Sex and flow: the consequences of fluid shear for sperm–egg interactions

Reinforcement learning of biomimetic navigation: a model problem for sperm chemotaxis

Motile biological cells can respond to local environmental cues and exhibit various navigation strategies to search for specific targets. These navigation strategies usually involve tuning of key biophysical parameters of the cells, such that the cells can modulate their trajectories to move in response to the detected signals. Here we introduce a reinforcement learning approach to modulate key biophysical parameters and realize navigation strategies reminiscent to those developed by biological cells. We present this approach using sperm chemotaxis toward an egg as a paradigm. By modulating the trajectory curvature of a sperm cell model, the navigation strategies informed by reinforcement learning are capable to resemble sperm chemotaxis observed in experiments. This approach provides an alternative method to capture biologically relevant navigation strategies, which may inform the necessary parameter modulations required for obtaining specific navigation strategies and guide the design of biomimetic micro-robotics.

Exploring sperm cell rheotaxis in microfluidic channel: the role of flow and viscosity

Rheotaxis is a fundamental mechanism of sperm cells that guides them in navigating towards the oocyte. The present study investigates the phenomenon of sperm rheotaxis in Newtonian and non-Newtonian fluid media, which for the first time explores a viscosity range equivalent to that of the oviductal fluid of the female reproductive tract in rectilinear microfluidic channels. Three parameters, the progressive velocity while performing rheotaxis, the radius of rotation during rheotaxis, and the percentage of rheotactic sperm cells in the bulk and near-wall regions of the microfluidic channel were measured. Numerical simulations of the flow were conducted to estimate the shear rate, flow velocity, and the drag force acting on the sperm head at specific locations where the sperms undergo rheotaxis. Increasing the flow velocity resulted in a change in the position of rheotactic sperm from the bulk center to the near wall region, an increase and subsequent decrease in the sperm's upstream progressive velocity, and a decrease in the radius of rotation. We observed that with an increase in viscosity, rheotactic sperms migrate to the near wall regions at lower flow rates, the upstream progressive velocity of the sperm decreases for Newtonian and increases for non-Newtonian media, and the radius of rotation increases for Newtonian and decreases for non-Newtonian media. These results quantify the effects of fluid properties such as viscosity and flow rate on sperm rheotaxis and navigation, thereby paving the way for manipulating sperm behavior in microfluidic devices, potentially leading to advancements in assisted reproduction techniques.

A simple reaction-diffusion system as a possible model for the origin of chemotaxis

Chemotaxis is a directed cell movement in response to external chemical stimuli. In this paper, we propose a simple model for the origin of chemotaxis - namely how a directed movement in response to an external chemical signal may occur based on purely reaction-diffusion equations reflecting inner working of the cells. The model is inspired by the well-studied role of the rho-GTPase Cdc42 regulator of cell polarity, in particular in yeast cells. We analyse several versions of the model to better understand its analytic properties and prove global regularity in one and two dimensions. Using computer simulations, we demonstrate that in the framework of this model, at least in certain parameter regimes, the speed of the directed movement appears to be proportional to the size of the gradient of signalling chemical. This coincides with the form of the chemical drift in the most studied mean field model of chemotaxis, the Keller-Segel equation.

Random Search in Fluid Flow Aided by Chemotaxis

In this paper, we consider the dynamics of a 2D target-searching agent performing Brownian motion under the influence of fluid shear flow and chemical attraction. The analysis is motivated by numerous situations in biology where these effects are present, such as broadcast spawning of marine animals and other reproduction processes or workings of the immune systems. We rigorously characterize the limit of the expected hit time in the large flow amplitude limit as corresponding to the effective one-dimensional problem. We also perform numerical computations to characterize the finer properties of the expected duration of the search. The numerical experiments show many interesting features of the process and in particular existence of the optimal value of the shear flow that minimizes the expected target hit time and outperforms the large flow limit.

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.

Recent Microfluidic Innovations for Sperm Sorting

Sperm selection is a clinical need for guided fertilization in men with low-quality semen. In this regard, microfluidics can provide an enabling platform for the precise manipulation and separation of high-quality sperm cells through applying various stimuli, including chemical agents, mechanical forces, and thermal gradients. In addition, microfluidic platforms can help to guide sperms and oocytes for controlled in vitro fertilization or sperm sorting using both passive and active methods. Herein, we present a detailed review of the use of various microfluidic methods for sorting and categorizing sperms for different applications. The advantages and disadvantages of each method are further discussed and future perspectives in the field are given.

Sperm chemotaxis in marine species is optimal at physiological flow rates according theory of filament surfing

Sperm of marine invertebrates have to find eggs cells in the ocean. Turbulent flows mix sperm and egg cells up to the millimeter scale; below this, active swimming and chemotaxis become important. Previous work addressed either turbulent mixing or chemotaxis in still water. Here, we present a general theory of sperm chemotaxis inside the smallest eddies of turbulent flow, where signaling molecules released by egg cells are spread into thin concentration filaments. Sperm cells ‘surf’ along these filaments towards the egg. External flows make filaments longer, but also thinner. These opposing effects set an optimal flow strength. The optimum predicted by our theory matches flow measurements in shallow coastal waters. Our theory quantitatively agrees with two previous fertilization experiments in Taylor-Couette chambers and provides a mechanistic understanding of these early experiments. ‘Surfing along concentration filaments’ could be a paradigm for navigation in complex environments in the presence of turbulent flow.

Many motile cells navigate in complex environments along concentration gradients of signaling molecules. This chemotaxis has been studied extensively both experimentally and theoretically, yet mostly for idealized conditions of perfect chemical gradients. But under physiological conditions, concentration fields are subject to distortions, e.g., by turbulent flows in the ocean. Pioneering experiments suggest that in species with external fertilization, chemotaxis of sperm cells towards the egg may even work better at an optimal flow strength compared to conditions of still water. Yet to date, the mechanistic cause for this optimum is not known. We present a general theory of chemotactic navigation in external flow. We characterize how external flow distorts concentration fields into long filaments, and show how chemotaxing cells can subsequently ‘surf’ along these filaments towards a chemoattractant source. Stronger flows make concentration filaments longer, but also thinner; together, these two counter-acting effects set an optimal flow strength. Beyond fertilization of marine invertebrates, we believe that ‘surfing along concentration filaments’ could be a more general paradigm, relevant also for the ecology of marine bacteria feeding on organic marine snow in the ocean, or chemotaxis inside multi-cellular organisms with internal flows.

Flagellar kinematics reveals the role of environment in shaping sperm motility

Swimming spermatozoa from diverse organisms often have very similar morphologies, yet different motilities as a result of differences in the flagellar waveforms used for propulsion. The origin of these differences has remained largely unknown. Using high-speed video microscopy and mathematical analysis of flagellar shape dynamics, we quantitatively compare sperm flagellar waveforms from marine invertebrates to humans by means of a novel phylokinematic tree. This new approach revealed that genetically dissimilar sperm can exhibit strikingly similar flagellar waveforms and identifies two dominant flagellar waveforms among the deuterostomes studied here, corresponding to internal and external fertilizers. The phylokinematic tree shows marked discordance from the phylogenetic tree, indicating that physical properties of the fluid environment, more than genetic relatedness, act as an important selective pressure in shaping the evolution of sperm motility. More broadly, this work provides a physical axis to complement morphological and genetic studies to understand evolutionary relationships.

Flow-induced buckling dynamics of sperm flagella

The swimming sperm of many external fertilizing marine organisms face complex fluid flows during their search for egg cells. Aided by chemotaxis, relatively weak flows are known to enhance sperm-egg fertilization rates through hydrodynamic guidance. However, strong flows have the potential to mechanically inhibit flagellar motility through elastohydrodynamic interactions-a phenomenon that remains poorly understood. Here we explore the effects of flow on the buckling dynamics of sperm flagella in an extensional flow through detailed numerical simulations, which are informed by microfluidic experiments and high-speed imaging. Compressional fluid forces lead to rich buckling dynamics of the sperm flagellum beyond a critical dimensionless sperm number, Sp, which represents the ratio of viscous force to elastic force. For nonmotile sperm, the maximum buckling curvature and the number of buckling locations, or buckling mode, increase with increasing sperm number. In contrast, motile sperm exhibit a local flagellar curvature due to the propagation of bending waves along the flagellum. In compressional flow, this preexisting curvature acts as a precursor for buckling, which enhances local curvature without creating new buckling modes and leads to asymmetric beating. However, in extensional flow, flagellar beating remains symmetric with a smaller head yawing amplitude due to tensile forces. The flagellar beating frequency also influences the maximum curvature of motile sperm by facilitating sperm reorientation relative to the compressional axis of the flow near stagnation points. These combined simulations and experiments directly illustrate the microscopic elastohydrodynamic mechanisms responsible for inhibiting flagellar motility in flow and have possible implications for our understanding of external fertilization in dynamic marine systems.

Sperm chemotaxis is driven by the slope of the chemoattractant concentration field

Spermatozoa of marine invertebrates are attracted to their conspecific female gamete by diffusive molecules, called chemoattractants, released from the egg investments in a process known as chemotaxis. The information from the egg chemoattractant concentration field is decoded into intracellular Ca²⁺ concentration ([Ca²⁺]_i) changes that regulate the internal motors that shape the flagellum as it beats. By studying sea urchin species-specific differences in sperm chemoattractant-receptor characteristics we show that receptor density constrains the steepness of the chemoattractant concentration gradient detectable by spermatozoa. Through analyzing different chemoattractant gradient forms, we demonstrate for the first time that Strongylocentrotus purpuratus sperm are chemotactic and this response is consistent with frequency entrainment of two coupled physiological oscillators: i) the stimulus function and ii) the [Ca²⁺]_i changes. We demonstrate that the slope of the chemoattractant gradients provides the coupling force between both oscillators, arising as a fundamental requirement for sperm chemotaxis.

Microfluidic techniques for separation of bacterial cells via taxis

The microbial environment is typically within a fluid and the key processes happen at the microscopic scale where viscosity dominates over inertial forces. Microfluidic tools are thus well suited to study microbial motility because they offer precise control of spatial structures and are ideal for the generation of laminar fluid flows with low Reynolds numbers at microbial lengthscales. These tools have been used in combination with microscopy platforms to visualise and study various microbial taxes. These include establishing concentration and temperature gradients to influence motility via chemotaxis and thermotaxis, or controlling the surrounding microenvironment to influence rheotaxis, magnetotaxis, and phototaxis. Improvements in microfluidic technology have allowed fine separation of cells based on subtle differences in motility traits and have applications in synthetic biology, directed evolution, and applied medical microbiology.

Microfluidic retention of progressively motile zebrafish sperms

Genetic manipulation of zebrafish results in thousands of mutant strains and to efficiently preserve them for future use, zebrafish sperms have been cryopreserved in various cryopreservation centers. However, cryopreservation protocols are known to alter genetic entities. Therefore, there is an urgent need for an efficient method that can select morphologically superior and progressively motile zebrafish sperms after their activation for in vitro fertilization success. However, unlike those of other mammalian species, fish sperms do not take any physical or chemical cues to travel towards the egg. Their inertness towards any external cues makes the control of their orientation in a microfluidic environment difficult. In this aspect, a new microfluidic concept was demonstrated where PDMS baffles were inserted in the sidewalls to form microscale confinement creating a flow stagnation zone towards sperm retention. Two distinct microfluidic device designs were selected to evidence the improvement in sperm retention through the unique hydrodynamic feature provided by the microchannel design. Under similar flow conditions, 44% improvement was noticed for the device with a modified baffle design in terms of sperm retrieving efficiency. It was further noticed that with a flow tuning of 0.7 μL min^-1, 80% of the total sperms swimming into the retention zones was retained within a specific time window. The present work further explains the significance of the hydrodynamic dependency of zebrafish sperm kinematics that paves the way for highly efficient spermatozoan manipulation.

Effect of external shear flow on sperm motility

The trajectory of sperm in the presence of background flow is of utmost importance for the success of fertilization, as sperm encounter background flow of different magnitude and direction on their way to the egg. Here, we have studied the effect of an unbounded simple shear flow as well as a Poiseuille flow on the sperm trajectory. In the presence of a simple shear flow, the sperm moves on an elliptical trajectory in the reference frame advecting with the local background flow. The length of the major-axis of this elliptical trajectory decreases with the shear rate. The flexibility of the flagellum and consequently the length of the major axis of the elliptical trajectories increases with the sperm number. The sperm number is a dimensionless number representing the ratio of viscous force to elastic force. The sperm moves downstream or upstream depending on the strength of background Poiseuille flow. In contrast to the simple shear flow, the sperm also moves toward the centerline in a Poiseuille flow. Far away from the centerline, the cross-stream migration velocity of the sperm increases as the transverse distance of the sperm from the centerline decreases. Close to the centerline, on the other hand, the cross-stream migration velocity decreases as the sperm further approaches the center. The cross-stream migration velocity of the sperm also increases with the sperm number.

Bacterial scattering in microfluidic crystal flows reveals giant active Taylor-Aris dispersion

The natural habitats of planktonic and swimming microorganisms, from algae in the oceans to bacteria living in soil or intestines, are characterized by highly heterogeneous fluid flows. The complex interplay of flow-field topology, self-propulsion, and porous microstructure is essential to a wide range of biophysical and ecological processes, including marine oxygen production, remineralization of organic matter, and biofilm formation. Although much progress has been made in the understanding of microbial hydrodynamics and surface interactions over the last decade, the dispersion of active suspensions in complex flow environments still poses unsolved fundamental questions that preclude predictive models for microbial transport and spreading under realistic conditions. Here, we combine experiments and simulations to identify the key physical mechanisms and scaling laws governing the dispersal of swimming bacteria in idealized porous media flows. By tracing the scattering dynamics of swimming bacteria in microfluidic crystal lattices, we show that hydrodynamic gradients hinder transverse bacterial dispersion, thereby enhancing stream-wise dispersion [Formula: see text]-fold beyond canonical Taylor-Aris dispersion of passive Brownian particles. Our analysis further reveals that hydrodynamic cell reorientation and Lagrangian flow structure induce filamentous density patterns that depend upon the incident angle of the flow and disorder of the medium, in striking analogy to classical light-scattering experiments.

Brief exposure to intense turbulence induces a sustained life-history shift in echinoids

In coastal ecosystems, attributes of fluid motion can prompt animal larvae to rise or sink in the water column and to select microhabitats within which they attach and commit to a benthic existence. In echinoid (sea urchin and sand dollar) larvae living along wave-exposed shorelines, intense turbulence characteristic of surf zones can cause individuals to undergo an abrupt life-history shift characterized by precocious entry into competence - the stage at which larvae will settle and complete metamorphosis in response to local cues. However, the mechanistic details of this turbulence-triggered onset of competence remain poorly defined. Here, we evaluate in a series of laboratory experiments the time course of this turbulence effect, both the rapidity with which it initiates and whether it perdures. We found that larvae become competent with turbulence exposures as brief as 30 s, with longer exposures inducing a greater proportion of larvae to become competent. Intriguingly, larvae can remember such exposures for a protracted period (at least 24 h), a pattern reminiscent of long-term potentiation. Turbulence also induces short-term behavioral responses that last less than 30 min, including cessation of swimming, that facilitate sinking and thus contact of echinoid larvae with the substratum. Together, these results yield a novel perspective on how larvae find their way to suitable adult habitat at the critical settlement transition, and also open new experimental opportunities to elucidate the mechanisms by which planktonic animals respond to fluid motion.

Analysis of sperm chemotaxis

In many species, sperm must locate the female gamete to achieve fertilization. Molecules diffusing from the egg envelope, or the female genital tract, guide the sperm toward the oocyte through a process called chemotaxis. Sperm chemotaxis has been studied for more than 100 years being a widespread phenomenon present from lower plants to mammals. This process has been mostly studied in external fertilizers where gametes undergo a significant dilution, as compared to internal fertilizers where the encounter is more defined by the topology of the female tract and only a small fraction of sperm appear to chemotactically respond. Here, we summarize the main methods to measure sperm swimming responses to a chemoattractant, both in populations and in individual sperm. We discuss a novel chemotactic index (CI) to score sperm chemotaxis in external fertilizers having circular trajectories. This CI is based on the sperm progressive displacement and its orientation angle to the chemoattractant source.

Sperm activation through orbital and self-axis revolutions using an artificial cilia embedded serpentine microfluidic platform

The zebrafish sperm activation profoundly depends upon the homogeneous mixing of the sperm cells with its diluent in a quick succession as it alters the cell's extracellular medium and initiates their motility. Manual stirring, the traditional method for zebrafish sperm activation is tedious, time-consuming, and has a poor outcome. In this aspect, an artificial cilia embedded serpentine microfluidic is designed through which hydrodynamic factors of the microfluidic environment can be precisely regulated to harness uniform mixing, hence ensuring a superior sperm activation. To quantify the sperm motility, computer assisted sperm analysis software (CASA) was used whereas to quantify the generated flow field, micro particle image velocimetry (μPIV) was used. With this proposed microfluidic, 74.4% of the zebrafish sperm were activated which is 20% higher than its currently existing manual measurements. The μPIV analysis demonstrates that the curvature of the microchannel induces an orbital rotation to the flow field along the length of the microchannel together with the artificial cilia actuation which instigates a local rotation to the flow field of the artificial cilia location. The collective rotation in the whole flow field induce vorticity that promotes the change in temporal dynamics of the sperm cells towards their activation.

Magnetotaxis Enables Magnetotactic Bacteria to Navigate in Flow

Magnetotactic bacteria (MTB) play an important role in Earth's biogeochemical cycles by transporting minerals in aquatic ecosystems, and have shown promise for controlled transport of microscale objects in flow conditions. However, how MTB traverse complex flow environments is not clear. Here, using microfluidics and high-speed imaging, it is revealed that magnetotaxis enables directed motion of Magnetospirillum magneticum over long distances in flow velocities ranging from 2 to 1260 µm s^-1 , corresponding to shear rates ranging from 0.2 to 142 s^-1 -a range relevant to both aquatic environments and biomedical applications. The ability of MTB to overcome a current is influenced by the flow, the magnetic field, and their relative orientation. MTB can overcome 2.3-fold higher flow velocities when directed to swim perpendicular to the flow as compared to upstream, as the latter orientation induces higher drag. The results indicate a threshold drag of 9.5 pN, corresponding to a flow velocity of 550 µm s^-1 , where magnetotaxis enables MTB to overcome counterdirectional flow. These findings bring new insights into the interactions of MTB with complex flow environments relevant to aquatic ecosystems, while suggesting opportunities for in vivo applications of MTB in microbiorobotics and targeted drug delivery.

CASA in invertebrates

Sperm movement has been described in several phyla of invertebrates. Yet, sperm motility has only been quantified using computer-aided sperm analysis (CASA-Mot) in externally fertilising species (broadcast spawners) of two phyla, molluscs and echinoderms. In the present study we quantified in detail the nature of the sperm tracks, percentage motility groupings and detailed kinematics of rapid-, medium- and slow-swimming spermatozoa in the oyster Crassostrea gigas and four species never previously studied by CASA-Mot, namely the molluscs Choromytilus meridionalis, Donax serra and Haliotis midae and the echinoderm Parechinus angulosus. A feature common to all these species are the helical tracks, the diameter of which seems to be species specific. Using CASA-Mot, the behaviour of spermatozoa was also studied over time and in the presence of egg water and Ca2+ modulators such as caffeine and procaine hydrochloride. For the first time, we show that hyperactivation can be induced in all species in the presence of egg water (sea water that was mixed with mature eggs and then centrifuged) and/or caffeine, and these hyperactivated sperm tracks were characterised using CASA-Mot. We relate the different patterns of sperm motility and behaviour to reproductive strategies such as broadcast spawning and spermcasting, and briefly review studies using CASA-Mot on other invertebrates.

Microfluidic Studies of Biofilm Formation in Dynamic Environments

The advent of microscale technologies, such as microfluidics, has revolutionized many areas of biology yet has only recently begun to impact the field of bacterial biofilms. By enabling accurate control and manipulation of physical and chemical conditions, these new microscale approaches afford the ability to combine important features of natural and artificial microbial habitats, such as fluid flow and ephemeral nutrient sources, with an unprecedented level of flexibility and quantification. Here, we review selected case studies to exemplify this potential, discuss limitations, and suggest that this approach opens new vistas into biofilm research over traditional setups, allowing us to expand our understanding of the formation and consequences of biofilms in a broad range of environments and applications.

Density Shock Waves in Confined Microswimmers

Motile and driven particles confined in microfluidic channels exhibit interesting emergent behavior, from propagating density bands to density shock waves. A deeper understanding of the physical mechanisms responsible for these emergent structures is relevant to a number of physical and biomedical applications. Here, we study the formation of density shock waves in the context of an idealized model of microswimmers confined in a narrow channel and subject to a uniform external flow. Interestingly, these density shock waves exhibit a transition from "subsonic" with compression at the back to "supersonic" with compression at the front of the population as the intensity of the external flow increases. This behavior is the result of a nontrivial interplay between hydrodynamic interactions and geometric confinement, and it is confirmed by a novel quasilinear wave model that properly captures the dependence of the shock formation on the external flow. These findings can be used to guide the development of novel mechanisms for controlling the emergent density distribution and the average population speed, with potentially profound implications on various processes in industry and biotechnology, such as the transport and sorting of cells in flow channels.

Upstream Swimming in Microbiological Flows

Interactions between microorganisms and their complex flowing environments are essential in many biological systems. We develop a model for microswimmer dynamics in non-Newtonian Poiseuille flows. We predict that swimmers in shear-thickening (-thinning) fluids migrate upstream more (less) quickly than in Newtonian fluids and demonstrate that viscoelastic normal stress differences reorient swimmers causing them to migrate upstream at the centerline, in contrast to well-known boundary accumulation in quiescent Newtonian fluids. Based on these observations, we suggest a sorting mechanism to select microbes by swimming speed.

Rheotaxis facilitates upstream navigation of mammalian sperm cells

A major puzzle in biology is how mammalian sperm maintain the correct swimming direction during various phases of the sexual reproduction process. Whilst chemotaxis may dominate near the ovum, it is unclear which cues guide spermatozoa on their long journey towards the egg. Hypothesized mechanisms range from peristaltic pumping to temperature sensing and response to fluid flow variations (rheotaxis), but little is known quantitatively about them. We report the first quantitative study of mammalian sperm rheotaxis, using microfluidic devices to investigate systematically swimming of human and bull sperm over a range of physiologically relevant shear rates and viscosities. Our measurements show that the interplay of fluid shear, steric surface-interactions, and chirality of the flagellar beat leads to stable upstream spiralling motion of sperm cells, thus providing a generic and robust rectification mechanism to support mammalian fertilisation. A minimal mathematical model is presented that accounts quantitatively for the experimental observations.DOI: http://dx.doi.org/10.7554/eLife.02403.001.

Sperm guidance to the egg finds calcium at the helm

Sperm respond to multiple cues during guidance to the egg including chemical attractants, temperature, and fluid flow. Of these, sperm chemotaxis has been studied most extensively-over 100 years-but only recently has it started to be understood at the molecular level. The long gestation in this understanding has largely been due to technical limitations that include the detection of calcium signal dynamics in a relatively small structure-the flagellum, measurement of actual chemoattractant gradients, the fact that only subpopulations of sperm respond at any given time, and the diversity in swimming behaviors that sperm exhibit from different species. Today, measurements of flagellar calcium signals on a fast time scale, discovery of the ion channels and organelles that may regulate these signals, and better understanding and quantitation of sperm swimming behaviors involved have given more certainty to our understanding of sperm directional swimming and its control by characteristic, calcium-directed asymmetric flagellar bends. Future research will need to apply these technical advances to other forms of sperm guidance such as thermotaxis and rheotaxis as well as gaining an understanding of how the flagellar apparatus is controlled by calcium.

Present-day nearshore pH differentially depresses fertilization in congeneric sea urchins

Ocean acidification impacts fertilization in some species of sea urchin, but whether sensitivity is great enough to be influenced by present-day pH variability has not been documented. In this study, fertilization in two congeneric sea urchins, Strongylocentrotus purpuratus and S. franciscanus, was found to be sensitive to reduced pH, <7.50, but only within a range of sperm-egg ratios that was species-specific. By further testing fertilization across a broad range of pH, pH-fertilization curves were generated and revealed that S. purpuratus was largely robust to pH, while fertilization in S. franciscanus was sensitive to even modest reductions in pH. Combining the pH-fertilization response curves with pH data collected from these species' habitat demonstrated that relative fertilization success remained high for S. purpuratus but could be as low as 79% for S. franciscanus during periods of naturally low pH. In order for S. franciscanus to maintain high fertilization success in the present and future, adequate adult densities, and thus sufficient sperm-egg ratios, will be required to negate the effects of low pH. In contrast, fertilization of S. purpuratus was robust to a broad range of pH, encompassing both present-day and future ocean acidification scenarios, even though the two congeners have similar habitats.

Effects of oscillatory flow on fertilization in the green sea urchin Strongylocentrotus droebachiensis

Broadcast spawning invertebrates that live in shallow, high-energy coastal habitats are subjected to oscillatory water motion that creates unsteady flow fields above the surface of animals. The frequency of the oscillatory fluctuations is driven by the wave period, which will influence the stability of local flow structures and may affect fertilization processes. Using an oscillatory water tunnel, we quantified the percentage of eggs fertilized on or near spawning green sea urchins, Strongylocentrotus droebachiensis. Eggs were sampled in the water column, wake eddy, substratum and aboral surface under a range of different periods (T = 4.5 – 12.7 s) and velocities of oscillatory flow. The root-mean-square wave velocity (rms(u_w)) was a good predictor of fertilization in oscillatory flow, although the root-mean-square of total velocity (rms(u)), which incorporates all the components of flow (current, wave and turbulence), also provided significant predictions. The percentage of eggs fertilized varied between 50 – 85% at low flows (rms(u_w) <0.02 m s⁻¹), depending on the location sampled, but declined to below 10% for most locations at higher rms(u_w). The water column was an important location for fertilization with a relative contribution greater than that of the aboral surface, especially at medium and high rms(u_w) categories. We conclude that gametes can be successfully fertilized on or near the parent under a range of oscillatory flow conditions.

The physics of broadcast spawning in benthic invertebrates

Most benthic invertebrates broadcast their gametes into the sea, whereupon successful fertilization relies on the complex interaction between the physics of the surrounding fluid flow and the biological properties and behavior of eggs and sperm. We present a holistic overview of the impact of instantaneous flow processes on fertilization across a range of scales. At large scales, transport and stirring by the flow control the distribution of gametes. Although mean dilution of gametes by turbulence is deleterious to fertilization, a variety of instantaneous flow phenomena can aggregate gametes before dilution occurs. We argue that these instantaneous flow processes are key to fertilization efficiency. At small scales, sperm motility and taxis enhance contact rates between sperm and chemoattractant-releasing eggs. We argue that sperm motility is a biological adaptation that replaces molecular diffusion in conventional mixing processes and enables gametes to bridge the gap that remains after aggregation by the flow.

Temporal sampling, resetting, and adaptation orchestrate gradient sensing in sperm

Sperm use temporal sampling, resetting of intracellular calcium level, and adaptation of their sensitivity to respond to a wide range of chemoattractant concentrations during their voyage toward the egg.

Sperm, navigating in a chemical gradient, are exposed to a periodic stream of chemoattractant molecules. The periodic stimulation entrains Ca²⁺ oscillations that control looping steering responses. It is not known how sperm sample chemoattractant molecules during periodic stimulation and adjust their sensitivity. We report that sea urchin sperm sampled molecules for 0.2–0.6 s before a Ca²⁺ response was produced. Additional molecules delivered during a Ca²⁺ response reset the cell by causing a pronounced Ca²⁺ drop that terminated the response; this reset was followed by a new Ca²⁺ rise. After stimulation, sperm adapted their sensitivity following the Weber–Fechner law. Taking into account the single-molecule sensitivity, we estimate that sperm can register a minimal gradient of 0.8 fM/µm and be attracted from as far away as 4.7 mm. Many microorganisms sense stimulus gradients along periodic paths to translate a spatial distribution of the stimulus into a temporal pattern of the cell response. Orchestration of temporal sampling, resetting, and adaptation might control gradient sensing in such organisms as well.

Periodic and quasiperiodic motion of an elongated microswimmer in Poiseuille flow

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

What is the core oscillator in the speract-activated pathway of the Strongylocentrotus purpuratus sperm flagellum?

Sperm chemotaxis has an important role in fertilization. Most of our knowledge regarding this phenomenon comes from studies in organisms whose fertilization occurs externally, like sea urchins. Sea urchin spermatozoa respond to sperm-activating peptides, which diffuse from the egg jelly coat and interact with their receptor in the flagellum, triggering several physiological responses: changes in membrane potential, intracellular pH, cyclic nucleotide levels, and intracellular Ca2+ concentration ([Ca2+]). In particular, flagellar [Ca2+] has been shown to oscillate. These [Ca2+] oscillations are correlated with changes in the flagellar shape and so with the regulation of the sperm swimming paths. In this study, we demonstrate, from a mathematical modeling perspective, that the reported speract-activated signaling pathway in Strongylocentrotus purpuratus (speract being a sperm-activating peptide specific to this species) has the necessary elements to replicate the reported [Ca2+] oscillations. We further investigate which elements of this signaling pathway constitute the core oscillator.

Nonlinear dynamics of a microswimmer in Poiseuille flow

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

Computational modelling of maternal interactions with spermatozoa: potentials and prospects

Understanding the complex interactions between gametes, embryos and the maternal tract is required knowledge for combating infertility and developing new methods of contraception. Here we present some main aspects of spermatozoa interactions with the mammalian oviduct before fertilisation and discuss how computational modelling can be used as an invaluable aid to experimental investigation in this field. A complete predictive computational model of gamete and embryo interactions with the female reproductive tract is a long way off. However, the enormity of this task should not discourage us from working towards it. Computational modelling allows us to investigate aspects of maternal communication with gametes and embryos, which are financially, ethically or practically difficult to look at experimentally. In silico models of maternal communication with gametes and embryos can be used as tools to complement in vivo experiments, in the same way as in vitro and in situ models.

The role of structured stirring and mixing on gamete dispersal and aggregation in broadcast spawning

Broadcast-spawning benthic invertebrates synchronously release sperm and eggs from separate locations into the surrounding flow, whereupon the process depends on structured stirring by the flow field (at large scales), and sperm motility and taxis (at small scales) to bring the gametes together. The details of the relevant physical and biological aspects of the problem that result in successful and efficient fertilization are not well understood. This review paper includes relevant work from both the physical and biological communities to synthesize a more complete understanding of the processes that govern fertilization success; the focus is on the role of structured stirring on the dispersal and aggregation of gametes. The review also includes a summary of current trends and approaches for numerical and experimental simulations of broadcast spawning.

Bacterial rheotaxis

The motility of organisms is often directed in response to environmental stimuli. Rheotaxis is the directed movement resulting from fluid velocity gradients, long studied in fish, aquatic invertebrates, and spermatozoa. Using carefully controlled microfluidic flows, we show that rheotaxis also occurs in bacteria. Excellent quantitative agreement between experiments with Bacillus subtilis and a mathematical model reveals that bacterial rheotaxis is a purely physical phenomenon, in contrast to fish rheotaxis but in the same way as sperm rheotaxis. This previously unrecognized bacterial taxis results from a subtle interplay between velocity gradients and the helical shape of flagella, which together generate a torque that alters a bacterium's swimming direction. Because this torque is independent of the presence of a nearby surface, bacterial rheotaxis is not limited to the immediate neighborhood of liquid-solid interfaces, but also takes place in the bulk fluid. We predict that rheotaxis occurs in a wide range of bacterial habitats, from the natural environment to the human body, and can interfere with chemotaxis, suggesting that the fitness benefit conferred by bacterial motility may be sharply reduced in some hydrodynamic conditions.

Allurin, an amphibian sperm chemoattractant having implications for mammalian sperm physiology

Eggs of many species are surrounded by extracellular coats that emit ligands to which conspecific sperm respond by undergoing chemotaxis and changes in metabolism, motility, and acrosomal status in preparation for fertilization. Here we review methods used to measure sperm chemotaxis and focus on recent studies of allurin, a 21-kDa protein belonging to the Cysteine-RIch Secretory Protein (CRISP) family that has chemoattraction activity for both amphibian and mammalian sperm. Allurin is unique in being the first extensively characterized Crisp protein found in the female reproductive tract and is the product of a newly discovered amphibian gene within a gene cluster that has been largely conserved in mammals. Study of its expression, function, and tertiary structure could lead to new insights in the role of Crisp proteins in sperm physiology.

Earliest ciliary swimming effects vertical transport of planktonic embryos in turbulence and shear flow

Eggs released by broadcast-spawning marine invertebrates are often negatively buoyant. Blastulae and gastrulae of these species are commonly motile, with passive stability that leads to upward swimming in still water. The earliest occurrence of swimming in developing embryos of diverse invertebrates may therefore permit vertical migration in nature. I used turbulent and laminar shear flows to investigate: (1) the speed and direction of transport of non-motile and newly swimming stages of the echinoids Dendraster excentricus and Strongylocentrotus purpuratus in turbulence, and (2) the limit of stable vertical orientation in swimming blastulae of D. excentricus. Swimming contributed significantly to the rate of upward transport of D. excentricus in turbulence experiments where the kinetic energy dissipation rate (ε) was ∼10–2cm2s–3. However, swimming significantly reduced the rate of upward transport of S. purpuratus blastulae in turbulence, suggesting that passively stable swimmers of this species were turned from the vertical, crossed flow-lines, and migrated into downwelling. Observations of swimming in laminar shear indicate that D. excentricus swimming blastulae maintain a vertical orientation until shear approaches 0.26s–1, equivalent to sub-microscale shear in turbulence where ε is ∼10–3cm2s–3. Swimming speeds of D. excentricus showed an unexpected dependence on shear, indicating that greater shear (within limits) can enhance speed of ciliary swimming. In D. excentricus, swimming by newly hatched blastulae should support upward migration in turbulence characteristic of coastal surface waters, whereas species differences in passive stability and swimming responses to shear may lead to differences in vertical transport and subsequent dispersal.

Two types of assays for detecting frog sperm chemoattraction

Sperm chemoattraction in invertebrates can be sufficiently robust that one can place a pipette containing the attractive peptide into a sperm suspension and microscopically visualize sperm accumulation around the pipette. Sperm chemoattraction in vertebrates such as frogs, rodents and humans is more difficult to detect and requires quantitative assays. Such assays are of two major types - assays that quantitate sperm movement to a source of chemoattractant, so-called sperm accumulation assays, and assays that actually track the swimming trajectories of individual sperm. Sperm accumulation assays are relatively rapid allowing tens or hundreds of assays to be done in a single day, thereby allowing dose response curves and time courses to be carried out relatively rapidly. These types of assays have been used extensively to characterize many well established chemoattraction systems - for example, neutrophil chemotaxis to bacterial peptides and sperm chemotaxis to follicular fluid. Sperm tracking assays can be more labor intensive but offer additional data on how chemoattractancts actually alter the swimming paths that sperm take. This type of assay is needed to demonstrate the orientation of sperm movement relative to the chemoattrractant gradient axis and to visualize characteristic turns or changes in orientation that bring the sperm closer to the egg. Here we describe methods used for each of these two types of assays. The sperm accumulation assay utilized is called a "two-chamber" assay. Amphibian sperm are placed in a tissue culture plate insert with a polycarbonate filter floor having 12 μm diameter pores. Inserts with sperm are placed into tissue culture plate wells containing buffer and a chemoatttractant carefully pipetted into the bottom well where the floor meets the wall (see Fig. 1). After incubation, the top insert containing the sperm reservoir is carefully removed, and sperm in the bottom chamber that have passed through the membrane are removed, pelleted and then counted by hemocytometer or flow cytometer. The sperm tracking assay utilizes a Zigmond chamber originally developed for observing neutrophil chemotaxis and modified for observation of sperm by Giojalas and coworkers. The chamber consists of a thick glass slide into which two vertical troughs have been machined. These are separated by a 1 mm wide observation platform. After application of a cover glass, sperm are loaded into one trough, the chemoattractant agent into the other and movement of individual sperm visualized by video microscopy. Video footage is then analyzed using software to identify two-dimensional cell movements in the x-y plane as a function of time (xyt data sets) that form the trajectory of each sperm.

Sperm chemotaxis, fluid shear, and the evolution of sexual reproduction

Chemical communication is fundamental to sexual reproduction, but how sperm search for and find an egg remains enigmatic. For red abalone (Haliotis rufescens), a large marine snail, the relationship between chemical signaling and fluid motion largely determines fertilization success. Egg-derived attractant plumes are dynamic, changing their size and shape in response to unique combinations of physical and chemical environmental features. Attractant plumes that promote sexual reproduction, however, are limited to a precise set of hydrodynamic conditions. Performance-maximizing shears are those that most closely match flows in native spawning habitats. Under conditions in which reproductive success is chronically limited by sperm availability, gametes are under selection for mechanisms that increase sperm-egg encounter. Here, chemoattraction is found to provide a cheap evolutionary alternative for enhancing egg target size without enlarging cytoplasmic and/or cell volume. Because egg signaling and sperm response may be tuned to meet specific fluid-dynamic constraints, shear could act as a critical selective pressure that drives gamete evolution and determines fitness.

Sperm chemotaxis as revealed with live and synthetic eggs

Fertilization is one of the least understood fundamental biological processes. How sperm search for and find an egg remains enigmatic. Sperm attraction to egg-derived chemical cues may be significant evolutionarily for maintaining species barriers and important ecologically for increasing gamete encounters. New tools are needed, however, to resolve the functional consequences of these dissolved signal molecules. Freshly spawned eggs from red abalone (Haliotis rufescens) naturally release l-tryptophan, which stimulates chemotactic responses by conspecific sperm. Here, microspheres were manufactured to the approximate size and the same shape as female gametes and formulated to emit controlled doses of chemoattractant, imitating natural l-tryptophan release rates. When experimentally tested for effectiveness, male gametes did not distinguish between chemically impregnated mimics and live eggs, demonstrating that l-tryptophan alone is both necessary and sufficient to promote chemotaxis, and confirming the identity of a native sperm attractant. The techniques that we describe can be used to create synthetic eggs for most animal and plant species, including humans. Egg mimics increase the capacity for experimental manipulation and enable realistic studies of sperm behavior even in the absence of female gametes.

Tuning sperm chemotaxis

Sperm chemotaxis is a long-term puzzle and most of our knowledge comes from studying marine animals that are external fertilizers. Sperm are attracted by diffusible chemical factors (chemoattractants) released from the egg which redirect their swimming paths towards their source. This redirection is driven by increases in flagellar curvature that correlate with transient flagellar Ca(2+) increases. Recent experimental and modelling results provide insights into the signal flow underlying the translation of an external chemical gradient into an intracellular molecular and motor response. A fundamental element of sea-urchin sperm chemotaxis lies in the ability of these cells to suppress Ca(2+)-mediated increases in flagellar curvature while experiencing an increasing chemoattractant gradient. The article considers this new evidence and summarizes the known underlying cellular mechanisms and behavioural strategies that sperm use to locate and fertilize the oocyte.

Modelling of energy expended by free swimming spermatozoa in temperature-dependent viscous semen

Derived models of fertilization kinetics have relied upon estimates of the swimming velocity of spermatozoa from the insemination site to a fallopian tube. However, limited derivations are available describing the probability and energy expended when spermatozoa collide with one another. An analytic approach of spermatozoon motion in a linear viscoelastic fluid is adopted to simplify the derivation. The complex kinematics of motion of an inextensible flagellum is modelled as planar flagellar wave of small amplitude. In humans, a temperature difference is expected between the cooler tubal isthmus and the warmer tubal ampulla. Thus, fluidic characteristics of semen such as viscosity can vary along the female reproductive tract. The results suggest that the probability of spermatozoa colliding in relatively lower viscous semen increases by 64.87% for a 0.5 degrees C surge in temperature. Moreover, this increases for a denser concentration of spermatozoa due to the limited semen volume available to manoeuvre. In addition, the propulsive forces and shear stress were 39.35% lower in less viscous semen due to an increase in temperature of only 0.5 degrees C. Hence, the described derivations herein can assist in the understanding of work done by a normal motile spermatozoon in a pool of semen.

Marine ecomechanics

The emerging field of marine ecomechanics provides an explicit physical framework for exploring interactions among marine organisms and between these organisms and their environments. It exhibits particular utility through its construction of predictive, mechanistic models, a number of which address responses to changing climatic conditions. Examples include predictions of (a) the change in relative abundance of corals as a function of colony morphology, ocean acidity, and storm intensity; (b) the rate of disturbance and patch formation in beds of mussels, a competitive dominant on many intertidal shores; (c) the dispersal and recruitment patterns of giant kelps, an important nearshore foundation species; (d) the effects of turbulence on external fertilization, a widespread method of reproduction in the sea; and (e) the long-term incidence of extreme ecological events. These diverse examples emphasize the breadth of marine ecomechanics. Indeed, its principles can be applied to any ecological system.