Velocity Condensation for Magnetotactic Bacteria

Role of Topology in Relaxation of One-Dimensional Stochastic Processes

Stochastic processes are commonly used models to describe dynamics of a wide variety of nonequilibrium phenomena ranging from electrical transport to biological motion. The transition matrix describing a stochastic process can be regarded as a non-Hermitian Hamiltonian. Unlike general non-Hermitian systems, the conservation of probability imposes additional constraints on the transition matrix, which can induce unique topological phenomena. Here, we reveal the role of topology in relaxation phenomena of classical stochastic processes. Specifically, we define a winding number that is related to topology of stochastic processes and show that it predicts the existence of a spectral gap that characterizes the relaxation time. Then, we numerically confirm that the winding number corresponds to the system-size dependence of the relaxation time and the characteristic transient behavior. One can experimentally realize such topological phenomena in magnetotactic bacteria and cell adhesions.

Magnetic Microswimmers Exhibit Bose-Einstein-like Condensation

We study an active matter system comprised of magnetic microswimmers confined in a microfluidic channel and show that it exhibits a new type of self-organized behavior. Combining analytical techniques and Brownian dynamics simulations, we demonstrate how the interplay of nonequilibrium activity, external driving, and magnetic interactions leads to the condensation of swimmers at the center of the channel via a nonequilibrium phase transition that is formally akin to Bose-Einstein condensation. We find that the effective dynamics of the microswimmers can be mapped onto a diffusivity-edge problem, and use the mapping to build a generalized thermodynamic framework, which is verified by a parameter-free comparison with our simulations. Our work reveals how driven active matter has the potential to generate exotic classical nonequilibrium phases of matter with traits that are analogous to those observed in quantum systems.

Persistence in Brownian motion of an ellipsoidal particle in two dimensions

We investigate the persistence probability p(t) of the position of a Brownian particle with shape asymmetry in two dimensions. The persistence probability is defined as the probability that a stochastic variable has not changed its sign in the given time interval. We explicitly consider two cases-diffusion of a free particle and that of a harmonically trapped particle. The latter is particularly relevant in experiments that use trapping and tracking techniques to measure the displacements. We provide analytical expressions of p(t) for both the scenarios and show that in the absence of the shape asymmetry, the results reduce to the case of an isotropic particle. The analytical expressions of p(t) are further validated against numerical simulation of the underlying overdamped dynamics. We also illustrate that p(t) can be a measure to determine the shape asymmetry of a colloid and the translational and rotational diffusivities can be estimated from the measured persistence probability. The advantage of this method is that it does not require the tracking of the orientation of the particle.

Chemotaxis in external fields: Simulations for active magnetic biological matter

The movement of microswimmers is often described by active Brownian particle models. Here we introduce a variant of these models with several internal states of the swimmer to describe stochastic strategies for directional swimming such as run and tumble or run and reverse that are used by microorganisms for chemotaxis. The model includes a mechanism to generate a directional bias for chemotaxis and interactions with external fields (e.g., gravity, magnetic field, fluid flow) that impose forces or torques on the swimmer. We show how this modified model can be applied to various scenarios: First, the run and tumble motion of E. coli is used to establish a paradigm for chemotaxis and investigate how it is affected by external forces. Then, we study magneto-aerotaxis in magnetotactic bacteria, which is biased not only by an oxygen gradient towards a preferred concentration, but also by magnetic fields, which exert a torque on an intracellular chain of magnets. We study the competition of magnetic alignment with active reorientation and show that the magnetic orientation can improve chemotaxis and thereby provide an advantage to the bacteria, even at rather large inclination angles of the magnetic field relative to the oxygen gradient, a case reminiscent of what is expected for the bacteria at or close to the equator. The highest gain in chemotactic velocity is obtained for run and tumble with a magnetic field parallel to the gradient, but in general a mechanism for reverse motion is necessary to swim against the magnetic field and a run and reverse strategy is more advantageous in the presence of a magnetic torque. This finding is consistent with observations that the dominant mode of directional changes in magnetotactic bacteria is reversal rather than tumbles. Moreover, it provides guidance for the design of future magnetic biohybrid swimmers.

In this paper, we propose a modified Active Brownian particle model to describe bacterial swimming behavior under the influence of external forces and torques, in particular of a magnetic torque. This type of interaction is particularly important for magnetic biohybrids (i.e. motile bacteria coupled to a synthetic magnetic component) and for magnetotactic bacteria (i.e. bacteria with a natural intracellular magnetic chain), which perform chemotaxis to swim along chemical gradients, but are also directed by an external magnetic field. The model allows us to investigate the benefits and disadvantages of such coupling between two different directionality mechanisms. In particular we show that the magnetic torque can speed chemotaxis up in some conditions, while it can hinder it in other cases. In addition to an understanding of the swimming strategies of naturally magnetotactic organisms, the results may guide the design of future biomedical devices.

Magnetotactic bacteria in a droplet self-assemble into a rotary motor

From intracellular protein trafficking to large-scale motion of animal groups, the physical concepts driving the self-organization of living systems are still largely unraveled. Self-organization of active entities, leading to novel phases and emergent macroscopic properties, recently shed new light on these complex dynamical processes. Here we show that under the application of a constant magnetic field, motile magnetotactic bacteria confined in water-in-oil droplets self-assemble into a rotary motor exerting a torque on the external oil phase. A collective motion in the form of a large-scale vortex, reversable by inverting the field direction, builds up in the droplet with a vorticity perpendicular to the magnetic field. We study this collective organization at different concentrations, magnetic fields and droplet radii and reveal the formation of two torque-generating areas close to the droplet interface. We characterize quantitatively the mechanical energy extractable from this new biological and self-assembled motor.

Viscotaxis: Microswimmer Navigation in Viscosity Gradients

The survival of many microorganisms, like Leptospira or Spiroplasma bacteria, can depend on their ability to navigate towards regions of favorable viscosity. While this ability, called viscotaxis, has been observed in several bacterial experiments, the underlying mechanism remains unclear. We provide a framework to study viscotaxis of biological or synthetic self-propelled swimmers in slowly varying viscosity fields and show that suitable body shapes create viscotaxis based on a systematic asymmetry of viscous forces acting on a microswimmer. Our results shed new light on viscotaxis in Spiroplasma and Leptospira and suggest that dynamic body shape changes exhibited by both types of microorganisms may have an unrecognized functionality: to prevent them from drifting to low viscosity regions where they swim poorly. The present theory classifies microswimmers regarding their ability to show viscotaxis and can be used to design synthetic viscotactic swimmers, e.g., for delivering drugs to a target region distinguished by viscosity.

Dynamics of a magnetic active Brownian particle under a uniform magnetic field

The dynamics of a magnetic active Brownian particle undergoing three-dimensional Brownian motion, both translation and rotation, under the influence of a uniform magnetic field is investigated. The particle self-propels at a constant speed along its magnetic dipole moment, which reorients due to the interplay between Brownian and magnetic torques, quantified by the Langevin parameter α. In this work, the time-dependent active diffusivity and the crossover time (τ^{cross})-from ballistic to diffusive regimes-are calculated through the time-dependent correlation function of the fluctuations of the propulsion direction. The results reveal that, for any value of α, the particle undergoes a directional (or ballistic) propulsive motion at very short times (t≪τ^{cross}). In this regime, the correlation function decreases linearly with time, and the active diffusivity increases with it. It the opposite time limit (t≫τ^{cross}), the particle moves in a purely diffusive regime with a correlation function that decays asymptotically to zero and an active diffusivity that reaches a constant value equal to the long-time active diffusivity of the particle. As expected in the absence of a magnetic field (α=0), the crossover time is equal to the characteristic time scale for rotational diffusion, τ_{rot}. In the presence of a magnetic field (α>0), the correlation function, the active diffusivity, and the crossover time decrease with increasing α. The magnetic field regulates the regimes of propulsion of the particle. Here, the field reduces the period of time at which the active particle undergoes a directional motion. Consequently, the active particle rapidly reaches a diffusive regime at τ^{cross}≪τ_{rot}. In the limit of weak fields (α≪1), the crossover time decreases quadratically with α, while in the limit of strong fields (α≫1) it decays asymptotically as α^{-1}. The results are in excellent agreement with those obtained by Brownian dynamics simulations.

Brownian motion of a circle swimmer in a harmonic trap

We study the dynamics of a Brownian circle swimmer with a time-dependent self-propulsion velocity in an external temporally varying harmonic potential. For several situations, the noise-free swimming paths, the noise-averaged mean trajectories, and the mean-square displacements are calculated analytically or by computer simulation. Based on our results, we discuss optimal swimming strategies in order to explore a maximum spatial range around the trap center. In particular, we find a resonance situation for the maximum escape distance as a function of the various frequencies in the system. Moreover, the influence of the Brownian noise is analyzed by comparing noise-free trajectories at zero temperature with the corresponding noise-averaged trajectories at finite temperature. The latter reveal various complex self-similar spiral or rosette-like patterns. Our predictions can be tested in experiments on artificial and biological microswimmers under dynamical external confinement.