistic parameters, were capable of displaying an array of behaviors such as proliferation, migration, chemotaxis and apoptosis. In this way the platform was shown to capture not only the impact of bioreactor transport processes on cellular behavior but also the influence that cellular activity wields on that very same local mass transport, thereby influencing overall cell growth. The platform was validated by simulating cellular chemotaxis in a virtual direct visualization chamber and comparing the simulation with its experimental analogue. The results presented in this paper are in agreement with published models of similar flavor. The modeling platform can be used as a concept selection tool to optimize bioreactor design specifications.     

Elastic network models for RNA: a comparative assessment with molecular dynamics and SHAPE experiments

Elastic network models (ENMs) are valuable and efficient tools for characterizing the collective internal dynamics of proteins based on the knowledge of their native structures. The increasing evidence that the biological functionality of RNAs is often linked to their innate internal motions poses the question of whether ENM approaches can be successfully extended to this class of biomolecules. This issue is tackled here by considering various families of elastic networks of increasing complexity applied to a representative set of RNAs. The fluctuations predicted by the alternative ENMs are stringently validated by comparison against extensive molecular dynamics simulations and SHAPE experiments. We find that simulations and experimental data are systematically best reproduced by either an all-atom or a three-beads-per-nucleotide representation (sugar-base-phosphate), with the latter arguably providing the best balance of accuracy and computational complexity.     

Principal component and normal mode analysis of proteins; a quantitative comparison using the GroEL subunit

Principal component analysis (PCA) and normal mode analysis (NMA) have emerged as two invaluable tools for studying conformational changes in proteins. To compare these approaches for studying protein dynamics, we have used a subunit of the GroEL chaperone, whose dynamics is well characterized. We first show that both PCA on trajectories from molecular dynamics (MD) simulations and NMA reveal a general dynamical behavior in agreement with what has previously been described for GroEL. We thus compare the reproducibility of PCA on independent MD runs and subsequently investigate the influence of the length of the MD simulations. We show that there is a relatively poor one-to-one correspondence between eigenvectors obtained from two independent runs and conclude that caution should be taken when analyzing principal components individually. We also observe that increasing the simulation length does not improve the agreement with the experimental structural difference. In fact, relatively short MD simulations are sufficient for this purpose. We observe a rapid convergence of the eigenvectors (after ca. 6 ns). Although there is not always a clear one-to-one correspondence, there is a qualitatively good agreement between the movements described by the first five modes obtained with the three different approaches; PCA, all-atoms NMA, and coarse-grained NMA. It is particularly interesting to relate this to the computational cost of the three methods. The results we obtain on the GroEL subunit contribute to the generalization of robust and reproducible strategies for the study of protein dynamics, using either NMA or PCA of trajectories from MD simulations.     

Correlating cell behavior with tissue topology in embryonic epithelia

Measurements on embryonic epithelial tissues in a diverse range of organisms have shown that the statistics of cell neighbor numbers are universal in tissues where cell proliferation is the primary cell activity. Highly simplified non-spatial models of proliferation are claimed to accurately reproduce these statistics. Using a systematic critical analysis, we show that non-spatial models are not capable of robustly describing the universal statistics observed in proliferating epithelia, indicating strong spatial correlations between cells. Furthermore we show that spatial simulations using the Subcellular Element Model are able to robustly reproduce the universal histogram. In addition these simulations are able to unify ostensibly divergent experimental data in the literature. We also analyze cell neighbor statistics in early stages of chick embryo development in which cell behaviors other than proliferation are important. We find from experimental observation that cell neighbor statistics in the primitive streak region, where cell motility and ingression are also important, show a much broader distribution. A non-spatial Markov process model provides excellent agreement with this broader histogram indicating that cells in the primitive streak may have significantly weaker spatial correlations. These findings show that cell neighbor statistics provide a potentially useful signature of collective cell behavior.     

Binding of antifusion peptides with HIVgp41 from molecular dynamics simulations: quantitative correlation with experiment

Peptides based on C-terminal regions of the human immunodeficiency virus (HIV) viral protein gp41 represent an important new class of antiviral therapeutics called peptide fusion inhibitors. In this study, computational methods were used to model the binding of six peptides that contain residues that pack into a conserved hydrophobic pocket on HIVgp41, an attractive target site for the development of small molecule inhibitors. Free energies of binding were computed using molecular mechanics Generalized Born surface area (MM-GBSA) methods from molecular dynamics (MD) simulations, which employed either explicit (TIP3P) or continuum Generalized Born (GB) water models and strong correlations between experimental and computational affinities were obtained in both cases. Energy decomposition of the TIP3P-MD results (r2 = 0.75) reveals that variation in experimental affinity is highly correlated with changes in intermolecular van der Waals energies (deltaE(vdw)) on both a local (residue-based, r2 = 0.94) and global (peptide-based, r2 = 0.84) scale. The results show that differential association of C-peptides with HIVgp41 is driven solely by changes within the conserved pocket supporting the hypothesis that this region is an important drug target site. Such strong agreement with experiment is notable given the large size of the ligands (34 amino-acids) relative to the small range of experimental affinities (2 kcal/mol) and demonstrates good sensitivity of this computational method for simulating peptide fusion inhibitors. Finally, inspection of simulation trajectories identified a highly populated pi-type hydrogen bond, which formed between Gln575 on the receptor and the aromatic ring of peptide ligand Phe631, which could have important implications for drug design.     

Information transfer in moving animal groups

Moving animal groups provide some of the most intriguing and difficult to characterise examples of collective behaviour. We review some recent (and not so recent) empirical research on the motion of animal groups, including fish, locusts and homing pigeons. An important concept which unifies our understanding of these groups is that of transfer of directional information. Individuals which change their direction of travel in response to the direction taken by their near neighbours can quickly transfer information about the presence of a predatory threat or food source. We show that such information transfer is optimised when the density of individuals in a group is close to that at which a phase transition occurs between random and ordered motion. Similarly, we show that even relatively small differences in information possessed by group members can lead to strong collective-level decisions for one of two options. By combining the use of self-propelled particle and social force models of collective motion with thinking about the evolution of flocking we aim to better understand how complexity arises within these groups.

---

Comparison of blood rheological models for physiological flow simulation

The present study investigates the flow effects that different blood constitutive equations induce when employed in numerical simulations in the framework of computational hemodynamics. In accord with experimental studies on the rheological behavior of blood, three blood constitutive equations namely the Casson, Power-Law and Quemada models were used for simulating the shear flow behavior of blood. The case studied is the flow in a channel with a moving part of the boundary and was selected because it reproduces the flow phenomena occurring in realistic arterial conditions. Flow simulation for every model is carried out assuming the same flow rate at the inlet of the channel and different Strouhal numbers reflecting different intensities of the boundary movement. Results show that the modeling of blood as non-Newtonian fluid has marked qualitative and quantitative effects on both the flow field and the wall shear stress whereas comparison of the different models shows good agreement between the flow effects by the Casson and Quemada models.     

Biogenic magnetite as a basis for magnetic field detection in animals

Bacteria, sharks, honey bees, and homing pigeons as well as other organisms seem to detect the direction of the earth's magnetic field. Indirect but reproducible evidence suggests that the bees and birds can also respond to very minute changes in its intensity. The mechanisms behind this sensitivity are not known. Naturally magnetic, biologically precipitated magnetite (Fe₃O₄) has been found in chitons, magnetotactic bacteria, honey bees, homing pigeons, and dolphins. Its mineralization in localized areas may be associated with the ability of these animals to respond to the direction and intensity of the earth's magnetic field. The presence of large numbers (～10⁸) of superparamagnetic magnetite crystals in honey bees and similar numbers of single-domain magnetite grains in pigeons suggests that there may be at least two basic types of ferrimagnetic magnetoreceptive organelles. Theoretical calculations show that ferrimagnetic organs using either type of grain when integrated by the nervous system are capable of accounting for even the most extreme magnetic field sensitivities reported. Indirect evidence suggests that organic magnetite may be a common biological component, and may account for the results of numerous high field and electromagnetic experiments on animals.