Auswahl der wissenschaftlichen Literatur zum Thema „Particules run-And-Tumble“

The run and tumble process is well established in order to describe the movement of bacteria in response to a chemical stimulus. However, the relation between the tumbling rate and the internal state of bacteria is poorly understood. This study aims at deriving macroscopic models as limits of the mesoscopic kinetic equation in different regimes. In particular, we are interested in the roles of the stiffness of the response and the adaptation time in the kinetic equation. Depending on the asymptotics chosen both the standard Keller–Segel equation and the flux-limited Keller–Segel (FLKS) equation can appear. An interesting mathematical issue arises with a new type of equilibrium equation leading to solution with singularities.

AbstractMost classical work on the hydrodynamics of low-Reynolds-number swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction, resulting in a transition from short-time ballistic dynamics to effective long-time diffusion. As most cells or synthetic swimmers are immersed in external flows, we consider theoretically in this paper the stochastic dynamics of a model active particle (a self-propelled sphere) in a steady general linear flow. The stochasticity arises both from translational diffusion in physical space, and from a combination of rotary diffusion and so-called run-and-tumble dynamics in orientation space. The latter process characterizes the manner in which the orientation of many bacteria decorrelates during their swimming motion. In contrast to rotary diffusion, the decorrelation occurs by means of large and impulsive jumps in orientation (tumbles) governed by a Poisson process. We begin by deriving a general formulation for all components of the long-time mean square displacement tensor for a swimmer with a time-dependent swimming velocity and whose orientation decorrelates due to rotary diffusion alone. This general framework is applied to obtain the convectively enhanced mean-squared displacements of a steadily swimming particle in three canonical linear flows (extension, simple shear and solid-body rotation). We then show how to extend our results to the case where the swimmer orientation also decorrelates on account of run-and-tumble dynamics. Self-propulsion in general leads to the same long-time temporal scalings as for passive particles in linear flows but with increased coefficients. In the particular case of solid-body rotation, the effective long-time diffusion is the same as that in a quiescent fluid, and we clarify the lack of flow dependence by briefly examining the dynamics in elliptic linear flows. By comparing the new active terms with those obtained for passive particles we see that swimming can lead to an enhancement of the mean-square displacements by orders of magnitude, and could be relevant for biological organisms or synthetic swimming devices in fluctuating environmental or biological flows.

Abstract We consider one-dimensional systems comprising either active run-and-tumble particles (RTPs) or passive Brownian random walkers. These particles are either noninteracting or have hardcore exclusions. We study the dynamics of a single tracer particle embedded in such a system—this tracer may be either active or passive, with hardcore exclusion from environmental particles. In an active hardcore environment, both active and passive tracers show long-time subdiffusion: displacements scale as t 1/4 with a density-dependent prefactor that is independent of tracer type, and differs from the corresponding result for passive-in-passive subdiffusion. In an environment of noninteracting active particles, the passive-in-passive results are recovered at low densities for both active and passive tracers, but transient caging effects slow the tracer motion at higher densities, delaying the onset of any t 1/4 regime. For an active tracer in a passive environment, we find more complex outcomes, which depend on details of the dynamical discretization scheme. We interpret these results by studying the density distribution of environmental particles around the tracer. In particular, sticking of environment particles to the tracer cause it to move more slowly in noninteracting than in interacting active environments, while the anomalous behaviour of the active-in-passive cases stems from a ‘snowplough’ effect whereby a large pile of diffusive environmental particles accumulates in front of an RTP tracer during a ballistic run.

We examine the stability of a suspension of swimming bacteria in a Newtonian medium. The bacteria execute a run-and-tumble motion, runs being periods when a bacterium on average swims in a given direction; runs are interrupted by tumbles, leading to an abrupt, albeit correlated, change in the swimming direction. An instability is predicted to occur in a suspension of ‘pushers’ (e.g.E. Coli,Bacillus subtilis, etc.), and owes its origin to the intrinsic force dipoles of such bacteria. Unlike the dipole induced in an inextensible fibre subject to an axial straining flow, the forces constituting the dipole of a pusher are directed outward along its axis. As a result, the anisotropy in the orientation distribution of bacteria due to an imposed velocity perturbation drives a disturbance velocity field that acts to reinforce the perturbation. For long wavelengths, the resulting destabilizing bacterial stress is Newtonian but with a negative viscosity. The suspension becomes unstable when the total viscosity becomes negative. In the dilute limit (nL3≪ 1), a linear stability analysis gives the threshold concentration for instability as (nL3)crit= ((30/Cℱ(r))(DrL/U)(1 + 1/(6τDr)))/(1−(15𝒢(r)/Cℱ(r))(DrL/U)(1 + 1/(6τDr))) for perfectly random tumbles; here,LandUare the length and swimming velocity of a bacterium,nis the bacterial number density,Drcharacterizes the rotary diffusion during a run and τ−1is the average tumbling frequency. The function ℱ(r) characterizes the rotation of a bacterium of aspect ratiorin an imposed linear flow; ℱ(r) = (r2−1)/(r2+ 1) for a spheroid, and ℱ(r) ≈ 1 for a slender bacterium (r≫ 1). The function 𝒢(r) characterizes the stabilizing viscous response arising from the resistance of a bacterium to a deforming ambient flow; 𝒢(r) = 5π/6 for a rigid spherical bacterium, and 𝒢(r)≈ π/45(lnr) for a slender bacterium. Finally, the constantCdenotes the dimensionless strength of the bacterial force dipole in units of μU L2; forE. Coli,C≈ 0.57. The threshold concentration diverges in the limit ((15𝒢(r)/Cℱ(r)) (DrL/U)(1 + 1/(6τDr))) → 1. This limit defines a critical swimming speed,Ucrit= (DrL)(15𝒢(r)/Cℱ(r))(1 + 1/(6τDr)). For speeds smaller than this critical value, the destabilizing bacterial stress remains subdominant and a dilute suspension of these swimmers therefore responds to long-wavelength perturbations in a manner similar to a suspension of passive rigid particles, that is, with a net enhancement in viscosity proportional to the bacterial concentration.On the other hand, the stability analysis predicts that the above threshold concentration reduces to zero in the limitDr→ 0, τ → ∞, and a suspension of non-interacting straight swimmers is therefore always unstable. It is then argued that the dominant effect of hydrodynamic interactions in a dilute suspension of such swimmers is via an interaction-driven orientation decorrelation mechanism. The latter arises from uncorrelated pair interactions in the limitnL3≪ 1, and for slender bacteria in particular, it takes the form of a hydrodynamic rotary diffusivity (Dhr); forE. Coli, we findDhr= 9.4 × 10−5(nUL2). From the above expression for the threshold concentration, it may be shown that even a weakly interacting suspension of slender smooth-swimming bacteria (r≫ 1, ℱ(r) ≈ 1, τ → ∞) will be stable providedDhr> (C/30)(nUL2) in the limitnL3≪ 1. The hydrodynamic rotary diffusivity ofE. Coliis, however, too small to stabilize a dilute suspension of these swimmers, and a weakly interacting suspension ofE. Coliremains unstable.

We present an in silico microswimmer motivated by peritrichous bacteria, E. coli, which can run and tumble by spinning their flagellar motors counterclockwise (CCW) or clockwise (CW). Runs are the directed movement driven by a flagellar bundle and tumbles are reorientations of cells caused by some motors' reversals from CCW to CW. In a viscous fluid without obstacles, our simulations reveal that material properties of the hook and the counterrotation of the cell body are important factors for efficient flagellar bundling, and that longer hooks in mutant cell models create an instability and disrupt the bundling process, resulting in a limited range of movement. In the presence of a planar wall, we demonstrate that microswimmers can explore environment near surface by making various types of tumble events as they swim close to the surface. In particular, the variation of tumble duration can lead the microswimmer to run in a wide range of direction. However, we find that cells near surface stay close to the surface even after tumbles, which suggests that the tumble motion may not promote cells' escape from the confinement but promote biofilm formation.

Abstract The connection between absorbing boundary conditions and hard walls is well established in the mathematical literature for a variety of stochastic models, including for instance the Brownian motion. In this paper we explore this duality for a different type of process which is of particular interest in physics and biology, namely the run-tumble-particle, a toy model of active particle. For a one-dimensional run-and-tumble particle subjected to an arbitrary external force, we provide a duality relation between the exit probability, i.e. the probability that the particle exits an interval from a given boundary before a certain time $t$, and the cumulative distribution of its position in the presence of hard walls at the same time $t$. We show this relation for a run-and-tumble particle in the stationary state by explicitly computing both quantities. At finite time, we provide a derivation using the Fokker-Planck equation. All the results are confirmed by numerical simulations.

AbstractRandom flights (also called run-and-tumble walks or transport processes) represent finite velocity random motions changing direction at any Poissonian time. These models in d-dimension, can be studied giving a general formulation of the problem valid at any spatial dimension. The aim of this paper is to extend this general analysis to time-fractional processes arising from a non-local generalization of the kinetic equations. The probabilistic interpretation of the solution of the time-fractional equations leads to a time-changed version of the original transport processes. The obtained results provide a clear picture of the role played by the time-fractional derivatives in this kind of random motions. They display an anomalous behavior and are useful to describe several complex systems arising in statistical physics and biology. In particular, we focus on the one-dimensional random flight, called telegraph process, studying the time-fractional version of the classical telegraph equation and providing a suitable interpretation of its stochastic solutions.

AbstractSuitable asymmetric microstructures can be used to control the direction of motion in microorganism populations. This rectification process makes it possible to accumulate swimmers in a region of space or to sort different swimmers. Here we study numerically how the separation process depends on the specific motility strategies of the microorganisms involved. Crucial properties such as the separation efficiency and the separation time for two bacterial strains are precisely defined and evaluated. In particular, the sorting of two bacterial populations inoculated in a box consisting of a series of chambers separated by columns of asymmetric obstacles is investigated. We show how the sorting efficiency is enhanced by these obstacles and conclude that this kind of sorting can be efficiently used even when the involved populations differ only in one aspect of their swimming strategy.

Abstract We study the extreme value statistics of a run and tumble particle (RTP) in one dimension till its first passage to the origin starting from the position $x_0~(>0)$. This model has recently drawn a lot of interest due to its biological application in modelling the motion of certain species of bacteria. Herein, we analytically study the exact time-dependent propagators for a single RTP in a finite interval with absorbing conditions at its two ends. By exploiting a path decomposition technique, we use these propagators appropriately to compute the joint distribution $\mathscr{P}(M,t_m)$ of the maximum displacement $M$ till first-passage and the time $t_m$ at which this maximum is achieved exactly. The corresponding marginal distributions $\mathbb{P}_M(M)$ and $P_M(t_m)$ are studied separately and verified numerically. In particular, we find that the marginal distribution $P_M(t_m)$ has interesting asymptotic forms for large and small $t_m$. While for small $t_m$, the distribution $P_M(t_m)$ depends sensitively on the initial velocity direction $\sigma _i$ and is completely different from the Brownian motion, the large $t_m$ decay of $P_M(t_m)$ is same as that of the Brownian motion although the amplitude crucially depends on the initial conditions $x_0$ and $\sigma _i$. We verify all our analytical results to high precision by numerical simulations.

Abstract Active fluids refer to the fluids that contain self-propelled particles such as bacteria or microalgae, whose properties differ fundamentally from the passive fluids. Such particles often exhibit an intermittent motion, with high-motility “run” periods broken by low-motility “tumble” periods. The average motion can be modified with external stresses, such as nutrient or light gradients, leading to a directed movement called chemotaxis and phototaxis, respectively. Using cyanobacterium Synechocystis sp. PCC 6803, a model microorganism to study photosynthesis, we track the bacterial response to light stimuli, under isotropic and nonisotropic (directional) conditions. In particular, we investigate how the intermittent motility is influenced by illumination. We find that just after a rise in light intensity, the probability to be in the run state increases. This feature vanishes after a typical characteristic time of about 1 h, when initial probability is recovered. Our results are well described by a mathematical model based on the linear response theory. When the perturbation is anisotropic, we observe a collective motion toward the light source (phototaxis). We show that the bias emerges due to more frequent runs in the direction of the light, whereas the run durations are longer whatever the direction.

1. Simuler des systèmes actifs et métastables avec des processus de Markov déterministes par morceaux (PDMPs): quelle dynamique choisir pour simuler efficacement des états métastables? comment exploiter directement la nature hors équilibre des PDMPs pour étudier les systèmes physiques modélisés? 2. Modéliser des systèmes actifs avec des PDMPs: quelles conditions doit remplir un système pour être modélisable par un PDMP? dans quels cas le système a-t-il un distribution stationnaire? comment calculer des quantités dynamiques (ex: rates de transition) dans ce cadre? 3. Améliorer les techniques de simulation de systèmes à l'équilibre: peut-on utiliser les résultats obtenus dans le cadre de systèmes hors équilibre pour accélérer la simulation de systèmes à l'équilibre? comment utiliser l'information topologique pour adapter la dynamique en temps réel?
1. Simulating active and metastable systems with piecewise deterministic Markov processes (PDMPs): - Which dynamics to choose to efficiently simulate metastable states? - How to directly exploit the non-equilibrium nature of PDMPs to study the modeled physical systems? 2. Modeling active systems with PDMPs: - What conditions must a system meet to be modeled by a PDMP? - In which cases does the system have a stationary distribution? - How to calculate dynamic quantities (e.g., transition rates) in this framework? 3. Improving simulation techniques for equilibrium systems: - Can results obtained in the context of non-equilibrium systems be used to accelerate the simulation of equilibrium systems? - How to use topological information to adapt the dynamics in real-time?

For increasing the thermal engine efficiency, faster combustion and low cycle-to-cycle variation are required. In PFI engines the organization of in-cylinder flow structure is thus mandatory for achieving increased efficiency. In particular the formation of a coherent tumble vortex with dimensions comparable to engine stroke largely promotes proper turbulence production extending the engine tolerance to dilute/lean mixture. For motorbike and scooter applications, tumble has been considered as an effective way to further improve combustion system efficiency and to achieve emission reduction since layout and weight constraints limit the adoption of more advanced concepts. In literature chamber geometry was found to have a significant influence on bulk motion and turbulence levels at ignition time, while intake system influences mainly the formation of tumble vortices during suction phase. The most common engine parameters believed to affect in-cylinder flow structure are: 1. Intake duct angle; 2. Inlet valve shape and lift; 3. Piston shape; 4. Pent-roof angle. The present paper deals with the computational analysis of three different head shapes equipping a scooter/motorcycle engine and their influence on the tumble flow formation and breakdown, up to the final turbulent kinetic energy distribution at spark plug. The engine in analysis is a 3-valves pent-roof motorcycle engine. The three dimensional CFD simulations were run at 6500 rpm with AVL FIRE code on the three engines characterised by the same piston, valve lift, pent-roof angle and compression ratio. They differ only in head shape and squish areas. The aim of the present paper is to demonstrate the influence of different head shapes on in-cylinder flow motion, with particular care to tumble motion and turbulence level at ignition time. Moreover, an analysis of the mutual influence between tumble motion and squish motion was carried out in order to assess the role of both these motions in promoting a proper level of turbulence at ignition time close to spark plug in small 3-valves engines.

Abstract Active fluids refer to the fluids that contain self-propelled particles such as bacteria or micro-algae, whose properties differ fundamentally from the passive fluids. Such particles often exhibit an intermittent motion; with high-motility “run” periods separated by low-motility “tumble” periods. The average motion can be modified with external stresses, such as nutrient or light gradient, leading to a directed movement called chemotaxis and phototaxis, respectively. Using cyanobacterium Synechocystis sp.PCC 6803, a model micro-organism to study photosynthesis, we track the bacterial response to light stimuli, under isotropic and non-isotropic conditions. In particular, we investigate how the intermittent motility is influenced by illumination. We find that just after a rise in light intensity, the probability to be in the run state increases. This feature vanishes after a typical time of about 1 hour, when initial probability is recovered. Our results are well described by a model based on the linear response theory. When the perturbation is anisotropic, the characteristic time of runs is longer whatever the direction, similar to what is observed with isotropic conditions. Yet we observe a collective motion toward the light source (phototaxis) and show that the bias emerges because of more frequent runs towards the light.