Abstract
Spermatozoa are attracted to their conspecific female gamete by diffusive molecules released from the egg investments in a process called chemotaxis. The decapeptide speract induces metabolic and permeability changes in Strongylocentrotus purpuratus sea urchin sperm. In the decades since speract purification from S. purpuratus egg investments, sperm chemotaxis has not been demonstrated in this species. By studying how the stimulus function, which spermatozoa experience during the accumulation of bound chemoattractants throughout their trajectory, influences both their motility response and their internal Ca2+ oscillations, we were able to show that S. purpuratus spermatozoa exhibit chemotaxis under sufficiently steep speract concentration gradients. We demonstrate that this process arises through frequency entrainment of the coupled metabolic oscillators.
Introduction
Broadcast spawning organisms, such as marine invertebrates, release their gametes into open sea, where they are often subject to extensive dilution that reduces the probability of gamete encounter (Lotterhos et al., 2010). In many marine organisms, female gametes release diffusible molecules that attract homologous spermatozoa (Lillie, 1913; Miller, 1985; Suzuki, 1995). Propelled by their beating flagella, spermatozoa detect and respond to chemoattractant concentration gradients by steering their swimming trajectory toward the gradient source: the egg. Though it was in bracken ferns where sperm chemotaxis was first identified (Pfeffer, 1884), sea urchins are currently the best-characterized model system for studying sperm chemotaxis at a molecular level (Alvarez et al., 2012; Cook et al., 1994; Darszon et al., 2008; Strünker et al., 2015; Wood et al., 2015).
The sea urchin egg is surrounded by an extracellular matrix which contains short sperm-activating peptides (SAPs), that modulate sperm motility through altering intracellular Ca2+ concentration ([Ca2+]i) and other signaling intermediates (Darszon et al., 2008; Suzuki, 1995). The probability of sperm-egg encounter is enhanced by the prompt transduction of the biochemical signals triggered by SAPs into the appropriate reorientation of the sperm trajectory.
The decapeptide speract is one of best characterized members of the SAP family due to its powerful stimulating effect on metabolism, permeability and motility in Strongylocentrotus purpuratus and Lytechinus pictus spermatozoa. The binding of speract to its receptor located in the flagellar plasma membrane, triggers a train of [Ca2+]i increases in immobilized S. purpuratus spermatozoa (Wood et al., 2003). This calcium signal was proposed to regulate the activity of dynein motor proteins in the flagellum, and thus potentially modulate the trajectory of free-swimming spermatozoa (Brokaw, 1979).
A direct link between [Ca2+]i signaling and sperm motility was established through the use of optochemical techniques to rapidly, and non-turbulently, expose swimming sea urchin spermatozoa to their conspecific attractant in a well-controlled experimental regime (Böhmer et al., 2005; Wood et al., 2005). Currently, it is well established that the transient [Ca2+]i increases triggered by chemoattractants produce a sequence of turns and straight swimming episodes (turn-and-run), where each turning event results from the rapid increase in the [Ca2+]i (Alvarez et al., 2012; Böhmer et al., 2005; Shiba et al., 2008; Wood et al., 2005). The turn-and-run response seems to be a general requirement for sperm chemotaxis in sea urchins, however it is not sufficient on its own to produce a chemotactic response (Guerrero et al., 2010; Strünker et al., 2015; Wood et al., 2007, 2005).
Our current understanding of chemotaxis, suggests that sperm first sample the chemoattractant concentration gradient while swimming in periodic paths (either circular 2D or helical 3D). During the sampling phase, the accumulation of bound chemoattractants triggers [Ca2+]i transients that control the symmetry of the waveform of the flagellar beat. In this way, the alternate periods of asymmetrical (turn) and symmetrical (run) flagellar beating give rise to a looping swimming pattern that guides cells to the source of the chemoattractant gradient.
Friedrich and Jülicher proposed a generic theory that captures the essence of sperm navigation following periodic paths in a non-homogeneous chemoattractant field, in which the sampling of a periodic concentration stimulus s(t) is translated by intracellular signaling i(t) into the periodic modulation of the swimming path curvature k(t) (Friedrich and Jülicher, 2008, 2007). As result, the periodic swimming path drifts in a direction that depends on the internal dynamics of the signaling system. In this theory, the latency of the intracellular signaling (i.e. the [Ca2+]i signal), expressed as the phase shift between s(t) and k(t), is a crucial determinant of the directed looping of the swimming trajectory up the chemical concentration field. This theory also predicts that chemotaxis is a robust property of the system that does not require fine-tuning of parameters if the signaling system is adaptive (Friedrich and Jülicher, 2009, 2008). In other words, there is a large range of parameters for which sperm chemotaxis is a robust outcome, providing an effective way for sampling the local chemoattractant concentration field and detecting the direction of the concentration gradient (Friedrich and Jülicher, 2008, 2007; Kashikar et al., 2012; Kaupp et al., 2003; Pichlo et al., 2014).
Even though the conceptual framework of Friedrich & Jülicher provides insights into the mechanism governing sperm chemotaxis, it does not explore the scenario whereby chemoattractants trigger an autonomous [Ca2+]i oscillator operating in the absence of a periodic stimulus. The existence of an autonomous [Ca2+]i oscillator triggered by chemoattractants (Aguilera et al., 2012; Espinal et al., 2011; Wood et al., 2003) suggests that sperm chemotaxis might operate in a dynamical space where two autonomous oscillators, namely the stimulus function and the internal Ca2+ oscillator, reach frequency entrainment.
In spite of 30 years of research since speract’s isolation from S. purpuratus oocytes (Hansbrough and Garbers, 1981; Suzuki, 1995), chemotaxis of S. purpuratus sperm towards this peptide has not yet been demonstrated (Cook et al., 1994; Darszon et al., 2008; Guerrero et al., 2010; Kaupp, 2012; Miller, 1985; Wood et al., 2015). A comparison between individual L. pictus and S. purpuratus sperm responses to a specific chemoattractant concentration gradient generated by photoactivating caged speract (CS) revealed that only L. pictus spermatozoa exhibit chemotaxis under these conditions (Guerrero et al., 2010). In that study, L. pictus spermatozoa experience [Ca2+]i fluctuations and pronounced turns while swimming in descending speract gradients, that result in spermatozoa reorienting their swimming behavior along the positive chemoattractant concentration gradient. In contrast, S. purpuratus spermatozoa experience similar trains of [Ca2+]i fluctuations that in turn drive them to relocate, but with no preference towards the center of the chemoattractant gradient (Guerrero et al., 2010).
In the present work, we investigate whether S. purpuratus spermatozoa can undergo chemotaxis. Particularly, we examined whether the chemoattractant concentration gradient has to have a minimum steepness to be adequately detected. If true, this limit may have prevented the observation and characterization of their chemotactic response to date. We report that S. purpuratus spermatozoa are chemotactic only when exposed to much steeper speract concentration gradients than those previously employed. Furthermore, we have explored the coupling between the recruitment of speract molecules during sperm translation, and the internal Ca2+ oscillator; and demonstrate that sperm chemotaxis arises through coupled metabolic oscillators.
Results
Constraints upon the detection of chemoattractant concentration fields
To examine why so far S. purpuratus spermatozoa have not been shown to be chemotactic, we asked ourselves what limits this response? The challenge for a sperm that must swim towards higher stimulus intensities (i.e. up a chemoattractant concentration gradient) is to determine the direction in which the intensity increases or decreases during its journey (Dusenbery, 2011). To do so, the minimum requirement is to detect the intensity of the stimulus at two distinct locations, and act on the expectation that the gradient continues beyond the limits of the measurement (Figure 1a).
To reliably measure a concentration gradient of chemoattractant, this difference in binding events detected by the spermatozoon in the measurement interval must be above the noise level (Figure 1a). Considering the biophysical constraints of the case in question, the probability that a spermatozoon has to detect a gradient of diffusible molecules depends of the sperm velocity (v), the sampling time (tint), the number of receptors (N), the radius of the receptor binding pocket (s), the size of the cell (a), the diffusion constant of the chemoattractant (D), the concentration of the chemoattractant (c), and the slope of the chemoattractant gradient (ξ) (Figure 1a, Table S1, for further explanation see Theory 2.4. Uncertainty in the detection of a chemoattractant concentration fields, in supplementary materials). The associated uncertainty to reliable determine the direction of the chemoattractant gradient u2, can be expressed as:
Equation (1) indicates that the slope of the chemoattractant concentration gradient, ξ = dc/dr, directly impinges on the ability to reliably determine the source of the attractant, being indirectly proportional to the uncertainty. In other words, the uncertainty associated with the detection of a large (i.e. steep) gradient is very low, and vice versa. The quantity ξ has units of concentration over distance, and it is indicative of the strength of the stimuli received when sampling a particular location r1 and r2, each with a given chemoattractant concentration c1 and c2 (Figure 1a). Typically, dc = c2 − c1 is in the order of picomolar and dr = r2 − r1 in microns. As ξ increases, the strength of chemotactic signal increases. In contrast, homogeneous concentration gradients are characterized by c1 ~ c2, hence there is no positional information for sperm guidance, where dc → 0.
The least fractional error attainable in the determination of chemoattractant gradient direction u2, has no upper boundary, however values greater than 1 indicate that stochastic fluctuations dominate over the signal. For simplicity, u2 will be considered to operate in the range [0, 1].
We modeled the uncertainties for different gradients (10−11 to 10−6 M) for the three sea urchin species. At high concentrations of speract (10−8 to 10−6 M) the change in receptor occupancy experienced by L. pictus spermatozoa, at two given distinct locations, allows the reliable assessment of relatively shallow chemical gradients, with u2 below 0.01 for a wide range of ξ (Figure 1c). However, at low concentrations of speract (below 10−10 M), keeping all other parameters equal, stochastic fluctuations tend to dominate over the signal. In this low-concentration regime, the slope of the chemoattractant gradient is determinant. Shallow gradients (ξ < 10−12 M μm−1) increase the uncertainty for detection of gradient polarity, while steeper chemoattractant gradients allow L. pictus spermatozoa to determine the orientation of the chemical gradient dependably (Figure 1c, orange and brown lines with u2 < 1%). In contrast to L. pictus, taking into account the previous considerations, S. purpuratus spermatozoa can only determine the orientation of the chemical gradient for high enough speract concentrations and steep, but not shallow, concentration gradients (Figure 1b, only orange line with u2 < 1%).
Noteworthy, our calculations indicate that in S. purpuratus and L. pictus spermatozoa act in a regime where the rate of chemoattractant uptake is slower than diffusion, then they cannot be considered as perfect absorbers, the actual number of speract receptors for both species is significantly lower than N1/2 ~ 3×105, which is the required receptor number for being a perfect absorber. Moreover, we show that such observation holds when considering the cylindrical geometry of the sperm flagellum (Figure S1, Table S1, and Theory 2.2. On the estimate of maximal chemoattractant absorption, in supplementary materials) (Nishigaki et al., 2001; Nishigaki and Darszon, 2000). The later suggests that the differences in the number of receptors amongst these species may contribute to their differential sensitivity to reliably determine the direction of the chemoattractant gradient.
To understand the differential sensitivity between the spermatozoa of S. purpuratus and L. pictus, we analyzed the scenario in which the probabilities of the detection of the gradient for both spermatozoa species were equal, i.e. they would have the same uncertainties upurpuratus = upictus. After mathematical simplification, we compute the ratio between the slopes of the gradient of both species, which represents a scaling factor (SF) in the gradient slope between S. purpuratus and L. pictus spermatozoa, expressed as:
Where is the probability that a molecule that has collided with the cell will find a receptor (Berg and Purcell, 1977), which represents the area fraction of the cell covered by chemoattractant receptors, and SF is a factor that scales the slope of the speract gradient to a regime that allows S. purpuratus spermatozoa to detect the local direction of the chemical gradient with the same uncertainty as the L. pictus spermatozoa would. In other words, the model predicts that S. purpuratus spermatozoa should undergo chemotaxis in a speract gradient approximately three times steeper than the gradient that drives chemotaxis in L. pictus spermatozoa, with ξpurpuratus ~ 3ξpictus.
In summary, the chemoreception model suggests that S. purpuratus spermatozoa detect chemoattractant gradients with less sensitivity than those of L. pictus. It also predicts that S. purpuratus spermatozoa may detect chemoattractant gradients in the 10−9 M regime with sufficient certainty only if the difference in sampling concentration is greater than 10−11 M μm−1 (i.e. steep concentration gradients). If the latter holds to be true, then S. purpuratus spermatozoa should be able to experience chemotaxis when exposed to steeper speract gradients than those tested experimentally so far. Given this prediction, we designed and implemented an experimental condition for which we expect S. purpuratus spermatozoa to experience chemotaxis.
S. purpuratus spermatozoa accumulate at steep speract concentration gradients
Our experimental setup is designed to generate specific concentration gradients by focusing a brief (200 ms) flash of UV light along an optical fiber, through the objective, and into a field of swimming S. purpuratus spermatozoa containing caged-speract (CS) at 10 nM in artificial sea water (Guerrero et al., 2010; Tatsu et al., 2002). To test experimentally whether S. purpuratus spermatozoa undergo chemotaxis, as predicted from the chemoreception model, we varied the slope of the chemoattractant gradient by separately employing four optical fibers of distinct diameters that could be arranged into five different configurations (f1, f2, f3, f4, f5) (Figure 2c).
Each configuration produces a characteristic pattern of UV illumination within the imaging field (Figure 2). The UV intensity was measured at the back focal plane of the objective for each fiber configuration (Table S2). The spatial derivative of the imaged UV light profile was computed for use as a proxy for the slope of the speract concentration gradient (Figure 2b). By examining these UV irradiation patterns, the highest concentration of speract released through photo-liberation from CS is generated by the f5 fiber, followed by f4 > f3 > f2 > f1 (Figure 2a). The steepest UV irradiation gradients are those generated by the f2, f3 and f5 fibers (Figure 2b).
Irrespective of the optical fiber used, the photo-activation of caged speract triggers the stereotypical Ca2+-dependent motility responses of S. purpuratus spermatozoa (Figure 2d, Movies 1, S1, S4, S5 and S6). To determine whether these changes lead to sperm accumulation, we developed an algorithm which automatically scores the number of spermatozoa at any of four defined concentric regions (R1, R2, R3, and R4) relative to the center of the speract concentration gradient (Figure S3).
Photo-liberation of speract through either the f2 or f3 fibers, but not through the f1, f4 or f5 fibers, lead to the accumulation of S. purpuratus spermatozoa towards the center of the speract gradient (zones R1 and R2) within the first 5-10 seconds after UV irradiation (Figure 3a, S4, Movies 1, and S1).
Interestingly, for f2, the number of spermatozoa increases in R1 and R2 and decreases in R3 and R4, indicating that cells from the R3 and R4 regions most probably relocate towards R1 and R2 (Figure 3a, S4, and Movie 1). In the case of the f3 gradient, the number of spermatozoa increases in the R1, R2 and R3 regions and decreases in the R4 region, suggesting that spermatozoa in R4 and possibly outside of the imaged field are entering the other regions (Figure 3a and Movie S2). The maximum sperm accumulation (about two-fold) occurs in R1 for the f3 gradient (Figure 3a).
In the case of exposure to the speract concentration gradient generated by illumination through the f5 fiber, the number of spermatozoa showed a tendency to increase in R2, R3 and R4 (Figure 3a, S4, and Movie S6). Gradients f1, f4 and negative controls (Low [Ca2+]i or High extracellular K+ ([K+]e)) did not show increased sperm numbers in any region (Figure 3a, S4, Movies S4, S5, S2 and S3, respectively).
We also evaluated the corresponding [Ca2+]i changes across the imaging field for each imposed speract concentration gradient. Gradients f2 to f5 increase [Ca2+]i in spermatozoa at least two-fold, while the increase for the f1 gradient was modest (Figure 3b). Interestingly, [Ca2+]i levels rose highest upon exposure to the f4 gradient, even though the number of spermatozoa did not increase significantly (Figure 3a), which underlines the notion that elevated [Ca2+]i levels are necessary, but not sufficient to drive the accumulation of spermatozoa (Figure 3), as previously suggested (Alvarez et al., 2012; Böhmer et al., 2005; Guerrero et al., 2010; Kaupp et al., 2003; Wood et al., 2005).
In summary, S. purpuratus spermatozoa significantly accumulate towards the center of the speract gradients generated by the f2- and f3-fibers, which are the two that generate UV light profiles with steeper slopes compared to the f1 and f4 fibers (Figure 2b). Notably, use of fibers f4 and f5 uncages higher concentrations of speract (by providing higher UV energies than other fibers) (Figure 2a, Table S2), yet they do not trigger the maximum accumulation of S. purpuratus spermatozoa at the center of the chemoattractant field.
S. purpuratus spermatozoa undergo chemotaxis upon exposure to steep speract gradients
The spatial derivative of the UV profiles shown in Figure 2b indicates that the steeper light gradients generated from UV irradiation are those of f2, f3 and f5, which are assumed to generate the most pronounced speract gradients of similar form. This assumption is strictly only valid at the instant of UV exposure, as subsequently the speract gradient dissipates over time with a diffusion constant of D ≈ 240 μm2s−1.
We further sought to understand how the stimulus function, which S. purpuratus spermatozoa experience during the accumulation of bound speract throughout their trajectory, influences their motility response. For this purpose, we computed the spatio-temporal dynamics of the speract gradient for f1, f2, f3, f4 and f5 fibers (Figure 4a, 4b and S5) and analyzed the trajectories of spermatozoa swimming in these five distinct speract gradient configurations (Figure 4c, S6a and S6c). Moreover, we computed the stimulus function of individual spermatozoa in response to each of the five speract gradient forms (Figure 4d, S6b, S6d and Movie 2).
From these trajectories, chemotactic behavior was quantified using a novel chemotactic index (CI) (see Figure 5a). This index takes values from −1 (negative chemotaxis) to 1 (positive chemotaxis), being 0 no chemotaxis at all (Movie 3). The temporal evolution of the CI, for each of f1, f2, f3, f4, f5 speract concentration fields, was computed (Figure 5b), and their distributions across time were analyzed by a binomial test (Figure 5c, and Movie S7).
The speract field regimes imposed by fibers f2, f3 and f5 result in a significant increase of CI, compared to other conditions (f4), confirming that the former steeper speract concentration gradients, trigger chemotactic responses on S. purpuratus spermatozoa. Again, the lack of chemotactic responses on S. purpuratus spermatozoa observed by Guerrero et al., 2010, was reproduced through stimulation with f4, zero Ca2+, or High K+ experimental regimes.
The model of chemoreception presented in the previous section (equations (9) and (10) of supplementary material) predicts a scaling rule for chemotactic responses between S. purpuratus and L. pictus spermatozoa of SF ~ 3. Moreover, the derivatives of the UV-irradiation profiles shown in Figure 2b indicate that the f2, f3, and f5 fibers generate steeper speract gradients than the f4 fiber.
To reliably determine the direction of the chemoattractant concentration gradient, the signal difference dc between two sampled positions dr must be greater than the noise (Figure 1a). To test the prediction of the chemoreception model, we computed the local relative slope ξ detected by single spermatozoa exposed to a given speract concentration gradient, with ξ = c−1/2dc/dr (Figure 4d).
We found that, in agreement with the chemoreception model, the maximum relative slope ξmax = Max(ξ1, ξ2, ξ3, …, ξn) required by S. purpuratus spermatozoa to perform chemotaxis occurs when exposed to f2 and f3 speract gradients, which are up to 2-3 times greater than the one they experience when exposed to the f4-generated speract gradient (Figure 6b). In addition, L. pictus spermatozoa are able to perform chemotaxis when exposed to the f4 speract gradient, which is 2-3 times smaller than that required by S. purpuratus (Figure 6b). These findings support the predicted scaling rule for the detection of the speract concentration gradient between L. pictus and S. purpuratus spermatozoa.
The slope of the speract gradient is the critical determinant for the strength of coupling between the stimulus function and the internal Ca2+ oscillator
To test the hypothesis that the slope of the speract gradient regulates the coupling between the stimulus function and the internal Ca2+ oscillator triggered by speract, we made use of a generic model for coupled phase oscillators (Pikovsky et al., 2003). In its simplest form, the model describes two phase oscillators of intrinsic frequencies ω1 and ω2 coupled with a strength γ through the antisymmetric function of their phase difference Φ = φ1 − φ2. The time evolution of Φ then follows an Adler equation dΦ/dt = Δω − 2γ sin(Φ), which is the leading order description for weakly-coupled non-linear oscillators. In the present case, the two coupled oscillators are the internal Ca2+ oscillator and the oscillations in the stimulus function induced in spermatozoa swimming across a speract gradient (Figure 6a). The former occurs even for immotile cells, for which there are no stimulus oscillations under a spatially uniform speract field (Figure S7, and Movie S8); while the later exists under two tested negative controls: cells swimming in Low Ca2+ and in High K+ artificial sea water, both of which inhibit Ca2+ oscillations (see Figure 3b, Movie S2 and S3).
There are two immediate predictions from the Adler model: first, there is a minimum coupling strength necessary for the two oscillators to synchronize (γmin = Δω/2). For weaker coupling (i.e. γ < γmin), the two oscillators run with independent frequencies and, hence, the phase difference increases monotonically with time; second, and within the synchronous region (i.e. γ > γmin), the phase difference between the oscillators is constant and does not take any arbitrary value, but rather follows a simple relation to the coupling strength (Φsync = arcsin(Δω/2γ)). Figure 6c shows the two regions in the parameter space given by Δω and γ. The boundary between these two regions corresponds to the condition γ = γmin and it delimits what is known as an Arnold’s tongue.
We measured the difference in intrinsic frequency by looking at the instantaneous frequency of the internal Ca2+ oscillator just before and after the speract gradient is established. The range of measured Δω is shown in Figure 6c as a band of accessible conditions in our experiments (mean of Δω, black line; mean ± standard deviation, green dashed lines). If the driving coupling force between the oscillators is the maximum slope of the speract gradient, i.e. γ = ξmax, we would expect to find a minimum slope below which no synchrony is observed.
This is indeed the case as clearly shown in Figure 6b, 6d and 6e (magenta line). Moreover, and for cells for which synchronization occurs, the measured phase difference is constrained by the predicted functional form of Φsync = Φsync(Δω, γ) as can be verified from the collapsed data shown in Figure 6d, and 6e within the theoretical estimates (see also Figure S8).
Altogether, the excellent agreement of this simple model of coupled phase oscillators with our data, points to the slope of the speract gradient as the driving force behind the observed synchronous oscillations and, as a result, for the chemotactic ability of sea urchin spermatozoa.
Discussion
Marine spermatozoa, together with many motile microorganisms, explore their environment via helical swimming paths, whereupon encountering a surface these helices collapse to circular trajectories. The intrinsic periodicity of either swimming behavior commonly results in the periodic sampling of the cell chemical environment with direct implications for their ability to accurately perform chemotaxis.
A strict requirement for sperm chemotaxis is the presence of extracellular Ca2+. For chemotaxis to occur, the timing of the Ca2+ transients (i.e. the intracellular Ca2+ oscillations) triggered by the chemoattractants must also be kept in phase with the polarity of the chemoattractant concentration field, which in this, and other studies, is referred as the stimulus function (Böhmer et al., 2005; Friedrich and Jülicher, 2008; Guerrero et al., 2010; Kaupp et al., 2008). This requisite coupling ensures that the turning events start at the descending phase of the chemoattractant concentration field; otherwise spermatozoa are driven away by Ca2+-dependent motility adjustments. The periodic sampling of chemoattractants by the sperm flagellum continuously feeds back to the signaling pathway governing the intracellular Ca2+ oscillator, hence providing a potential coupling mechanism for sperm chemotaxis. Indirect evidence for the existence of a feedback loop operating between the stimulus function and the Ca2+ oscillator triggered by chemoattractants has been found in L. pictus, Arbacia punctulata and Ciona intestinalis species, whose spermatozoa show robust chemotactic responses towards their conspecific chemoattractants (Böhmer et al., 2005; Guerrero et al., 2010; Jikeli et al., 2015; Shiba et al., 2008).
For almost three decades, chemotaxis had not been observed for the widely studied S. purpuratus species under diverse experimental conditions, raising doubts about their capabilities to respond to the spatial cues provided by the speract concentration gradients. To tackle whether S. purpuratus spermatozoa are able to derive spatial information from a candidate-chemoattractant concentration gradient, we use a model of chemoreception developed by Berg and Purcell, 1977, which considers the minimal requirements needed for a single searcher (i.e. a sperm cell) to gather sufficient information to determine the orientation of a non-uniform concentration field. By considering the difference between L. pictus and S. purpuratus spermatozoa in terms of the number of chemoattractant receptors, receptor pocket size, sampling time, swimming velocity, sampling distance, and the local mean and slope of the chemoattractant concentration field, we predicted that S. purpuratus should be able to detect the polarity of a speract concentration field. The model predicts that speract gradient necessary to guide S. purpuratus spermatozoa would be up to three times steeper than the gradient that drives chemotactic responses on L. pictus spermatozoa. We tested this prediction experimentally by exposing S. purpuratus spermatozoa to various defined speract concentration gradients. To objectively compare the responses to these gradients we defined a chemotactic index, which incorporates information regarding changes in direction and progressive velocity of the sperm when responding to a chemoattractant gradient (Figure 5 and Movie 3). We show that S. purpuratus spermatozoa exhibit chemotactic responses but, as predicted by the chemoreception model, only if the speract concentration gradients are sufficiently steep (i.e. speract gradients that are at least three times steeper than the speract concentration gradient that drives chemotaxis in L. pictus spermatozoa). The shallower speract gradients previously tested are therefore unable to generate any chemotactic response in S. purpuratus spermatozoa.
To investigate further the molecular mechanism involved in sperm chemotaxis, we measured both the stimulus function and the triggered [Ca2+]i oscillations for up to one thousand S. purpuratus spermatozoa exposed to five distinct speract concentration gradients. We demonstrate that the slope of the chemoattractant concentration field is a major determinant for sperm chemotaxis in S. purpuratus and might be an uncovered feature of sperm chemotaxis in general. A steep slope of the speract gradient entrains the frequencies of the stimulus function and the internal Ca2+ oscillator triggered by the periodic sampling of a non-uniform speract concentration field. We assessed the transition boundary of the coupling term (the slope of the speract concentration field) for the two oscillators to synchronize and found it to be very close to the boundary where S. purpuratus starts to experience chemotaxis. The agreement of our data with a model of weakly coupled phase oscillators, suggest that the slope of the speract gradient is the driving force behind the observed synchronous oscillations and, as a result, for the chemotactic ability of sea urchin spermatozoa.
One can further hypothesize about the evolutionary origin of the described differences in sensitivity to chemoattractant concentration gradients between S. purpuratus and L. pictus spermatozoa given the significant dissimilarities between their ecological reproductive niches. The turbulent environment where sea urchin reproduces directly impinges on the dispersion rates of small molecules such as speract, hence, imposing ecological limits that constrain permissive chemoattractant gradient topologies within different hydrodynamic regimes. For instance, the reproduction success of L. pictus, S. purpuratus and Abalone species has been shown to peak at particular hydrodynamic shearing values (Hussain et al., 2017; Mead and Denny, 1995; Riffell and Zimmer, 2007; Zimmer and Riffell, 2011). What are the typical values of the chemoattractant gradients encountered by the different species in their natural habitat? The correct scale to consider when discussing the small-scale distribution of chemicals in the ocean is the Batchelor scale, lB = (ηD2/ζ)1/4, where η is kinematic viscosity, D the molecular diffusivity and ζ is the turbulent dissipation rate (Aref et al., 2014; Batchelor, 1959). Turbulence stirs dissolved chemicals in the ocean, stretching and folding them into sheets and filaments at spatial dimensions down to the Batchelor scale: below 1B molecular diffusion dominates and chemical gradients are smoothened out.
S. purpuratus is primarily found in the low intertidal zone. The purple sea urchin lives in an habitat with strong wave action and areas with shaking aerated water. These more energetic zones, including tidal channels and breaking waves, generate relatively high levels of turbulence (ζ ~ 10−4 m2s−3) which lead to somewhat small values of lB and, hence, to steep gradients (i.e. l/lB). L. pictus, on the contrary, is mostly found at the edge of or inside kelp beds, well below the low tide mark where the levels of turbulence are much more moderate (ζ ~ 10−6 m2s−3) (Jiménez, 1997; Thorpe, 2007). This difference in turbulent kinetic energy dissipation rate has a significant effect on the spatial dimensions of chemical gradients for sperm chemotaxis present in a particular habitat. The ratio of lB for the different habitats scales as lBpurpuratus/lBpictus ~ (ζpictus/ζpurpuratus)1/4> ~ 3, which fits considerably well with the relative sensitivity to speract of the two species. Furthermore, we have shown that S. purpuratus spermatozoa experience chemotaxis toward steeper speract gradients than those that guide L. pictus spermatozoa, which is also compatible with the distinct chemoattractant gradients they might naturally encounter during their voyage searching for the egg.
The chemoattractant concentration gradients generated in the present study were near-instantaneously set up by the photo-release of speract in still water. Further experimental studies are needed to assess the chemotactic ability of sea urchin spermatozoa in more realistic chemoattractant gradients (as those shaped, for instance, by hydrodynamic forces in their natural environment) and to shed light into the mechanisms governing chemotaxis and their ecological implications.
Materials and Methods
Materials
Artificial seawater (ASW), and Low Ca2+ ASW were prepared as in (Guerrero et al., 2010), their detailed composition, together with an extended list of other materials is presented in the supplementary materials. Caged speract (CS), was prepared as described previously (Tatsu et al., 2002).
Loading of Ca2+-fluorescent indicator into spermatozoa and microscopy imaging
Undiluted S. purpuratus or L. pictus were loaded with fluo-4-AM, and their swimming behavior was studied at the water-glass interface on an epifluorescence microscope stage (Eclipse TE-300; Nikon). The cover slips were covered with a poly-HEME to prevent the attachment of the cells to the glass. Images were collected with a Nikon Plan Fluor 40x 1.3 NA oil-immersion objective. Temperature was controlled directly on the imaging chamber at a constant 15 °C. Stroboscopic fluorescence excitation was provided by a Cyan LED synchronized to the exposure output signal of the iXon camera (2 ms illumination per individual exposure, observation field of 200 × 200 μm), the florescence cube was set up accordingly (see supplementary material).
Image processing and quantification of global changes of spermatozoa number and [Ca2+]i
To study the dynamics of overall sperm motility and [Ca2+]i signals triggered by the distinct speract gradients, we developed an algorithm that provides an efficient approach to automatically detect the head of every spermatozoa in every frame of a given video-microscopy file. A detailed description of the algorithm is provided as supplementary material. Briefly, images are filtered for shot noise, sperm heads are segmented based on global thresholding methods, following by an automatic quantification of head fluorescence and sperm trajectories. Up to 267 videos of S. purpuratus spermatozoa, each containing tens of swimming cells, exposed to five distinct speract concentration gradients, were automatically analyzed.
Computing the dynamics of speract concentration gradients
The dynamics of the chemoattractant gradient was computed using Green’s function of the diffusion equation:
This equation for the concentration tells us that the profile has a Gaussian form. The width of the Gaussian is , and hence it increases as the square root of time. Cb is the basal concentration of the chemoattractant, D is the molecular diffusivity.
The speract concentration gradients were generated via the photolysis of 10 nM caged speract (CS) with a 200 ms UV pulse delivered through each of four different optical fibers with internal diameters of 200 μm, 600 μm, 2 mm and 4 mm (at two different positions). Light intensity was normalized dividing each point by the sum of all points of light intensity for each fiber and multiplying it by the fiber potency (measured at the back focal plane of the objective) in miliwatts (mW) (Table S2). Each spatial distribution of instantaneously-generated speract concentration gradient was computed by fitting their corresponding normalized spatial distribution of UV light (Residual standard error: 2.738 × 10−5 on 97 degrees of freedom), considering an uncaging efficiency of 5%, as reported (Tatsu et al., 2002).
The diffusion coefficient of a molecule is related to its size by the Stokes-Einstein equation: , where k is Boltzmann’s constant, T is the temperature, η is the viscosity of the solvent, and Rh is the hydrodynamic radius (Lakowicz, 2006). The hydrodynamic radius Rh of speract was calculated by modeling the molecules in terms of equivalent hydrodynamic spheres. , where M is the molecular weight, and is the specific gravity (Lakowicz, 2006). The volume of an equivalent spherical particle is . These equations show that the radius and diffusion coefficient are weakly dependent on the molecular weight.
The diffusion coefficient of speract has not been measured experimentally, nonetheless it can be estimated following equations 6 and 7 (supplementary material). The diffusion coefficient of a similar chemoattractant molecule, resact (with fourteen amino acids), has been reported, Dresact = 239 ± 7 μm2 s−1 (Kashikar et al., 2012). If we consider that speract is a decapeptide, the 1.4 fold difference in molecular weight between speract and resact would imply a (1.4)1/3 fold difference in their diffusion coefficients, which is close to the experimental error reported (Kashikar et al., 2012). For the sake of simplicity, the spatio-temporal dynamics of the distinct instantaneously generated speract gradients was modeled considering a speract diffusion coefficient of Dsperact = 240 μm2 s−1.
The hydrodynamic radius of speract (Rh = 8.8 Å) was computed with Dsperact = 240 μm2 s−1, k = 1.38 × 10−23 J K−1, T = 288.15 K and η = 0.001 N s /m2.
Computing [Ca2+]i dynamics and the stimulus function of single spermatozoa
Spermatozoa were tracked semi-automatically by following the head centroid with the MtrackJ plugin (Meijering et al., 2012) of ImageJ 1.49u. Single cell [Ca2+]i signals were computed from the mean value of a 5 × 5 pixel region, centered at each sperm head along the time. The head position of each spermatozoa was used to compute the local concentration of speract at r(x, y) over each frame. The stimulus function of single spermatozoa s = c(r, t) was computed by solving equation (3), considering both their swimming trajectories, and the spatio-temporal evolution of a given speract concentration gradient. The profiles of UV light were used to compute the initial conditions at c(r, to).
The phase- and temporal-shifts between time derivative of the stimulus function ds/dt and the internal Ca2+ oscillator triggered by speract, were computed from their normalized cross-correlation function.
Programs were written in R statistical software.
Chemotactic index
Each sperm trajectory was smoothened using a moving average filter, with a window of 60 frames (two seconds approximately) (Figure 5a and Movie 3). A linear model was then fitted to the smoothed trajectory, the corresponding line was forced to go through the mean point of the smoothed trajectory (orange point in Figure 5a and Movie 3). The θ angle between red and black vectors was calculated in each frame from the second 4.5 to 10.
The chemotactic index was defined based on the progressive displacement of the sperm trajectory as , being ϕ and θ the angles between gray and magenta, and red and black vectors, respectively; and |v| and |u| the magnitude of the sperm progressive velocity before and after speract uncaging, respectively (Figure 5a and Movie 3). The CI considers the sperm displacement before speract uncaging (i.e. unstimulated drift movement at 0-3 seconds), and then subtracts it from the speract induced effect (at 3-10 seconds). The CI takes values from −1 (negative chemotaxis) to 1 (positive chemotaxis), being 0 no chemotaxis at all.
Statistical analyses
The normality of the CI distributions, each obtained from f1 to f5 speract gradient stimuli, was first assessed using the Shapiro-Wilk test; none of them were normal (Gaussian), so each CI distribution was analyzed using non-parametric statistics (Movie S7). The curves obtained from medians of each CI distribution were smoothed using a moving average filter, with a window of 20 frames (0.6 seconds).
Data are presented for individual spermatozoa (n) collected from up to three sea urchins. All statistical tests were performed using R software (R Development Core Team, 2016). The significance level was set at 95%.
Author contributions
A.G., A.D. and I.T. conceived the project; A.G. and V.J.S. performed the experiments; H.R., A.G., I.T., V.J.S. and M.V. analyzed the data; A.G., I.T. and H.R. performed the mathematical model calculations and wrote the corresponding section; H.R. and I.T. developed the chemotactic index; A.D., A.G., H.R. and I.T. participated in the design and drafting of the manuscript; J.C., C.D.W. and C.B. provide feedback for conceptualization and drafting of the manuscript. All authors approved the final version of the article.
Competing interests
The authors declared that no competing interests exist.
Funding
A.D. and A.G. acknowledge grants from the Consejo Nacional de Ciencia y Tecnología (CONACyT Fronteras 71, CONACyT Ciencia Básica 252213 and CONACyT 255914), A.G., A.D. and C.B to Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica UNAM (PAPIIT/DGAPA) (IA202417, IN205516, IN206016 and IN112514). We acknowledge CONACYT and PAPIIT for fellowships to M.V.P. and H.R.; the panish inistr of conom and Competitiveness Grants No. FIS2013-48444-C2-1-P, FIS2016-77692-C2-1-P, the Subprogram Ramón-y-Cajal and the Ibero-America Program-Santander Universities 2015 (I.T.).
Acknowledgements
The authors thank Dr. Tatsu Yoshiro for providing the caged speract, and Drs. Hermes Gadêlha, David Smith and Nina Pastor for stimulating discussions and a critical reading of the manuscript. AG thanks Dr. Manabu Yoshida and Dr. Kaoru Yoshida for feedback regarding sperm chemotaxis in marine invertebrates, and to the Japan Society for the Promotion of Science (JSPS invitation fellowship for research in Japan to A.G., short term JSPS/236, ID no. S16172).