Gil Ariel

Swarming bacteria migrate by Lévy Walk.

Individual swimming bacteria are known to bias their random trajectories in search of food and to optimize survival. The motion of bacteria within a swarm, wherein they migrate as a collective group over a solid surface, is fundamentally different as typical bacterial swarms show large-scale swirling and streaming motions involving millions to billions of cells. Here by tracking trajectories of fluorescently labelled individuals within such dense swarms, we find that the bacteria are performing super-diffusion, consistent with Lévy walks. Lévy walks are characterized by trajectories that have straight stretches for extended lengths whose variance is infinite. The evidence of super-diffusion consistent with Lévy walks in bacteria suggests that this strategy may have evolved considerably earlier than previously thought.

Lethal protein produced in response to competition between sibling bacterial colonies

Sibling Paenibacillus dendritiformis bacterial colonies grown on low-nutrient agar medium mutually inhibit growth through secretion of a lethal factor. Analysis of secretions reveals the presence of subtilisin (a protease) and a 12 kDa protein, termed sibling lethal factor (Slf). Purified subtilisin promotes the growth and expansion of P. dendritiformis colonies, whereas Slf is lethal and lyses P. dendritiformis cells in culture. Slf is encoded by a gene belonging to a large family of bacterial genes of unknown function, and the gene is predicted to encode a protein of approximately 20 kDa, termed dendritiformis sibling bacteriocin. The 20 kDa recombinant protein was produced and found to be inactive, but exposure to subtilisin resulted in cleavage to the active, 12 kDa form. The experimental results, combined with mathematical modeling, show that subtilisin serves to regulate growth of the colony. Below a threshold concentration, subtilisin promotes colony growth and expansion. However, once it exceeds a threshold, as occurs at the interface between competing colonies, Slf is then secreted into the medium to rapidly reduce cell density by lysis of the bacterial cells. The presence of genes encoding homologs of dendritiformis sibling bacteriocin in other bacterial species suggests that this mechanism for self-regulation of colony growth might not be limited to P. dendritiformis.

Locust Collective Motion and Its Modeling

Over the past decade, technological advances in experimental and animal tracking techniques have motivated a renewed theoretical interest in animal collective motion and, in particular, locust swarming. This review offers a comprehensive biological background followed by comparative analysis of recent models of locust collective motion, in particular locust marching, their settings, and underlying assumptions. We describe a wide range of recent modeling and simulation approaches, from discrete agent-based models of self-propelled particles to continuous models of integro-differential equations, aimed at describing and analyzing the fascinating phenomenon of locust collective motion. These modeling efforts have a dual role: The first views locusts as a quintessential example of animal collective motion. As such, they aim at abstraction and coarse-graining, often utilizing the tools of statistical physics. The second, which originates from a more biological perspective, views locust swarming as a scientific problem of its own exceptional merit. The main goal should, thus, be the analysis and prediction of natural swarm dynamics. We discuss the properties of swarm dynamics using the tools of statistical physics, as well as the implications for laboratory experiments and natural swarms. Finally, we stress the importance of a combined-interdisciplinary, biological-theoretical effort in successfully confronting the challenges that locusts pose at both the theoretical and practical levels.

Collective motion of spherical bacteria.

A large variety of motile bacterial species exhibit collective motions while inhabiting liquids or colonizing surfaces. These collective motions are often characterized by coherent dynamic clusters, where hundreds of cells move in correlated whirls and jets. Previously, all species that were known to form such motion had a rod-shaped structure, which enhances the order through steric and hydrodynamic interactions. Here we show that the spherical motile bacteria Serratia marcescens exhibit robust collective dynamics and correlated coherent motion while grown in suspensions. As cells migrate to the upper surface of a drop, they form a monolayer, and move collectively in whirls and jets. At all concentrations, the distribution of the bacterial speed was approximately Rayleigh with an average that depends on concentration in a non-monotonic way. Other dynamical parameters such as vorticity and correlation functions are also analyzed and compared to rod-shaped bacteria from the same strain. Our results demonstrate that self-propelled spherical objects do form complex ordered collective motion. This opens a door for a new perspective on the role of cell aspect ratio and alignment of cells with regards to collective motion in nature.

A Multiscale Method for Highly Oscillatory Dynamical Systems Using a Poincaré Map Type Technique

We propose a new heterogeneous multiscale method (HMM) for computing the effective behavior of a class of highly oscillatory ordinary differential equations (ODEs). Without the need for identifying hidden slow variables, the proposed method is constructed based on the following ideas: a nonstandard splitting of the vector field (the right hand side of the ODEs); comparison of the solutions of the split equations; construction of effective paths in the state space whose projection onto the slow subspace has the correct dynamics; and a novel on-the-fly filtering technique for achieving a high order accuracy. Numerical examples are given.

Numerical Multiscale Methods for Coupled Oscillators

A multiscale method for computing the effective slow behavior of a system of weakly coupled nonlinear planar oscillators is presented. The oscillators may be either in the form of a periodic solution or a stable limit cycle. Furthermore, the oscillators may be in resonance with one another and thereby generate some hidden slow dynamics. The proposed method relies on correctly tracking a set of slow variables that is sufficient to approximate any variable and functional that are slow under the dynamics of the ordinary differential equation. The technique is more efficient than existing methods, and its advantages are demonstrated with examples. The algorithm follows the framework of the heterogeneous multiscale method.

Gaussian beam decomposition of high frequency wave fields using expectation-maximization

A new numerical method for approximating highly oscillatory wave fields as a superposition of Gaussian beams is presented. The method estimates the number of beams and their parameters automatically. This is achieved by an expectation-maximization algorithm that fits real, positive Gaussians to the energy of the highly oscillatory wave fields and its Fourier transform. Beam parameters are further refined by an optimization procedure that minimizes the difference between the Gaussian beam superposition and the highly oscillatory wave field in the energy norm.

From organized internal traffic to collective navigation of bacterial swarms

Bacterial swarming resulting in collective navigation over surfaces provides a valuable example of cooperative colonization of new territories. The social bacterium Paenibacillus vortex exhibits successful and diverse swarming strategies. When grown on hard agar surfaces with peptone, P. vortex develops complex colonies of vortices (rotating bacterial aggregates). In contrast, during growth on Mueller?Hinton broth gelled into a soft agar surface, a new strategy of multi-level organization is revealed: the colonies are organized into a special network of swarms (or ?snakes? of a fraction of millimeter in width) with intricate internal traffic. More specifically, cell movement is organized in two or three lanes of bacteria traveling between the back and the front of the swarm. This special form of cellular logistics suggests new methods in which bacteria can share resources and risk while searching for food or migrating into new territories. While the vortices-based organization on hard agar surfaces has been modeled before, here, we introduce a new multi-agent bacterial swarming model devised to capture the swarms-based organization on soft surfaces. We test two putative generic mechanisms that may underlie the observed swarming logistics: (i) chemo-activated taxis in response to chemical cues and (ii) special align-and-push interactions between the bacteria and the boundary of the layer of lubricant collectively generated by the swarming bacteria. Using realistic parameters, the model captures the observed phenomena with semi-quantitative agreement in terms of the velocity as well as the dynamics of the swarm and its envelope. This agreement implies that the bacteria interactions with the swarm boundary play a crucial role in mediating the interplay between the collective movement of the swarm and the internal traffic dynamics.

Collective navigation of cargo-carrying swarms

Much effort has been devoted to the study of swarming and collective navigation of micro-organisms, insects, fish, birds and other organisms, as well as multi-agent simulations and to the study of real robots. It is well known that insect swarms can carry cargo. The studies here are motivated by a less well-known phenomenon: cargo transport by bacteria swarms. We begin with a concise review of how bacteria swarms carry natural, micrometre-scale objects larger than the bacteria (e.g. fungal spores) as well as man-made beads and capsules (for drug delivery). A comparison of the trajectories of virtual beads in simulations (using different putative coupling between the virtual beads and the bacteria) with the observed trajectories of transported fungal spores implies the existence of adaptable coupling. Motivated by these observations, we devised new, multi-agent-based studies of cargo transport by agent swarms. As a first step, we extended previous modelling of collective navigation of simple bacteria-inspired agents in complex terrain, using three putative models of agent–cargo coupling. We found that cargo-carrying swarms can navigate efficiently in a complex landscape. We further investigated how the stability, elasticity and other features of agent–cargo bonds influence the collective motion and the transport of the cargo, and found sharp phase shifts and dual successful strategies for cargo delivery. Further understanding of such mechanisms may provide valuable clues to understand cargo-transport by smart swarms of other organisms as well as by man-made swarming robots.

Oscillatory Systems with Three Separated Time Scales: Analysis and Computation

We study a few interesting issues that occur in multiscale modeling and computation for oscillatory dynamical systems that involve three or more separated scales. A new type of slow variables which do not formally have bounded derivatives emerge from averaging in the fastest time scale. We present a few systems which have such new slow variables and discuss their characterization. The examples motivate a numerical multiscale algorithm that uses nested tiers of integrators which numerically solve the oscillatory system on different time scales. The communication between the scales follows the framework of the Heterogeneous Multiscale Method. The method’s accuracy and efficiency are evaluated and its applicability is demonstrated by examples.