Geometrical guidance and trapping transition of human sperm cells

Demixing of an active-passive binary mixture through a two-dimensional elastic meshwork

Separation of particles based on motility is a daunting task, especially when the particles are of the same size and the density is low. We propose and demonstrate how a dilute monodisperse mixture of active-passive particles can be separated by introducing an elastic meshwork. Our in silico method does not rely on any external stimuli, rather the mesh size and stiffness of the meshwork control the demixing. There is a threshold activity above which demixing starts and below this, particles exert pressure on the meshwork that relaxes upon permeation. Our findings are in principle experimentally testable and open up new avenues for active-passive separation, where clustering of particles is not feasible.

Migration of an active particle in mixtures of rigid and flexible rings

The migration of active particles in slowly moving, crowded, and heterogeneous media is fundamental to various biological processes and technological applications. In this study, we numerically investigate the dynamics of a single active particle in a multicomponent medium composed of mixtures of rigid and flexible rings. We observe a nonmonotonic dependence of diffusivity on the relative fraction of rigid to flexible rings, leading to the identification of an optimal composition for enhanced diffusion. This long-time nonmonotonic diffusion, resulting from the different responses of the active particle to rigid and flexible rings, is coupled with transient short-time trapping. The probability distribution of trapping durations is well described by the herein-proposed extended entropic-trap model. We further theoretically establish a universal relationship between particle activity and the optimal rigid-to-flexible ring ratio for diffusion, which aligns closely with our numerical results.

Geometry of obstructed pathway regulates upstream navigational pattern of sperm population

Sperm navigation through the complex microarchitecture of the fallopian tube is essential for successful fertilization. Spatiotemporal structural alteration due to folded epithelium or muscle contractions in the fallopian tube changes the geometry of the sperm pathways. The role of structural complexity in sperm navigational patterns has been investigated for single sperm cells but has not been fully addressed at the population level. Here, we studied the dynamics of the navigation of a bull sperm population through obstructed pathways mimicking the architecture of the female reproductive tract. We observed that slightly tapered barriers enhance navigation by 20% compared to straight pathway; however, tapered barriers with a 90° angle restrict sperm passage. We demonstrated sperm cooperation while passing through a tapered pathway in a low-viscosity medium under elevated shear rates. These findings propose a fresh perspective on how sperm move through the fallopian tube, suggesting that the convoluted pathways' shape influences sperm navigation locally.

Ratchet effect and jamming in dense mixtures of active and passive colloids in narrow pores

Using the framework of generalized exclusion processes, we study mixtures of passive and active particles interacting by steric repulsion. The particles move in a pore with a periodically modulated aperture, which is modeled by a quasi-one-dimensional channel with a periodic tooth-shaped profile. Internal driving of the active particles induces a ratchet current of these particles. In the current-density diagram, we observe three main regimes: of free flow, of thermally activated processes, and of spinodal decomposition. When the density of particles is increased, we observe a transition to a jammed state, where the ratchet current is substantially reduced. In time evolution, the transition to a jammed state is seen as a sudden drop of current at a certain time. The probability distribution of these jamming times follows an exponential law. The average jamming time depends exponentially on the density of active particles. The coefficient in this exponential is nearly independent of the switching rate of the active particles as well as the presence or absence of passive particles. Due to the interaction, the current of active particles imposes a drag on the passive particles. In the limit of both large systems and long times, the current of passive particles always has the same direction as the ratchet current of active particles. However, during the evolution of the system, we observe a very slow (logarithmic in time) approach to the asymptotic value, sometimes accompanied by current reversal, i.e., the current of active and passive particles may go in opposite directions.

A Lifetime of Catalytic Micro-/Nanomotors

Microscopic and nanoscopic motors, often referred to as micro-/nanomotors, are autonomous devices capable of converting chemical energy from their surroundings into mechanical motion or forces necessary for propulsion. These devices draw inspiration from natural biomolecular motor proteins, and in recent years, synthetic micro-/nanomotors have attracted significant attention. Among these, catalytic micro-/nanomotors have emerged as a prominent area of research. Despite considerable progress in their design and functionality, several obstacles remain, especially regarding the development of biocompatible materials and fuels, the integration of intelligent control systems, and the translation of these motors into practical applications. Thus, a comprehensive understanding of the current advancements in catalytic micro-/nanomotors is critical. This review aims to provide an in-depth overview of their fabrication techniques, propulsion mechanisms, key influencing factors, control methodologies, and potential applications. Furthermore, we examine their physical and hydrodynamic properties in fluidic environments to optimize propulsion efficiency. Lastly, we evaluate their biosafety and biocompatibility to facilitate their use in biological systems. The review also addresses key challenges and proposes potential solutions to advance their practical deployment.

Transport and energetics of bacterial rectification

Randomly moving active particles can be herded into directed motion by asymmetric geometric structures. Although such a rectification process has been extensively studied due to its fundamental, biological, and technological relevance, a comprehensive understanding of active matter rectification based on single particle dynamics remains elusive. Here, by combining experiments, simulations, and theory, we study the directed transport and energetics of swimming bacteria navigating through funnel-shaped obstacles-a paradigmatic model of rectification of living active matter. We develop a microscopic parameter-free model for bacterial rectification, which quantitatively explains experimental and numerical observations and predicts the optimal geometry for the maximum rectification efficiency. Furthermore, we quantify the degree of time irreversibility and measure the extractable work associated with bacterial rectification. Our study provides quantitative solutions to long-standing questions on bacterial rectification and establishes a generic relationship between time irreversibility, particle fluxes, and extractable work, shedding light on the energetics of nonequilibrium rectification processes in living systems.

Propulsion mechanisms of micro/nanorobots: a review

Micro/nanomotors (MNMs) are intelligent, efficient and promising micro/nanorobots (MNR) that can respond to external stimuli (e.g., chemical energy, temperature, light, pH, ultrasound, magnetic, biosignals, ions) and perform specific tasks. The MNR can adapt to different external stimuli and transform into various functional forms to match different application scenarios. So far, MNR have found extensive application in targeted therapy, drug delivery, tissue engineering, environmental remediation, and other fields. Despite the promise of MNR, there are few reviews that focus on them. To shed new light on the further development of the field, it is necessary to provide an overview of the current state of development of these MNR. Therefore, this paper reviews the research progress of MNR in terms of propulsion mechanisms, and points out the pros and cons of different stimulus types. Finally, this paper highlights the current challenges faced by MNR and proposes possible solutions to facilitate the practical application of MNR.

Analysis of the number of topological defects in active nematic fluids under applied shear flow

The number of topological defects in the shear flow of active nematic fluids is numerically investigated in this study. The evolution of the flow state of extensile active nematic fluids is explored by increasing the activity of active nematic fluids. Evidently, medium-activity active nematic fluids exhibit a highly ordered vortex lattice fluid state. However, high-activity active nematic fluids exhibit a meso-scale turbulent flow accompanied by topological defects. The number of topological defects (Ndef) increases with increasing shear Reynolds number (Res). Fluid viscosity strongly influences Ndef, while the influence of fluid density is relatively weak. Ndef decreases with increasing activity length scale (lζ) value. A small Res value strongly influences Ndef, whereas a large lζ value only weakly influences Ndef. As the activity increases, Ndef in contractile active nematic fluids becomes larger than that of extensile active nematic fluids.

Faster sperm selected by rheotaxis leads to superior early embryonic development in vitro

To understand the impact of sperm speed as they swim against the flow on fertilization rates, we created conditions similar to the female reproductive tract (FRT) on a microfluidic platform for sperm selection. Selected sperm were evaluated based on early development of fertilized embryos. Bovine and human spermatozoa were selected at various fluid flow rates within the device. We found that the speed of bovine spermatozoa increases as the flow rate increases and that the amount of DNA fragmentation index is lowered by increasing the flow rate. Bovine spermatozoa selected by our platform at low (150 μL h-1, shear rate 3 s-1), medium (250 μL h-1, shear rate 5 s-1), and high flow rates (350 μL h-1, shear rate 7 s-1) were used for fertilization and compared to sperm sorted by centrifugation. The samples collected at the highest flow rate resulted in the formation of 23% more blastocysts compared to the control. While selecting for higher quality sperm by increasing the flow rate does result in lower sperm yield, quality improvement and yield may be balanced by better embryonic development.

Selecting active matter according to motility in an acoustofluidic setup: self-propelled particles and sperm cells

Active systems - including sperm cells, living organisms like bacteria, fish, birds, or active soft matter systems like synthetic "microswimmers" - are characterized by motility, i.e., the ability to propel using their own "engine". Motility is the key feature that distinguishes active systems from passive or externally driven systems. In a large ensemble, motility of individual species can vary in a wide range. Selecting active species according to their motility represents an exciting and challenging problem. We propose a new method for selecting active species based on their motility using an acoustofluidic setup where highly motile species escape from the acoustic trap. This is demonstrated in simulations and in experiments with self-propelled Janus particles and human sperm. The immediate application of this method is selecting highly motile sperm for medically assisted reproduction (MAR). Due to the tunable acoustic trap, the proposed method is more flexible than the existing passive microfluidic methods. The proposed selection method based on motility can also be applied to other active systems that require selecting highly motile species or removing immotile species.

Mixtures of self-propelled particles interacting with asymmetric obstacles

In the presence of an obstacle, active particles condensate into a surface "wetting" layer due to persistent motion. If the obstacle is asymmetric, a rectification current arises in addition to wetting. Asymmetric geometries are therefore commonly used to concentrate microorganisms like bacteria and sperms. However, most studies neglect the fact that biological active matter is diverse, composed of individuals with distinct self-propulsions. Using simulations, we study a mixture of "fast" and "slow" active Brownian disks in two dimensions interacting with large half-disk obstacles. With this prototypical obstacle geometry, we analyze how the stationary collective behavior depends on the degree of self-propulsion "diversity," defined as proportional to the difference between the self-propulsion speeds, while keeping the average self-propulsion speed fixed. A wetting layer rich in fast particles arises. The rectification current is amplified by speed diversity due to a superlinear dependence of rectification on self-propulsion speed, which arises from cooperative effects. Thus, the total rectification current cannot be obtained from an effective one-component active fluid with the same average self-propulsion speed, highlighting the importance of considering diversity in active matter.

Role of translational noise on current reversals of active particles on ratchet

In this study, we explore using Langevin dynamics simulations, the role of thermal fluctuations on the rectification of non-interacting inertial active (self-propelled) particles in a rocking ratchet setup in the absence and in the presence of the external time periodic drive. The system is first studied in the absence of the external drive. It is found that the average velocity is always positive and a peaked function of the translational noise, indicating that the asymmetry effects dominate at intermediate values of the strength of the thermal noise. In the second part of this work, we study the effect of the external drive on the dynamics of the system by exploring a phase diagram in the parameter space of translational noise and driving frequency for two different strengths of rotational diffusion. For a given constant amplitude of the active force and amplitude of external drive less than the maximum force due to the potential, the average velocity magnitude as well as the direction ([Formula: see text]) is found to depend on the rotational diffusion, frequency of the external drive and the strength of the translational noise. We discover certain critical parameters in the phase space at which current reversals happen. It is found that when the average particle energy is lower than the potential energy of the barrier, symmetry breaking dominates and the currents are in the 'easy' direction of the ratchet. On the other hand, when the energy available per particle crosses the potential energy of the barrier, the competition between inertial effects and diffusion effects decides the direction of currents. We explain our findings by constructing phase difference datum, velocity probability distribution, and current probability analyses. Our results provide a novel method for controlling the direction of transport of inertial active particles.

Biphasic Chemokinesis of Mammalian Sperm

The female reproductive tract (FRT) continuously modulates mammalian sperm motion by releasing various clues as sperm migrate toward the fertilization site. An existing gap in our understanding of sperm migration within the FRT is a quantitative picture of how sperm respond to and navigate the biochemical clues within the FRT. In this experimental study, we have found that in response to biochemical clues, mammalian sperm display two distinct chemokinetic behaviors which are dependent upon the rheological properties of the media: chiral, characterized by swimming in circles; and hyperactive, characterized by random reorientation events. We used minimal theoretical modeling, along with statistical characterization of the chiral and hyperactive trajectories, to show that the effective diffusivity of these motion phases decreases with increasing concentration of chemical stimulant. In the context of navigation this concentration dependent chemokinesis suggests that the chiral or hyperactive motion refines the sperm search area within different FRT functional regions. Further, the ability to switch between phases indicates that sperm may use various stochastic navigational strategies, such as run and tumble or intermittent search, within the fluctuating and spatially heterogeneous environment of the FRT.

A microfluidic method for passive trapping of sperms in microstructures

Sperm motility is a prerequisite for male fertility. Enhancing the concentration of motile sperms in assisted reproductive technologies - for human and animal reproduction - is typically achieved through aggressive methods such as centrifugation. Here, we propose a passive technique for the amplification of motile sperm concentration, with no externally imposed forces or flows. The technique is based on the disparity between probability rates, for motile cells, of entering and escaping from complex structures. The effectiveness of the technique is demonstrated in microfluidic experiments with microstructured devices, comparing the trapping power in different geometries. In these micro-traps, we observe an enhancement of cells' concentration close to 10, with a contrast between motile and non-motile cells increased by a similar factor. Simulations of suitable interacting model sperms in realistic geometries reproduce quantitatively the experimental results, extend the range of observations and highlight the components that are key to the optimal trap design.

Fluid circulation driven by collectively organized metachronal waves in swimming T. aceti nematodes

Recent experiments have shown that the nematode T. aceti can assemble into collectively undulating groups at the edge of fluid drops. This coordinated state consists of metachronal waves and drives fluid circulation inside the drop. We find that the circulation velocity is about 2 mm/s and nearly half the speed of the metachronal wave. We develop a quasi-two-dimensional hydrodynamics model using the Stokes flow approximation. The periodic motion of the nematodes constitute our moving boundary condition that drives the flow. Our model suggests that large-amplitude excursions of the nematode tails produce the fluid circulation. We discuss the constraints on containers that would enhance fluid motion, which could be used in the future design of on demand flow generating systems.

Long-Range Influence of a Pump on a Critical Fluid

A pump coupled to a conserved density generates long-range modulations, resulting from the non-equilibrium nature of the dynamics. We study how these modulations are modified at the critical point where the system exhibits intrinsic long-range correlations. To do so, we consider a pump in a diffusive fluid, which is known to generate a density profile in the form of an electric dipole potential and a current in the form of a dipolar field above the critical point. We demonstrate that while the current retains its form at the critical point, the density profile changes drastically. At criticality, in d<4 dimensions, the deviation of the density from the average is given by sgn[cos(θ)]|cos(θ)/r^{(d-1)}|^{1/δ} at large distance r from the pump and angle θ with respect to the pump's orientation. At short distances, there is a crossover to a cos(θ)/r^{d-3+η} profile. Here δ and η are Ising critical exponents. The effect of the local pump on the domain wall structure below the critical point is also considered.

Microscopic Theory for the Diffusion of an Active Particle in a Crowded Environment

We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a closure approximation that goes beyond trivial mean field and provides the diffusion coefficient for an arbitrary density of crowders in the system. We show that our approximation is accurate for a very wide range of parameters, and that it correctly captures numerous nonequilibrium effects, which are the signature of the activity in the system. In addition to the determination of the diffusion coefficient of the tracer, our approach allows us to characterize the perturbation of the environment induced by the displacement of the active tracer. Finally, we consider the asymptotic regimes of low and high densities, in which the expression of the diffusion coefficient of the tracer becomes explicit, and which we argue to be exact.

Dichotomic ratchet in a two-dimensional corrugated channel

We consider a particle diffusing in a two-dimensional (2D) channel of varying width h(x). It is driven by a force of constant magnitude f but random orientation there or back along the channel. We derive the effective generalized Fick-Jacobs equation for this system, which describes the dynamics of such a particle in the longitudinal coordinate x. Aside from the effective diffusion coefficient D(x), our mapping also generates an additional effective potential -γ(x) added to the entropic potential -log[h(x)]. It acquires an increasing or decreasing component in asymmetric periodic channels, and thus it explains appearance of the ratchet current. We study this effect on a trial example and compare the results of our true 2D theory with a commonly used effective one-dimensional description; the data are verified by the numerical solution of the full 2D problem.

Mammalian sperm hyperactivation regulates navigation via physical boundaries and promotes pseudo-chemotaxis

Mammalian sperm migration within the complex and dynamic environment of the female reproductive tract toward the fertilization site requires navigational mechanisms, through which sperm respond to the tract environment and maintain the appropriate swimming behavior. In the oviduct (fallopian tube), sperm undergo a process called "hyperactivation," which involves switching from a nearly symmetrical, low-amplitude, and flagellar beating pattern to an asymmetrical, high-amplitude beating pattern that is required for fertilization in vivo. Here, exploring bovine sperm motion in high-aspect ratio microfluidic reservoirs as well as theoretical and computational modeling, we demonstrate that sperm hyperactivation, in response to pharmacological agonists, modulates sperm-sidewall interactions and thus navigation via physical boundaries. Prior to hyperactivation, sperm remained swimming along the sidewalls of the reservoirs; however, once hyperactivation caused the intrinsic curvature of sperm to exceed a critical value, swimming along the sidewalls was reduced. We further studied the effect of noise in the intrinsic curvature near the critical value and found that these nonthermal fluctuations yielded an interesting "Run-Stop" motion on the sidewall. Finally, we observed that hyperactivation produced a "pseudo-chemotaxis" behavior, in that sperm stayed longer within microfluidic chambers containing higher concentrations of hyperactivation agonists.

Curved ratchets improve bacteria rectification in microfluidic devices

We study how bacteria rectification in microfluidics devices can be optimized by performing experiments with eight ratchets of different shape and size. Results show that curved ratchets perform best and that their radius of curvature influences how well they perform, as it affects the time bacteria spend on the ratchet surface. We find that the optimal bacterial ratchet is a 60μm radius semicircle witch 15μm concavities. We also show that the angle at which bacteria leave the ratchets can play an important role in their efficiency. Lastly, we reproduce our experimental conditions in a simple numerical simulation to confirm our findings.

Rotation reversal of a ratchet gear powered by active particles

Rotation of a gear powered by active particles is numerically investigated in a circular chamber. Due to the nonequilibrium properties of active particles, net gear rotation is achieved in a bath composed of self-propelling particles. Our setup can convert the random motion of active particles into the directional rotation of the ratchet gear. The direction of rotation is determined by the asymmetry of the gear and the persistence length (the ratio of the self-propulsion speed to the rotation diffusion coefficient) of active particles. Remarkably, the direction of rotation for large persistence length is opposite to the direction of rotation for small persistence length. Therefore, for a given asymmetric gear, we can observe the rotation reversal when tuning the system parameters (e.g., the self-propulsion speed, the rotation diffusion coefficient, and the packing fraction of active particles). Our findings are relevant to the experimental pursuit of rectifying random motion to directional motion in active matter.

Rolling controls sperm navigation in response to the dynamic rheological properties of the environment

Mammalian sperm rolling around their longitudinal axes is a long-observed component of motility, but its function in the fertilization process, and more specifically in sperm migration within the female reproductive tract, remains elusive. While investigating bovine sperm motion under simple shear flow and in a quiescent microfluidic reservoir and developing theoretical and computational models, we found that rolling regulates sperm navigation in response to the rheological properties of the sperm environment. In other words, rolling enables a sperm to swim progressively even if the flagellum beats asymmetrically. Therefore, a rolling sperm swims stably along the nearby walls (wall-dependent navigation) and efficiently upstream under an external fluid flow (rheotaxis). By contrast, an increase in ambient viscosity and viscoelasticity suppresses rolling, consequently, non-rolling sperm are less susceptible to nearby walls and external fluid flow and swim in two-dimensional diffusive circular paths (surface exploration). This surface exploration mode of swimming is caused by the intrinsic asymmetry in flagellar beating such that the curvature of a sperm's circular path is proportional to the level of asymmetry. We found that the suppression of rolling is reversible and occurs in sperm with lower asymmetry in their beating pattern at higher ambient viscosity and viscoelasticity. Consequently, the rolling component of motility may function as a regulatory tool allowing sperm to navigate according to the rheological properties of the functional region within the female reproductive tract.

Progressive bovine sperm separation using parallelized microchamber-based microfluidics

Motility is one of the most important factors in sperm migration toward an egg. Therefore, sperm separation based on motility might enhance sperm selection for infertility treatments. Conventional centrifugation-based methods increase the risk of damage to sperm cells. Microfluidic systems, on the other hand, can sort sperm in a less intrusive way, but their efficiency and throughput still needs improvement, especially in low-concentration samples (oligozoospermia). Here, a microchamber-based microfluidic platform is demonstrated that can separate progressively motile sperm from non-viable sperm and debris, and trap nonprogressive sperm in microchambers. This platform can be operated in a short period of time (<10 min) with an excellent degree of controllability with no sample preparation. Sperm were screened in a 384-microchamber platform. The mean average-path velocity of the motile sperm in the collected sample increased significantly, from 57 ± 10 μm s^-1 in the raw semen sample to 81 ± 13 μm s^-1. The DNA Integrity of the separated sperm showed 20% improvement over the raw sample which indicated that separated sperm were of higher quality. We began with a 22.5 μL raw bovine sperm sample which had a concentration of 8.5 million sperm per milliliter (M mL^-1) with 38% motility. After separation, the concentration of the collected sperm was 2.1 M mL^-1 with a motility rate of 90%. This corresponds to a 75% retrieval efficiency and the selection of approximately 5.2 × 10⁴ progressively motile spermatozoa. Our results show that the microchamber depth does not affect the residence time of motile sperm; therefore, it is possible to inspect higher sample volumes within the same time frame. This microfluidic platform may provide an easy-to-implement solution for high-throughput, robust, and efficient, collection of progressive sperm with the DNA integrity needed for assisted reproductive technologies (ARTs). However, further studies are necessary to show the implications of this method in human cases.

Co-Adaptation of Physical Attributes of the Mammalian Female Reproductive Tract and Sperm to Facilitate Fertilization

The functions of the female reproductive tract not only encompass sperm migration, storage, and fertilization, but also support the transport and development of the fertilized egg through to the birth of offspring. Further, because the tract is open to the external environment, it must also provide protection against invasive pathogens. In biophysics, sperm are considered “pusher microswimmers”, because they are propelled by pushing fluid behind them. This type of swimming by motile microorganisms promotes the tendency to swim along walls and upstream in gentle fluid flows. Thus, the architecture of the walls of the female tract, and the gentle flows created by cilia, can guide sperm migration. The viscoelasticity of the fluids in the tract, such as mucus secretions, also promotes the cooperative swimming of sperm that can improve fertilization success; at the same time, the mucus can also impede the invasion of pathogens. This review is focused on how the mammalian female reproductive tract and sperm interact physically to facilitate the movement of sperm to the site of fertilization. Knowledge of female/sperm interactions can not only explain how the female tract can physically guide sperm to the fertilization site, but can also be applied for the improvement of in vitro fertilization devices.

Getting to and away from the egg, an interplay between several sperm transport mechanisms and a complex oviduct physiology

In mammals, the architecture and physiology of the oviduct are very complex, and one long-lasting intriguing question is how spermatozoa are transported from the sperm reservoir in the isthmus to the oocyte surface. In recent decades, several studies have improved knowledge of the factors affecting oviduct fluid movement and sperm transport. They report sperm-guiding mechanisms that move the spermatozoa towards (rheotaxis, thermotaxis, and chemotaxis) or away from the egg surface (chemorepulsion), but only a few provide evidence of their occurrence in vivo. This gives rise to several questions: how and when do the sperm transport mechanisms operate inside such an active oviduct? why are there so many sperm guidance processes? is one dominant over the others, or do they cooperate to optimise the success of fertilisation? Assuming that sperm guidance evolved alongside oviduct physiology, in this review we propose a theoretical model that integrates oviduct complexity in space and time with the sperm-orienting mechanisms. In addition, since all of the sperm-guidance processes recruit spermatozoa in a better physiological condition than those not selected, they could potentially be incorporated into assisted reproductive technology (ART) to improve fertility treatment and/or to develop innovative contraceptive methods. All these issues are discussed in this review.

An attraction-repulsion transition of force on two asymmetric wedges induced by active particles

Effective interaction between two asymmetric wedges immersed in a two-dimensional active bath is investigated by computer simulations. The attraction–repulsion transition of effective force between two asymmetric wedges is subjected to the relative position of two wedges, the wedge-to-wedge distance, the active particle density, as well as the apex angle of two wedges. By exchanging the position of the two asymmetric wedges in an active bath, firstly a simple attraction–repulsion transition of effective force occurs, completely different from passive Brownian particles. Secondly the transition of effective force is symmetric for the long-range distance between two asymmetric wedges, while it is asymmetric for the short-range case. Our investigations may provide new possibilities to govern the motion and assembly of microscopic objects by taking advantage of the self-driven behaviour of active particles.

Medical micro/nanorobots in complex media

Medical micro/nanorobots have received tremendous attention over the past decades owing to their potential to be navigated into hard-to-reach tissues for a number of biomedical applications ranging from targeted drug/gene delivery, bio-isolation, detoxification, to nanosurgery. Despite the great promise, the majority of the past demonstrations are primarily under benchtop or in vitro conditions. Many developed micro/nanoscale propulsion mechanisms are based on the assumption of a homogeneous, Newtonian environment, while realistic biological environments are substantially more complex. Moving toward practical medical use, the field of micro/nanorobotics must overcome several major challenges including propulsion through complex media (such as blood, mucus, and vitreous) as well as deep tissue imaging and control in vivo. In this review article, we summarize the recent research efforts on investigating how various complexities in biological environments impact the propulsion of micro/nanoswimmers. We also highlight the emerging technological approaches to enhance the locomotion of micro/nanorobots in complex environments. The recent demonstrations of in vivo imaging, control and therapeutic medical applications of such micro/nanorobots are introduced. We envision that continuing materials and technological innovations through interdisciplinary collaborative efforts can bring us steps closer to the fantasy of "swallowing a surgeon".

Hitting the wall: Human sperm velocity recovery under ultra-confined conditions

Infertility is a common medical condition encountered by health systems throughout the world. Despite the development of complex in vitro fertilization techniques, only one-third of these procedures are successful. New lab-on-a-chip systems that focus on spermatozoa selection require a better understanding of sperm behavior under ultra-confined conditions in order to improve outcomes. Experimental studies combined with models and simulations allow the evaluation of the efficiency of different lab-on-a-chip devices during the design process. In this work, we provide experimental evidence of the dynamics of sperm interacting with a lateral wall in a shallow chamber. We observe a decrease in average sperm velocity during initial wall interaction and partial recovery after the alignment of the trajectory of the cell. To describe this phenomenon, we propose a simple model for the sperm alignment process with a single free parameter. By incorporating experimental motility characterization into the model, we achieve an accurate description of the average velocity behavior of the sperm population close to walls. These results will contribute to the design of more efficient lab-on-a-chip devices for the treatment of human infertility.

Phase separation in a two-dimensional binary colloidal mixture by quorum sensing activity

We present results from Langevin dynamics simulations of a glassy active-passive mixture of soft-repulsive binary colloidal disks. Activity on the smaller particles is applied according to the quorum sensing scheme, in which a smaller particle will be active for a persistence time if its local nearest neighbors are equal to or greater than a certain threshold value. We start with a passive glassy state of the system and apply activity to the smaller particles, which shows a nonmonotonous glassy character of the active particles with the persistence time of the active force, from its passive limit (zero activity). On the other hand, passive particles of the active-passive mixture phase separate at the intermediate persistence time of the active force, resulting in the hexatic-liquid and solid-liquid phases. Thus, our system shows three regimes as active glass, phase separation, and active liquid, as the persistence time increases from its smaller values. We show that the solidlike and hexatic phases consisting of passive large particles are stable due to the smaller momentum transfer from active to passive particles, compared to the higher persistence time where the positional and orientational ordering vanishes. Our model is relevant to active biological systems, where glassy dynamics is present, e.g., bacterial cytoplasm, biological tissues, dense quorum sensing bacteria, and synthetic smart amorphous glasses.

Self-propelled particle in a nonconvex external potential: Persistent limit in one dimension

Equilibrium mapping techniques for nonaligning self-propelled particles have made it possible to predict the density profile of an active ideal gas in a wide variety of external potentials. However, they fail when the self-propulsion is very persistent and the potential is nonconvex, which is precisely when the most uniquely active phenomena occur. Here, we show how to predict the density profile of a 1D active Ornstein-Uhlenbeck particle in an arbitrary external potential in the persistent limit and discuss the consequences of the potential's nonconvexity on the structure of the solution, including the central role of the potential's inflection points and the nonlocal dependence of the density profile on the potential.

High-throughput characterisation of bull semen motility using differential dynamic microscopy

We report a high-throughput technique for characterising the motility of spermatozoa using differential dynamic microscopy. A movie with large field of view (∼10mm2) records thousands of cells (e.g. ≈ 5000 cells even at a low cell density of 20 × 106 cells/ml) at once and yields averaged measurements of the mean ([Formula: see text]) and standard deviation (σ) of the swimming speed, head oscillation amplitude (A0) and frequency (f0), and the fraction of motile spermatozoa (α). Interestingly, we found that the measurement of α is facilitated because the swimming spermatozoa enhance the motion of the non-swimming population. We demonstrate the ease and rapidity of our method by performing on-farm characterisation of bull spermatozoa motility, and validate the technique by comparing laboratory measurements with tracking. Our results confirm the long-standing theoretical prediction that [Formula: see text] for swimming spermatozoa.

Diffusion of active particles in a complex environment: Role of surface scattering

Experiments have shown that self-propelled particles can slide along the surface of a circular obstacle without becoming trapped over long times. Using simulations and theory, we study the impact of boundary conditions on the diffusive transport of active particles in an obstacle lattice. We find that particle dynamics with sliding boundary conditions result in large diffusivities even at high obstacle density, unlike classical specular reflection. These dynamics are very well described by a model based on run-and-tumble particles with microscopically derived reorientation functions arising from obstacle-induced tumbles. This model, however, fails to describe fine structure in the diffusivity at high obstacle density predicted by simulations for pusherlike collisions. Using a simple deterministic model, we show that this structure results from particles being guided by the lattice. Our results thus show how nonclassical surface scattering introduces a dependence on the lattice geometry at high densities. We discuss implications for the study of bacteria in complex environments.

Strictures of a microchannel impose fierce competition to select for highly motile sperm

Investigating sperm locomotion in the presence of external fluid flow and geometries simulating the female reproductive tract can lead to a better understanding of sperm motion during fertilization. Using a microfluidic device featuring a stricture that simulates the fluid mechanical properties of narrow junctions inside the female reproductive tract, we documented the gate-like role played by the stricture in preventing sperm with motilities below a certain threshold from advancing through the stricture to the other side (i.e., fertilization site). All the slower sperm accumulate below (i.e., in front of) the stricture and swim in a butterfly-shaped path between the channel walls, thus maintaining the potential for penetrating the stricture and ultimately advancing toward the fertilization site. Accumulation below the stricture occurs in a hierarchical manner so that dense concentrations of sperm with higher velocities remain closer to the stricture, with more sparsely distributed arrays of lower-velocity sperm lagging behind.

Ideal circle microswimmers in crowded media

Microswimmers are exposed in nature to crowded environments and their transport properties depend in a subtle way on the interaction with obstacles. Here, we investigate a model for a single ideal circle swimmer exploring a two-dimensional disordered array of impenetrable obstacles. The microswimmer moves on circular orbits in the freely accessible space and follows the surface of an obstacle for a certain time upon collision. Depending on the obstacle density and the radius of the circular orbits, the microswimmer displays either long-range transport or is localized in a finite region. We show that there are transitions from two localized states to a diffusive state each driven by an underlying static percolation transition. We determine the non-equilibrium state diagram and calculate the mean-square displacements and diffusivities by computer simulations. Close to the transition lines transport becomes subdiffusive which is rationalized as a dynamic critical phenomenon.

Cellular geometry controls the efficiency of motile sperm aggregates

Sperm that swim collectively to the fertilization site have been observed across several vertebrate and invertebrate species, with groups ranging in size from sperm pairs to massive aggregates containing hundreds of cells. Although the molecular mechanisms that regulate sperm-sperm adhesion are still unclear, aggregation can enhance sperm motility and thus offer a fertilization advantage. Here, we report a thorough computational investigation on the role of cellular geometry in the performance of sperm aggregates. The sperm head is modelled as a persistent random walker characterized by a non-trivial three-dimensional shape and equipped with an adhesive region where cell-cell binding occurs. By considering both, a simple parametric head shape and a computer reconstruction of a real head shape based on morphometric data, we demonstrate that the geometry of the head and the structure of the adhesive region crucially affects both the stability and motility of the aggregates. Our analysis further suggests that the apical hook commonly found in the sperm of muroid rodents might serve to shield portions of the adhesive region and promote efficient alignment of the velocities of the interacting cells.

Current reversals of active particles in time-oscillating potentials

Rectification of interacting active particles is numerically investigated in a two-dimensional time-oscillating potential. It is found that the oscillation of the potential and the self-propulsion of active particles are two different types of nonequilibrium driving, which can induce net currents with opposite directions. For a given asymmetry of the potential, the direction of the transport is determined by the competition of the self-propulsion and the oscillation of the potential. There exists an optimal oscillating angular frequency (or self-propulsion speed) at which the average velocity takes its maximal positive or negative value. Remarkably, when the oscillation of the potential competes with the self-propulsion, the average velocity can change direction several times due to the change in the oscillating frequency. Especially, particles with different self-propulsion velocities will move in opposite directions and can be separated. Our results provide a novel and convenient method for controlling and manipulating the transport (or separation) of active particles.

An attraction-repulsion transition of force on wedges induced by active particles

Effective forces between two micro-wedges immersed in an active bath are investigated using Brownian dynamics simulations. Two anti-parallel and parallel wedge-like obstacles are considered respectively, and the effective forces between two wedges rely on the wedge-to-wedge distance, the apex angle of the wedge, as well as the particle density and aspect ratio. For two anti-parallel wedges, a transition from repulsion to attraction occurs by varying the apex angle, which is also sensitive to the particle density and aspect ratio. The optimal apex angle θr* (or θa*) and particle density ρ* are characterized by the saturated trapping of active particles inside a wedge. For two parallel wedges, the effective force also experiences a transition from repulsion to attraction as the wedge-to-wedge distance increases. These results originate from the collective trapping effect which is driven by the many-body dynamics of self-propelled particles in the confinement (near the boundary) of obstacles. Our results can provide insight into controlling the motion and assembly of microscopic objects through the suspension of active particles.

Optimized Diffusion of Run-and-Tumble Particles in Crowded Environments

We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of run-and-tumble particles (RTPs) moving in discrete time on a d-dimensional cubic lattice in the presence of diffusing hard-core obstacles. We derive an explicit expression for the diffusivity of the RTP, which is exact in the limit of low density of fixed obstacles. To do so, we introduce a generalization of Kac's theorem on the mean return times of Markov processes, which we expect to be relevant for a large class of lattice gas problems. Our results show the diffusivity of RTPs to be nonmonotonic in the tumbling probability for low enough obstacle mobility. These results prove the potential for the optimization of the transport of RTPs in crowded and disordered environments with applications to motile artificial and biological systems.

Memory effects in active particles with exponentially correlated propulsion

The Ornstein-Uhlenbeck particle (OUP) model imagines a microscopic swimmer propelled by an active force which is correlated with itself on a finite time scale. Here we investigate the influence of external potentials on an ideal suspension of OUPs, in both one and two spatial dimensions, with particular attention paid to the pressure exerted on "confining walls." We employ a mathematical connection between the local density of OUPs and the statistics of their propulsion force to demonstrate the existence of an equation of state in one dimension. In higher dimensions we show that active particles generate a nonconservative force field in the surrounding medium. A simplified far-from-equilibrium model is proposed to account for OUP behavior in the vicinity of potentials. Building on this, we interpret simulations of OUPs in more complicated situations involving asymmetrical and spatially curved potentials, and characterize the resulting inhomogeneous stresses in terms of competing active length scales.

Pressure and flow of exponentially self-correlated active particles

Microscopic swimming particles, which dissipate energy to execute persistent directed motion, are a classic example of a nonequilibrium system. We investigate the noninteracting Ornstein-Uhlenbeck Particle (OUP), which is propelled through a viscous medium by a force which is correlated over a finite time. We obtain an exact expression for the steady-state phase-space density of a single OUP confined by a quadratic potential, and use the result to explore more complex geometries, both through analytical approximations and numerical simulations. In a "Casimir"-style setup involving two narrowly spaced walls, we describe a particle-trapping phenomenon, which leads to a repulsive effective interaction between the walls, while in a two-dimensional annulus geometry, we observe net stresses which resemble the Laplace pressure.

Equilibrium mappings in polar-isotropic confined active particles

Despite their fundamentally nonequilibrium nature, the individual and collective behavior of active systems with polar propulsion and isotropic interactions (polar-isotropic active systems) are remarkably well captured by equilibrium mapping techniques. Here we examine two signatures of equilibrium systems --the existence of a local free energy function and the independence of the coarse-grained behavior on the details of the microscopic dynamics-- in polar-isotropic active particles confined by hard walls of arbitrary geometry at the one-particle level. We find that boundaries that possess concave regions make the density profile strongly dynamics-dependent and give it a nonlocal dependence on the geometry of the confining box. This in turn constrains the scope of equilibrium mapping techniques in polar-isotropic active systems.

Transport of alignment active particles in funnel structures

We study the transport of alignment active particles in complex confined structures (an array of asymmetric funnels). It is found that due to the existence of the multiple pathways, the alignment interaction can enrich the transport behavior of active particles. In an array of asymmetric funnels, the purely nematic alignment always suppresses the rectification. However, the polar alignment does not always promote the rectification, the rectification is suppressed for large self-propulsion speed. In addition, we also found the existence of optimal parameters (the self-propulsion speed and the rotational diffusion coefficient) at which the directed velocity takes its maximal value.

Effects of hydrodynamic interactions on rectified transport of self-propelled particles

Directed transport of self-propelled particles is numerically investigated in a three-dimensional asymmetric potential. Beside the steric repulsive forces, hydrodynamic interactions between particles have been taken into account in an approximate way. From numerical simulations, we find that hydrodynamic interactions can strongly affect the rectified transport of self-propelled particles. Hydrodynamic interactions enhance the performance of the rectified transport when particles can easily pass across the barrier of the potential, and reduce the rectified transport when particles are mainly trapped in the potential well.

Microorganism billiards in closed plane curves

Recent experiments have shown that many species of microorganisms leave a solid surface at a fixed angle determined by steric interactions and near-field hydrodynamics. This angle is completely independent of the incoming angle. For several collisions in a closed body this determines a unique type of billiard system, an aspecular billiard in which the outgoing angle is fixed for all collisions. We analyze such a system using numerical simulation of this billiard for varying tables and outgoing angles, and also utilize the theory of one-dimensional maps and wavefront dynamics. When applicable we cite results from and compare our system to similar billiard systems in the literature. We focus on examples from three broad classes: the ellipse, the Bunimovich billiards, and the Sinai billiards. The effect of a noisy outgoing angle is also discussed.

Active Brownian particles and run-and-tumble particles separate inside a maze

A diverse range of natural and artificial self-propelled particles are known and are used nowadays. Among them, active Brownian particles (ABPs) and run-and-tumble particles (RTPs) are two important classes. We numerically study non-interacting ABPs and RTPs strongly confined to different maze geometries in two dimensions. We demonstrate that by means of geometrical confinement alone, ABPs are separable from RTPs. By investigating Matryoshka-like mazes with nested shells, we show that a circular maze has the best filtration efficiency. Results on the mean first-passage time reveal that ABPs escape faster from the center of the maze, while RTPs reach the center from the rim more easily. According to our simulations and a rate theory, which we developed, ABPs in steady state accumulate in the outermost region of the Matryoshka-like mazes, while RTPs occupy all locations within the maze with nearly equal probability. These results suggest a novel technique for separating different types of self-propelled particles by designing appropriate confining geometries without using chemical or biological agents.

Predominance of sperm motion in corners

Sperm migration through the female tract is crucial to fertilization, but the role of the complex and confined structure of the fallopian tube in sperm guidance remains unknown. Here, by confocal imaging microchannels head-on, we distinguish corner- vs. wall- vs. bulk-swimming bull sperm in confined geometries. Corner-swimming dominates with local areal concentrations as high as 200-fold that of the bulk. The relative degree of corner-swimming is strongest in small channels, decreases with increasing channel size, and plateaus for channels above 200 μm. Corner-swimming remains predominant across the physiologically-relevant range of viscosity and pH. Together, boundary-following sperm account for over 95% of the sperm distribution in small rectangular channels, which is similar to the percentage of wall swimmers in circular channels of similar size. We also demonstrate that wall-swimming sperm travel closer to walls in smaller channels (~100 μm), where the opposite wall is within the hydrodynamic interaction length-scale. The corner accumulation effect is more than the superposition of the influence of two walls, and over 5-fold stronger than that of a single wall. These findings suggest that folds and corners are dominant in sperm migration in the narrow (sub-mm) lumen of the fallopian tube and microchannel-based sperm selection devices.