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.

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.

Absolute proteomic quantification reveals design principles of sperm flagellar chemosensation

Cilia serve as cellular antennae that translate sensory information into physiological responses. In the sperm flagellum, a single chemoattractant molecule can trigger a Ca2+ rise that controls motility. The mechanisms underlying such ultra-sensitivity are ill-defined. Here, we determine by mass spectrometry the copy number of nineteen chemosensory signaling proteins in sperm flagella from the sea urchin Arbacia punctulata. Proteins are up to 1,000-fold more abundant than the free cellular messengers cAMP, cGMP, H+ , and Ca2+ . Opto-chemical techniques show that high protein concentrations kinetically compartmentalize the flagellum: Within milliseconds, cGMP is relayed from the receptor guanylate cyclase to a cGMP-gated channel that serves as a perfect chemo-electrical transducer. cGMP is rapidly hydrolyzed, possibly via "substrate channeling" from the channel to the phosphodiesterase PDE5. The channel/PDE5 tandem encodes cGMP turnover rates rather than concentrations. The rate-detection mechanism allows continuous stimulus sampling over a wide dynamic range. The textbook notion of signal amplification-few enzyme molecules process many messenger molecules-does not hold for sperm flagella. Instead, high protein concentrations ascertain messenger detection. Similar mechanisms may occur in other small compartments like primary cilia or dendritic spines.

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.

Individual female differences in chemoattractant production change the scale of sea urchin gamete interactions

Sperm selection by females is an important process influencing fertilization and, particularly in broadcast-spawning organisms, often occurs before sperm reach the egg. Waterborne sperm chemoattractants are one mechanism by which eggs selectively influence conspecific sperm behavior, but it remains an open question whether the eggs from different females produce different amounts of sperm chemoattractant, and how that might influence sperm behavior. Here, we quantify the differences in attractant production between females of the sea urchin species Lytechinus pictus and use computational models and microfluidic sperm chemotaxis assays to determine how differences in chemoattractant production between females affects their ability to attract sperm. Our study demonstrates that there is significant individual female variation in egg chemoattractant production, and that this variation changes the scope and strength of sperm attraction. These results provide evidence for the importance of individual female variability in differential sperm attraction and fertilization success.

Chang's meaning of capacitation: A molecular perspective

Dr. Min Chue Chang's contributions to the field of reproductive biology set the stage for the development of the contraceptive pill and in vitro fertilization. Throughout his publications, Dr. Chang was also able to transmit his view of the fertilization process in ways that organized research for newer generations of reproductive biologists. Particularly relevant for the achievement of in vitro fertilization in mammals was the discovery that the sperm required a period of residence in the female tract to become fertilization-competent; Dr. Chang and Dr. Austin, in Australia, independently reported this process, now known as sperm capacitation. This review discusses Dr. Chang's views on capacitation, and puts them in the context of recent advances in the understanding of the molecular basis of this process. Mol. Reprod. Dev. 83: 860-874, 2016 © 2016 Wiley Periodicals, Inc.

Speract, a sea urchin egg peptide that regulates sperm motility, also stimulates sperm mitochondrial metabolism

Sea urchin sperm have only one mitochondrion, that in addition to being the main source of energy, may modulate intracellular Ca(2+) concentration ([Ca(2+)]i) to regulate their motility and possibly the acrosome reaction. Speract is a decapeptide from the outer jelly layer of the Strongylocentrotus purpuratus egg that upon binding to its receptor in the sperm, stimulates sperm motility, respiration and ion fluxes, among other physiological events. Altering the sea urchin sperm mitochondrial function with specific inhibitors of this organelle, increases [Ca(2+)]i in an external Ca(2+) concentration ([Ca(2+)]ext)-dependent manner (Ardón, et al., 2009. BBActa 1787: 15), suggesting that the mitochondrion is involved in sperm [Ca(2+)]i homeostasis. To further understand the interrelationship between the mitochondrion and the speract responses, we measured mitochondrial membrane potential (ΔΨ) and NADH levels. We found that the stimulation of sperm with speract depolarizes the mitochondrion and increases the levels of NADH. Surprisingly, these responses are independent of external Ca(2+) and are due to the increase in intracellular pH (pHi) induced by speract. Our findings indicate that speract, by regulating pHi, in addition to [Ca(2+)]i, may finely modulate mitochondrial metabolism to control motility and ensure that sperm reach the egg and fertilize it.

Sperm chemotaxis promotes individual fertilization success in sea urchins

Reproductive success fundamentally shapes an organism's ecology and evolution, and gamete traits mediate fertilization, which is a critical juncture in reproduction. Individual male fertilization success is dependent on the ability of sperm from one male to outcompete the sperm of other males when searching for a conspecific egg. Sperm chemotaxis, the ability of sperm to navigate towards eggs using chemical signals, has been studied for over a century, but such studies have long assumed that this phenomenon improves individual male fitness without explicit evidence to support this claim. Here, we assess fertilization changes upon use of a chemoattractant-digesting peptidase and use a microfluidic device coupled with a fertilization assay to determine the effect of sperm chemotaxis on individual male fertilization success in the sea urchin Lytechinus pictus. We show that removing chemoattractant from the gametic environment decreases fertilization success. We further find that individual male differences in chemotaxis to a well-defined gradient of attractant correlate with individual male differences in fertilization success. These results demonstrate that sperm chemotaxis is an important contributor to individual reproductive success.

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.