Sperm chemotaxis, fluid shear, and the evolution of sexual reproduction

Abstract

Chemical communication is fundamental to sexual reproduction, but how sperm search for and find an egg remains enigmatic. For red abalone (Haliotis rufescens), a large marine snail, the relationship between chemical signaling and fluid motion largely determines fertilization success. Egg-derived attractant plumes are dynamic, changing their size and shape in response to unique combinations of physical and chemical environmental features. Attractant plumes that promote sexual reproduction, however, are limited to a precise set of hydrodynamic conditions. Performance-maximizing shears are those that most closely match flows in native spawning habitats. Under conditions in which reproductive success is chronically limited by sperm availability, gametes are under selection for mechanisms that increase sperm–egg encounter. Here, chemoattraction is found to provide a cheap evolutionary alternative for enhancing egg target size without enlarging cytoplasmic and/or cell volume. Because egg signaling and sperm response may be tuned to meet specific fluid-dynamic constraints, shear could act as a critical selective pressure that drives gamete evolution and determines fitness.

Chemical communication is pervasive among gametes of taxa with diverse reproductive strategies. Sperm activation and chemotaxis occur in marine animals and plants that broadcast gametes into the sea, as well as in terrestrial organisms with internal fertilization (1–6). At the scale of gamete interactions (0.01–1 mm; Re << 1; the Reynolds number is a dimensionless ratio, reflecting the magnitude of inertial forces to viscous forces that act on a body in flow), sperm encounter eggs while being transported within a laminar (i.e., viscous) shear flow. The magnitudes of shear forces in mammalian reproductive tracts are remarkably similar to those in many coastal ocean environments (7–14). Consequently, mechanisms that drive sperm–egg interactions for external-fertilizing marine organisms are informative of processes that operate in their internal-fertilizing terrestrial counterparts.

Experimental studies on sperm behavior traditionally have been conducted in still water. However, most gametes populate a natural world of fluid motion. In the ocean, sperm and eggs usually are smaller than the tiniest vortices at these viscous-dominated scales (11, 12). The microscopic flow fields consist of instabilities that give rise to laminar shear (10)—the change in velocity divided by change in distance. Such shears also are generated in a terrestrial, mammalian reproductive tract, in which flows are driven by muscular contractions, ciliary beating, and/or convective heating (8, 9, 14). Here, laminar shears result from the viscous flows produced in confined passages. Whether gametes are suspended in a relatively unbounded (e.g., ocean) or bounded (e.g., vessel) medium, or attached to a surface, the magnitude of shear has important consequences for sperm–egg interactions.

A given shear can positively or negatively affect gamete performance. In excessive shears, for example, sperm may lose control of their swimming direction, which would impede chemotaxis and inhibit fertilization (12, 13). Alternatively, higher shears could thin the boundary layer in specific regions near a rotating egg, steepening concentration gradients (11, 13) and thus promoting chemotaxis. Previous investigations have elucidated specific mechanisms that underlie sperm motility (reviewed in refs. 15, 16). They have not, however, provided the information necessary for predicting emergent properties of sperm–egg interactions as a consequence of combined physical, chemical, and biological factors.

Soluble sperm attractants could mediate fertilization success and drive speciation, operating upstream of cell-surface proteins and before gamete contact (17–19). Although purportedly critical in sexual reproduction, the influence of gamete chemical communication on fertilization in flow has been inferred, but never tested directly to our knowledge. Recent discoveries have considerably improved knowledge on the molecular basis of signal transduction and sperm chemotaxis (20, 21). Still, we are aware of no experimental evidence demonstrating, unequivocally, a cause-and-effect relationship among sperm chemoattraction, fluid motion, and fertilization success.

The identification of a signal molecule links behavioral performance with ecological and evolutionary consequences. Red abalone (Haliotis rufescens) sperm detect a waterborne chemical cue emitted by conspecific eggs, and change their swimming behavior to increase the likelihood of successful contact (22). As determined by bioassay-guided fractionation of natural egg-conditioned seawater, male gamete attraction is dose-dependent and stereospecific for the l-isomer of tryptophan (23). This same compound fails to elicit behavioral responses from the sperm of three congeneric abalone species (Haliotis sorenseni, Haliotis corrugata, or Haliotis fulgens) that inhabit the same coastal environments and overlap in reproductive timing with H. rufescens. Waterborne compounds, upon release from each of the three species, do not affect the sperm of red abalone. Moreover, l-tryptophan metabolites, including serotonin, tyramine, and seven other structural analogues, do not impact H. rufescens sperm motility or orientation toward eggs (24). Consequently, red abalone sperm require only a single, identified compound for conspecific gamete attraction.

In this study, we simulated critical aspects of small-scale turbulence within the natural habitats of spawning red abalone (Fig. 1). Laminar-shear was manipulated systematically in large Taylor–Couette flow tanks (Fig. S1). Sperm motility, gamete encounter rate, and fertilization success all were quantified, simultaneously, by using a custom-built IR laser and computer-assisted digital imaging system. Combining theoretical and empirical approaches, egg-derived tryptophan plumes were described accurately and linked to sperm locomotory performance. Boundary conditions for 3D numerical modeling (flow speed, fluid shear, tryptophan release rate and diffusion coefficient, egg rotational velocity) reflected actual plumes of this natural attractant from freshly spawned abalone eggs. Accordingly, we established the basic contributions of chemical communication and fluid dynamics to fertilization success and we identified shear as a critical selective pressure that may drive the evolution of gamete behavior.

Fig. 1.

(A) Open habitat of giant kelp forest in shallow (10–15 m depth) coastal waters offshore of Point Loma, San Diego, California (photo by Eric Hanauer). (Scale bar, 25 cm.) (B) Within this forest (and others like it), adult red abalone aggregate underneath ledges and in crevices among rocky reefs. Hydrodynamic measurements have characterized the physical properties of these environments (13). Relatively strong cross-shelf and weak longshore currents are typical of open reef habitats. In contrast, flow speeds among the rocky ledges and crevices harboring groups of red abalone (”hot spots”) are two to three times slower than in exposed areas. These hot spots exhibit significantly smaller Reynolds stresses, turbulent energy dissipation rates, and shears (ranging from 0.3 to 2.4 s⁻¹ and from 4.8 to 13.4 s⁻¹ in hot spots and open habitats, respectively; ref. 13). Red abalone thus aggregate and spawn at sites where water motion is relatively tranquil. Critical aspects of these flow environments can be simulated within a Taylor–Couette apparatus (photo by Eric Hanauer). (Scale bar, 15 cm.) (C) Each adult male or female spawns gametes into the sea via excurrent tremata, small holes in the shell that connect the mantle cavity (i.e., exit site for reproductive products) and surrounding ocean. The epipodium (i.e., lateral lobe of the foot) contains many small tentacles that are used in sensing water motion; two large cephalic tentacles (not shown) protrude from the head (arrow at left) and function primarily in olfaction (photo by Luis Ignacio-Vilchis). (Scale bar, 1.0 cm.) (D) Spawning of sperm by a single adult male. Propulsive forces generated by the muscular contractions of its foot ultimately produce a gamete jet, or plume. In nature, both mature males and females are gravid yearround and spawn synchronously. Individuals can be systematically induced to spawn in the laboratory, and a single gravid male or female releases approximately 10 billion sperm or 3 million eggs, respectively. Profuse gamete material is therefore available at almost all times for laboratory experiments (photo by Larry Friesen and Daniel Morse). (Scale bar, 0.5 cm.)

Results and Discussion

Attractant Plumes Surrounding Eggs.

Field measurements within giant kelp forests (Macrocystis pyrifera) previously characterized the mixing properties of fluid into which abalone naturally spawn (13). These determinations specified the range of fluid-dynamic conditions for testing in present laboratory trials. Shears were 4.8 to 13.4 s⁻¹ in adjacent open habitats, in contrast to 0.3 to 2.4 s⁻¹ within the native crevices and under ledges where adult red abalone live and spawn (13). Spawning abalone thus aggregated at sites where water motion was substantially retarded (Fig. 1).

Theoretically, surface areas and volumes of egg-derived tryptophan plumes peaked in still water or in weak shears and decreased thereafter (Fig. 2 and Table S1). Weak shears (0.1–0.5 s⁻¹) and slow flows [Pe of 1.5–7.5; Peclet number is a dimensionless ratio, reflecting flow speed (i.e., advection) relative to coefficient of molecular diffusion for l-tryptophan) resulted in elevated concentrations that decreased with increasing distance from an egg. The plumes thus expanded along the principal flow axis, relative to diffusion alone (i.e., still water; Fig. 2B and Table S1). In contrast, strong shears (2.0–10.0 s⁻¹) and fast flows (Pe of 30–151) rapidly reduced tryptophan concentrations below threshold in all but a very small region near the eggs (Fig. 2 E and G). Consequently, plume-maximizing shears were those most closely simulating flows in native spawning habitats (13).

Fig. 2.

Theoretical concentration distributions (nmol L⁻¹, in pseudocolor) of tryptophan surrounding red abalone eggs (black spheres) in still-water and in Taylor–Couette flows. Each plot is a 2D slice, cut through the center of an egg (A–G). White arrows denote flow velocity vectors (speeds and directions). The x axis is parallel to the direction of flow and the y axis is orthogonal to flow, but parallel to the direction of shear. Tryptophan plumes were produced through 3D numerical simulations that used a coupled convection-diffusion model, taking into account egg rotation rate at each shear, and assuming a constant and continuous tryptophan release over the entire egg surface for 4 min at 0.18 fmol egg⁻¹ min⁻¹ (SI Materials and Methods). Model parameters (flow speed and direction, fluid shear, attractant release rate and diffusion coefficient, egg diameter and rotational velocity, water temperature) accurately portrayed conditions in our current experiments on sperm behavior, gamete encounter rates, and fertilization success. (Scale bar, 200 μm.)

Effects of Chemical Communication and Fluid Shear on Sperm Behavior.

Results of Taylor–Couette flow experiments strongly supported the theoretical predictions, validating the physical model of tryptophan plume dynamics (Materials and Methods provides details on Taylor–Couette apparatus and experimental protocols). Sperm swam faster and navigated directly toward egg surfaces within the predicted plumes (Fig. 3 A and B and 4 A and C). In contrast, male gametes positioned outside of the plumes swam slower and did not orient significantly with respect to an egg (Figs. 3 A and C and 4 F and H). Shear exerted a strong modulatory effect on sperm behavior (Tables S2 and S3). Swim speed and orientation toward an egg peaked at the weakest shears tested (0.1–0.5 s⁻¹) and then decreased as shear strengthened. At 2.0 to 10.0 s⁻¹, flow-generated torques increasingly overwhelmed sperm behavior (13). These higher shears prevented male gametes from swimming actively across streamlines. Sperm aligned parallel to streamlines and cells tumbled at frequencies predicted by theory for passively transported particles (13). Whereas weak shears promoted, strong shears inhibited sperm locomotory performance and suppressed the attractant plume of egg-derived chemical signals.

Fig. 3.

(A) Representative swimming paths of individual red abalone sperm surrounding conspecific eggs in FSW as a function of shear. For each experimental treatment, a dashed line denotes the predicted behavioral threshold concentration (3 × 10⁻¹⁰ mol L⁻¹). This line demarcates the theoretical active space (i.e., closer to egg) from inactive space (i.e., further from egg) of an attractant plume. Active space was defined as the portion of a plume maintaining tryptophan greater than the threshold level that caused faster sperm swimming and orientation with respect to a chemical gradient. Small circles are successive digital images of sperm heads captured at 0.033-s intervals, and each arrowhead denotes the direction of travel for an individual cell. Sperm displacement caused by flow was subtracted on a frame-by-frame basis, so each computer-generated path reflects the actual track swum. To eliminate selection bias, a random numbers generator was used in choosing representative paths for each flow treatment. Orientation rosettes show distributions of directional tracks by sperm populations positioned inside (B) or outside (C) the active spaces of hypothesized tryptophan plumes. For B and C, complete data sets, not representative paths, were used to establish distributions and in calculating mean unit vector lengths (r) and angular headings (θ) relative to a line between each sperm head and the center of an egg. Sperm moving directly toward an egg would follow a 0° heading. A Rayleigh test (z-value) was used to compare each mean direction against a uniform circular distribution, and to calculate the P value. Sperm orientation toward an egg was significant inside the predicted active space at 0, 0.1, 0.5, 1.0, and 2.0 s⁻¹ (V test: u ≥ 2.65, n ≥ 26; P < 0.04, all comparisons).

Fig. 4.

Effects of fluid shear on direction of sperm swimming with respect to an egg (A and F) (as described in more detail in Fig. 3), direction of sperm swimming with respect to flow (B and G), sperm translational swim speed (C and H), sperm encounter rate with a theoretical, tryptophan active space surrounding an egg (D), and sperm–egg encounter rate (E). Male gametes were imaged while swimming either “inside” or “outside” the active spaces of theoretical tryptophan plumes. Complete data sets, not representative paths, were used to establish mean unit vector lengths (r) with respect to an origin in A, B, F, and G. Experiments were performed in the presence of FSW alone (solid line) or with addition of active or denatured tryptophanase (dotted or dashed lines, respectively). Each dependent variable was described as a function of log-shear, using least-squares regression to establish the best fit (F tests for FSW and denatured enzyme treatments: F ≥ 7.39, df ≥ 1, 116; P < 0.001, all comparisons). Symbols are mean values (±SEM), and error bars are smaller than symbol sizes in some cases.

Effects of Chemical Communication and Fluid Shear on Sperm–Egg Encounter Rate and Fertilization Success.

Straighter and faster paths need not indicate that chemically mediated behavior increases encounter rates, or ultimately enhances fertilization success. As a function of shear, magnitudes of sperm swim speed and orientation (relative to an egg surface), male–female gamete contact rates, and percentages of fertilized eggs, all were highly correlated (Pearson product–moment correlation, r² ≥ 0.73, df = 6; P < 0.05, all comparisons; Figs. 4 and 5 and Tables S2–S5). Thus, fertilization success could be forecasted accurately from sperm swimming behavior alone.

Fig. 5.

Effects of fluid shear on fertilization success (i.e., percentage of fertilized eggs). Egg density was held constant (10³ cells mL⁻¹) and, in separate treatments, sperm density was tested at (A) 10⁶, (B) 10⁵, or (C) 10⁴ cells mL⁻¹. Experiments were performed in the presence of FSW alone (solid line) or with addition of active or denatured tryptophanase (dotted or dashed lines, respectively). Fertilization success was described as a function of log-shear, using least-squares regression to establish the best fit (F tests: F ≥ 50.5, df ≥ 1, 58; P < 0.001, all comparisons). Symbols are mean values (±SEM), and error bars are smaller than symbols in some cases.

Similar trends emerged across all sperm treatments. The percentages of fertilized eggs peaked at 0.1 to 0.5 s⁻¹, and then decreased as shear increased. At sperm concentrations of 10⁵ and 10⁴ cells mL⁻¹, maximal percentages of fertilized eggs were approximately 1.5 times those measured in still water (Fig. 5 B and C). In contrast, the maximal value decreased (1.2 times) slightly at a higher sperm density (10⁶ cells mL⁻¹), as overall fertilization levels approached saturation (an asymptote of 100% eggs fertilized; Fig. 5A). Compared with still water, fertilization success was elevated significantly at 0.1 to 0.5 s⁻¹, was approximately the same at 1.0 to 2.0 s⁻¹, and was depressed significantly at 4.0 to 10.0 s⁻¹ (Fig. 5 and Table S5). Weak shears therefore promoted sperm chemoattraction as well as reproductive success.

As always, correlation does not imply causation. Whereas results showed a strong association between egg-derived attractant plumes and sperm behavioral performance, these experiments were not designed to show a cause-and-effect relationship. Consequently, we determined whether eliminating the chemical signal around eggs would prevent fertilization. Freshly spawned eggs and sperm were placed in Taylor–Couette chambers containing filtered seawater (FSW) as before, but now with addition of activated or denatured (i.e., boiled) tryptophanase (2 μg mL⁻¹). This enzyme, when active, selectively digests free tryptophan in solution.

The addition of activated tryptophanase had profound consequences for sperm–egg interactions. First, the enzyme did not affect sperm membranes, receptors, or behaviors, or the proclivity of male or female gametes for fertilization (22). It did, however, extinguish the signal surrounding an egg, as evidenced by sperm inability to navigate within hypothesized plumes, even from a distance of 100 μm, or less (Fig. 6 and Tables S6 and S7). HPLC indicated no measurable accumulation of tryptophan in seawater, when both enzyme and eggs were present. Second, elimination of the tryptophan and sperm chemoattraction precipitated a significant decrease in gamete encounter rate and fertilization success (Figs. 4 and 5 and Tables S8 and S9). Conversely, there was no decay in sperm navigation (toward an egg) and swim speed, encounter rate, or fertilization with the denatured tryptophanase (Figs. 4 and 5, Fig. S2, and Tables S6–S9). Tryptophan release by eggs, therefore, was a causative agent and critical determinant of fertilization success.

Fig. 6.

Effects of fluid shear and tryptophanase on representative swimming paths of individual red abalone sperm (A) and on orientation distributions of directional tracks by sperm populations positioned inside (B) or outside (C) of theoretical tryptophan plumes surrounding eggs. All experimental procedures and analyses, except for enzyme addition, were the same as described for Fig. 3. A Rayleigh test (z-value) was used to compare each mean direction against a uniform circular distribution, and to calculate the P value. Sperm orientation toward an egg was not significant in still water and at each tested shear (V tests: u ≤ 1.38; P ≥ 0.39).

Sperm chemoattraction and fluid shear each had significant effects on fertilization dynamics. Which process plays the ascendant role? To answer this question, we performed a series of stepwise multiple regressions on the fertilization data. Taken as a whole, our experiments measured percentages of fertilized eggs over a wide range of shears (0–10 s⁻¹, from abalone spawning to open kelp forest habitats), sperm densities (10⁴–10⁶ cells mL⁻¹, from sperm-limiting to sperm-saturating conditions), and in the presence of active or denatured tryptophanase. Shear—not chemoattraction—explained most (55–64%) of the variation in fertilization success at low sperm densities (10⁴ and 10⁵ sperm mL⁻¹; Table S10). In contrast, at a high sperm density (10⁶ mL⁻¹), chemoattraction had a significantly greater impact (67% of variation in fertilization). Thus, shear dominated chemical communication only under limiting sperm conditions. Shear did not damage either sperm or eggs (13). Instead, acting to facilitate or inhibit, it modulated the strength of chemically mediated, gamete interactions.

Chemical Communication, Fluid Shear, and Evolution of Sexual Reproduction.

The evolution of gamete size and morphology is a major unsolved problem in reproductive biology. Under conditions in which reproductive success is chronically limited by sperm availability, adults and gametes are under selection for mechanisms that increase sperm–egg contact (25). One such mechanism could involve changes in the physical size of the egg, because enlarging the “target” increases the probability of sperm–egg collision (25–27). Models of evolution have focused, traditionally, on postzygotic consequences of egg size for larval or juvenile survivorship (28, 29). Another implication of the target size hypothesis, however, is that prezygotic benefits to fertilization could drive the evolution of egg size and, in turn, anisogamy (25).

To date, theoretical models of gamete size evolution have not considered effects of fluid motion on sperm–egg encounter probabilities. Because shear is a natural feature of nearly all reproductive habitats, it may exert strong selective pressure on gamete morphology. In fact, shear initiates egg rotation at an angular velocity directly proportional to gamete size (i.e., radius) (11, 13, 30). As a consequence of this rotation, fluid accelerates when it approaches an egg, compressing or closing streamlines and locally increasing shear stress near an egg surface. The likelihood of sperm “slipping” around an egg surface, rather than encountering it, increases significantly with rotation rate (13). Thus, a larger egg is not always a better target.

For red abalone, chemoattraction provides a cheap evolutionary alternative for increasing egg target size without enlarging cytoplasmic and/or cell volume. Egg cytoplasm is an expensive commodity. It contains a vast array of organic molecules and provides a rich biochemical environment for synthesizing natural products after fusion, as required in embryo development (31). In contrast, the free amino acid l-tryptophan is taken up by maternal abalone from a dietary source and incorporated directly in egg cytoplasm during oogenesis. Thus, signal production, as well as release (via diffusion), consumes little or no metabolic energy and expends less than 1% of total cytoplasmic tryptophan reserves (24). Whereas tryptophan acts as a sperm attractant, it also is a precursor for synthesizing many neurotransmitters and neuromodulators. As a metabolic substrate essential to the development of the larval nervous system, tryptophan could be an honest indicator of egg fitness for prospective sperm suitors (32). Furthermore, red abalone eggs stop releasing tryptophan as they age and become infertile (24). Our results, therefore, suggest that endogenous signaling pathways have been coopted for external communication, as an adaptation to increase the likelihood of reproductive success. Because egg signaling and sperm response are possibly tuned to meet specific fluid-dynamic constraints, shear may act as a critical selective pressure that drives gamete evolution and determines fitness.

Materials and Methods

Procedures for the maintenance and spawning of abalones, instrumentation, analysis and construction of the Taylor–Couette apparatus, chemosensory treatments on sperm behavior, and theoretical flow fields and attractant plumes around eggs are detailed in SI Materials and Methods.

Effects of Chemical Communication and Fluid Shear on Fertilization Success.

Relationships among fluid shear, chemical communication, and fertilization success were determined in a Taylor–Couette apparatus. This device consists of two nested cylinders with radii of 6.1 cm and 6.9 cm for the inner and outer cylinders, respectively (Fig. S1; details of theory and construction are provided in refs. 11, 12). The gap between the cylinders was filled with sperm at a concentration of 10⁴, 10⁵, or 10⁶ cells mL⁻¹. In each trial, the gap contained FSW alone, FSW with tryptophanase (2 μg mL⁻¹), or FSW with denatured (i.e., boiled) tryptophanase (2 μg mL⁻¹). Before use, tryptophanase was activated by incubation with 100 μmol L⁻¹ pyridoxal-5′-phosphate in FSW (pH 7.9) at 37 °C for 1 h to ensure maximum formation of the holoenzyme (22). The addition of denatured tryptophanase controlled for nonspecific effects of increased protein concentration. A computer-controlled stepper motor system was activated after all visible air bubbles were purged from the tank (standing upright). Within 5 s, this unit brought the spinning cylinders to a designated shear of 0.1, 0.5, 1.0, 2.0, 4.0, or 10.0 s⁻¹. For comparison, trials also were performed in still water, without motor activation. Eggs were placed in custom-built mesh tubes in the absence of flow. Because filament size was inconsequential compared with the size of the mesh openings, these compartments failed to significantly affect sperm swim speeds or directions under test conditions (13). Ten to 15 replicate trials were conducted for each sperm concentration, shear (or still water), and enzyme treatment (N = 773 total trials).

Shear effects on fertilization were quantified at a single contact time. Fifteen seconds after egg introduction, 10 mL of mixed gamete suspension were withdrawn from the middle of the gap, 4 cm below the water surface. This time reflected a short, but realistic, gamete encounter interval in field environments (33, 34). Moreover, we previously calculated the Kolmogorov time scales from hydrodynamic measurements of flows within the crevices and ledges that were inhabited by adult red abalone (13). These scales reflect the lifetimes of the tiniest turbulent eddies (called the Kolmogorov microscales) in which spawned sperm and eggs resided naturally, before kinetic energy dissipation by fluid viscosity to heat. As determined empirically, Kolmogorov times of 2 to 13 s compared favorably to the duration of our current fertilization assays and thus provided an immediate ecological context (13). In present experiments, eggs (at ∼10³ mL⁻¹) were captured from suspension on a 100-μm mesh screen, and then rinsed thoroughly with 50 mL of FSW. Repeated microscopic examinations indicated that the rinse eliminated all sperm from egg surfaces, except those attached to the vitelline envelope. After 3-h incubation in FSW, eggs were fixed in 5% buffered formalin and assessed for percentage fertilized as cleavage into four- or eight-celled embryos.

Measurements of Sperm Swimming Speed and Direction in Shear Flows.

Timing and precise location of each encounter between sperm and egg was recorded from digital images. Swim speed and position of each sperm cell also were determined within a 1,000 × 800 μm field (parallel × perpendicular to flow direction) surrounding an egg. To control for effects of flow on measurements of swim speed, heat-killed sperm (20 min exposure at 40 °C) were substituted for their live counterparts, and the measurements repeated (n = 8 replicate trials for each shear). The dead sperm served as passive particles, revealing background fluid movement experienced by live gametes. From paths of dead sperm, 2D velocity fields were mapped with respect to positions (x,y coordinates) within the gap. The computed velocities based on dead sperm paths were then subtracted from live sperm paths on a frame-by-frame basis, by using a customized MATLAB program (as detailed in ref. 13).

Elimination of the flow component from a live cell path revealed the direction of swimming within a circular coordinate system. Here, θ is the angle relative to an operationally defined origin (0°) and r is the unit vector for n cells in a population:

A unit vector length of 1 indicates that all sperm swam on a single trajectory for a given treatment. In contrast, a length of zero denotes random movements without a shared bearing. Two relative orientations were evaluated: did cells orient relative to flow or egg surface? If the former, cells swimming in straight paths, downstream or upstream, would move with an θ of 0° or 180°, respectively. The coordinate system was set up with the origin facing away from flow. According to the latter, sperm swimming trajectory was evaluated with respect to the nearest egg. In this case, 0° was defined as the angle between each cell body and the center of the egg. Sperm moving directly toward an egg thus would follow a 0° heading. For each treatment, these two separate analyses were performed on the same data set. A Rayleigh test was applied initially to compare the mean direction swum against a uniform circular distribution. If significantly different, a V test was used to determine the fit with respect to each of the origins (0°) as defined earlier.