Turbulence of swarming sperm

Self-organization of spermatozoa via unsteady elastohydrodynamic interactions enhances their swimming speed and efficiency

Sperm bundling, swarming, and aggregation are observed in various species, suggesting that grouping enhances motility. In this study, we developed a numerical model of sperm computed by fluid-structure interactions between multiple flagella, showing that hydrodynamic interactions allow the sperm model to form polar orders, in which they swim alongside each other. The time required for order formation depends on the density n and is scaled by lnn/n. A wave propagation model controlled by the time derivative of flagellar curvature was introduced to represent flagellar synchronization via hydrodynamic interactions. The polar state results in hydrodynamic flagellar synchronization due to relatively long contact time, which increases swimming speed and flagellar beat speed by approximately 10% compared with no synchronization. During coordinated locomotion, the mechanical power performed by cells is similar to that in isolated systems, but grouping lowers the viscous resistance per cell and increases swimming speed by a factor of 2 compared to solitary swimming under high-density physiological conditions. Thus swimming efficiency increases with density (under physiological conditions, two- to fivefold times higher than in isolated systems). These numerical results show that, in the ordered state, sperm swim faster while expending less energy, suggesting that ordered swimming aids long-distance swimming from an energy perspective.

Collective sperm movement in mammalian reproductive tracts

Mammalian sperm cells travel from their origin in the male reproductive tract to fertilization in the female tract through a complex process driven by coordinated mechanical and biochemical mechanisms. Recent experimental and theoretical advances have illuminated the collective behaviors of sperm both in vivo and in vitro. However, our understanding of the underlying mechano-chemical processes remains incomplete. This review integrates current insights into sperm group movement, examining both immotile and motile states, which are essential for passive transport and active swimming through the reproductive tracts. We provide an overview of the current understanding of collective sperm movement, focusing on the experimental and theoretical mechanisms behind these behaviors. We also explore how sperm motility is regulated through the coordination of mechanical and chemical processes. Emerging evidence highlights the mechanosensitive properties of a sperm flagellum, suggesting that mechanical stimuli regulate flagellar beating at both individual and collective levels. This self-regulatory, mechano-chemical system reflects a broader principle observed in multicellular systems, offering a system-level insight into the regulation of motility and collective dynamics in biological systems.

Swarm Autonomy: From Agent Functionalization to Machine Intelligence

Swarm behaviors are common in nature, where individual organisms collaborate via perception, communication, and adaptation. Emulating these dynamics, large groups of active agents can self-organize through localized interactions, giving rise to complex swarm behaviors, which exhibit potential for applications across various domains. This review presents a comprehensive summary and perspective of synthetic swarms, to bridge the gap between the microscale individual agents and potential applications of synthetic swarms. It is begun by examining active agents, the fundamental units of synthetic swarms, to understand the origins of their motility and functionality in the presence of external stimuli. Then inter-agent communications and agent-environment communications that contribute to the swarm generation are summarized. Furthermore, the swarm behaviors reported to date and the emergence of machine intelligence within these behaviors are reviewed. Eventually, the applications enabled by distinct synthetic swarms are summarized. By discussing the emergent machine intelligence in swarm behaviors, insights are offered into the design and deployment of autonomous synthetic swarms for real-world applications.

Controlling wall-particle interactions with activity

We theoretically determine the effective forces on hard disks near walls embedded inside active nematic liquid crystals. When the disks are sufficiently close to the wall and the flows are sufficiently slow, we can obtain exact expressions for the effective forces. We find these forces and the dynamics of disks near the wall depend both on the properties of the active nematic and on the anchoring conditions on the disks and the wall. Our results show that the presence of active stresses attract planar anchored disks to walls if the activity is extensile, and repel them if contractile. For normal anchored disks the reverse is true; they are attracted in contractile systems, and repelled in extensile ones. By choosing the activity and anchoring, these effects may be helpful in controlling the self assembly of active nematic colloids.

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.

Scaling Transition of Active Turbulence from Two to Three Dimensions

Turbulent flows are observed in low-Reynolds active fluids, which display similar phenomenology to the classical inertial turbulence but are of a different nature. Understanding the dependence of this new type of turbulence on dimensionality is a fundamental challenge in non-equilibrium physics. Real-space structures and kinetic energy spectra of bacterial turbulence are experimentally measured from two to three dimensions. The turbulence shows three regimes separated by two critical confinement heights, resulting from the competition of bacterial length, vortex size and confinement height. Meanwhile, the kinetic energy spectra display distinct universal scaling laws in quasi-2D and 3D regimes, independent of bacterial activity, length, and confinement height, whereas scaling exponents transition in two steps around the critical heights. The scaling behaviors are well captured by the hydrodynamic model we develop, which employs image systems to represent the effects of confining boundaries. The study suggests a framework for investigating the effect of dimensionality on non-equilibrium self-organized systems.

Self-organized vortex phases and hydrodynamic interactions in Bos taurus sperm cells

Flocking behavior is observed in biological systems from the cellular to superorganismal length scales, and the mechanisms and purposes of this behavior are objects of intense interest. In this paper, we study the collective dynamics of bovine sperm cells in a viscoelastic fluid. These cells appear not to spontaneously flock, but transition into a long-lived flocking phase after being exposed to a transient ordering pulse of fluid flow. Surprisingly, this induced flocking phase has many qualitative similarities with the spontaneous polar flocking phases predicted by Toner-Tu theory, such as anisotropic giant number fluctuations and nontrivial transverse density correlations, despite the induced nature of the phase and the clearly important role of momentum conservation between the swimmers and the surrounding fluid in these experiments. We also find a self-organized global vortex state of the sperm cells, and map out an experimental phase diagram of states of collective motion as a function of cell density and motility statistics. We compare our experiments with a parameter-matched computational model of persistently turning active particles and find that the experimental order-disorder phase boundary as a function of cell density and persistence time can be approximately predicted from measures of single-cell properties. Our results may have implications for the evaluation of sample fertility by studying the collective phase behavior of dense groups of swimming sperm.

Orientational order and topological defects in a dilute solutions of rodlike polymers at low Reynolds number

The relationship between the polymer orientation and the chaotic flow, in a dilute solution of rigid rodlike polymers at low Reynolds number, is investigated by means of direct numerical simulations. It is found that the rods tend to align with the velocity field in order to minimize the friction with the solvent fluid, while regions of rotational disorder are related to strong vorticity gradients, and therefore to the chaotic flow. The "turbulent-like" behavior of the system is therefore associated with the emergence and interaction of topological defects of the mean director field, similarly to active nematic turbulence. The analysis has been carried out in both two and three spatial dimensions.

Nonequilibrium hyperuniform states in active turbulence

We demonstrate that the complex spatiotemporal structure in active fluids can feature characteristics of hyperuniformity. Using a hydrodynamic model, we show that the transition from hyperuniformity to nonhyperuniformity and antihyperuniformity depends on the strength of active forcing and can be related to features of active turbulence without and with scaling characteristics of inertial turbulence. Combined with identified signatures of Levy walks and nonuniversal diffusion in these systems, this allows for a biological interpretation and the speculation of nonequilibrium hyperuniform states in active fluids as optimal states with respect to robustness and strategies of evasion and foraging.

Fluid flow reconstruction around a free-swimming sperm in 3D

We investigate the dynamics and hydrodynamics of a human spermatozoa swimming freely in 3D. We simultaneously track the sperm flagellum and the sperm head orientation in the laboratory frame of reference via high-speed high-resolution 4D (3D+t) microscopy, and extract the flagellar waveform relative to the body frame of reference, as seen from a frame of reference that translates and rotates with the sperm in 3D. Numerical fluid flow reconstructions of sperm motility are performed utilizing the experimental 3D waveforms, with excellent accordance between predicted and observed 3D sperm kinematics. The reconstruction accuracy is validated by directly comparing the three linear and three angular sperm velocities with experimental measurements. Our microhydrodynamic analysis reveals a novel fluid flow pattern, characterized by a pair of vortices that circulate in opposition to each other along the sperm cell. Finally, we show that the observed sperm counter-vortices are not unique to the experimental beat, and can be reproduced by idealised waveform models, thus suggesting a fundamental flow structure for free-swimming sperm propelled by a 3D beating flagellum.

Oscillating edge current in polar active fluid

Dense bacterial suspensions exhibit turbulent behavior called bacterial turbulence. The behavior of the bulk unconstrained bacterial turbulence is described well by the Toner-Tu-Swift-Hohenberg (TTSH) equation for the velocity field. However, it remains unclear how we should treat boundary conditions on bacterial turbulence in contact with some boundaries (e.g., solid walls). To be more specific, although the importance of the edge current, the flow along the boundary, has been demonstrated in several experimental studies on confined bacterial suspensions, previous numerical studies based on the TTSH equation employ nonslip boundary conditions and do not seem to properly describe the behavior of bacteria near the boundaries. In this paper, we impose a slip boundary condition on the TTSH equation to describe the bacterial motion at boundaries. We develop a method to implement the slip boundary condition. Using this method, we have successfully produced edge current and discovered that the direction of the edge current temporally oscillates. The oscillation can be attributable to the advection term in the TTSH equation. Our paper demonstrates that boundary conditions could play an important role in the collective dynamics of active systems.

Order, chaos, and dimensionality transition in a system of swarmalators

Similarly to sperm, where individuals self-organize in space while also striving for coherence in their tail swinging, several natural and engineered systems exhibit the emergence of swarming and synchronization. The arising and interplay of these phenomena have been captured by collectives of hypothetical particles named swarmalators, each possessing a position and a phase whose dynamics are affected reciprocally and also by the space-phase states of their neighbors. In this work, we introduce a solvable model of swarmalators able to move in two-dimensional spaces. We show that several static and active collective states can emerge and derive necessary conditions for each to show up as the model parameters are varied. These conditions elucidate, in some cases, the displaying of multistability among states. Notably, in the active regime, the system exhibits hyperchaos, maintaining spatial correlation under certain conditions and breaking it under others on what we interpret as a dimensionality transition.

On particle motion in a confined square domain filled with active fluids

The motion of passive particles in a confined square domain filled with active fluids has been numerically simulated using a direct-fictitious domain method. The ratio of particle diameter to the side length of the square domain (dp/L) is adopted to classify the degree of confinement (i.e., strong or weak confinement). The translational mean-squared displacement (MSDT) of weakly-confined particles scales well with the reported theoretical and experimental results in a short time and eventually reaches a plateau because of the confined environment. Additionally, the radial probability densities of the particle positions gradually increase with increasing distance from the center of the square domain at relatively high activity levels, displaying an apparent rise near the boundary and maximize near the corner. Conversely, the strongly confined particles migrate toward the center of the square domain or approach the corner with continuous rotation. In addition, the localized minima of the angular velocity of the particles show a periodic behavior, with the vortices periodically becoming more organized. Moreover, with increasing activity, two distinct linearly correlated regimes emerge in the relationship between the particle's rotational velocity and the activity. A comprehensive analysis of the collective dynamics reveals that the cutoff length is Rc ≈ 0.19(2.375dp), pointing to the distance at which the velocities of two particles are uncorrelated. Moreover, the spatial correlation function (Ip) shows a small peak at Rr ≈ 0.12(1.5dp), suggesting a relatively strong correlation between a given particle and another particle located at a distance Rr from it. Interestingly, both Rc and Rr are smaller than those observed in an unbounded flow, which indicates that boundary confinement significantly influences the ability of the particles to form coherent structures.

Tracking bacteria at high density with FAST, the Feature-Assisted Segmenter/Tracker

Most bacteria live attached to surfaces in densely-packed communities. While new experimental and imaging techniques are beginning to provide a window on the complex processes that play out in these communities, resolving the behaviour of individual cells through time and space remains a major challenge. Although a number of different software solutions have been developed to track microorganisms, these typically require users either to tune a large number of parameters or to groundtruth a large volume of imaging data to train a deep learning model-both manual processes which can be very time consuming for novel experiments. To overcome these limitations, we have developed FAST, the Feature-Assisted Segmenter/Tracker, which uses unsupervised machine learning to optimise tracking while maintaining ease of use. Our approach, rooted in information theory, largely eliminates the need for users to iteratively adjust parameters manually and make qualitative assessments of the resulting cell trajectories. Instead, FAST measures multiple distinguishing 'features' for each cell and then autonomously quantifies the amount of unique information each feature provides. We then use these measurements to determine how data from different features should be combined to minimize tracking errors. Comparing our algorithm with a naïve approach that uses cell position alone revealed that FAST produced 4 to 10 fold fewer tracking errors. The modular design of FAST combines our novel tracking method with tools for segmentation, extensive data visualisation, lineage assignment, and manual track correction. It is also highly extensible, allowing users to extract custom information from images and seamlessly integrate it into downstream analyses. FAST therefore enables high-throughput, data-rich analyses with minimal user input. It has been released for use either in Matlab or as a compiled stand-alone application, and is available at https://bit.ly/3vovDHn, along with extensive tutorials and detailed documentation.

Friction-mediated phase transition in confined active nematics

Using a minimal continuum model, we investigate the interplay between circular confinement and substrate friction in active nematics. Upon increasing the friction from low to high, we observe a dynamical phase transition from a circulating flow phase to an anisotropic flow phase in which the flow tends to align perpendicular to the nematic director at the boundary. We demonstrate that both the flow structure and dynamic correlations in the latter phase differ from those of an unconfined, active turbulent system and may be controlled by the prescribed nematic boundary conditions. Our results show that substrate friction and geometric confinement act as valuable control parameters in active nematics.

Semen rheology and its relation to male infertility

Infertility affects 15% of couples of reproductive age worldwide. In spite of many advances in understanding and treating male infertility, there is still a number of issues that need further investigation and translation to the clinic. Here, we review the current knowledge and practice concerning semen rheology and its relation with pathological states affecting male infertility. Although it is well recognized that altered rheological properties of semen can impair normal sperm movement in the female reproductive tract, routine semen analysis is mostly focused on number, motility and morphology of spermatozoa, and includes only an approximate, operator-dependent measure of semen viscosity. The latter is based on the possible formation of a liquid thread from a pipette where a semen sample has been aspirated, a method that is sensitive not only to viscosity but also to elongational properties and surface tension of semen. The formation of a liquid thread is usually associated with a gel-like consistency of the sample and changes in spermatozoa motility in such a complex medium are still to be fully elucidated. The aim of this review is to point out that a more quantitative and reliable characterization of semen rheology is in order to improve the current methods of semen analysis and to develop additional tools for the diagnosis and treatment of male infertility.

Giant vortex dynamics in confined bacterial turbulence

We report the numerical evidence of a new state of bacterial turbulence in confined domains. By means of extensive numerical simulations of the Toner-Tu-Swift-Hohenberg model for dense bacterial suspensions in circular geometry, we discover the formation a stable, ordered state in which the angular momentum symmetry is broken. This is achieved by self-organization of a turbulent-like flow into a single, giant vortex of the size of the domain. The giant vortex is surrounded by an annular region close to the boundary, characterized by small-scale, radial vorticity streaks. The average radial velocity profile of the vortex is found to be in agreement with a simple analytical prediction. We also provide an estimate of the temporal and spatial scales of a suitable experimental setup comparable with our numerical findings.

Tubulation and dispersion of oil by bacterial growth on droplets

Bacteria on surfaces exhibit collective behaviors, such as active turbulence and active stresses, which result from their motility, growth, and interactions with their local surroundings. However, interfacial deformations on soft surfaces and liquid interfaces caused by active growth, particularly over long time scales, are not well understood. Here, we describe experimental observations on the emergence of tubular structures arising from the growth of rod-shaped bacteria at the interface of oil droplets in water. Using microfluidics and timelapse microscopy, the dimensions and extension rates of individual tubular structures as well as bulk bio-aggregate formation are quantified for hundreds of droplets over 72 hours. Tubular structures are comparable in length to the initial droplet radius and are composed of an outer shell of bacteria that stabilize an inner filament of oil. The oil filament breaks up into smaller microdroplets dispersed within the bacterial shell. This work provides insight into active stresses at deformable interfaces and improves our understanding of microbial oil biodegradation and its potential influence on the transport of droplets in the ocean water column.

Biological benefits of collective swimming of sperm in a viscoelastic fluid

Collective swimming is evident in the sperm of several mammalian species. In bull (Bos taurus) sperm, high viscoelasticity of the surrounding fluid induces the sperm to form dynamic clusters. Sperm within the clusters swim closely together and align in the same direction, yet the clusters are dynamic because individual sperm swim into and out of them over time. As the fluid in part of the mammalian female reproductive tract contains mucus and, consequently, is highly viscoelastic, this mechanistic clustering likely happens in vivo. Nevertheless, it has been unclear whether clustering could provide any biological benefit. Here, using a microfluidic in vitro model with viscoelastic fluid, we found that the collective swimming of bull sperm in dynamic clusters provides specific biological benefits. In static viscoelastic fluid, clustering allowed sperm to swim in a more progressive manner. When the fluid was made to flow in the range of 2.43-4.05 1/sec shear rate, clustering enhanced the ability of sperm to swim upstream. We also found that the swimming characteristics of sperm in our viscoelastic fluid could not be fully explained by the hydrodynamic model that has been developed for sperm swimming in a low-viscosity, Newtonian fluid. Overall, we found that clustered sperm swam more oriented with each other in the absence of flow, were able to swim upstream under intermediate flows, and better withstood a strong flow than individual sperm. Our results indicate that the clustering of sperm can be beneficial to sperm migrating against an opposing flow of viscoelastic fluid within the female reproductive tract.

Fluid-structure interaction of bio-inspired flexible slender structures: a review of selected topics

Flexible slender structures are ubiquitous in biological systems and engineering applications. Fluid-structure interaction (FSI) plays a key role in the dynamics of such structures immersed in fluids. Here, we survey recent studies on highly simplified bio-inspired models (either mathematical or mechanical) that aim to revealthe flow physics associated with FSI. Various models from different sources of biological inspiration are included, namely flexible flapping foil inspired by fish and insects, deformable membrane inspired by jellyfish and cephalopods, beating filaments inspired by flagella and cilia of microorganisms, and flexible wall-mounted filaments inspired by terrestrial and aquatic plants. Suggestions on directions for future research are also provided.

Exploring order in active turbulence: Geometric rule and pairing order transition in confined bacterial vortices

Ordered collective motion emerges in a group of autonomously motile elements (known as active matter) as their density increases. Microswimmers, such as swimming bacteria, have been extensively studied in physics and biology. A dense suspension of bacteria forms seemingly chaotic turbulence in viscous fluids. Interestingly, this active turbulence driven by bacteria can form a hidden ensemble of many vortices. Understanding the active turbulence in a bacterial suspension can provide physical principles for pattern formation and insight into the instability underlying biological phenomena. This review presents recent findings regarding ordered structures causing active turbulence and discusses a physical approach for controlling active turbulence via geometric confinement. When the active matter is confined in a compartment with a size comparable to the correlation length of the collective motion, vortex-like rotation appears, and the vortex pairing order is indicated by the patterns of interacting vortices. Additionally, we outline the design principle for controlling collective motions via the geometric rule of the vortex pairing, which may advance engineering microdevices driven by a group of active matter. This article is an extended version of the Japanese article, Ordered Structure and Geometric Control of Active Matter in Dense Bacterial Suspensions, published in SEIBUTSU BUTSURI Vol. 60, p. 13–18 (2020).

Density fluctuations and energy spectra of 3D bacterial suspensions

Giant number fluctuations are often considered as a hallmark of the emergent nonequilibrium dynamics of active fluids. However, these anomalous density fluctuations have only been reported experimentally in two-dimensional dry active systems heretofore. Here, we investigate density fluctuations of bulk Escherichia coli suspensions, a paradigm of three-dimensional (3D) wet active fluids. Our experiments demonstrate the existence and quantify the scaling relation of giant number fluctuations in 3D bacterial suspensions. Surprisingly, the anomalous scaling persists at small scales in low-concentration suspensions well before the transition to active turbulence, reflecting the long-range nature of hydrodynamic interactions of 3D wet active fluids. To illustrate the origin of the density fluctuations, we measure the energy spectra of suspension flows and explore the density-energy coupling in both the steady and transient states of active turbulence. A scale-invariant density-independent correlation between density fluctuations and energy spectra is uncovered across a wide range of length scales. In addition, our experiments show that the energy spectra of bacterial turbulence exhibit the scaling of 3D active nematic fluids, challenging the common view of dense bacterial suspensions as active polar fluids.

Emergence and melting of active vortex crystals

Melting of two-dimensional (2D) equilibrium crystals is a complex phenomenon characterized by the sequential loss of positional and orientational order. In contrast to passive systems, active crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Currently, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using a generalized Toner-Tu theory. Performing extensive hydrodynamic simulations, we find rich transition scenarios. On small domains, we identify a hysteretic transition as well as a transition featuring temporal coexistence of active vortex lattices and active turbulence, both of which can be controlled by self-propulsion and active stresses. On large domains, an active vortex crystal with solid order forms within the parameter range corresponding to active vortex lattices. The melting of this crystal proceeds through an intermediate hexatic phase. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts.

Anomalous Diffusion and Lévy Walks Distinguish Active from Inertial Turbulence

Bacterial swarms display intriguing dynamical states like active turbulence. Now, using a hydrodynamic model, we show that such dense active suspensions manifest superdiffusion, via Lévy walks, which masquerades as a crossover from ballistic to diffusive scaling in measurements of mean-squared displacements, and is tied to the emergence of hitherto undetected oscillatory streaks in the flow. Thus, while laying the theoretical framework of an emergent advantageous strategy in the collective behavior of microorganisms, our Letter underlines the essential differences between active and inertial turbulence.

Modelling Motility: The Mathematics of Spermatozoa

In one of the first examples of how mechanics can inform axonemal mechanism, Machin's study in the 1950s highlighted that observations of sperm motility cannot be explained by molecular motors in the cell membrane, but would instead require motors distributed along the flagellum. Ever since, mechanics and hydrodynamics have been recognised as important in explaining the dynamics, regulation, and guidance of sperm. More recently, the digitisation of sperm videomicroscopy, coupled with numerous modelling and methodological advances, has been bringing forth a new era of scientific discovery in this field. In this review, we survey these advances before highlighting the opportunities that have been generated for both recent research and the development of further open questions, in terms of the detailed characterisation of the sperm flagellum beat and its mechanics, together with the associated impact on cell behaviour. In particular, diverse examples are explored within this theme, ranging from how collective behaviours emerge from individual cell responses, including how these responses are impacted by the local microenvironment, to the integration of separate advances in the fields of flagellar analysis and flagellar mechanics.

Collective dynamics of sperm cells

While only a single sperm may fertilize the egg, getting to the egg can be facilitated, and possibly enhanced, by sperm group dynamics. Examples range from the trains formed by wood mouse sperm to the bundles exhibited by echidna sperm. In addition, observations of wave-like patterns exhibited by ram semen are used to score prospective sample fertility for artificial insemination in agriculture. In this review, we discuss these experimental observations of collective dynamics, as well as describe recent mechanistic models that link the motion of individual sperm cells and their flagella to observed collective dynamics. Establishing this link in models involves negotiating the disparate time- and length scales involved, typically separated by a factor of 1000, to capture the dynamics at the greatest length scales affected by mechanisms at the shortest time scales. Finally, we provide some outlook on the subject, in particular, the open questions regarding how collective dynamics impacts fertility. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Self-organization and multi-line transport of human spermatozoa in rectangular microchannels due to cell-cell interactions

The journey of sperm navigation towards ovum is one of the most important questions in mammalian fertilisation and reproduction. However, we know very little about spermatozoa propagation in a complex fluidic, chemical and topographic environment of a fertility tract. Using microfluidics techniques, we investigate the influence of cell-cell interactions on spermatozoa swimming behavior in constrained environment at different concentrations. Our study shows that at high enough cell concentration the interaction between boundary-following cells leads to formation of areas with preferential direction of cell swimming. In the microchannel of a rectangular cross-section, this leads to formation of a “four-lane” swimming pattern with the asymmetry of the cell distribution of up to 40%. We propose that this is caused by the combination of cell-cell collisions in the corners of the microchannel and the existence of morphologically different spermatozoa: slightly asymmetric cells with trajectories curved left and the symmetric ones, with trajectories curved right. Our findings suggest that cell-cell interactions in highly folded environment of mammalian reproductive tract are important for spermatozoa swimming behavior and play role in selection of highly motile cells.

Understanding Dense Active Nematics from Microscopic Models

We study dry, dense active nematics at both particle and continuous levels. Specifically, extending the Boltzmann-Ginzburg-Landau approach, we derive well-behaved hydrodynamic equations from a Vicsek-style model with nematic alignment and pairwise repulsion. An extensive study of the phase diagram shows qualitative agreement between the two levels of description. We find in particular that the dynamics of topological defects strongly depends on parameters and can lead to "arch" solutions forming a globally polar, smecticlike arrangement of Néel walls. We show how these configurations are at the origin of the defect ordered states reported previously. This work offers a detailed understanding of the theoretical description of dense active nematics directly rooted in their microscopic dynamics.

Particle-resolved lattice Boltzmann simulations of 3-dimensional active turbulence

Collective behaviour in suspensions of microswimmers is often dominated by the impact of long-ranged hydrodynamic interactions. These phenomena include active turbulence, where suspensions of pusher bacteria at sufficient densities exhibit large-scale, chaotic flows. To study this collective phenomenon, we use large-scale (up to N = 3 × 106) particle-resolved lattice Boltzmann simulations of model microswimmers described by extended stresslets. Such system sizes enable us to obtain quantitative information about both the transition to active turbulence and characteristic features of the turbulent state itself. In the dilute limit, we test analytical predictions for a number of static and dynamic properties against our simulation results. For higher swimmer densities, where swimmer-swimmer interactions become significant, we numerically show that the length- and timescales of the turbulent flows increase steeply near the predicted finite-system transition density.

New objective measurements of semen wave motion are associated with fertility in sheep

In sheep, wave motion in semen is currently used by AI centres to select ejaculates for insemination. Despite its low cost, convenience and established ability to predict fertility, the subjectivity of this assessment is a limiting factor for its applicability. The aims of the present study were to establish an objective method for the analysis of wave motion and to assess the associations of objective parameters with fertility after cervical insemination. Collective sperm motion in undiluted semen was observed by phase contrast microscopy at low magnification in a 100-µm deep glass chamber. Images of moving dark waves over a grey background were recorded and analysed by the optic flow method, producing several velocity-related parameters. Turbulence was assessed from the motion of fluorescent polystyrene beads. Among objective parameters, optical flow entropy and the average speed of beads were both able to discriminate ejaculates suitable for insemination. Two synthetic variables of optic flow and bead motion and a global objective variable were computed from linear combinations of individual parameters and compared with the subjective motion score for their predictive value. These were as efficient as the wave motion score for assessing fertility and can be proposed for the assessment of ram semen in routine AI procedures.

Lattice Boltzmann methods and active fluids

We review the state of the art of active fluids with particular attention to hydrodynamic continuous models and to the use of Lattice Boltzmann Methods (LBM) in this field. We present the thermodynamics of active fluids, in terms of liquid crystals modelling adapted to describe large-scale organization of active systems, as well as other effective phenomenological models. We discuss how LBM can be implemented to solve the hydrodynamics of active matter, starting from the case of a simple fluid, for which we explicitly recover the continuous equations by means of Chapman-Enskog expansion. Going beyond this simple case, we summarize how LBM can be used to treat complex and active fluids. We then review recent developments concerning some relevant topics in active matter that have been studied by means of LBM: spontaneous flow, self-propelled droplets, active emulsions, rheology, active turbulence, and active colloids.

From flagellar undulations to collective motion: predicting the dynamics of sperm suspensions

Swimming cells and microorganisms are as diverse in their collective dynamics as they are in their individual shapes and propulsion mechanisms. Even for sperm cells, which have a stereotyped shape consisting of a cell body connected to a flexible flagellum, a wide range of collective dynamics is observed spanning from the formation of tightly packed groups to the display of larger-scale, turbulence-like motion. Using a detailed mathematical model that resolves flagellum dynamics, we perform simulations of sperm suspensions containing up to 1000 cells and explore the connection between individual and collective dynamics. We find that depending on the level of variation in individual dynamics from one swimmer to another, the sperm exhibit either a strong tendency to aggregate, or the suspension exhibits large-scale swirling. Hydrodynamic interactions govern the formation and evolution of both states. In addition, a quantitative analysis of the states reveals that the flows generated at the time scale of flagellum undulations contribute significantly to the overall energy in the surrounding fluid, highlighting the importance of resolving these flows.

Geometrical Control of Active Turbulence in Curved Topographies

We investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal constrained to a curved surface. Using a combination of hydrodynamic and particle-based simulations, we demonstrate that the fundamental structural features of the fluid, such as the topological charge density, the defect number density, the nematic order parameter, and defect creation and annihilation rates, are approximately linear functions of the substrate Gaussian curvature, which then acts as a control parameter for the chaotic flow. Our theoretical predictions are then compared with experiments on microtubule-kinesin suspensions confined on toroidal droplets, finding excellent qualitative agreement.

Dynamical subclasses of dry active nematics

We show that the dominant mode of alignment plays an important role in dry active nematics, leading to two dynamical subclasses defined by the nature of the instability of the nematic bands that characterize, in these systems, the coexistence phase separating the isotropic and fluctuating nematic states. In addition to the well-known instability inducing long undulations along the band, another stronger instability leading to the breakup of the band in many transversal segments may arise. We elucidate the origin of this strong instability for a realistic model of self-propelled rods and determine the high-order nonlinear terms responsible for it at the hydrodynamic level.

Data-driven quantitative modeling of bacterial active nematics

Active matter comprises individual units that convert energy into mechanical motion. In many examples, such as bacterial systems and biofilament assays, constituent units are elongated and can give rise to local nematic orientational order. Such "active nematics" systems have attracted much attention from both theorists and experimentalists. However, despite intense research efforts, data-driven quantitative modeling has not been achieved, a situation mainly due to the lack of systematic experimental data and to the large number of parameters of current models. Here, we introduce an active nematics system made of swarming filamentous bacteria. We simultaneously measure orientation and velocity fields and show that the complex spatiotemporal dynamics of our system can be quantitatively reproduced by a type of microscopic model for active suspensions whose important parameters are all estimated from comprehensive experimental data. This provides unprecedented access to key effective parameters and mechanisms governing active nematics. Our approach is applicable to different types of dense suspensions and shows a path toward more quantitative active matter research.

Active nematics

Active matter extracts energy from its surroundings at the single particle level and transforms it into mechanical work. Examples include cytoskeleton biopolymers and bacterial suspensions. Here, we review experimental, theoretical and numerical studies of active nematics - a type of active system that is characterised by self-driven units with elongated shape. We focus primarily on microtubule-kinesin mixtures and the hydrodynamic theories that describe their properties. An important theme is active turbulence and the associated motile topological defects. We discuss ways in which active turbulence may be controlled, a pre-requisite to harvesting energy from active materials, and we consider the appearance, and possible implications, of active nematics and topological defects to cellular systems and biological processes.

Role of Correlations in the Collective Behavior of Microswimmer Suspensions

In this Letter, we study the collective behavior of a large number of self-propelled microswimmers immersed in a fluid. Using unprecedentedly large-scale lattice Boltzmann simulations, we reproduce the transition to bacterial turbulence. We show that, even well below the transition, swimmers move in a correlated fashion that cannot be described by a mean-field approach. We develop a novel kinetic theory that captures these correlations and is nonperturbative in the swimmer density. To provide an experimentally accessible measure of correlations, we calculate the diffusivity of passive tracers and reveal its nontrivial density dependence. The theory is in quantitative agreement with the lattice Boltzmann simulations and captures the asymmetry between pusher and puller swimmers below the transition to turbulence.

Nonequilibrium fluctuations during diffusion in liquid layers

Theoretical analysis and experiments have provided compelling evidence of the presence of long-range nonequilibrium concentration fluctuations during diffusion processes in fluids. In this paper, we investigate the dependence of the features of the fluctuations from the dimensionality of the system. In three-dimensional fluids the amplitude of nonequilibrium fluctuations can become several orders of magnitude larger than that of equilibrium fluctuations. Notwithstanding that, the amplitude of nonequilibrium fluctuations remains small with respect to the concentration difference driving the diffusion process. By extending the theory to two-dimensional systems, such as liquid monolayers and bilayers, we show that the amplitude of the fluctuations becomes much stronger than in three-dimensional systems. We investigate the properties of the fronts of diffusion and show that they have a self-affine structure characterized by a Hurst exponent H=1. We discuss the implications of these results for diffusion in liquid crystals and in cellular membranes of living organisms.

Dancing disclinations in confined active nematics

The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterised by swirls, jets, and topological disclinations in their orientation field. However, the ability to achieve structured flows and ordered disclinations is of particular importance in the design and control of active systems. By confining an active nematic fluid within a channel, we find a regular motion of disclinations, in conjunction with a well defined and dynamic vortex lattice. As pairs of moving disclinations travel through the channel, they continually exchange partners producing a dynamic ordered state, reminiscent of Ceilidh dancing. We anticipate that this biomimetic ability to self-assemble organised topological disclinations and dynamically structured flow fields in engineered geometries will pave the road towards establishing new active topological microfluidic devices.

Symmetry-breaking phase transitions in highly concentrated semen

New experimental evidence of self-motion of a confined active suspension is presented. Depositing fresh semen sample in an annular shaped microfluidic chip leads to a spontaneous vortex state of the fluid at sufficiently large sperm concentration. The rotation occurs unpredictably clockwise or counterclockwise and is robust and stable. Furthermore, for highly active and concentrated semen, richer dynamics can occur such as self-sustained or damped rotation oscillations. Experimental results obtained with systematic dilution provide a clear evidence of a phase transition towards collective motion associated with local alignment of spermatozoa akin to the Vicsek model. A macroscopic theory based on previously derived self-organized hydrodynamics models is adapted to this context and provides predictions consistent with the observed stationary motion.

Collective Motion of Microorganisms in a Viscoelastic Fluid

We study the collective motion of a suspension of rodlike microswimmers in a two-dimensional film of viscoelastic fluids. We find that the fluid elasticity has a small effect on a suspension of pullers, while it significantly affects the pushers. The attraction and orientational ordering of the pushers are enhanced in viscoelastic fluids. The induced polymer stresses break down the large-scale flow structures and suppress velocity fluctuations. In addition, the energy spectra and induced mixing in the suspension of pushers are greatly modified by fluid elasticity.

Large scale flow visualization and anemometry applied to lab-on-a-chip models of porous media

The following is a report on an experimental technique that allows one to quantify and map the velocity field with very high resolution and simple equipment in large 2D devices. Illumination through a grid is proposed to reinforce the contrast in the images and allow one to detect seeded particles that are pixel-sized or even smaller. The velocimetry technique that we have reported is based on the auto-correlation functions of the pixel intensity, which we have shown are directly related to the magnitude of the local average velocity. The characteristic time involved in the decorrelation of the signal is proportional to the tracer size and inversely proportional to the average velocity. We have reported on a detailed discussion about the optimization of relevant involved parameters, the spatial resolution and the accuracy of the method. The technique is then applied to a model porous medium made of a random channel network. We show that it is highly efficient to determine the magnitude of the flow in each of the channels of the network, opening the door to the fundamental study of the flows of complex fluids. The latter is illustrated with a yield stress fluid, in which the flow becomes highly heterogeneous at small flow rates.

Active micromachines: Microfluidics powered by mesoscale turbulence

Dense active matter, from bacterial suspensions and microtubule bundles driven by motor proteins to cellular monolayers and synthetic Janus particles, is characterized by mesoscale turbulence, which is the emergence of chaotic flow structures. By immersing an ordered array of symmetric rotors in an active fluid, we introduce a microfluidic system that exploits spontaneous symmetry breaking in mesoscale turbulence to generate work. The lattice of rotors self-organizes into a spin state where neighboring discs continuously rotate in permanent alternating directions due to combined hydrodynamic and elastic effects. Our virtual prototype demonstrates a new research direction for the design of micromachines powered by the nematohydrodynamic properties of active turbulence.