J. Tailleur, M. E. Cates
We consider self-propelled particles undergoing run-and-tumble dynamics (as exhibited by E. coli) in one dimension. Building on previous analyses at drift-diffusion level for the one-particle density, we add both interactions and noise, enabling discussion of domain formation by "self-trapping", and other collective phenomena. Mapping onto detailed-balance systems is possible in certain cases.
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{\it E. coli} bacteria swim in straight runs interrupted by sudden reorientation events called tumbles. The resulting random walks give rise to density fluctuations that can be derived analytically in the limit of non interacting particles or equivalently of very low concentrations. However, in situations of practical interest, the concentration of bacteria is always large enough to make interactions an important factor. Using molecular dynamics simulations, we study the dynamic structure factor of a model bacterial bath for increasing values of densities. We show that it is possible to reprod…
In our article we present a computational model for the simulation of self-propelled anisotropic bacteria. To this end we use a self-propelled particle model and augment it with a statistical algorithm for the run-and-tumble motion. We derive an equation for the distribution of reorientations of the bacteria that we use to analyze the statistics of the random walk and that allows us to tune the behavior of our model to the characteristics of an E.coli bacterium. We validate our implementation in terms of a single swimmer and demonstrate that our model is capable of reproducing E.coli's run-and…
Bacterial dimensions sensitively regulate surface diffusivity and residence time
本研究揭示了细菌尺寸如何敏感调节其游动-翻滚策略及动力学行为，发现尺寸微小变化可导致停留时间巨大变化，并使最佳翻滚偏置和表面扩散率产生显著分化。
The random energy landscapes developed by speckle fields can be used to confine and manipulate a large number of micro-particles with a single laser beam. By means of molecular dynamics simulations, we investigate the static and dynamic properties of an active suspension of swimming bacteria embedded into speckle patterns. Looking at the correlation of the density fluctuations and the equilibrium density profiles, we observe a crossover phenomenon when the forces exerted by the speckles are equal to the bacteria's propulsion.
The run-and-tumble (RT) dynamics followed by bacterial swimmers gives rise first to a ballistic motion due to their persistence, and later, through consecutive tumbles, to a diffusive process. Here we investigate how long it takes for a dilute swimmer suspension to reach the diffusive regime as well as what is the amplitude of the deviations from the diffusive dynamics. A linear time dependence of the mean-squared displacement (MSD) is insufficient to characterize diffusion and thus we also focus on the excess kurtosis of the displacement distribution. Four swimming strategies are considered: …
We simulate by lattice Boltzmann the nonequilibrium steady states of run-and-tumble particles (inspired by a minimal model of bacteria), interacting by far-field hydrodynamics, subject to confinement. Under gravity, hydrodynamic interactions barely perturb the steady state found without them, but for particles in a harmonic trap such a state is quite changed if the run length is larger than the confinement length: a self-assembled pump is formed. Particles likewise confined in a narrow channel show a generic upstream flux in Poiseuille flow: chiral swimming is not required.
Recent experiments on the green alga Chlamydomonas that swims using synchronized beating of a pair of flagella have revealed that it exhibits a run-and-tumble behavior similar to that of bacteria such as E. Coli. Using a simple purely hydrodynamic model that incorporates a stroke cycle and an intrinsic Gaussian white noise, we show that a stochastic run-and-tumble behavior could emerge, due to the nonlinearity of the combined synchronization-rotation-translation dynamics. This suggests the intriguing possibility that the alga might exploit nonlinear mechanics---as opposed to sophisticated bioc…
We study a generic model for quorum-sensing bacteria in circular confinement. Every bacterium produces signaling molecules, the local concentration of which triggers a response when a certain threshold is reached. If this response lowers the motility then an aggregation of bacteria occurs, which differs fundamentally from standard motility-induced phase separation due to the long-ranged nature of the concentration of signal molecules. We analyze this phenomenon analytically and by numerical simulations employing two different protocols leading to stationary cluster and ring morphologies, respe…
Magnetotactic swimmers tend to align along magnetic field lines against stochastic reorientations. We show that the swimming strategy, e.g. active Brownian motion versus run-and-tumble dynamics, strongly affects the orientation statistics. The latter can exhibit a velocity condensation whereby the alignment probability density diverges. As a consequence, we find that the swimming strategy affects the nature of the phase transition to collective motion, indicating that Lévy run-and-tumble walks can outperform active Brownian processes as strategies to trigger collective behavior.
We solve the problem of first-passage time for run-and-tumble particles in one dimension. Exact expression is derived for the mean first-passage time in the general case, considering external force-fields and chemotactic-fields, giving rise to space dependent swim-speed and tumble rate. Agreement between theoretical formulae and numerical simulations is obtained in the analyzed case studies -- constant and sinusoidal force fields, constant gradient chemotactic field. Reported findings can be useful to get insights into very different phenomena involving active particles, such as bacterial moti…
The run-and-tumble dynamics of bacteria, as exhibited by \textit{E. coli}, offers a simple experimental realization of non-Brownian, yet diffusive, particles. Here we present some analytic and numerical results for models of the ideal (low-density) limit in which the particles have no hydrodynamic or other interactions and hence undergo independent motions. We address three cases: sedimentation under gravity; confinement by a harmonic external potential; and rectification by a strip of `funnel gates' which we model by a zone in which tumble rate depends on swim direction. We compare our result…
We study a model of self propelled particles exhibiting run and tumble dynamics on lattice. This non-Brownian diffusion is characterised by a random walk with a finite persistence length between changes of direction, and is inspired by the motion of bacteria such as E. coli. By defining a class of models with multiple species of particle and transmutation between species we can recreate such dynamics. These models admit exact analytical results whilst also forming a counterpart to previous continuum models of run and tumble dynamics. We solve the externally driven non-interacting and zero-rang…
Run-and-tumble dynamics is a wide-spread mechanism of swimming bacteria. The accumulation of run-and-tumble microswimmers near impermeable surfaces is studied theoretically and numerically in the low-density limit in two and three spatial dimensions. Both uni-modal and exponential distributions of the run lengths are considered. Constant run lengths lead to {peaks and depletions regions} in the density distribution of particles near the surface, in contrast to {exponentially-distributed run lengths}. Finally, we present a universal accumulation law for large channel widths, which applies not o…
We numerically study the dynamics of run-and-tumble particles confined in two chambers connected by thin channels. Two dominant dynamical behaviors emerge: (i) an oscillatory pumping state, in which particles periodically fill the two vessels and (ii) a circulating flow state, dynamically maintaining a near constant population level in the containers when connected by two channels. We demonstrate that the oscillatory behaviour arises from the combination of a narrow channel, preventing bacteria reorientation, and a density dependent motility inside the chambers.
The run-and-tumble walk, consisting in randomly reoriented ballistic excursions, models phenomena ranging from gas kinetics to bacteria motility. We evaluate the mean time required for this walk to find a fixed target within a 2D or 3D spherical confinement. We find that the mean search time admits a minimum as a function of the mean run duration for various types of boundary conditions and run duration distributions (exponential, power-law, deterministic). Our result stands in sharp contrast to the pure ballistic motion, which is predicted to be the optimal search strategy in the case of Pois…
Microbiology is the science of microbes, particularly bacteria. Many bacteria are motile: they are capable of self-propulsion. Among these, a significant class execute so-called run-and-tumble motion: they follow a fairly straight path for a certain distance, then abruptly change direction before repeating the process. This dynamics has something in common with Brownian motion (it is diffusive at large scales), and also something in contrast. Specifically, motility parameters such as the run speed and tumble rate depend on the local environment and hence can vary in space. When they do so, eve…
We consider the dynamics of self-propelled particles subject to external torques. Two models for the reorientation of self-propulsion are considered, run-and-tumble particles, and active Brownian particles. Using the standard tools of non-equilibrium statistical mechanics we show that the run and tumble particles have a more robust response to torques. This macroscopic signature of the underlying reorientation statistics can be used to differentiate between the two types of self propelled particles. Further this result might indicate that run and tumble motion is indeed the evolutionarily stab…
Run-and-tumble motion in trapping environments
本文研究活性粒子在含捕获区域环境中的跑动-翻滚运动，求解一维动力学方程，给出稳态分布和平均捕获时间，并扩展模型以解释细菌黏附中的亚扩散行为。
The effect of crowding on the run-and-tumble dynamics of swimmers such as bacteria is studied using a discrete lattice model of mutually excluding particles that move with constant velocity along a direction that is randomized at a rate $α$. In stationary state, the system is found to break into dense clusters in which particles are trapped or stopped from moving. The characteristic size of these clusters predominantly scales as $α^{-0.5}$ both in 1D and 2D. For a range of densities, due to cooperative effects, the stopping time scales as ${\cal T}_{1d}^{0.85}$ and as ${\cal T}_{2d}^{0.8}$, wh…
We study a one-dimensional three-state run-and-tumble model motivated by the bacterium Caulobacter crescentus which displays a cell cycle between two non-proliferation mobile phase and a proliferating sedentary phase. Our model implements kinetic transitions between the two mobile and one sedentary states described in terms of their number densities, where mobility is allowed with different running speeds in forward and backward direction. We start by analyzing the stationary states of the system and compute the mean and squared-displacements for the distribution of all cells, as well as for t…
Run-and-tumble particles, frequently considered today for modeling bacterial locomotion, naturally appear outside a biological context as well, e.g. for producing waves in the telegraph process. Here, we use a wave function to drive their propulsion and tumbling. Such quantum-active motion realizes a jittery motion of Dirac electrons (as in the famous Zitterbewegung): the Dirac electron is a run-and-tumble particle, where the tumbling is between chiralities. We visualize the trajectories in diffraction and double slit experiments for electrons. In particular, that yields the time-of-arrival st…
Optimal run-and-tumble in slit-like confinement
该研究针对狭缝约束下平行边界的输运研究不足的问题，提出可解的离散方向奔跑-翻滚模型得到精确扩散系数，经模拟验证可近似连续方向情况，并找出扩散最大化条件及细菌最优奔跑长度规律。
Shortcut engineering of active matter: run-and-tumble particles
本文将捷径工程方法拓展至 run-and-tumble 粒子，给出谐振子势中一维系统的快速控制通用解，并通过数值模拟证明其相比淬火方案能显著加速，为活性物质控制提供了新工具。
Run-and-Tumble Particles Learning Chemotaxis
研究通过机器学习方法，探讨了具备时间比较能力的奔跑-翻滚粒子在趋化运动中更高效地定位目标的能力。
Local entropy production rate of run-and-tumble particles
本文研究热浴中无相互作用跑动-翻滚粒子的局部熵产生率与熵流，证明稳态下二者相等且仅由分布函数及其空间导数决定，并通过光动细菌速度场和外力场案例验证解析结果与数值模拟的一致性。
Active Brownian particles (ABPs, such as self-phoretic colloids) swim at fixed speed $v$ along a body-axis ${\bf u}$ that rotates by slow angular diffusion. Run-and-tumble particles (RTPs, such as motile bacteria) swim with constant $\u$ until a random tumble event suddenly decorrelates the orientation. We show that when the motility parameters depend on density $ρ$ but not on ${\bf u}$, the coarse-grained fluctuating hydrodynamics of interacting ABPs and RTPs can be mapped onto each other and are thus strictly equivalent. In both cases, a steeply enough decreasing $v(ρ)$ causes phase separati…
We study a model of bacterial dynamics where two interacting random walkers perform run-and-tumble motion on a one-dimensional lattice under mutual exclusion and find an exact expression for the probability distribution in the steady state. This stationary distribution has a rich structure comprising three components: a jammed component, where the particles are adjacent and block each other; an attractive component, where the probability distribution for the distance between particles decays exponentially; and an extended component in which the distance between particles is uniformly distribut…
A one-dimensional run-and-tumble particle (RTP) switches randomly between a left and right moving state of constant speed $v$. This type of motion arises in a wide range of applications in cell biology, including the unbiased growth and shrinkage of microtubules or cytonemes, the bidirectional motion of molecular motors, and the "run-and-tumble" motion of bacteria such as {\em E. coli}. RTPs are also of more general interest within the non-equilibrium statistical physics community, both at the single particle level and at the interacting population level, where it provides a simple example of …
We investigate the statistics of the convex hull for a single run-and-tumble particle in two dimensions. Run-and-tumble particle, also known as persistent random walker, has gained significant interest in the recent years due to its biological application in modelling the motion of bacteria. We consider two different statistical ensembles depending on whether (i) the total number of tumbles $n$ or (ii) the total observation time $t$ is kept fixed. Benchmarking the results on perimeter, we study the statistical properties of the area of the convex hull for RTP. Exploiting the connections to ext…
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 m…
We present an analysis of the stationary distributions of run-and-tumble particles trapped in external potentials in terms of a thermophoretic potential, that emerges when trapped active motion is mapped to trapped passive Brownian motion in a fictitious inhomogeneous thermal bath. We elaborate on the meaning of the non-Boltzmann-Gibbs stationary distributions that emerge as a consequence of the persistent motion of active particles. These stationary distributions are interpreted as a class of distributions in nonequilibrium statistical mechanics known as superstatistics. Our analysis provides…
Spontaneous Emergence of Run-and-Tumble-Like Dynamics in a Robotic Analog of \textit{Chlamydomonas}: Experiment and Theory
本研究通过刚性杆连接的干燥自推进机器人模拟莱茵衣藻，发现系统自发涌现类跑-翻滚动力学，并通过理论模型揭示其物理机制，为微游动者运动提供新见解。
Jamming pair of general run-and-tumble particles: Exact results, symmetries and steady-state universality classes
本文利用分段确定性马尔可夫过程（PDMP）直接建模游走-翻滚粒子系统，解析推导出设定稳态不变分布的守恒条件，并显式构造了精细阻塞与全局阻塞两个普适类，揭示了其非平衡特征及不变测度的类悬链约束。
Exploring run-and-tumble movement in confined settings through simulation
本研究通过理论与数值模拟探讨了受限二维圆形区域内游走与翻滚粒子的动力学，验证了MPLT的适用条件并揭示了边界效应、非均匀角分布和记忆过程导致的偏差，为受限空间中的运动机制提供了新见解。
Improving estimation of entropy production rate for run-and-tumble particle systems by high-order thermodynamic uncertainty relation
本文针对一维非对称 run-and-tumble 粒子系统，引入高阶热力学不确定性关系（HTUR）并解析求得流的累积量生成函数，从而在远离平衡条件下显著改进熵产生率与能量耗散率的估计。
Steady state and mixing of two run-and-tumble particles interacting through jamming and attractive forces
研究两个跑停粒子在吸引力与堵塞作用下的长时间行为，给出显式不变测度并分析弛豫性质，发现线性势下总变差距离指数衰减，谐波势下给出Wasserstein型指数界。
When active matter particles such as swimming bacteria are placed in an asymmetric array of funnels, it has been shown that a ratchet effect can occur even in the absence of an external drive. Here we examine active ratchets for two dimensional arrays of funnels or L-shapes where there is also an externally applied dc drive or drift. We show that for certain conditions, the ratchet effect can be strongly enhanced, and that it is possible to have conditions under which run-and-tumble particles with one run length move in the opposite direction from particles with a different run length. For the…
Intermittent Run Motility of Bacteria in Gels Exhibits Power-Law Distributed Dwell Times
研究 P. putida 在不同浓度琼脂凝胶中的间歇奔跑运动，发现停留时间呈幂律分布，并提出可再现均方位移时间依赖性的最小主动粒子模型。
Integral equation formulation of run-and-tumble particles in a harmonic trap: the special status of a system in two-dimensions
本研究采用积分方程表述研究谐振阱中的奔跑-翻滚粒子模型，发现二维系统的跃迁算符具有可逆性，可通过细致平衡直接得到稳态分布，且该可逆性依赖于等待时间的指数分布。
Many of the chemical reactions that take place within a living cell are irreversible. Due to evolutionary pressures, the number of allowable reactions within these systems are highly constrained and thus the resulting metabolic networks display considerable asymmetry. In this paper, we explore possible evolutionary factors pertaining to the reduced symmetry observed in these networks, and demonstrate the important role environmental variability plays in shaping their structural organization. Interpreting the returnability index as an equilibrium constant for a reaction network in equilibrium w…
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