Collective dynamics of sperm cells

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

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

Collective cell dynamics and luminal fluid flow in the epididymis: A mechanobiological perspective

BACKGROUND

The mammalian epididymis is a specialized duct system that serves a critical role in sperm maturation and storage. Its distinctive, highly coiled tissue morphology provides a unique opportunity to investigate the link between form and function in reproductive biology. Although recent genetic studies have identified key genes and signaling pathways involved in the development and physiological functions of the epididymis, there has been limited discussion about the underlying dynamic and mechanical processes that govern these phenomena.

AIMS

In this review, we aim to address this gap by examining two key aspects of the epididymis across its developmental and physiological phases.

RESULTS AND DISCUSSION

First, we discuss how the complex morphology of the Wolffian/epididymal duct emerges through collective cell dynamics, including duct elongation, cell proliferation, and arrangement during embryonic development. Second, we highlight dynamic aspects of luminal fluid flow in the epididymis, essential for regulating the microenvironment for sperm maturation and motility, and discuss how this phenomenon emerges and interplays with epididymal epithelial cells.

CONCLUSION

This review not only aims to summarize current knowledge but also to provide a starting point for further exploration of mechanobiological aspects related to the cellular and extracellular fluid dynamics in the epididymis.

The tri-flow adaptiveness of codes in major evolutionary transitions

Life codes increase in both number and variety with biological complexity. Although our knowledge of codes is constantly expanding, the evolutionary progression of organic, neural, and cultural codes in response to selection pressure remains poorly understood. Greater clarification of the selective mechanisms is achieved by investigating how major evolutionary transitions reduce spatiotemporal and energetic constraints on transmitting heritable code to offspring. Evolution toward less constrained flows is integral to enduring flow architecture everywhere, in both engineered and natural flow systems. Beginning approximately 4 billion years ago, the most basic level for transmitting genetic material to offspring was initiated by protocell division. Evidence from ribosomes suggests that protocells transmitted comma-free or circular codes, preceding the evolution of standard genetic code. This rudimentary information flow within protocells is likely to have first emerged within the geo-energetic and geospatial constraints of hydrothermal vents. A broad-gauged hypothesis is that major evolutionary transitions overcame such constraints with tri-flow adaptations. The interconnected triple flows incorporated energy-converting, spatiotemporal, and code-based informational dynamics. Such tri-flow adaptations stacked sequence splicing code on top of protein-DNA recognition code in eukaryotes, prefiguring the transition to sexual reproduction. Sex overcame the spatiotemporal-energetic constraints of binary fission with further code stacking. Examples are tubulin code and transcription initiation code in vertebrates. In a later evolutionary transition, language reduced metabolic-spatiotemporal constraints on inheritance by stacking phonetic, phonological, and orthographic codes. In organisms that reproduce sexually, each major evolutionary transition is shown to be a tri-flow adaptation that adds new levels of code-based informational exchange. Evolving biological complexity is also shown to increase the nongenetic transmissibility of code.

Synchronization of Sakaguchi swarmalators

Swarmalators are phase oscillators that cluster in space, like fireflies flashing in a swarm to attract mates. Interactions between particles, which tend to synchronize their phases and align their motion, decrease with the distance and phase difference between them, coupling the spatial and phase dynamics. In this work, we explore the effects of inducing phase frustration on a system of swarmalators that move on a one-dimensional ring. Our model is inspired by the well-known Kuramoto-Sakaguchi equations. We find, numerically and analytically, the ordered and disordered states that emerge in the system. The active states, not present in the model without frustration, resemble states found previously in numerical studies for the two-dimensional swarmalators system. One of these states, in particular, shows similarities to turbulence generated in a flattened media. We show that all ordered states can be generated for any values of the coupling constants by tuning the phase frustration parameters only. Moreover, many of these combinations display multistability.

Biological benefits of collective swimming of sperm in a viscoelastic fluid

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

Conservation Biology and Reproduction in a Time of Developmental Plasticity

The objective of this review is to ask whether, and how, principles in conservation biology may need to be revisited in light of new knowledge about the power of epigenetics to alter developmental pathways. Importantly, conservation breeding programmes, used widely by zoological parks and aquariums, may appear in some cases to reduce fitness by decreasing animals' abilities to cope when confronted with the 'wild side' of their natural habitats. Would less comfortable captive conditions lead to the selection of individuals that, despite being adapted to life in a captive environment, be better able to thrive if relocated to a more natural environment? While threatened populations may benefit from advanced reproductive technologies, these may actually induce undesirable epigenetic changes. Thus, there may be inherent risks to the health and welfare of offspring (as is suspected in humans). Advanced breeding technologies, especially those that aim to regenerate the rarest species using stem cell reprogramming and artificial gametes, may also lead to unwanted epigenetic modifications. Current knowledge is still incomplete, and therefore ethical decisions about novel breeding methods remain controversial and difficult to resolve.

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

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

Postcopulatory sexual selection is associated with sperm aggregate quality in Peromyscus mice

In some species, sperm form coordinated groups that are hypothesized to improve their swimming performance in competitive contexts or to navigate through the viscous fluids of the female reproductive tract. Here we investigate sperm aggregation across closely related species of Peromyscus mice that naturally vary by mating system to test the predictions that sperm aggregates 1) are faster than solitary sperm in species that females mate multiply to aid cells in sperm competition, and 2) outperform solitary sperm cells in viscous environments. We find significant variation in the size of sperm aggregates, which negatively associates with relative testis mass, a proxy for sperm competition risk, suggesting that postcopulatory sexual selection has a stabilizing effect on sperm group size. Moreover, our results show that sperm aggregates are faster than solitary sperm in some, but not all, species, and this can vary by fluid viscosity. Of the two species that produce the largest and most frequent groups, we find that sperm aggregates from the promiscuous P. maniculatus are faster than solitary sperm in every experimentally viscous environment but aggregation provides no such kinematic advantage under these same conditions for the monogamous P. polionotus. The reduced performance of P. polionotus aggregates is associated with less efficient aggregate geometry and the inclusion of immotile or morphological abnormal sperm. Our cross-species comparison yields insight into the evolution of sperm social behaviors, provides evidence of extensive variation in the Peromyscus lineage, and reveals that differences in sperm aggregate quality associate with postcopulatory sexual selection.

Recent Progress in Spermatology Contributing to the Knowledge and Conservation of Rare and Endangered Species

There is a remarkable diversity in the animal kingdom regarding mechanisms underlying the production, maturation, structure, and function of sperm cells. Spermatology studies contribute to the knowledge of species diversity and also provide information about individual or population fitness. Furthermore, this fundamental research is required before collected spermatozoa can be used for conservation breeding, including assisted reproduction and cryobanking. This article aims to (a) review the most recent knowledge on sperm morphology and function in wild animal species, (b) analyze how this knowledge can be used to save species in their natural habitat or ex situ, and (c) propose future scientific directions in wildlife spermatology that could positively impact animal conservation. Variations in sperm structure and performance within and between species have multiple origins and significance. This collective body of knowledge enables the design and implementation of conservation strategies and action plans that integrate several disciplines. Expected final online publication date for the Annual Review of Animal Biosciences, Volume 10 is February 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

The social shape of sperm: using an integrative machine-learning approach to examine sperm ultrastructure and collective motility

Sperm is one of the most morphologically diverse cell types in nature, yet they also exhibit remarkable behavioural variation, including the formation of collective groups of cells that swim together for motility or transport through the female reproductive tract. Here, we take advantage of natural variation in sperm traits observed across Peromyscus mice to test the hypothesis that the morphology of the sperm head influences their sperm aggregation behaviour. Using both manual and automated morphometric approaches to quantify their complex shapes, and then statistical modelling and machine learning to analyse their features, we show that the aspect ratio of the sperm head is the most distinguishing morphological trait and statistically associates with collective sperm movements obtained from in vitro observations. We then successfully use neural network analysis to predict the size of sperm aggregates from sperm head morphology and show that species with relatively wider sperm heads form larger aggregates, which is consistent with the theoretical prediction that an adhesive region around the equatorial region of the sperm head mediates these unique gametic interactions. Together these findings advance our understanding of how even subtle variation in sperm design can drive differences in sperm function and performance.

MODELING OF FLAGELLUM BEHAVIOR AND TWO-DIMENSIONAL SPERM CELL MOTILITY WITHIN THE CONTEXT OF FLUID–SOLID INTERACTIONS

In this study, the flagellar motility of a swimmer microorganism as a model of a human sperm cell, inside a two-dimensional channel as a model of the female reproductive tract containing a viscous fluid, is numerically investigated. The Navier–Stokes equations governing the fluid are coupled with the equations governing the models flagellum via applying a fluid–solid interaction approach and then solved using the finite element method. To stimulate the flagellum to move, a prescribed sinusoidal waveform is applied to it. The strain induced by this waveform along the flagellum initiates a continuous interaction between the flagellum and the fluid. The simulations are validated using data available in the literature. A very good agreement is seen between them. The results show that by decreasing the Young modulus of the flagellum as well as increasing the fluid viscosity, the swimming velocity of the model significantly decreases. It is found that for lower Young modulus of the flagellum, the effect of the fluid viscosity on the flagellar deformation is stronger. It is also found that for higher amplitude of the waveform applied to stimulate the flagellum, both the swimming velocity of the model and the average work rate are greater. Moreover, it is found that in a channel with a smaller height, the model swims at a higher speed and with a higher average work rate.

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.

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

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

Multi-scale analysis and modelling of collective migration in biological systems

Collective migration has become a paradigm for emergent behaviour in systems of moving and interacting individual units resulting in coherent motion. In biology, these units are cells or organisms. Collective cell migration is important in embryonic development, where it underlies tissue and organ formation, as well as pathological processes, such as cancer invasion and metastasis. In animal groups, collective movements may enhance individuals' decisions and facilitate navigation through complex environments and access to food resources. Mathematical models can extract unifying principles behind the diverse manifestations of collective migration. In biology, with a few exceptions, collective migration typically occurs at a 'mesoscopic scale' where the number of units ranges from only a few dozen to a few thousands, in contrast to the large systems treated by statistical mechanics. Recent developments in multi-scale analysis have allowed linkage of mesoscopic to micro- and macroscopic scales, and for different biological systems. The articles in this theme issue on 'Multi-scale analysis and modelling of collective migration' compile a range of mathematical modelling ideas and multi-scale methods for the analysis of collective migration. These approaches (i) uncover new unifying organization principles of collective behaviour, (ii) shed light on the transition from single to collective migration, and (iii) allow us to define similarities and differences of collective behaviour in groups of cells and organisms. As a common theme, self-organized collective migration is the result of ecological and evolutionary constraints both at the cell and organismic levels. Thereby, the rules governing physiological collective behaviours also underlie pathological processes, albeit with different upstream inputs and consequences for the group. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.