Discrete dynamics model for the speract-activated Ca2+ signaling network relevant to sperm motility

Reviewing mathematical models of sperm signaling networks

Dave Garbers' work significantly contributed to our understanding of sperm's regulated motility, capacitation, and the acrosome reaction. These key sperm functions involve complex multistep signaling pathways engaging numerous finely orchestrated elements. Despite significant progress, many parameters and interactions among these elements remain elusive. Mathematical modeling emerges as a potent tool to study sperm physiology, providing a framework to integrate experimental results and capture functional dynamics considering biochemical, biophysical, and cellular elements. Depending on research objectives, different modeling strategies, broadly categorized into continuous and discrete approaches, reveal valuable insights into cell function. These models allow the exploration of hypotheses regarding molecules, conditions, and pathways, whenever they become challenging to evaluate experimentally. This review presents an overview of current theoretical and experimental efforts to understand sperm motility regulation, capacitation, and the acrosome reaction. We discuss the strengths and weaknesses of different modeling strategies and highlight key findings and unresolved questions. Notable discoveries include the importance of specific ion channels, the role of intracellular molecular heterogeneity in capacitation and the acrosome reaction, and the impact of pH changes on acrosomal exocytosis. Ultimately, this review underscores the crucial importance of mathematical frameworks in advancing our understanding of sperm physiology and guiding future experimental investigations.

Mathematical model reveals that heterogeneity in the number of ion transporters regulates the fraction of mouse sperm capacitation

Capacitation is a complex maturation process mammalian sperm must undergo in the female genital tract to be able to fertilize an egg. This process involves, amongst others, physiological changes in flagellar beating pattern, membrane potential, intracellular ion concentrations and protein phosphorylation. Typically, in a capacitation medium, only a fraction of sperm achieve this state. The cause for this heterogeneous response is still not well understood and remains an open question. Here, one of our principal results is to develop a discrete regulatory network, with mostly deterministic dynamics in conjunction with some stochastic elements, for the main biochemical and biophysical processes involved in the early events of capacitation. The model criterion for capacitation requires the convergence of specific levels of a select set of nodes. Besides reproducing several experimental results and providing some insight on the network interrelations, the main contribution of the model is the suggestion that the degree of variability in the total amount and individual number of ion transporters among spermatozoa regulates the fraction of capacitated spermatozoa. This conclusion is consistent with recently reported experimental results. Based on this mathematical analysis, experimental clues are proposed for the control of capacitation levels. Furthermore, cooperative and interference traits that become apparent in the modelling among some components also call for future theoretical and experimental studies.

Modularity in Biological Networks

Network modeling, from the ecological to the molecular scale has become an essential tool for studying the structure, dynamics and complex behavior of living systems. Graph representations of the relationships between biological components open up a wide variety of methods for discovering the mechanistic and functional properties of biological systems. Many biological networks are organized into a modular structure, so methods to discover such modules are essential if we are to understand the biological system as a whole. However, most of the methods used in biology to this end, have a limited applicability, as they are very specific to the system they were developed for. Conversely, from the statistical physics and network science perspective, graph modularity has been theoretically studied and several methods of a very general nature have been developed. It is our perspective that in particular for the modularity detection problem, biology and theoretical physics/network science are less connected than they should. The central goal of this review is to provide the necessary background and present the most applicable and pertinent methods for community detection in a way that motivates their further usage in biological research.

Discrete Dynamic Model of the Mammalian Sperm Acrosome Reaction: The Influence of Acrosomal pH and Physiological Heterogeneity

The acrosome reaction (AR) is an exocytotic process essential for mammalian fertilization. It involves diverse physiological changes (biochemical, biophysical, and morphological) that culminate in the release of the acrosomal content to the extracellular medium as well as a reorganization of the plasma membrane (PM) that allows sperm to interact and fuse with the egg. In spite of many efforts, there are still important pending questions regarding the molecular mechanism regulating the AR. Particularly, the contribution of acrosomal alkalinization to AR triggering physiological conditions is not well understood. Also, the dependence of the proportion of sperm capable of undergoing AR on the physiological heterogeneity within a sperm population has not been studied. Here, we present a discrete mathematical model for the human sperm AR based on the physiological interactions among some of the main components of this complex exocytotic process. We show that this model can qualitatively reproduce diverse experimental results, and that it can be used to analyze how acrosomal pH (pH a ) and cell heterogeneity regulate AR. Our results confirm that a pH a increase can on its own trigger AR in a subpopulation of sperm, and furthermore, it indicates that this is a necessary step to trigger acrosomal exocytosis through progesterone, a known natural inducer of AR. Most importantly, we show that the proportion of sperm undergoing AR is directly related to the detailed structure of the population physiological heterogeneity.

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

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

Modular analysis of the control of flagellar Ca2+-spike trains produced by CatSper and CaV channels in sea urchin sperm

Intracellular calcium ([Ca²⁺]_i) is a basic and ubiquitous cellular signal controlling a wide variety of biological processes. A remarkable example is the steering of sea urchin spermatozoa towards the conspecific egg by a spatially and temporally orchestrated series of [Ca²⁺]_i spikes. Although this process has been an experimental paradigm for reproduction and sperm chemotaxis studies, the composition and regulation of the signalling network underlying the cytosolic calcium fluctuations are hitherto not fully understood. Here, we used a differential equations model of the signalling network to assess which set of channels can explain the characteristic envelope and temporal organisation of the [Ca²⁺]_i-spike trains. The signalling network comprises an initial membrane hyperpolarisation produced by an Upstream module triggered by the egg-released chemoattractant peptide, via receptor activation, cGMP synthesis and decay. Followed by downstream modules leading to intraflagellar pH (pH_i), voltage and [Ca²⁺]_i fluctuations. The Upstream module outputs were fitted to kinetic data on cGMP activity and early membrane potential changes measured in bulk cell populations. Two candidate modules featuring voltage-dependent Ca²⁺-channels link these outputs to the downstream dynamics and can independently explain the typical decaying envelope and the progressive spacing of the spikes. In the first module, [Ca²⁺]_i-spike trains require the concerted action of a classical Ca_V-like channel and a potassium channel, BK (Slo1), whereas the second module relies on pH_i-dependent CatSper dynamics articulated with voltage-dependent neutral sodium-proton exchanger (NHE). We analysed the dynamics of these two modules alone and in mixed scenarios. We show that the [Ca²⁺]_i dynamics observed experimentally after sustained alkalinisation can be reproduced by a model featuring the CatSper and NHE module but not by those including the pH-independent Ca_V and BK module or proportionate mixed scenarios. We conclude in favour of the module containing CatSper and NHE and highlight experimentally testable predictions that would corroborate this conclusion.

Fertilisation in marine invertebrates, such as the sea urchin, occurs during broadcast spawning events in which males and females of co-localised species ejaculate sperm and spawn eggs synchronously. During these events, spermatozoa have to find and fertilise conspecific eggs in the midst of all the other ones, which is a remarkable navigation and mating choice achievement. Sperm cells do this by navigating towards the source of species-specific peptides released by the egg, steered by spatial and temporally orchestrated peaks in intracellular calcium concentration that trigger sudden reorientations. How these calcium spikes are regulated and timed remains elusive. Different calcium channels have been implicated by indirect experimental evidence giving rise to a complex network of putative interacting components. We gained insight into the structure and function of this network by modelling it as a set of candidate modules that could be studied separately. By using this ‘divide and conquer’ approach to the complexity of the network, we could characterise the potential dynamics of each module and confront these dynamics with specific quantitative data. Our results indicate that the channel mediating calcium signals in sea urchin sperm is likely CatSper, a calcium channel necessary for human male fertility.

The Molecular Mechanisms of Gametic Incompatibility in Invertebrates

Fertilization (gamete fusion followed by zygote formation) is a multistage process. Each stage is mediated by ligand-receptor recognition of gamete interaction molecules. This recognition includes the movement of sperm in the gradient of egg chemoattractants, destruction of the egg envelope by acrosomal proteins, etc. Gametic incompatibility is one of the mechanisms of reproductive isolation. It is based on species-specific molecular interactions that prevent heterospecific fertilization. Although gametic incompatibility may occur in any sexually reproducing organism, it has been studied only in a few model species. Gamete interactions in different taxa involve generally similar processes, but they often employ non-homologous molecules. Gamete recognition proteins evolve rapidly, like immunity proteins, and include many taxon-specific families. In fact, recently appeared proteins particularly contribute to reproductive isolation via gametic incompatibility. Thus, we can assume a multiple, independent origin of this type of reproductive isolation throughout animal evolution. Gametic incompatibility can be achieved at any fertilization stage and entails different consequences at different taxonomic levels and ranges, from complete incompatibility between closely related species to partial incompatibility between distantly related taxa.

Network model predicts that CatSper is the main Ca2+ channel in the regulation of sea urchin sperm motility

Spermatozoa sea urchin swimming behaviour is regulated by small peptides from the egg outer envelope. Speract, such a peptide, after binding to its receptor in Strongylocentrotus purpuratus sperm flagella, triggers a signaling pathway that culminates with a train of intracellular calcium oscillations, correlated with changes in sperm swimming pattern. This pathway has been widely studied but not fully characterized. Recent work on Arbacia punctulata sea urchin spermatozoa has documented the presence of the Ca²⁺ CatSper channel in their flagella and its involvement in chemotaxis. However, if other calcium channels participate in chemotaxis remains unclear. Here, based on an experimentally-backed logical network model, we conclude that CatSper is fundamental in the S. purpuratus speract-activated sea urchin sperm signaling cascade, although other Ca²⁺ channels could still be relevant. We also present for the first time experimental corroboration of its active presence in S. purpuratus sperm flagella. We argue, prompted by in silico knock-out calculations, that CatSper is the main generator of calcium oscillations in the signaling pathway and that other calcium channels, if present, have a complementary role. The approach adopted here allows us to unveil processes, which are hard to detect exclusively by experimental procedures.

Sodium affects the sperm motility in the European eel

The role of seminal plasma sodium and activation media sodium on sperm motility was examined by selectively removing the element from these two media, in European eel sperm. Sperm size (sperm head area) was also measured using an ASMA (Automated Sperm Morphometry Analyses) system, in the different conditions. Intracellular sodium [Na(+)]i was quantitatively analyzed by first time in the spermatozoa from a marine fish species. Measurement of [Na(+)]i was done before and after motility activation, by Flow Cytometry, using CoroNa Green AM as a dye. Sperm motility activation induced an increase in [Na(+)]i, from 96.72mM in quiescent stage to 152.21mM post-activation in seawater. A significant decrease in sperm head area was observed post-activation in seawater. There was a notable reduction in sperm motility when sodium was removed from the seminal plasma, but not when it was removed from the activation media. Sodium removal was also linked to a significant reduction in sperm head area in comparison to the controls. Our results indicate that the presence of the ion Na(+) in the seminal plasma (or in the extender medium) is necessary for the preservation of sperm motility in European eel, probably because it plays a role in maintaining an appropriate sperm cell volume in the quiescent stage of the spermatozoa.

In silico determination of the effect of multi-target drugs on calcium dynamics signaling network underlying sea urchin spermatozoa motility

The motility of spermatozoa of both Lytechinus pictus and Strongylocentrotus purpuratus sea urchin species is modulated by the egg-derived decapeptide speract via an oscillatory [Ca2+]-dependent signaling pathway. Comprehension of this pathway is hence directly related to the understanding of regulated sperm swimming. Niflumic acid (NFA), a nonsteroidal anti-inflammatory drug alters several ion channels. Though unspecific, NFA profoundly affects how sea urchin sperm respond to speract, increasing the [Ca2+]i oscillation period, amplitude, peak and average level values of the responses in immobilized and swimming cells. A previous logical network model we developed for the [Ca2+] dynamics of speract signaling cascade in sea urchin sperm allows integrated dissection of individual and multiple actions of NFA. Among the channels affected by NFA are: hyperpolarization-activated and cyclic nucleotide gated Na+ channels (HCN), [Ca2+]-dependent Cl- channels (CaCC) and [Ca2+]-dependent K+ channels (CaKC), all present in the sea urchin genome. Here, using our model we investigated the effect of blocking in silico HCN and CaCC channels suggested by experiments. Regarding CaKC channels, arguments can be provided for either their blockage or activation by NFA. Our study yielded two scenarios compliant with experimental observations: i) under CaKC inhibition, this [Ca2+]-dependent K+ channel should be different from the Slo1 channel and ii) under activation of the CaKC channel, another [Ca2+] channel not considered previously in the network is required, such as the pH-dependent CatSper channel. Additionally, our findings predict cause-effect relations resulting from a selective inhibition of those channels. Knowledge of these relations may be of consequence for a variety of electrophysiological studies and have an impact on drug related investigations. Our study contributes to a better grasp of the network dynamics and suggests further experimental work.

Soluble adenylyl cyclase of sea urchin spermatozoa

Fertilization, a key step in sexual reproduction, requires orchestrated changes in cAMP concentrations. It is notable that spermatozoa (sperm) are among the cell types with extremely high adenylyl cyclase (AC) activity. As production and consumption of this second messenger need to be locally regulated, the discovery of soluble AC (sAC) has broadened our understanding of how such cells deal with these requirements. In addition, because sAC is directly regulated by HCO(3)(-) it is able to translate CO₂/HCO(3)(-)/pH changes into cAMP levels. Fundamental sperm functions such as maturation, motility regulation and the acrosome reaction are influenced by cAMP; this is especially true for sperm of the sea urchin (SU), an organism that has been a model in the study of fertilization for more than 130 years. Here we summarize the discovery and properties of SU sperm sAC, and discuss its involvement in sperm physiology. This article is part of a Special Issue entitled: The role of soluble adenylyl cyclase in health and disease.

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.

Modeling of progesterone-induced intracellular calcium signaling in human spermatozoa

Calcium ion is a secondary messenger of mammalian spermatozoa. The dynamic change of its concentration plays a vital role in the process of sperm motility, capacitation, acrosome and fertilization. Progesterone released by the cumulus cells, as a potent stimulator of fertilization, can activate the calcium channels on the plasma membrane, which in turn triggers the dynamic change of intracellular calcium concentration. In this paper, a mathematical model of calcium dynamic response in mammalian spermatozoa induced by progesterone is proposed and numerical simulation of the dynamic model is conducted. The results show that the dynamic response of calcium concentration predicted by the model is in accordance with experimental evidence. The proposed dynamic model can be used to explain the phenomena observed in the experiments and predict new phenomena to be revealed by experimental investigations, which will provide the basis to quantitatively investigate the fluid mechanics and biochemistry for the sperm motility induced by progesterone.

Niflumic acid disrupts marine spermatozoan chemotaxis without impairing the spatiotemporal detection of chemoattractant gradients

In many broadcast-spawning marine organisms, oocytes release chemicals that guide conspecific spermatozoa towards their source through chemotaxis. In the sea urchin Lytechinus pictus, the chemoattractant peptide speract triggers a train of fluctuations of intracellular Ca2+ concentration in the sperm flagella. Each transient Ca2+ elevation leads to a momentary increase in flagellar bending asymmetry, known as a chemotactic turn. Furthermore, chemotaxis requires a precise spatiotemporal coordination between the Ca2+-dependent turns and the form of chemoattractant gradient. Spermatozoa that display Ca2+-dependent turns while swimming down the chemoattractant gradient, and conversely suppress turning events while swimming up gradient, successfully approach the center of the gradient. Previous experiments in Strongylocentrotus purpuratus sea urchin spermatozoa showed that niflumic acid (NFA), an inhibitor of several ion channels, drastically altered the speract-induced Ca2+ fluctuations and swimming patterns. In this study, mathematical modeling of the speract-dependent Ca2+ signaling pathway suggests that NFA, by potentially affecting HCN, CaCC and CaKC channels, may alter the temporal organization of Ca2+ fluctuations, and therefore disrupt chemotaxis. Here we investigate our hypothesis using a novel automated method for analyzing sperm behavior. We show that NFA does indeed disrupt chemotactic responses of L. pictus spermatozoa, although the temporal coordination between the Ca2+-dependent turns and the form of chemoattractant gradient is unaltered. Instead, NFA disrupts sperm chemotaxis by altering the arc length traveled during each chemotactic turning event. This alteration in the chemotactic turn trajectory disorientates spermatozoa at the termination of the turning event. We conclude that NFA disrupts chemotaxis without affecting how the spermatozoa decode environmental cues.

AMP-activated kinase AMPK is expressed in boar spermatozoa and regulates motility

The main functions of spermatozoa required for fertilization are dependent on the energy status and metabolism. AMP-activated kinase, AMPK, acts a sensor and regulator of cell metabolism. As AMPK studies have been focused on somatic cells, our aim was to investigate the expression of AMPK protein in spermatozoa and its possible role in regulating motility. Spermatozoa from boar ejaculates were isolated and incubated under different conditions (38,5°C or 17°C, basal medium TBM or medium with Ca(2+) and bicarbonate TCM, time from 1-24 hours) in presence or absence of AMPK inhibitor, compound C (CC, 30 µM). Western blotting reveals that AMPK is expressed in boar spermatozoa at relatively higher levels than in somatic cells. AMPK phosphorylation (activation) in spermatozoa is temperature-dependent, as it is undetectable at semen preservation temperature (17°C) and increases at 38,5°C in a time-dependent manner. AMPK phosphorylation is independent of the presence of Ca(2+) and/or bicarbonate in the medium. We confirm that CC effectively blocks AMPK phosphorylation in boar spermatozoa. Analysis of spermatozoa motility by CASA shows that CC treatment either in TBM or in TCM causes a significant reduction of any spermatozoa motility parameter in a time-dependent manner. Thus, AMPK inhibition significantly decreases the percentages of motile and rapid spermatozoa, significantly reduces spermatozoa velocities VAP, VCL and affects other motility parameters and coefficients. CC treatment does not cause additional side effects in spermatozoa that might lead to a lower viability even at 24 h incubation. Our results show that AMPK is expressed in spermatozoa at high levels and is phosphorylated under physiological conditions. Moreover, our study suggests that AMPK regulates a relevant function of spermatozoa, motility, which is essential for their ultimate role of fertilization.

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

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