Principles of Biological and Robotic Navigation

The survival of microorganisms in limited nutrient conditions hinges on their foraging strategies. Bacteria have evolved cellular biochemical circuits that can detect, and even anticipate, variations in the environment. However, the motion of individual cells is highly stochastic, and it remains unclear to what extent the colony as a whole benefits from the anticipation achieved by individual cells. Here we address this question in E. coli chemotaxis using a novel mathematical approach that combines kinetic theory and optimal control theory. The model describes the evolution of the population under chemoattractant profiles assuming single cells optimise their tumbling rate based on anticipated environmental conditions. Moreover, it recovers the classical Keller-Segel model in the limit of no anticipation. We map the dynamics to a mean field game, from which we extract a fitness function governing the dynamics of the single cell. This also implies that the benefit of random population dispersal is weighed against its cost in the sense of a game-theoretic equilibrium. Simulations and theory show that the benefit from anticipation at the population level is only realised above a critical anticipation horizon. The maximum population gain occurs at a horizon which is trade-off between signal-to-noise ratio and the time and length scales of chemoattractant gradients relative to the motion of individual cells. In addition, anticipation allows for more efficient exploration of complex landscapes (e.g., with multiple sources of nutrients) leading to distinct spatial patterns corresponding to mixed strategies. Finally, we investigate the role of cell-to-cell communication in reinforcing, or disrupting, the anticipated response. Our framework is general and allows a wide range of collective phenomena in population biology to be systematically formulated as optimisation problems.

We adress the question of how self-propulsion affects the synchronization of motile physical entities, like fireflies, robots or bacteria synchronizing their internal genetic clocks. We consider hard particles carriying an internal phase oscillator. The dynamics of the internal degrees of freedom is based on the Kuramoto model of phase coupled oscillators. We consider first the case where the oscillators are identical and not affect the motion of the particles. We find that self-propulsion promotes synchronization and that the presence of steric interactions give rise to an optimal self-propulsion which minimises the synchronization time. We analyse the relaxation of the system and show that synchronization proceeds throught a coarsening mechanism that verifies the dynamic scaling hypothesis. Then, we consider the case where the internal phase of the oscillator dictates the direction of self-propulsion of the particles. Our general model includes, as limiting cases, a Vicsek-like model where repulsive particles align their velocities, and the Active Brownian Particles model where particles are pushed by a force that reorients by rotational diffusion. We analyse the phase behaviour of the system and show that the system exhibits a flocking/synchronization transition, a motility induced phase separation and a rich active liquid behaviour in between, depending on the values of the coupling strength between the oscillators. We finally consider the general Kuramoto set-up where the internal oscillators have a distribution of natural frequencies. We find that despite the tendency of the particles to align their phases (or velocities), there is a regime where global synchronization is not reached and particles seggregate accordingly to their natural frequencies, opening a novel generic route to control self-sustained dynamical patterns. We discuss the connexions of these results in the context of recent experimental studies of colloidal systems, bacterial collonies and collections of self-propelled macroscopic robots.

Diffusion of a spherical particle in polymer solution is studied using coarse-grained molecular dynamics simulations. Dependence of the particle diffusion coefficient on the polymer concentration is obtained at different values of the polymers bending rigidity. The obtained results show that reduction of the diffusion coefficient with increasing the polymer concentration is stronger in the case of rod-like polymers relative to flexible ones. It seems that study of the diffusion dynamics of such a tracer particle can be a tool for distinguishing the flexible polymers from the stiff ones. The orientational ordering of rod-like polymers at high concentrations is shown to cause the local structure of available volume around the tracer particle to be anisotropic and the diffusion of the tracer to be effectively one-dimensional which corresponds to smaller diffusion coefficient.

Honeybees are central-place foragers, with extraordinary navigational abilities. Those include, the for insects typical, strategies like path-integration, supported by an elaborate sun-compass, or view-matching strategies. On top of that, honeybees show behaviour which suggests a much richer repertoire of navigational mechanisms, while the composition of which is still debated. For starters honeybees are known to communicate foraging sites to their nest-mates via a sophisticated dance language, which represents a unique view into the internal representation of position and may give a hint on the complex interplay of different navigational strategies. Furthermore honeybees not only can find their way home, after being displaced up to several kilometres from their hive, but are known to perform shortcut flights over novel terrain, follow routes without compass information available, use landmarks for guidance and much more. All this is achieved by a central nervous system with roughly a million neurons. Recently a model for route following in ants has been proposed, by Baddeley et al. and others, which achieves robust route following, with only the help of directional view-matching. The proposed algorithm evaluates views to their familiarity. As the heading and movement direction in insects are directly linked, a route can be followed by pursuing the most familiar direction. Ardin et al. showed, that this familiarity-algorithm can be realized by a biological plausible, spiking neural model of the ant mushroom body. We are investigating if this promising concept may be relevant for the honeybee. First we investigated if the strategy of familiarity guided navigation fits into a general model for honeybee navigation, and may be one of the underlying strategies which give rise to the observed complex behaviour. Now it is our goal to build a neural model, based on the one proposed by Ardin et al., that is adjusted to the specifics of the honeybee and test it in a virtual environment resembling natural foraging grounds.

Mechanically induced polarity and its use for micro transport Oliver Nagel, Manuel Fry, Matthias Gerhardt, and Carsten Beta Institute of Physics and Astronomy, University of Potsdam, Potsdam, Germany The transport and positioning of micron-sized objects in complex geometries is often accomplished by fluid flow. However, under geometric constrains, like in dead-end structures, this is difficult to achieve. Alternative approaches include, for example, the use of magnetic or optical tweezers. Yet these techniques are costly and time consuming as the objects have to be rearranged manually and one by one. Here, we propose a novel alternative approach exploiting the behavior of single motile cells. First, we show that Dictyostelium discoideum cells can spontaneously polarize and undergo persistent unidirectional motion when confined in narrow micro-channels. We explore the potential of this type of motion to transport micron-sized objects along these geometries. Secondly, we use the chemotactic motion of Dictyostelium cells to transport objects of different sizes and shapes. In particular, the collective behavior of these cells can be exploited to assemble micro-objects and fit them together.

Chemically active Janus particles in solution create gradients in the chemical composition of the solution along their surfaces, as well as along any nearby container walls. The former leads to self-phoresis; the latter, which strongly depends on the molecular interactions between the diffusing chemical species and the wall, gives rise to chemi-osmosis. The chemi-osmotic flow driven at the wall extend into the solution and couple back to the active particle, thus providing an additional contribution to self-motility. Here we present results of numerical calculations, complemented by theoretical arguments based on an approximate ``point-particle'' approach, evidencing that by chemically patterning a planar substrate (e.g., by adsorbing two different materials) one can direct the motion of Janus particles via "tuning" the induced chemi-osmotic flows. The motion in the vicinity of Various types of chemical patterns is discussed, and the physical mechanisms governing the guidance of the chemically active particles are highlighted.

Intriguing physics underlies the random search mechanisms, or foraging, of living organisms: experimental studies show that often foraging of organisms, e.g., in search of food or mates, can be described by a super-diffusive model and the distribution of the steps in their trajectories follows a class of fat-tailed functions known as Levy distributions. While seeking for targets, random walkers might switch from Brownian motion to Lévy motion where the step size of each walk is no longer fixed and normally distributed. Searchers showing distinct displacement characteristics have recently attracted interests from many communities at the crossroad between physics and biology, such as the active matter community. Recent developments in this area largely consists of investigating the search patterns[1], animal foraging behaviour (e.g. marine predators [2]) and different searching strategies for detecting targets in homogeneous and patchy environment [3]. In this work, we investigated the search strategy of a Lévy walker inside complex environments. In particular, we observe that the complexity in the environment directly influence the trajectory of a Lévy walker as well as its optimal search strategy and target detecting abilities. [1]O.Bénichou, C.Loverdo, M.Moreau and R.Voituriez, Rev.Mod.Phys, 83, 81-129(2011) [2]N.E.Humphries et al., Nature, 465, 1066-1069(2010) [3]E.P.Raposo et al., PLoS Comp.Bio. 7, e1002233(2011)

The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors and some artificial micro-engines operate. As described by stochastic thermodynamics, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit. Here we report an experimental realization of a Carnot engine with a single optically trapped Brownian particle as the working substance. We present an exhaustive study of the energetics of the engine and analyse the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency—an insight that could inspire new strategies in the design of efficient nano-motors. Reference I. A. Martínez, É. Roldán, L. Dinis, D. Petrov, J. M. R. Parrondo and R. A. Rica Nature Physics 12, 67–70 (2016)

Cytoskeletal motor proteins are involved in major intracellular transport processes which are vital for maintaining appropriate cellular function. The motor exhibits distinct states of motility: active motion along filaments, and effectively stationary phase in which it detaches from the filaments and performs passive diffusion in the vicinity of the detachment point due to cytoplasmic crowding. The transition rates between motion and pause phases are asymmetric in general, and considerably affected by changes in environmental conditions which influences the efficiency of cargo delivery to specific targets. By considering the motion of molecular motor on a single filament as well as a dynamic filamentous network, we present an analytical model for the dynamics of self-propelled particles which undergo frequent pause phases. The interplay between motor processivity, structural properties of filamentous network, and transition rates between the two states of motility drastically changes the dynamics: multiple transitions between different types of anomalous diffusive dynamics occur and the crossover time to the asymptotic diffusive or ballistic motion varies by several orders of magnitude. We map out the phase diagrams in the space of transition rates, and address the role of initial conditions of motion on the resulting dynamics.

Motor systems must adapt to perturbations and changing conditions both within and outside the body. We refer to the ability of a system to maintain performance despite perturbations as ``robustness,'' and the ability of a system to deploy alternative strategies that improve fitness as ``flexibility.'' Different classes of pattern-generating circuits yield dynamics with differential sensitivities to perturbations and parameter variation. Depending on the task and the type of perturbation, high sensitivity can either facilitate or hinder robustness and flexibility. In this work we explore the role of multiple coexisting oscillatory modes and sensory feedback in allowing multiphasic motor pattern generation to be both robust and flexible. As a concrete example, we focus on a nominal neuromechanical model of triphasic motor patterns in the feeding apparatus of the marine mollusk Aplysia californica. We find that the model can operate within two distinct oscillatory modes, and that the system exhibits bistability between the two. In the ``heteroclinic mode,'' higher sensitivity makes the system more robust to changing mechanical loads, but less robust to internal parameter variations. In the ``limit cycle mode,'' lower sensitivity makes the system more robust to changes in internal parameter values, but less robust to changes in mechanical load. Finally, we show that overall performance on a variable feeding task is improved when the system can flexibly transition between oscillatory modes in response to the changing demands of the task. Thus, our results suggest that the interplay of sensory feedback and multiple oscillatory modes can allow motor systems to be both robust and flexible in a variable environment. David N. Lyttle, Jeffrey P. Gill, Kendrick M. Shaw, Peter J. Thomas, Hillel J. Chiel Department of Biology Department of Cognitive Science Department of Electrical Engineering and Computer Science Department of Mathematics, Applied Mathematics, and Statistics Case Western Reserve University Cleveland, Ohio USA