Non-Gaussian limit fluctuations in active swimmer suspensions

Enhanced Diffusion and Non-Gaussian Displacements of Colloids in Quasi-2D Suspensions of Motile Bacteria

In the real world, active agents interact with surrounding passive objects, thus introducing additional degrees of complexity. The relative contributions of far-field hydrodynamic and near-field contact interactions to the anomalous diffusion of passive particles in suspensions of active swimmers remain a subject of ongoing debate. We constructed a quasi-two-dimensional microswimmer-colloid mixed system by taking advantage of Serratia marcescens' tendency to become trapped at the air-water interface to investigate the origins of the enhanced diffusion and non-Gaussianity of the displacement distributions of passive colloidal tracers. Our findings reveal that the diffusion behavior of colloidal particles exhibits a strong dependence on bacterial density. At moderate densities, the collective dynamics of bacteria dominate the diffusion of tracer particles. In dilute bacterial suspensions, although there are multiple dynamic types present, near-field contact interactions such as collisions play a major role in the enhancement of colloidal transport and the emergence of non-Gaussian displacement distributions characterized by heavy exponential tails in short times. Despite the distinct types of microorganisms and their diverse self-propulsion mechanisms, a generality in the diffusion behavior of passive colloids and their underlying dynamics is observed.

Harnessing density to control the duration of intermittent Lévy walks in bacterial turbulence

Dense bacterial suspensions display collective motion exhibiting coherent flow structures reminiscent of turbulent flows. However, in contrast to inertial turbulence, the microscopic dynamics underlying bacterial turbulence is only beginning to be understood. Here, we report experiments revealing correlations between microscopic dynamics and the emergence of collective motion in bacterial suspensions. Our results demonstrate the existence of three microscopic dynamical regimes: initial ballistic dynamics followed by an intermittent Lévy walk before the intriguing decay to random Gaussian fluctuations. Our experiments capture that the fluid correlation time earmarks the transition from Lévy to Gaussian fluctuations demonstrating the microscopic reason underlying the observation. By harnessing the flow activity via bacterial concentration, we reveal systematic control over the flow correlation timescales, which, in turn, allows controlling the duration of the Lévy walk.

Activity-dependent glassy cell mechanics II: Nonthermal fluctuations under metabolic activity

The glassy cytoplasm, crowded with bio-macromolecules, is fluidized in living cells by mechanical energy derived from metabolism. Characterizing the living cytoplasm as a nonequilibrium system is crucial in elucidating the intricate mechanism that relates cell mechanics to metabolic activities. In this study, we conducted active and passive microrheology in eukaryotic cells, and quantified nonthermal fluctuations by examining the violation of the fluctuation-dissipation theorem. The power spectral density of active force generation was estimated following the Langevin theory extended to nonequilibrium systems. However, experiments performed while regulating cellular metabolic activity showed that the nonthermal displacement fluctuation, rather than the active nonthermal force, is linked to metabolism. We discuss that mechano-enzymes in living cells do not act as microscopic objects. Instead, they generate meso-scale collective fluctuations with displacements controlled by enzymatic activity. The activity induces structural relaxations in glassy cytoplasm. Even though the autocorrelation of nonthermal fluctuations is lost at long timescales due to the structural relaxations, the nonthermal displacement fluctuation remains regulated by metabolic reactions. Our results therefore demonstrate that nonthermal fluctuations serve as a valuable indicator of a cell's metabolic activities, regardless of the presence or absence of structural relaxations.

Statistics of long-range force fields in random environments: Beyond Holtsmark

Since the times of Holtsmark (1911), statistics of fields in random environments have been widely studied, for example in astrophysics, active matter, and line-shape broadening. The power-law decay of the two-body interaction of the form 1/|r|^{δ}, and assuming spatial uniformity of the medium particles exerting the forces, imply that the fields are fat-tailed distributed, and in general are described by stable Lévy distributions. With this widely used framework, the variance of the field diverges, which is nonphysical, due to finite size cutoffs. We find a complementary statistical law to the Lévy-Holtsmark distribution describing the large fields in the problem, which is related to the finite size of the tracer particle. We discover biscaling with a sharp statistical transition of the force moments taking place when the order of the moment is d/δ, where d is the dimension. The high-order moments, including the variance, are described by the framework presented in this paper, which is expected to hold for many systems. The new scaling solution found here is nonnormalized similar to infinite invariant densities found in dynamical systems.

Measuring fluctuating dynamics of sparsely crosslinked actin gels with dual-feedback nonlinear microrheology

We investigate the fluctuating dynamics of colloidal particles in weakly crosslinked F-actin networks with optical-trap-based microrheology. Using the dual-feedback technology, embedded colloidal particles were stably forced beyond the linear regime in a manner that does not suppress spontaneous fluctuations of particles. Upon forcing, a particle that was stably confined in a cage made of the network's crosslinks started to intermittently jump to the next caging microenvironments. By investigating the statistics of the jump dynamics, we discuss how heterogeneous relaxations observed in equilibrium systems became homogeneous when similar jumps were activated under constant forcing beyond the linear regime.

Exponential increase of transition rates in metastable systems driven by non-Gaussian noise

Noise-induced escape from metastable states governs a plethora of transition phenomena in physics, chemistry, and biology. While the escape problem in the presence of thermal Gaussian noise has been well understood since the seminal works of Arrhenius and Kramers, many systems, in particular living ones, are effectively driven by non-Gaussian noise for which the conventional theory does not apply. Here we present a theoretical framework based on path integrals that allows the calculation of both escape rates and optimal escape paths for a generic class of non-Gaussian noises. We find that non-Gaussian noise always leads to more efficient escape and can enhance escape rates by many orders of magnitude compared with thermal noise, highlighting that away from equilibrium escape rates cannot be reliably modelled based on the traditional Arrhenius-Kramers result. Our analysis also identifies a new universality class of non-Gaussian noises, for which escape paths are dominated by large jumps.

Anomalous Transport of Tracers in Active Baths

We derive the long-time dynamics of a tracer immersed in a one-dimensional active bath. In contrast to previous studies, we find that the damping and noise correlations possess long-time tails with exponents that depend on the tracer symmetry. For generic tracers, shape asymmetry induces ratchet effects that alter fluctuations and lead to superdiffusion and friction that grows with time when the tracer is dragged at a constant speed. In the singular limit of a completely symmetric tracer, we recover normal diffusion and finite friction. Furthermore, for small symmetric tracers, the active contribution to the friction becomes negative: active particles enhance motion rather than oppose it. These results show that, in low-dimensional systems, the motion of a passive tracer in an active bath cannot be modeled as a persistent random walker with a finite correlation time.

Active gels, heavy tails, and the cytoskeleton

The eukaryotic cell's cytoskeleton is a prototypical example of an active material: objects embedded within it are driven by molecular motors acting on the cytoskeleton, leading to anomalous diffusive behavior. Experiments tracking the behavior of cell-attached objects have observed anomalous diffusion with a distribution of displacements that is non-Gaussian, with heavy tails. This has been attributed to "cytoquakes" or other spatially extended collective effects. We show, using simulations and analytical theory, that a simple continuum active gel model driven by fluctuating force dipoles naturally creates heavy power-law tails in cytoskeletal displacements. We predict that this power law exponent should depend on the geometry and dimensionality of where force dipoles are distributed through the cell; we find qualitatively different results for force dipoles in a 3D cytoskeleton and a quasi-two-dimensional cortex. We then discuss potential applications of this model both in cells and in synthetic active gels.

Noise-Induced Acceleration of Single Molecule Kinesin-1

The movement of single kinesin molecules was observed while applying noisy external forces that mimic intracellular active fluctuations. We found kinesin accelerates under noise, especially when a large hindering load is added. The behavior quantitatively conformed to a theoretical model that describes the kinesin movement with simple two-state reactions. The universality of the kinetic theory suggests that intracellular enzymes share a similar noise-induced acceleration mechanism, i.e., active fluctuations in cells are not just noise but are utilized to promote various physiological processes.

Rapid-prototyping a Brownian particle in an active bath

Particles kicked by external forces to produce mobility distinct from thermal diffusion are an iconic feature of the active matter problem. Here, we map this onto a minimal model for experiment and theory covering the wide time and length scales of usual active matter systems. A particle diffusing in a harmonic potential generated by an optical trap is kicked by programmed forces with time correlation at random intervals following the Poisson process. The model's generic simplicity allows us to find conditions for which displacements are Gaussian (or not), how diffusion is perturbed (or not) by kicks, and quantifying heat dissipation to maintain the non-equilibrium steady state in an active bath. The model reproduces experimental results of tracer mobility in an active bath of swimming algal cells. It can be used as a stochastic dynamic simulator for Brownian objects in various active baths without mechanistic understanding, owing to the generic framework of the protocol.

Loopy Lévy flights enhance tracer diffusion in active suspensions

Brownian motion is widely used as a model of diffusion in equilibrium media throughout the physical, chemical and biological sciences. However, many real-world systems are intrinsically out of equilibrium owing to energy-dissipating active processes underlying their mechanical and dynamical features¹. The diffusion process followed by a passive tracer in prototypical active media, such as suspensions of active colloids or swimming microorganisms², differs considerably from Brownian motion, as revealed by a greatly enhanced diffusion coefficient^3-10 and non-Gaussian statistics of the tracer displacements^6,9,10. Although these characteristic features have been extensively observed experimentally, there is so far no comprehensive theory explaining how they emerge from the microscopic dynamics of the system. Here we develop a theoretical framework to model the hydrodynamic interactions between the tracer and the active swimmers, which shows that the tracer follows a non-Markovian coloured Poisson process that accounts for all empirical observations. The theory predicts a long-lived Lévy flight regime¹¹ of the loopy tracer motion with a non-monotonic crossover between two different power-law exponents. The duration of this regime can be tuned by the swimmer density, suggesting that the optimal foraging strategy of swimming microorganisms might depend crucially on their density in order to exploit the Lévy flights of nutrients¹². Our framework can be applied to address important theoretical questions, such as the thermodynamics of active systems¹³, and practical ones, such as the interaction of swimming microorganisms with nutrients and other small particles¹⁴ (for example, degraded plastic) and the design of artificial nanoscale machines¹⁵.

Pair dispersion in dilute suspension of active swimmers

Ensembles of biological and artificial microswimmers produce long-range velocity fields with strong nonequilibrium fluctuations, which result in a dramatic increase in diffusivity of embedded particles (tracers). While such enhanced diffusivity may point to enhanced mixing of the fluid, a rigorous quantification of the mixing efficiency requires analysis of pair dispersion of tracers, rather than simple one-particle diffusivity. Here, we calculate analytically the scale-dependent coefficient of relative diffusivity of passive tracers embedded in a dilute suspension of run-and-tumble microswimmers. Although each tracer is subject to strong fluctuations resulting in large absolute diffusivity, the small-scale relative dispersion is suppressed due to the correlations in fluid velocity which are relevant when the inter-tracer separation is below the persistence length of the swimmer's motion. Our results suggest that the reorientation of swimming direction plays an important role in biological mixing and should be accounted in the design of potential active matter devices capable of effective fluid mixing at microscale.