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Many microorganisms swim by performing larger non-reciprocal shape deformations that are initiated locally by molecular motors. However, it remains unclear how decentralized shape control determines the movement of the entire organism. Here, we investigate how efficient locomotion emerges from coordinated yet simple and decentralized decision-making of the body parts using neuroevolution techniques. Our approach allows us to investigate optimal locomotion policies for increasingly large microswimmer bodies, with emerging long-wavelength body shape deformations corresponding to surprisingly efficient swimming gaits. The obtained decentralized policies are robust and tolerant concerning morphological changes or defects and can be applied to artificial microswimmers for cargo transport or drug delivery applications without further optimization "out of the box". Our work is of relevance to understanding and developing robust navigation strategies of biological and artificial microswimmers and, in a broader context, for understanding emergent levels of individuality and the role of collective intelligence in Artificial Life.

We apply monomer-resolved computer simulations of supercoiled ring polymers under shear, taking full account of the hydrodynamic interactions, accompanied, in parallel, by simulations in which these are switched off. The combination of bending and torsional rigidities inherent in these polymers, in conjunction with hydrodynamics, has a profound impact on their flow properties. In contrast to their flexible counterparts, which dramatcially deform and inflate under shear [Liebetreu et al., Commun. Mater. 1, 4 (2020)], supercoiled rings undergo only weak changes in their overall shape and they display both a reduced propensity to tumbling (at fixed Weissenberg number) and a much stronger orientational resistance with respect to their flexible counterparts. In the presence of hydrodynamic interactions, the coupling of the polymer to solvent flow is capable of bringing about a topological transformation of writhe to twist at strong shear upon conservation of the overall linking number., Comment: 19 pages, 12 figures; accepted for publication in Nanoscale

Biological microswimmers such as bacteria and sperm cells often encounter complex biological fluid environments. Here we use the well-known squirmer microswimmer model to show the importance of the local fluid microstructure and non-continuum effects on their swimming speed in different polymeric and filamentous fluids. Surprisingly, we find that different squirmer types move at considerably different speed in filamentous fluids which cannot be explained by existing continuum models, but by considering the local fluid and polymer properties around the squirmers. Furthermore, direct squirmer-polymer interactions slow down in particular pushers by trapping large stiff filaments in a self-generated recirculation region in front of them., Comment: 13 pages (including SI), 5+3 figures. accepted for publication in EPL

The migration of helical particles in viscous shear flows plays a crucial role in chiral particle sorting. Attaching a non-chiral head to a helical particle leads to a rheotactic torque inducing particle reorientation. This phenomenon is responsible for bacterial rheotaxis observed for flagellated bacteria as Escherichia coli in shear flows. Here we use a high-resolution microprinting technique to fabricate micro-particles with controlled and tunable chiral shape consisting of a spherical head and helical tails of various pitch and handedness. By observing the fully time-resolved dynamics of these micro-particles in microfluidic channel flow, we gain valuable insights into chirality-induced orientation dynamics. Our experimental model system allows us to examine the effects of particle elongation, chirality, and head-heaviness for different flow rates on the orientation dynamics, while minimizing the influence of Brownian noise. Through our model experiments we demonstrate the existence of asymmetric bistability of the particle orientation perpendicular to the flow direction. We quantitatively explain the particle equilibrium orientations as a function of particle properties, initial conditions and flow rates, as well as the time-dependence of the reorientation dynamics through a theoretical model. The model parameters are determined using boundary element simulations and excellent agreement with experiments is obtained without any adjustable parameters. Our findings lead to a better understanding of chiral particle transport, bacterial rheotaxis and might allow the development of targeted delivery applications., Comment: 14 pages, 5+9 figures; accepted for publication in PNAS

Various microorganisms and some mammalian cells are able to swim in viscous fluids by performing nonreciprocal body deformations, such as rotating attached flagella or by distorting their entire body. In order to perform chemotaxis, i.e. to move towards and to stay at high concentrations of nutrients, they adapt their swimming gaits in a nontrivial manner. We propose a model how microswimmers are able to autonomously adapt their shape in order to swim in one dimension towards high field concentrations using an internal decision making machinery modeled by an artificial neural network. We present two methods to measure chemical gradients, spatial and temporal sensing, as known for swimming mammalian cells and bacteria, respectively. Using the NEAT genetic algorithm surprisingly simple neural networks evolve which control the shape deformations of the microswimmer and allow them to navigate in static and complex time-dependent chemical environments. By introducing noisy signal transmission in the neural network the well-known biased run-and-tumble motion emerges. Our work demonstrates that the evolution of a simple internal decision-making machinery, which we can fully interpret and is coupled to the environment, allows navigation in diverse chemical landscapes. These findings are of relevance for intracellular biochemical sensing mechanisms of single cells, or for the simple nervous system of small multicellular organisms such as C. elegans., Comment: 9 pages, 4 figures

In this review we discuss the recent progress in the simulation of soft active matter systems and in particular the hydrodynamics of microswimmers using the method of multiparticle collision dynamics, which solves the hydrodynamic flows around active objects on a coarse-grained level. We first present a brief overview of the basic simulation method and the coupling between microswimmers and fluid. We then review the current achievements in simulating flexible and rigid microswimmers using multiparticle collision dynamics, and briefly conclude and discuss possible future directions., Comment: 14 pages, 4 figures

Interaction of swimming bacteria with flows controls their ability to explore complex environments, crucial to many societal and environmental challenges and relevant for microfluidic applications as cell sorting. Combining experimental, numerical and theoretical analysis, we present a comprehensive study of the transport of motile bacteria in shear flows. Experimentally, we obtain with high accuracy and for a large range of flow rates, the spatially resolved velocity and orientation distributions. They are in excellent agreement with the simulations of a kinematic model accounting for stochastic and microhydrodynamic properties and in particular the flagella chirality. Theoretical analysis reveals the scaling laws behind the average rheotactic velocity at moderate shear rates using a chirality parameter and explains the reorientation dynamics leading to a saturation at large shear rates from the marginal stability of a fixed point. Our findings constitute a full understanding of the physical mechanisms and relevant parameters of bacteria bulk rheotaxis., Comment: 13 pages, 6 figures

We use mesoscale simulations to gain insight into the digestion of biopolymers by studying the break-up dynamics of polymer aggregates (boluses) bound by physical cross-links. We investigate aggregate evolution, establishing that the linking bead fraction and the interaction energy are the main parameters controlling stability with respect to diffusion. We show $\textit{via}$ a simplified model that chemical breakdown of the constituent molecules causes aggregates that would otherwise be stable to disperse. We further investigate breakdown of biopolymer aggregates in the presence of fluid flow. Shear flow in the absence of chemical breakdown induces three different regimes depending on the flow Weissenberg number ($Wi$). i) At $Wi \ll 1$, shear flow has a negligible effect on the aggregates. ii) At $Wi \sim 1$, the aggregates behave approximately as solid bodies and move and rotate with the flow. iii) At $Wi \gg 1$, the energy input due to shear overcomes the attractive cross-linking interactions and the boluses are broken up. Finally, we study bolus evolution under the combined action of shear flow and chemical breakdown, demonstrating a synergistic effect between the two at high reaction rates.

The emerging field of self-driven active particles in fluid environments has recently created significant interest in the biophysics and bioengineering communities owing to their promising future biomedical and technological applications. These microswimmers move autonomously through aqueous media where under realistic situations they encounter a plethora of external stimuli and confining surfaces with peculiar elastic properties. Based on a far-field hydrodynamic model, we present an analytical theory to describe the physical interaction and hydrodynamic couplings between a self-propelled active microswimmer and an elastic interface that features resistance toward shear and bending. We model the active agent as a superposition of higher-order Stokes singularities and elucidate the associated translational and rotational velocities induced by the nearby elastic boundary. Our results show that the velocities can be decomposed in shear and bending related contributions which approach the velocities of active agents close to a no-slip rigid wall in the steady limit. The transient dynamics predict that contributions to the velocities of the microswimmer due to bending resistance are generally more pronounced than to shear resistance. Our results provide insight into the control and guidance of artificial and synthetic self-propelling active microswimmers near elastic confinements., Comment: 20 pages, 3 figures. To appear in PRE. Abstract shortened to comply with the arXiv limit of 1920 characters

We study the orientational dynamics of heavy silica microrods flowing through a microfluidic channel. Comparing experiments and Brownian dynamics simulations we identify different particle orbits, in particular in-plane tumbling behavior, which cannot be explained by classical Jeffery theory, and we relate this behavior to the rotational diffusion of the rods. By constructing the full, three-dimensional, orientation distribution, we describe the rod trajectories and quantify the persistence of Jeffery orbits using temporal correlation functions of the Jeffery constant. We find that our colloidal rods lose memory of their initial configuration in about a second, corresponding to half a Jeffery period., Comment: 5 pages, 4 figures

Understanding the transport of driven nano- and micro-particles in complex fluids is of relevance for many biological and technological applications. Here we perform hydrodynamic multiparticle collision dynamics simulations of spherical and elongated particles driven through polymeric fluids containing different concentrations of polymers. We determine the mean particle velocities which are larger than expected from Stokes law for all particle shapes and polymer densities. Furthermore we measure the fluid flow fields and local polymer density and polymer conformation around the particles. We find that polymer-depleted regions close to the particles are responsible for an apparent tangential slip velocity which accounts for the measured flow fields and transport velocities. A simple two-layer fluid model gives a good match to the simulation results., Comment: 12 pages, 9 figures

Multiparticle collision dynamics is a modern coarse-grained simulation technique to treat the hydrodynamics of Newtonian fluids by solving the Navier-Stokes equations. Naturally, it also includes thermal noise. Initially it has been applied extensively to spherical colloids or bead-spring polymers immersed in a fluid. Here, we review and discuss the use of multiparticle collision dynamics for studying the motion of spherical model microswimmers called squirmers moving in viscous fluids., Comment: 11 pages, 6 figures, open access article

Bacterial contamination of biological conducts, catheters or water resources is a major threat to public health and can be amplified by the ability of bacteria to swim upstream. The mechanisms of this rheotaxis, the reorientation with respect to flow gradients, often in complex and confined environments, are still poorly understood. Here, we follow individual E. coli bacteria swimming at surfaces under shear flow with two complementary experimental assays, based on 3D Lagrangian tracking and fluorescent flagellar labelling and we develop a theoretical model for their rheotactic motion. Three transitions are identified with increasing shear rate: Above a first critical shear rate, bacteria shift to swimming upstream. After a second threshold, we report the discovery of an oscillatory rheotaxis. Beyond a third transition, we further observe coexistence of rheotaxis along the positive and negative vorticity directions. A full theoretical analysis explains these regimes and predicts the corresponding critical shear rates. The predicted transitions as well as the oscillation dynamics are in good agreement with experimental observations. Our results shed new light on bacterial transport and reveal new strategies for contamination prevention., Comment: 12 pages, 5 figures

We report a method to control the positions of ellipsoidal magnets in flowing channels of rectangular or circular cross section at low Reynolds number.A static uniform magnetic field is used to pin the particle orientation, and the particles move with translational drift velocities resulting from hydrodynamic interactions with the channel walls which can be described using Blake's image tensor.Building on his insights, we are able to present a far-field theory predicting the particle motion in rectangular channels, and validate the accuracy of the theory by comparing to numerical solutions using the boundary element method.We find that, by changing the direction of the applied magnetic field, the motion can be controlled so that particles move either to a curved focusing region or to the channel walls.We also use simulations to show that the particles are focused to a single line in a circular channel.Our results suggest ways to focus and segregate magnetic particles in lab-on-a-chip devices.

The locomotion of swimming bacteria in simple Newtonian fluids can successfully be described within the framework of low Reynolds number hydrodynamics. The presence of polymers in biofluids generally increases the viscosity, which is expected to lead to slower swimming for a constant bacterial motor torque. Surprisingly, however, several experiments have shown that bacterial speeds increase in polymeric fluids, and there is no clear understanding why. Therefore we perform extensive coarse-grained simulations of a bacterium swimming in explicitly modeled solutions of macromolecular polymers of different lengths and densities. We observe an increase of up to 60% in swimming speed with polymer density and demonstrate that this is due to a depletion of polymers in the vicinity of the bacterium leading to an effective slip. However this in itself cannot predict the large increase in swimming velocity: coupling to the chirality of the bacterial flagellum is also necessary., Comment: 8 pages + 9 figures

Microbial flagellates typically inhabit complex suspensions of polymeric material which can impact the swimming speed of motile microbes, filter-feeding of sessile cells, and the generation of biofilms. There is currently a need to better understand how the fundamental dynamics of polymers near active cells or flagella impacts these various phenomena, in particular the hydrodynamic and steric influence of a rotating helical filament on suspended polymers. Our Stokesian dynamics simulations show that as a stationary rotating helix pumps fluid along its long axis, polymers migrate radially inwards while being elongated. We observe that the actuation of the helix tends to increase the probability of finding polymeric material within its pervaded volume. This accumulation of polymers within the vicinity of the helix is stronger for longer polymers. We further analyse the stochastic work performed by the helix on the polymers and show that this quantity is positive on average and increases with polymer contour length., Comment: 14 pages, 6 figures

We present a simple method to control the position of ellipsoidal magnetic particles in microchannel Poiseuille flow using a static uniform magnetic field. The magnetic field is utilized to pin the particle orientation, and the hydrodynamic interactions between ellipsoids and channel walls allow control of the transverse position of the particles. We employ a far-field hydrodynamic theory and simulations using the boundary element method and Brownian dynamics to show how magnetic particles can be focussed and segregated by size and shape. This is of importance for particle manipulation in lab-on-a-chip devices.

A striking feature of the collective behavior of spherical microswimmers is that for sufficiently strong self-propulsion they phase-separate into a dense cluster coexisting with a low-density dis- ordered surrounding. Extending our previous work, we use the squirmer as a model swimmer and the particle-based simulation method of multi-particle collision dynamics to explore the influence of hydrodynamics on their phase behavior in a quasi-two-dimensional geometry. The coarsening dynamics towards the phase-separated state is diffusive in an intermediate time regime followed by a final ballistic compactification of the dense cluster. We determine the binodal lines in a phase diagram of P\'eclet number versus density. Interestingly, the gas binodals are shifted to smaller densities for increasing mean density or dense-cluster size, which we explain using a recently introduced pressure balance [S. C. Takatori et al., Phys. Rev. Lett. 113, 028103 (2014)] extended by a hydrodynamic contribution. Furthermore, we find that for pushers and pullers the binodal line is shifted to larger P\'eclet numbers compared to neutral squirmers. Finally, when lowering the P\'eclet number, the dense phase transforms from a hexagonal "solid" to a disordered "fluid" state., Comment: 10 pages, 15 figures

Active colloids are microscopic particles, which self-propel through viscous fluids by converting energy extracted from their environment into directed motion. We first explain how articial microswimmers move forward by generating near-surface flow fields via self-phoresis or the self-induced Marangoni effect. We then discuss generic features of the dynamics of single active colloids in bulk and in confinement, as well as in the presence of gravity, field gradients, and fluid flow. In the third part, we review the emergent collective behavior of active colloidal suspensions focussing on their structural and dynamic properties. After summarizing experimental observations, we give an overview on the progress in modeling collectively moving active colloids. While active Brownian particles are heavily used to study collective dynamics on large scales, more advanced methods are necessary to explore the importance of hydrodynamic and phoretic particle interactions. Finally, the relevant physical approaches to quantify the emergent collective behavior are presented., Comment: 31 pages, 14 figures

After colliding with a surface, microswimmers reside there during the detention time. They accumulate and may form complex structures such as biofilms. We introduce a general framework to calculate the distribution of detention times using the method of first-passage times and study how rotational noise and hydrodynamic interactions influence the escape from a surface. We compare generic swimmer models to the simple active Brownian particle. While the respective detention times of source dipoles are smaller, the ones of pullers are larger by up to several orders of magnitude, and pushers show both trends. We apply our results to the more realistic squirmer model, for which we use lubrication theory, and validate them by simulations with multi-particle collision dynamics., Comment: 6+6 pages, 4+5 figures

We study the collective motion of confined spherical microswimmers such as active colloids which we model by so-called squirmers. To simulate hydrodynamic flow fields including thermal noise, we use the method of multi-particle collision dynamics. We demonstrate that hydrodynamic near fields acting between squirmers as well as squirmers and bounding walls crucially determine their collective motion. In particular, with increasing density we observe a clear phase separation into a gas-like and cluster phase for neutral squirmers whereas strong pushers and pullers more gradually approach the hexagonal cluster state.

We study the dynamics of a prolate spheroidal microswimmer in Poiseuille flow for different flow geometries. When moving between two parallel plates or in a cylindrical microchannel, the swimmer performs either periodic swinging or periodic tumbling motion. Although the trajectories of spherical and elongated swimmers are qualitatively similar, the swinging and tumbling frequency strongly depends on the aspect ratio of the swimmer. In channels with reduced symmetry the swimmers perform quasiperiodic motion which we demonstrate explicitely for swimming in a channel with elliptical cross section.

We study the three-dimensional dynamics of a spherical microswimmer in cylindrical Poiseuille flow which can be mapped onto a Hamiltonian system. Swinging and tumbling trajectories are identified. In 2D they are equivalent to oscillating and circling solutions of a mathematical pendulum. Hydrodynamic interactions between the swimmer and confining channel walls lead to dissipative dynamics and result in stable trajectories, different for pullers and pushers. We demonstrate this behavior in the dipole approximation of the swimmer and with simulations using the method of multi-particle collision dynamics., Comment: 5 pages, 4 figures