Tracking sperm in three-dimensions

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.

Feature-based 3D+t descriptors of hyperactivated human sperm beat patterns

The flagellar movement of the mammalian sperm plays a crucial role in fertilization. In the female reproductive tract, human spermatozoa undergo a process called capacitation which promotes changes in their motility. Only capacitated spermatozoa may be hyperactivated and only those that transition to hyperactivated motility are capable of fertilizing the egg. Hyperactivated motility is characterized by asymmetric flagellar bends of greater amplitude and lower frequency. Historically, clinical fertilization studies have used two-dimensional analysis to classify sperm motility, despite the inherently three-dimensional (3D) nature of sperm motion. Recent research has described several 3D beating features of sperm flagella. However, the 3D motility pattern of hyperactivated spermatozoa has not yet been characterized. One of the main challenges in classifying these patterns in 3D is the lack of a ground-truth reference, as it can be difficult to visually assess differences in flagellar beat patterns. Additionally, it is worth noting that only a relatively small proportion, approximately 10-20% of sperm incubated under capacitating conditions exhibit hyperactivated motility. In this work, we used a multifocal image acquisition system that can acquire, segment, and track sperm flagella in 3D+t. We developed a feature-based vector that describes the spatio-temporal flagellar sperm motility patterns by an envelope of ellipses. The classification results obtained using our 3D feature-based descriptors can serve as potential label for future work involving deep neural networks. By using the classification results as labels, it will be possible to train a deep neural network to automatically classify spermatozoa based on their 3D flagellar beating patterns. We demonstrated the effectiveness of the descriptors by applying them to a dataset of human sperm cells and showing that they can accurately differentiate between non-hyperactivated and hyperactivated 3D motility patterns of the sperm cells. This work contributes to the understanding of 3D flagellar hyperactive motility patterns and provides a framework for research in the fields of human and animal fertility.

Human sperm rotate with a conserved direction during free swimming in four dimensions

Head rotation in human spermatozoa is essential for different swimming modes and fertilisation, as it links the molecular workings of the flagellar beat with sperm motion in three-dimensional (3D) space over time. Determining the direction of head rotation has been hindered by the symmetry and translucent nature of the sperm head, and by the fast 3D motion driven by the helical flagellar beat. Analysis has been mostly restricted to two-dimensional (2D) single focal plane image analysis, which enables tracking of head centre position but not tracking of head rotation. Despite the conserved helical beating of the human sperm flagellum, human sperm head rotation has been reported to be uni- or bi-directional, and even to intermittently change direction in a given cell. Here, we directly measure the head rotation of freely swimming human sperm using multi-plane 4D (3D+t) microscopy and show that: (1) 2D microscopy is unable to distinguish head rotation direction in human spermatozoa; (2) head rotation direction in non-capacitating and capacitating solutions, for both aqueous and viscous media, is counterclockwise (CCW), as seen from head to tail, in all rotating spermatozoa, regardless of the experimental conditions; and (3) head rotation is suppressed in 36% of spermatozoa swimming in non-capacitating viscous medium, although CCW rotation is recovered after incubation in capacitating conditions within the same viscous medium, possibly unveiling an unexplored aspect of the essential need of capacitation for fertilisation. Our observations show that the CCW head rotation in human sperm is conserved. It constitutes a robust and persistent helical driving mechanism that influences sperm navigation in 3D space over time, and thus is of critical importance in cell motility, propulsion of flagellated microorganisms, sperm motility assessments, human reproduction research, and self-organisation of flagellar beating patterns and swimming in 3D space.

Hydrodynamic Synchronization of Chiral Microswimmers

We study synchronization in bulk suspensions of spherical microswimmers with chiral trajectories using large scale numerics. The model is generic. It corresponds to the lowest order solution of a general model for self-propulsion at low Reynolds numbers, consisting of a nonaxisymmetric rotating source dipole. We show that both purely circular and helical swimmers can spontaneously synchronize their rotation. The synchronized state corresponds to velocity alignment with high orientational order in both the polar and azimuthal directions. Finally, we consider a racemic mixture of helical swimmers where intraspecies synchronization is observed while the system remains as a spatially uniform fluid. Our results demonstrate hydrodynamic synchronization as a natural collective phenomenon for microswimmers with chiral trajectories.

Recent advances in experimental design and data analysis to characterize prokaryotic motility

Bacterial motility plays a key role in important cell processes such as chemotaxis and biofilm formation, but is challenging to quantify due to the small size of the individual microorganisms and the complex interplay of biological and physical factors that influence motility phenotypes. Swimming, the first type of motility described in bacteria, still remains largely unquantified. Light microscopy has enabled qualitative characterization of swimming patterns seen in different strains, such as run and tumble, run-reverse-flick, run and slow, stop and coil, and push and pull, which has allowed for elucidation of the underlying physics. However, quantifying these behaviors (e.g., identifying run distances and speeds, turn angles and behavior by surfaces or cell-cell interactions) remains a challenging task. A qualitative and quantitative understanding of bacterial motility is needed to bridge the gap between experimentation, omics analysis, and bacterial motility theory. In this review, we discuss the strengths and limitations of how phase contrast microscopy, fluorescence microscopy, and digital holographic microscopy have been used to quantify bacterial motility. Approaches to automated software analysis, including cell recognition, tracking, and track analysis, are also discussed with a view to providing a guide for experimenters to setting up the appropriate imaging and analysis system for their needs.

Motility Assessment of Ram Spermatozoa

For successful fertilisation to occur, spermatozoa need to successfully migrate through the female reproductive tract and penetrate the oocyte. Predictably, poor sperm motility has been associated with low rates of fertilisation in many mammalian species, including the ram. As such, motility is one of the most important parameters used for in vitro evaluation of ram sperm quality and function. This review aims to outline the mechanical and energetic processes which underpin sperm motility, describe changes in motility which occur as a result of differences in sperm structure and the surrounding microenvironment, and assess the effectiveness of the various methods used to assess sperm motility in rams. Methods of subjective motility estimation are convenient, inexpensive methods widely used in the livestock industries, however, the subjective nature of these methods can make them unreliable. Computer-assisted sperm analysis (CASA) technology accurately and objectively measures sperm motility via two-dimensional tracing of sperm head motion, making it a popular method for sperm quality assurance in domesticated animal production laboratories. Newly developed methods of motility assessment including flagellar tracing, three-dimensional sperm tracing, in vivo motility assessment, and molecular assays which quantify motility-associated biomarkers, enable analysis of a new range of sperm motion parameters with the potential to reveal new mechanistic insights and improve ram semen assessment. Experimental application of these technologies is required to fully understand their potential to improve semen quality assessment and prediction of reproductive success in ovine artificial breeding programs.

3D+t feature-based descriptor for unsupervised flagellar human sperm beat classification

Human spermatozoa must swim through the female reproductive tract, where they undergo a series of biochemical and biophysical reactions called capacitation, a necessary step to fertilize the egg. Capacitation promotes changes in the motility pattern. Historically, a two-dimensional analysis has been used to classify sperm motility and clinical fertilization studies. Nevertheless, in a natural environment sperm motility is three-dimensional (3D). Imaging flagella of freely swimming sperm is a difficult task due to their high beating frequency of up to 25 Hz. Very recent studies have described several sperm flagellum 3D beating features (curvature, torsion, asymmetries, etc.). However, up to date, the 3D motility pattern of hyperactivated spermatozoa has not been characterized. The main difficulty in classifying these patterns in 3D is the lack of a ground truth reference since differences in flagellar beat patterns are very difficult to assess visually. Moreover, only around 10-20% of induced to capacitate spermatozoa are truly capacitated, i.e., hyperactivated. We used an image acquisition system that can acquire, segment, and track spermatozoa flagella in 3D+t. In this work, we propose an original three-dimensional feature vector formed by ellipses describing the envelope of the 3D+t spatio-temporal flagellar sperm motility patterns. These features allowed compressing an unlabeled 3D+t dataset to separate hyperactivated cells from others (capacitated from non-capacitated cells) using unsupervised hierarchical clustering. Preliminary results show three main clusters of flagellar motility patterns. The first principal component of these 3D flagella measurements correlated with 2D OpenCASA head determinations as a first approach to validate the unsupervised classification, showing a reasonable correlation coefficient near to 0.7. Clinical relevance- The novelty of this work is defining a 3D+t feature-based descriptor consisting of a set of ellipses enveloping the flagellar motion of human sperm for its unsu-pervised classification. This is a new promising tool to determine the viability of human sperm to fertilize the egg.

Unraveling the Kinematics of Sperm Motion by Reconstructing the Flagellar Wave Motion in 3D

Sperm swim through the female reproductive tract by propagating a 3D flagellar wave that is self-regulatory in nature and driven by dynein motors. Traditional microscopy methods fail to capture the full dynamics of sperm flagellar activity as they only image and analyze sperm motility in 2D. Here, an automated platform to analyze sperm swimming behavior in 3D by using thin-lens approximation and high-speed dark field microscopy to reconstruct the flagellar waveform in 3D is presented. It is found that head-tethered mouse sperm exhibit a rolling beating behavior in 3D with the beating frequency of 6.2 Hz using spectral analysis. The flagellar waveform bends in 3D, particularly in the distal regions, but is only weakly nonplanar and ambidextrous in nature, with the local helicity along the flagellum fluctuating between clockwise and counterclockwise handedness. These findings suggest a nonpersistent flagellar helicity. This method provides new opportunities for the accurate measurement of the full motion of eukaryotic flagella and cilia which is essential for a biophysical understanding of their activation by dynein motors.

Reconstruction of the three-dimensional beat pattern underlying swimming behaviors of sperm

 The eukaryotic flagellum propels sperm cells and simultaneously detects physical and chemical cues that modulate the waveform of the flagellar beat. Most previous studies have characterized the flagellar beat and swimming trajectories in two space dimensions (2D) at a water/glass interface. Here, using refined holographic imaging methods, we report high-quality recordings of three-dimensional (3D) flagellar bending waves. As predicted by theory, we observed that an asymmetric and planar flagellar beat results in a circular swimming path, whereas a symmetric and non-planar flagellar beat results in a twisted-ribbon swimming path. During swimming in 3D, human sperm flagella exhibit torsion waves characterized by maxima at the low curvature regions of the flagellar wave. We suggest that these torsion waves are common in nature and that they are an intrinsic property of beating axonemes. We discuss how 3D beat patterns result in twisted-ribbon swimming paths. This study provides new insight into the axoneme dynamics, the 3D flagellar beat, and the resulting swimming behavior.

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.

Tunable depletion force in active and crowded environments

We adopt two-dimensional Langevin dynamics simulations to study the effective interactions between two passive colloids in a bath crowded with active particles. We mainly pay attention to the significant effects of active particle size, crowding-activity coupling, and chirality. First, a transition of depletion force from repulsion to attraction is revealed by varying particle size. Moreover, larger active crowders with sufficient activity can generate strong attractive force, which is in contrast to the cage effect in passive media. It is interesting that the attraction induced by large active crowders follows a linear scaling with the persistence length of active particles. Second, the effective force also experiences a transition from repulsion to attraction as volume fraction increases, as a consequence of the competition between the two contrastive factors of activity and crowding. As bath volume fraction is relatively small, activity generates a dominant repulsion force, while as the bath becomes concentrated, crowding-induced attraction becomes overwhelming. Lastly, in a chiral bath, we observe a very surprising oscillation phenomenon of active depletion force, showing an evident quasiperiodic variation with increasing chirality. Aggregation of active particles in the vicinity of the colloids is carefully examined, which serves as a reasonable picture for our observations. Our findings provide an inspiring strategy for the tunable active depletion force by crowding, activity, and chirality.

Human sperm uses asymmetric and anisotropic flagellar controls to regulate swimming symmetry and cell steering

Flagellar beating drives sperm through the female reproductive tract and is vital for reproduction. Flagellar waves are generated by thousands of asymmetric molecular components; yet, paradoxically, forward swimming arises via symmetric side-to-side flagellar movement. This led to the preponderance of symmetric flagellar control hypotheses. However, molecular asymmetries must still dictate the flagellum and be manifested in the beat. Here, we reconcile molecular and microscopic observations, reconnecting structure to function, by showing that human sperm uses asymmetric and anisotropic controls to swim. High-speed three-dimensional (3D) microscopy revealed two coactive transversal controls: An asymmetric traveling wave creates a one-sided stroke, and a pulsating standing wave rotates the sperm to move equally on all sides. Symmetry is thus achieved through asymmetry, creating the optical illusion of bilateral symmetry in 2D microscopy. This shows that the sperm flagellum is asymmetrically controlled and anisotropically regularized by fast-signal transduction. This enables the sperm to swim forward.

Bioinspired reorientation strategies for application in micro/nanorobotic control

Engineers have recently been inspired by swimming methodologies of microorganisms in creating micro-/nanorobots for biomedical applications. Future medicine may be revolutionized by the application of these small machines in diagnosing, monitoring, and treating diseases. Studies over the past decade have often concentrated on propulsion generation. However, there are many other challenges to address before the practical use of robots at the micro-/nanoscale. The control and reorientation ability of such robots remain as some of these challenges. This paper reviews the strategies of swimming microorganisms for reorientation, including tumbling, reverse and flick, direction control of helical-path swimmers, by speed modulation, using complex flagella, and the help of mastigonemes. Then, inspired by direction change in microorganisms, methods for orientation control for microrobots and possible directions for future studies are discussed. Further, the effects of solid boundaries on the swimming trajectories of microorganisms and microrobots are examined. In addition to propulsion systems for artificial microswimmers, swimming microorganisms are promising sources of control methodologies at the micro-/nanoscale.

Computer Aided Sperm Analysis (CASA) in domestic animals: Current status, three D tracking and flagellar analysis

Computer Aided Sperm Analysis is currently well established in domestic animals. Apart from sperm concentration and sperm motility assessment (percentage groupings, kinematics groupings) sperm morphology, sperm viability, sperm fragmentation and the acrosome reaction are automated as part of modern CASA systems. This review cum new original research paper focuses on providing baseline data on sperm concentration and motility in common domestic species of animals of proven fertility including bull, boar, horse, ram, goat, dog, donkey, chicken. There is a great need to establish quantitative baseline values for sperm quality, breed differences and to develop and apply relevant sperm functional tests that relates to fertilization outcome. These approaches need to be standardized. Two new approaches are presented in this work that are complimentary to CASA and provide a whole range of new visualizations and parameters that may assist to define sperm function and quality better. The first new approach shows how Two-D analysis using X and Y coordinates of CASA can be converted to Three-dimensional (3^D) tracks. This method shows how sperm movement can be visualized in 3^D despite several shortcomings. The second approach of flagellar analysis through the use of the FAST programme (Flagellar and Sperm Tracking) of the University of Birmingham group represents a new development and provides several new quantitative measures such as flagellar speed and energy output (in Watts) expended by each sperm. Together with CASA and other sperm functional parameters, FAST may provide new and novel insights in sperm biology and assist in fertility assessment.

High-resolution 4-D acquisition of freely swimming human sperm cells without staining

We present a new acquisition method that enables high-resolution, fine-detail full reconstruction of the three-dimensional movement and structure of individual human sperm cells swimming freely. We achieve both retrieval of the three-dimensional refractive-index profile of the sperm head, revealing its fine internal organelles and time-varying orientation, and the detailed four-dimensional localization of the thin, highly-dynamic flagellum of the sperm cell. Live human sperm cells were acquired during free swim using a high-speed off-axis holographic system that does not require any moving elements or cell staining. The reconstruction is based solely on the natural movement of the sperm cell and a novel set of algorithms, enabling the detailed four-dimensional recovery. Using this refractive-index imaging approach, we believe that we have detected an area in the cell that is attributed to the centriole. This method has great potential for both biological assays and clinical use of intact sperm cells.

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

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

Three dimensional spatiotemporal nano-scale position retrieval of the confined diffusion of nano-objects inside optofluidic microstructured fibers

Understanding the dynamics of single nano-scale species at high spatiotemporal resolution is of utmost importance within fields such as bioanalytics or microrheology. Here we introduce the concept of axial position retrieval via scattered light at evanescent fields inside a corralled geometry using optofluidic microstructured optical fibers allowing to unlock information about diffusing nano-scale objects in all three spatial dimensions at kHz acquisition rate for several seconds. Our method yields the lateral positions by localizing the particle in a wide-field microscopy image. In addition, the axial position is retrieved via the scattered light intensity of the particle, as a result of the homogenized evanescent fields inside a microchannel running parallel to an optical core. This method yields spatial localization accuracies <3 nm along the transverse and <21 nm along the retrieved directions. Due to its unique properties such as three dimensional tracking, straightforward operation, mechanical flexibility, strong confinement, fast and efficient data recording, long observation times, low background scattering, and compatibility with microscopy and fiber circuitry, our concept represents a new paradigm in light-based nanoscale detection techniques, extending the capabilities of the field of nanoparticle tracking analysis and potentially allowing for the observation of so far inaccessible processes at the nanoscale level.

Assembled superlattice with dynamic chirality in a mixture of biased-active and passive particles

We introduce a general model of biased-active particles (BAPs) with anisotropic interactions, where the direction of the active force has a nonzero biased angle from the principal orientation of the anisotropic interaction between particles, and investigate the self-assembly behaviors of a mixture of BAPs with passive particles by using Langevin dynamics simulations. Remarkably, a highly ordered superlattice consisting of small hexagonal clusters with dynamic chirality emerges within a proper range of active force, given that the biased angle is not too small. In addition, there exists an optimal level of particle activity, being dependent on the biased-angle, which is the most favorable for both the long-range order and global dynamic chirality of the system. Our results demonstrate that fascinating collective behaviors can be explored through a proper design of new active particle models.

Current perspectives of CASA applications in diverse mammalian spermatozoa

Since the advent of computer-aided sperm analysis (CASA) some four decades ago, advances in computer technology and software algorithms have helped establish it as a research and diagnostic instrument for the analysis of spermatozoa. Despite mammalian spermatozoa being the most diverse cell type known, CASA is a great tool that has the capacity to provide rapid, reliable and objective quantitative assessment of sperm quality. This paper provides contemporary research findings illustrating the scientific and commercial applications of CASA and its ability to evaluate diverse mammalian spermatozoa (human, primates, rodents, domestic mammals, wildlife species) at both structural and functional levels. The potential of CASA to quantitatively measure essential aspects related to sperm subpopulations, hyperactivation, morphology and morphometry is also demonstrated. Furthermore, applications of CASA are provided for improved mammalian sperm quality assessment, evaluation of sperm functionality and the effect of different chemical substances or pathologies on sperm fertilising ability. It is clear that CASA has evolved significantly and is currently superior to many manual techniques in the research and clinical setting.

3D imaging of sex-sorted bovine spermatozoon locomotion, head spin and flagellum beating

With the advent of sperm sex sorting methods and computer-aided sperm analysis platforms, comparative 2D motility studies showed that there is no significant difference in the swimming speeds of X-sorted and Y-sorted sperm cells, clarifying earlier misconceptions. However, other differences in their swimming dynamics might have been undetectable as conventional optical microscopes are limited in revealing the complete 3D motion of free-swimming sperm cells, due to poor depth resolution and the trade-off between field-of-view and spatial resolution. Using a dual-view on-chip holographic microscope, we acquired the full 3D locomotion of 235X-sorted and 289 Y-sorted bovine sperms, precisely revealing their 3D translational head motion and the angular velocity of their head spin as well as the 3D flagellar motion. Our results confirmed that various motility parameters remain similar between X- and Y-sorted sperm populations; however, we found out that there is a statistically significant difference in Y-sorted bovine sperms' preference for helix-shaped 3D swimming trajectories, also exhibiting an increased linearity compared to X-sorted sperms. Further research on e.g., the differences in the kinematic response of X-sorted and Y-sorted sperm cells to the surrounding chemicals and ions might shed more light on the origins of these results.

3-D Human Sperm Flagellum Tracing in Low SNR Fluorescence Images

Tracing tubular structures from biomedical images is important for a wide range of applications. Particularly, the spermatozoon is an essential cell whose flagella have a tubular form. Its main function is to fertilize the egg, and the flagellum is fundamental to achieve this task which depends importantly on the dynamics of intracellular calcium ([Ca²⁺]_i). Measuring [Ca²⁺]_i along the flagellum in 3-D is not a simple matter since it requires: 1) sophisticated fluorescence imaging techniques dealing with low intensity and signal to noise ratio (SNR) and 2) tracing the flagellum's centerline. Most of the algorithms proposed to trace tubular structures have been developed for multi-branch structures not being adequate for single tubular structures with low SNR. Taking into account the prior knowledge that the flagellum is constituted by a single tubular structure, we propose an automatic method to trace and track multiple single tubular structures from 3-D images. First, an algorithm based on one-class classification allows enhancement of the flagellum. This enhanced 3-D image permits guiding an iterative centerline algorithm toward the flagellum's centerline. Each sperm is assigned an ID to keep track of it in 3-D . Our algorithm was quantitatively evaluated using a ground truth 564 semi-manual traces (six 3-D image stacks) comparing them to those obtained from state-of-the-art tubular structure centerline extraction algorithms. The qualitative and quantitative results show that our algorithm is extracting similar traces as compared with ground truth, and it is more robust and accurate to trace the flagellum's centerline than multi-branch algorithms.

Computational imaging of sperm locomotion

Not only essential for scientific research, but also in the analysis of male fertility and for animal husbandry, sperm tracking and characterization techniques have been greatly benefiting from computational imaging. Digital image sensors, in combination with optical microscopy tools and powerful computers, have enabled the use of advanced detection and tracking algorithms that automatically map sperm trajectories and calculate various motility parameters across large data sets. Computational techniques are driving the field even further, facilitating the development of unconventional sperm imaging and tracking methods that do not rely on standard optical microscopes and objective lenses, which limit the field of view and volume of the semen sample that can be imaged. As an example, a holographic on-chip sperm imaging platform, only composed of a light-emitting diode and an opto-electronic image sensor, has emerged as a high-throughput, low-cost and portable alternative to lens-based traditional sperm imaging and tracking methods. In this approach, the sample is placed very close to the image sensor chip, which captures lensfree holograms generated by the interference of the background illumination with the light scattered from sperm cells. These holographic patterns are then digitally processed to extract both the amplitude and phase information of the spermatozoa, effectively replacing the microscope objective lens with computation. This platform has further enabled high-throughput 3D imaging of spermatozoa with submicron 3D positioning accuracy in large sample volumes, revealing various rare locomotion patterns. We believe that computational chip-scale sperm imaging and 3D tracking techniques will find numerous opportunities in both sperm related research and commercial applications.

Are there intracellular Ca2+ oscillations correlated with flagellar beating in human sperm? A three vs. two-dimensional analysis

STUDY QUESTION

Are there intracellular Ca2+ ([Ca2+]i) oscillations correlated with flagellar beating in human sperm?

SUMMARY ANSWER

The results reveal statistically significant [Ca2+]i oscillations that are correlated with the human sperm flagellar beating frequency, when measured in three-dimensions (3D).

WHAT IS KNOWN ALREADY

Fast [Ca2+]i oscillations that are correlated to the beating flagellar frequency of cells swimming in a restricted volume have been detected in hamster sperm. To date, such findings have not been confirmed in any other mammalian sperm species. An important question that has remained regarding these observations is whether the fast [Ca2+]i oscillations are real or might they be due to remaining defocusing effects of the Z component arising from the 3D beating of the flagella.

STUDY DESIGN, SIZE, DURATION

Healthy donors whose semen samples fulfill the WHO criteria between the age of 18-28 were selected. Cells from at least six different donors were utilized for analysis. Approximately the same number of experimental and control cells were analyzed.

PARTICIPANTS/MATERIALS, SETTING, METHODS

Motile cells were obtained by the swim-up technique and were loaded with Fluo-4 (Ca2+ sensitive dye) or with Calcein (Ca2+ insensitive dye). Ni2+ was used as a non-specific plasma membrane Ca2+ channel blocker. Fluorescence data and flagella position were acquired in 3D. Each cell was recorded for up to 5.6 s within a depth of 16 microns with a high speed camera (coupled to an image intensifier) acquiring at a rate of 3000 frames per second, while an oscillating objective vibrated at 90 Hz via a piezoelectric device. From these samples, eight experimental and nine control sperm cells were analyzed in both 2D and 3D.

MAIN RESULTS AND THE ROLE OF CHANCE

We have implemented a new system that allows [Ca2+]i measurements of the human sperm flagellum beating in 3D. These measurements reveal statistically significant [Ca2+]i oscillations that correlate with the flagellar beating frequency. These oscillations may arise from intracellular sources and/or Ca2+ transporters, as they were insensitive to external Ni2+, a non-specific plasma membrane Ca2+ channel blocker.

LARGE SCALE DATA

N/A.

LIMITATIONS REASONS FOR CAUTION

Analysis in 3D needs a very fast image acquisition rate to correctly sample a volume containing swimming sperm. This condition requires a very short exposure time per image making it necessary to use an image intensifier which also increases noise. The lengthy analysis time required to obtain reliable results limited the number of cells that could be analyzed.

WIDER IMPLICATIONS OF THE FINDINGS

The possibility of recording flagellar [Ca2+]i oscillations described here may open a new avenue to better understand ciliary and flagellar beating that are fundamental for mucociliary clearance, oocyte transport, fertilization, cerebrospinal fluid pressure regulation and developmental left-right symmetry breaking in the embryonic node.

STUDY FUNDING AND COMPETING INTEREST(S)

This work was supported by Consejo Nacional de Ciencia y Tecnología (CONACyT) (grants 253952 to G.C.; 156667 to F.M.M. and Fronteras 71 39908-Q to A.D. and Post-doctoral scholarships 366844 to P.H.-H. and 291028 to F.M.) and the Dirección General de Asuntos del Personal Académico of the Universidad Nacional Autónoma de México (DGAPA-UNAM) (grants CJIC/CTIC/4898/2016 to F.M. and IN205516 to A.D.). There are no conflicts of interest to declare.

Multi-Target Tracking of Human Spermatozoa in Phase-Contrast Microscopy Image Sequences using a Hybrid Dynamic Bayesian Network

Male infertility is mostly related to semen and spermatozoa, and any diagnosis or treatment requires the investigation of the motility patterns of spermatozoa. The movements of spermatozoa are fast and involve collision and occlusion with each other. In order to extract the motility patterns of spermatozoa, multi-target tracking (MTT) of spermatozoa is necessary. One of the most important steps of MTT is data association, in which the newly arrived observations are used to update the previous tracks. Dynamic Bayesian network (DBN) is a powerful tool for modeling and solving various types of problems such as tracking and classification. There can also be a hybrid-DBN (HDBN), in which both continuous and discrete nodes are present. HDBN has a suitable structure for modeling problems that have both discrete and continuous parameters like MTT. In this research, the data association for MTT of human spermatozoa has been studied. The proposed algorithm was tested over hundreds of manually extracted spermatozoa tracks and evaluated using several standard measures. The superior results of the proposed algorithm in comparison to the other well-known algorithms, show that it could be considered as an improved alternative to traditional computer assisted sperm analysis (CASA) algorithms.

In vivo three-dimensional tracking of sperm behaviors in the mouse oviduct

Mammalian sperm evolutionarily acquired complex mechanisms to regulate their behaviors, which are thought to be crucial in navigating through the female reproductive tract toward fertilization. However, all current knowledge of this process is largely extrapolated from in vitro and ex vivo studies, because in vivo analysis of sperm in their native fertilization environment has not been possible. Here, we report a functional optical coherence tomography approach that allows, for the first time, in vivo three-dimensional tracking of sperm behaviors in the mouse oviduct. Motile sperm are identified with their intrinsic dynamic characteristics. Sperm trajectories are reconstructed in three dimensions with a ∼5 µm spatial resolution, allowing for quantitative analysis of the sperm velocity and location relative to the oviduct. Using this method, we found different behavior patterns, including sperm collection by the oviduct epithelium, spatial dependence of sperm velocity, and sperm grouping and separation as the first in vivo evidence of sperm cooperation in the ampulla, the site of fertilization. This approach opens new avenues to study sperm-oviduct interactions in vivo toward a more complete understanding of fertility and reproductive disorders.

Label-free 3D computational imaging of spermatozoon locomotion, head spin and flagellum beating over a large volume

We report a high-throughput and label-free computational imaging technique that simultaneously measures in three-dimensional (3D) space the locomotion and angular spin of the freely moving heads of microswimmers and the beating patterns of their flagella over a sample volume more than two orders-of-magnitude larger compared to existing optical modalities. Using this platform, we quantified the 3D locomotion of 2133 bovine sperms and determined the spin axis and the angular velocity of the sperm head, providing the perspective of an observer seated at the moving and spinning sperm head. In this constantly transforming perspective, flagellum-beating patterns are decoupled from both the 3D translation and spin of the head, which provides the opportunity to truly investigate the 3D spatio-temporal kinematics of the flagellum. In addition to providing unprecedented information on the 3D locomotion of microswimmers, this computational imaging technique could also be instrumental for micro-robotics and sensing research, enabling the high-throughput quantification of the impact of various stimuli and chemicals on the 3D swimming patterns of sperms, motile bacteria and other micro-organisms, generating new insights into taxis behaviors and the underlying biophysics.

CASA: tracking the past and plotting the future

The human semen sample carries a wealth of information of varying degrees of accessibility ranging from the traditional visual measures of count and motility to those that need a more computational approach, such as tracking the flagellar waveform. Although computer-aided sperm analysis (CASA) options are becoming more widespread, the gold standard for clinical semen analysis requires trained laboratory staff. In this review we characterise the key attitudes towards the use of CASA and set out areas in which CASA should, and should not, be used and improved. We provide an overview of the current CASA landscape, discussing clinical uses as well as potential areas for the clinical translation of existing research technologies. Finally, we discuss where we see potential for the future of CASA, and how the integration of mathematical modelling and new technologies, such as automated flagellar tracking, may open new doors in clinical semen analysis.

A coordinated sequence of distinct flagellar waveforms enables a sharp flagellar turn mediated by squid sperm pH-taxis

Animal spermatozoa navigate by sensing ambient chemicals to reach the site of fertilization. Generally, such chemicals derive from the female reproductive organs or cells. Exceptionally, squid spermatozoa mutually release and perceive carbon dioxide to form clusters after ejaculation. We previously identified the pH-taxis by which each spermatozoon can execute a sharp turn, but how flagellar dynamics enable this movement remains unknown. Here, we show that initiation of the turn motion requires a swim down a steep proton gradient (a theoretical estimation of ≥0.025 pH/s), crossing a threshold pH value of ~5.5. Time-resolved kinematic analysis revealed that the turn sequence results from the rhythmic exercise of two flagellar motions: a stereotypical flagellar ‘bent-cane’ shape followed by asymmetric wave propagation, which enables a sharp turn in the realm of low Reynolds numbers. This turning episode is terminated by an ‘overshoot’ trajectory that differs from either straight-line motility or turning. As with bidirectional pH-taxes in some bacteria, squid spermatozoa also showed repulsion from strong acid conditions with similar flagellar kinematics as in positive pH-taxis. These findings indicate that squid spermatozoa might have a unique reorientation mechanism, which could be dissimilar to that of classical egg-guided sperm chemotaxis in other marine invertebrates.

Sperm Sensory Signaling

Fertilization is exceptionally complex and, depending on the species, happens in entirely different environments. External fertilizers in aquatic habitats, like marine invertebrates or fish, release their gametes into the seawater or freshwater, whereas sperm from most internal fertilizers like mammals cross the female genital tract to make their way to the egg. Various chemical and physical cues guide sperm to the egg. Quite generally, these cues enable signaling pathways that ultimately evoke a cellular Ca2+ response that modulates the waveform of the flagellar beat and, hence, the swimming path. To cope with the panoply of challenges to reach and fertilize the egg, sperm from different species have developed their own unique repertoire of signaling molecules and mechanisms. Here, we review the differences and commonalities for sperm sensory signaling in marine invertebrates (sea urchin), fish (zebrafish), and mammals (mouse, human).

The tailored sperm cell

Sperm are ubiquitous and yet unique. Genes involved in sexual reproduction are more divergent than most genes expressed in non-reproductive tissues. It has been argued that sperm have been altered during evolution more than any somatic cell. Profound variations are found at the level of morphology, motility, search strategy for the egg, and the underlying signalling mechanisms. Sperm evolutionary adaptation may have arisen from sperm competition (sperm from rival males compete within the female's body to fertilize eggs), cryptic female choice (the female's ability to choose among different stored sperm), social cues tuning sperm quality or from the site of fertilization (internal vs. external fertilization), to name a few. Unquestionably, sperm represent an invaluable source for the exploration of biological diversity at the level of signalling, motility, and evolution. Despite the richness in sperm variations, only a few model systems for signalling and motility have been studied in detail. Using fast kinetic techniques, electrophysiological recordings, and optogenetics, the molecular players and the sequence of signalling events of sperm from a few marine invertebrates, mammals, and fish are being elucidated. Furthermore, recent technological advances allow studying sperm motility with unprecedented precision; these studies provide new insights into flagellar motility and navigation in three dimensions (3D). The scope of this review is to highlight variations in motile sperm across species, and discuss the great promise that 3D imaging techniques offer into unravelling sperm mysteries.

Lagrangian 3D tracking of fluorescent microscopic objects in motion

We describe the development of a tracking device, mounted on an epi-fluorescent inverted microscope, suited to obtain time resolved 3D Lagrangian tracks of fluorescent passive or active micro-objects in microfluidic devices. The system is based on real-time image processing, determining the displacement of a x, y mechanical stage to keep the chosen object at a fixed position in the observation frame. The z displacement is based on the refocusing of the fluorescent object determining the displacement of a piezo mover keeping the moving object in focus. Track coordinates of the object with respect to the microfluidic device as well as images of the object are obtained at a frequency of several tenths of Hertz. This device is particularly well adapted to obtain trajectories of motile micro-organisms in microfluidic devices with or without flow.

Rapid, high-throughput tracking of bacterial motility in 3D via phase-contrast holographic video microscopy

Tracking fast-swimming bacteria in three dimensions can be extremely challenging with current optical techniques and a microscopic approach that can rapidly acquire volumetric information is required. Here, we introduce phase-contrast holographic video microscopy as a solution for the simultaneous tracking of multiple fast moving cells in three dimensions. This technique uses interference patterns formed between the scattered and the incident field to infer the three-dimensional (3D) position and size of bacteria. Using this optical approach, motility dynamics of multiple bacteria in three dimensions, such as speed and turn angles, can be obtained within minutes. We demonstrated the feasibility of this method by effectively tracking multiple bacteria species, including Escherichia coli, Agrobacterium tumefaciens, and Pseudomonas aeruginosa. In addition, we combined our fast 3D imaging technique with a microfluidic device to present an example of a drug/chemical assay to study effects on bacterial motility.

Investigating the Swimming of Microbial Pathogens Using Digital Holography

To understand much of the behaviour of microbial pathogens, it is necessary to image living cells, their interactions with each other and with host cells. Species such as Escherichia coli are difficult subjects to image: they are typically microscopic, colourless and transparent. Traditional cell visualisation techniques such as fluorescent tagging or phase-contrast microscopy give excellent information on cell behaviour in two dimensions, but no information about cells moving in three dimensions. We review the use of digital holographic microscopy for three-dimensional imaging at high speeds, and demonstrate its use for capturing the shape and swimming behaviour of three important model pathogens: E. coli, Plasmodium spp. and Leishmania spp.

Imaging of the 3D dynamics of flagellar beating in human sperm

The study of the mechanical and environmental factors that regulate a fundamental event such as fertilization have been subject of multiple studies. Nevertheless, the microscopical size of the spermatozoa and the high beating frequency of their flagella (up to 20 Hz) impose a series of technological challenges for the study of the mechanical factors implicated. Traditionally, due to the inherent characteristics of the rapid sperm movement, and to the technological limitations of microscopes (optical or confocal) to follow in three dimensions (3D) their movement, the analysis of their dynamics has been studied in two dimensions, when the head is confined to a surface. Flagella propel sperm and while their head can be confined to a surface, flagellar movement is not restricted to 2D, always displaying 3D components. In this work, we present a highly novel and useful tool to analyze sperm flagella dynamics in 3D. The basis of the method is a 100 Hz oscillating objective mounted on a bright field optical microscope covering a 16 microns depth space at a rate of ~ 5000 images per second. The best flagellum focused subregions were associated to their respective Z real 3D position. Unprecedented graphical results making evident the 3D movement of the flagella are shown in this work and supplemental material illustrating a 3D animation using the obtained experimental results is also included.

Sperm navigation along helical paths in 3D chemoattractant landscapes

Sperm require a sense of direction to locate the egg for fertilization. They follow gradients of chemical and physical cues provided by the egg or the oviduct. However, the principles underlying three-dimensional (3D) navigation in chemical landscapes are unknown. Here using holographic microscopy and optochemical techniques, we track sea urchin sperm navigating in 3D chemoattractant gradients. Sperm sense gradients on two timescales, which produces two different steering responses. A periodic component, resulting from the helical swimming, gradually aligns the helix towards the gradient. When incremental path corrections fail and sperm get off course, a sharp turning manoeuvre puts sperm back on track. Turning results from an ‘off' Ca²⁺ response signifying a chemoattractant stimulation decrease and, thereby, a drop in cyclic GMP concentration and membrane voltage. These findings highlight the computational sophistication by which sperm sample gradients for deterministic klinotaxis. We provide a conceptual and technical framework for studying microswimmers in 3D chemical landscapes.

Sperm use external cues to find the egg using ill-defined principles. Here the authors use holographic microscopy and optochemical tools to study sperm swimming in light-sculpted chemical 3D landscapes; they show that sperm translate the temporal stimulation pattern into multiple swimming behaviours to orient deterministically in a gradient.

Effect of non-Newtonian fluid properties on bovine sperm motility

The swimming process by which mammal spermatozoa progress towards an egg within the reproductive organs is important in achieving successful internal fertilization. The viscosity of oviductal mucus is more than two orders of magnitude greater than that of water, and oviductal mucus also has non-Newtonian properties. In this study, we experimentally observed sperm motion in fluids with various fluid rheological properties and investigated the influence of varying the viscosity and whether the fluid was Newtonian or non-Newtonian on the sperm motility. We selected polyvinylpyrrolidone and methylcellulose as solutes to create solutions with different rheological properties. We used the semen of Japanese cattle and investigated the following parameters: the sperm velocity, the straight-line velocity and the amplitude from the trajectory, and the beat frequency from the fragellar movement. In a Newtonian fluid environment, as the viscosity increased, the motility of the sperm decreased. However, in a non-Newtonian fluid, the straight-line velocity and beat frequency were significantly higher than in a Newtonian fluid with comparable viscosity. As a result, the linearity of the sperm movement increased. Additionally, increasing the viscosity brought about large changes in the sperm flagellar shape. At low viscosities, the entire flagellum moved in a curved flapping motion, whereas in the high-viscosity, only the tip of the flagellum flapped. These results suggest that the bovine sperm has evolved to swim toward the egg as quickly as possible in the actual oviduct fluid, which is a high-viscosity non-Newtonian fluid.

Disrupting the wall accumulation of human sperm cells by artificial corrugation

Many self-propelled microorganisms are attracted to surfaces. This makes their dynamics in restricted geometries very different from that observed in the bulk. Swimming along walls is beneficial for directing and sorting cells, but may be detrimental if homogeneous populations are desired, such as in counting microchambers. In this work, we characterize the motion of human sperm cells ∼60 μm long, strongly confined to ∼25 μm shallow chambers. We investigate the nature of the cell trajectories between the confining surfaces and their accumulation near the borders. Observed cell trajectories are composed of a succession of quasi-circular and quasi-linear segments. This suggests that the cells follow a path of intermittent trappings near the top and bottom surfaces separated by stretches of quasi-free motion in between the two surfaces, as confirmed by depth resolved confocal microscopy studies. We show that the introduction of artificial petal-shaped corrugation in the lateral boundaries removes the tendency of cells to accumulate near the borders, an effect which we hypothesize may be valuable for microfluidic applications in biomedicine.

A fully three-dimensional model of the interaction of driven elastic filaments in a Stokes flow with applications to sperm motility

In many animals, sperm flagella exhibit primarily planar waveforms. An isolated sperm with a planar flagellar beat in a three-dimensional unbounded fluid domain would remain in a plane. However, because sperm must navigate through complex, three-dimensional confined spaces along with other sperm, forces that bend or move the flagellum out of its current beat plane develop. Here we present an extension of previous models of an elastic sperm flagellar filament whose shape change is driven by the pursuit of a preferred curvature wave. In particular, we extend the energy of the generalized elastica to include a term that penalizes out-of-plane motion. We are now able to study the interaction of free-swimmers in a 3D Stokes flow that do not start out beating in the same plane. We demonstrate the three-dimensional nature of swimming behavior as neighboring sperm swim close to each other and affect each others' trajectories via fluid-structure coupling.

Chemotactic response with a constant delay-time mechanism in Ciona spermatozoa revealed by a high time resolution analysis of flagellar motility

During their chemotactic swimming toward eggs, sperm cells detect their species-specific chemoattractant and sense concentration gradients by unknown mechanisms. After sensing the attractant, sperm cells commonly demonstrate a series of responses involving different swimming patterns by changing flagellar beats, gradually approaching a swimming path toward the eggs, which is the source of chemoattractants. Shiba et al. observed a rapid increase in intracellular Ca(2+) concentrations in Ciona spermatozoa after sensing chemoattractants; however, the biochemical processes occurring inside the sperm cells are unclear. In the present study, we focused on the timing and sensing mechanism of chemical signal detection in Ciona. One of the most crucial problems to be solved is defining the initial epoch of chemotactic responses. We adopted a high rate of video recording (600 Hz) for detailed analysis of sperm motion and a novel method for detecting subtle signs of beat forms and moving paths of sperm heads. From these analyses, we estimated a virtual sensing point of the attractant before initiation of motility responses and found that the time delay from sensing to motility responses was almost constant. To evaluate the efficiency of this constant delay model, we performed computer simulation of chemotactic behaviors of Ciona spermatozoa.

Computer-assisted sperm analysis (CASA): capabilities and potential developments

Computer-assisted sperm analysis (CASA) systems have evolved over approximately 40 years, through advances in devices to capture the image from a microscope, huge increases in computational power concurrent with amazing reduction in size of computers, new computer languages, and updated/expanded software algorithms. Remarkably, basic concepts for identifying sperm and their motion patterns are little changed. Older and slower systems remain in use. Most major spermatology laboratories and semen processing facilities have a CASA system, but the extent of reliance thereon ranges widely. This review describes capabilities and limitations of present CASA technology used with boar, bull, and stallion sperm, followed by possible future developments. Each marketed system is different. Modern CASA systems can automatically view multiple fields in a shallow specimen chamber to capture strobe-like images of 500 to >2000 sperm, at 50 or 60 frames per second, in clear or complex extenders, and in <2 minutes, store information for ≥ 30 frames and provide summary data for each spermatozoon and the population. A few systems evaluate sperm morphology concurrent with motion. CASA cannot accurately predict 'fertility' that will be obtained with a semen sample or subject. However, when carefully validated, current CASA systems provide information important for quality assurance of semen planned for marketing, and for the understanding of the diversity of sperm responses to changes in the microenvironment in research. The four take-home messages from this review are: (1) animal species, extender or medium, specimen chamber, intensity of illumination, imaging hardware and software, instrument settings, technician, etc., all affect accuracy and precision of output values; (2) semen production facilities probably do not need a substantially different CASA system whereas biology laboratories would benefit from systems capable of imaging and tracking sperm in deep chambers for a flexible period of time; (3) software should enable grouping of individual sperm based on one or more attributes so outputs reflect subpopulations or clusters of similar sperm with unique properties; means or medians for the total population are insufficient; and (4) a field-use, portable CASA system for measuring one motion and two or three morphology attributes of individual sperm is needed for field theriogenologists or andrologists working with human sperm outside urban centers; appropriate hardware to capture images and process data apparently are available.

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.

Digital inline holographic microscopy (DIHM) of weakly-scattering subjects

Weakly-scattering objects, such as small colloidal particles and most biological cells, are frequently encountered in microscopy. Indeed, a range of techniques have been developed to better visualize these phase objects; phase contrast and DIC are among the most popular methods for enhancing contrast. However, recording position and shape in the out-of-imaging-plane direction remains challenging. This report introduces a simple experimental method to accurately determine the location and geometry of objects in three dimensions, using digital inline holographic microscopy (DIHM). Broadly speaking, the accessible sample volume is defined by the camera sensor size in the lateral direction, and the illumination coherence in the axial direction. Typical sample volumes range from 200 µm x 200 µm x 200 µm using LED illumination, to 5 mm x 5 mm x 5 mm or larger using laser illumination. This illumination light is configured so that plane waves are incident on the sample. Objects in the sample volume then scatter light, which interferes with the unscattered light to form interference patterns perpendicular to the illumination direction. This image (the hologram) contains the depth information required for three-dimensional reconstruction, and can be captured on a standard imaging device such as a CMOS or CCD camera. The Rayleigh-Sommerfeld back propagation method is employed to numerically refocus microscope images, and a simple imaging heuristic based on the Gouy phase anomaly is used to identify scattering objects within the reconstructed volume. This simple but robust method results in an unambiguous, model-free measurement of the location and shape of objects in microscopic samples.

The computational sperm cell

Sperm are guided to the egg by a gradient of chemical attractants - a process called chemotaxis. The binding of the chemoattractant to receptors on the surface of the flagellum triggers a cascade of signaling events that eventually lead to an influx of Ca(2+) ions. Based on these Ca(2+) surges, which control the waveform of the flagellar beat, sperm adjust their swimming path toward the egg. In past years, many components of chemotactic signaling have been identified. Moreover, kinetic spectroscopy and imaging techniques unraveled the sequence of cellular events controlling swimming behavior. During navigation in a chemical gradient, sperm perform a surprising variety of computational operations. Here we discuss theoretical concepts of navigation strategies and the cellular underpinnings.

Sperm trajectories form chiral ribbons

We report the discovery of an entirely new three-dimensional (3D) swimming pattern observed in human and horse sperms. This motion is in the form of ‘chiral ribbons’, where the planar swing of the sperm head occurs on an osculating plane creating in some cases a helical ribbon and in some others a twisted ribbon. The latter, i.e., the twisted ribbon trajectory, also defines a minimal surface, exhibiting zero mean curvature for all the points on its surface. These chiral ribbon swimming patterns cannot be represented or understood by already known patterns of sperms or other micro-swimmers. The discovery of these unique patterns is enabled by holographic on-chip imaging of >33,700 sperm trajectories at >90–140 frames/sec, which revealed that only ~1.7% of human sperms exhibit chiral ribbons, whereas it increases to ~27.3% for horse sperms. These results might shed more light onto the statistics and biophysics of various micro-swimmers' 3D motion.

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.

Acute slices of mice testis seminiferous tubules unveil spontaneous and synchronous Ca2+ oscillations in germ cell clusters

Spermatogenic cell differentiation involves changes in the concentration of cytoplasmic Ca(2+) ([Ca(2+)]i); however, very few studies exist on [Ca(2+)]i dynamics in these cells. Other tissues display Ca(2+) oscillations involving multicellular functional arrangements. These phenomena have been studied in acute slice preparations that preserve tissue architecture and intercellular communications. Here we report the implementation of intracellular Ca(2+) imaging in a sliced seminiferous tubule (SST) preparation to visualize [Ca(2+)]i changes of living germ cells in situ within the SST preparation. Ca(2+) imaging revealed that a subpopulation of male germ cells display spontaneous [Ca(2+)]i fluctuations resulting from Ca(2+) entry possibly throughout Ca(V)3 channels. These [Ca(2+)]i fluctuation patterns are also present in single acutely dissociated germ cells, but they differ from those recorded from germ cells in the SST preparation. Often, spontaneous Ca(2+) fluctuations of spermatogenic cells in the SST occur synchronously, so that clusters of cells can display Ca(2+) oscillations for at least 10 min. Synchronous Ca(2+) oscillations could be mediated by intercellular communication via gap junctions, although intercellular bridges could also be involved. We also observed an increase in [Ca(2+)]i after testosterone application, suggesting the presence of functional Sertoli cells in the SST. In summary, we believe that the SST preparation is suitable to explore the physiology of spermatogenic cells in their natural environment, within the seminiferous tubules, in particular Ca(2+) signaling phenomena, functional cell-cell communication, and multicellular functional arrangements.

High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories

Dynamic tracking of human sperms across a large volume is a challenging task. To provide a high-throughput solution to this important need, here we describe a lensfree on-chip imaging technique that can track the three-dimensional (3D) trajectories of > 1,500 individual human sperms within an observation volume of approximately 8-17 mm(3). This computational imaging platform relies on holographic lensfree shadows of sperms that are simultaneously acquired at two different wavelengths, emanating from two partially-coherent sources that are placed at 45° with respect to each other. This multiangle and multicolor illumination scheme permits us to dynamically track the 3D motion of human sperms across a field-of-view of > 17 mm(2) and depth-of-field of approximately 0.5-1 mm with submicron positioning accuracy. The large statistics provided by this lensfree imaging platform revealed that only approximately 4-5% of the motile human sperms swim along well-defined helices and that this percentage can be significantly suppressed under seminal plasma. Furthermore, among these observed helical human sperms, a significant majority (approximately 90%) preferred right-handed helices over left-handed ones, with a helix radius of approximately 0.5-3 μm, a helical rotation speed of approximately 3-20 rotations/s and a linear speed of approximately 20-100 μm/s. This high-throughput 3D imaging platform could in general be quite valuable for observing the statistical swimming patterns of various other microorganisms, leading to new insights in their 3D motion and the underlying biophysics.