Guanylyl cyclases (GCs), which synthesize the messenger cyclic guanosine 3′,5′-monophosphate, control several sensory functions, such as phototransduction, chemosensation, and thermosensation, in many species from worms to mammals. The GC chemoreceptor in sea urchin sperm can decode chemoattractant concentrations with single-molecule sensitivity. The molecular and cellular underpinnings of such ultrasensitivity are not known for any eukaryotic chemoreceptor. In this paper, we show that an exquisitely high density of 3 × 105 GC chemoreceptors and subnanomolar ligand affinity provide a high ligand-capture efficacy and render sperm perfect absorbers. The GC activity is terminated within 150 ms by dephosphorylation steps of the receptor, which provides a means for precise control of the GC lifetime and which reduces “molecule noise.” Compared with other ultrasensitive sensory systems, the 10-fold signal amplification by the GC receptor is surprisingly low. The hallmarks of this signaling mechanism provide a blueprint for chemical sensing in small compartments, such as olfactory cilia, insect antennae, or even synaptic boutons.

Some cells are endowed with exquisite sensitivity: they can sense environmental cues at the physical limit. Photoreceptors respond to single photons (Pugh and Lamb, 2000; Yau and Hardie, 2009), sperm can register single molecules of chemoattractants (Kaupp et al., 2003; Strünker et al., 2006; Bönigk et al., 2009), olfactory neurons can generate single-molecule responses (Bhandawat et al., 2010) and register subpicomolar pheromone concentrations (Leinders-Zufall et al., 2000; Zufall and Munger, 2010), and Caenorhabditis elegans can track temperature changes as small as 0.1°C (Hedgecock and Russell, 1975; Ramot et al., 2008). Several of these sensory feats involve synthesis of cyclic guanosine 3′,5′-monophosphate (cGMP) by receptor guanylyl cyclases (GCs). They serve from worms to mice as chemoreceptors for semiochemicals such as small peptides (Leinders-Zufall et al., 2007), carbon dioxide (Sun et al., 2009; Hallem et al., 2011), carbon disulfides (Munger et al., 2010), and extracellular pH (Murayama et al., 2013). GCs are also key to pathogen defense in plants (Irving et al., 2012). Despite their prominent role in chemosensory signaling, the mechanisms have not been established by which chemoreceptor GCs encode spatiotemporal stimulus patterns. In fact, the molecular and cellular underpinnings of single-molecule sensitivity are not known for any eukaryotic chemosensory cell.

Sperm of the sea urchin Arbacia punctulata provide a unique system to reveal the cellular makings underlying single-molecule detection in quantitative terms. For sensing a chemical gradient, sperm perform a variety of computational operations (Alvarez et al., 2014). Sperm temporally sample single chemoattractant molecules impinging on their flagella and integrate the binding events to generate a summed Ca2+ response (Kashikar et al., 2012; Kaupp, 2012). The signaling pathway involves a chemoreceptor GC (Singh et al., 1988) and three different ion channels (Gauss et al., 1998; Strünker et al., 2006) that generate the voltage and Ca2+ response. Whereas the signaling mechanisms downstream of the receptor have been elucidated, it is not known how the chemoreceptor encodes single binding events by rapid sampling (0.5 s) and maintains its sensitivity over a wide dynamic range.

Here, we identify four novel features of the GC receptor that provide insight into ultrasensitive signaling: (1) an exquisitely high GC density, (2) a high ligand affinity combined with a wide dynamic range spanning several orders of magnitude of chemoattractant, (3) rapid inactivation by multiple dephosphorylations of the receptor, and (4) a surprisingly low signal amplification that, however, is sufficient to produce a single-molecule response in sperm. The high density, wide dynamic range and rapid receptor inactivation allow sperm to maintain a high sensitivity during rapid, repetitive probing of chemoattractant concentrations at sampling rates ≤1 Hz.

### The receptor density is extraordinarily high

In a landmark paper, Berg and Purcell (1977) derived from first physical principles the precision by which cells can measure the concentration of a chemical ligand. A crucial determinant of sensitivity is the number of absorbing chemoreceptors on the cell surface. For bacteria operating at micromolar concentrations of chemoattractant, ∼15,000 receptors/cell are required to track down a chemical gradient precisely (Sourjik and Wingreen, 2012). However, sperm operate in the picomolar regime of concentrations when only a few molecules hit the cell surface (Kaupp et al., 2003; Kashikar et al., 2012). To explain the precision by which sperm can sample molecules, we determined the copy number of GC/sperm cell by two independent methods. First, we used quantitative mass spectrometry (MS) in combination with stable-isotope dilution. As a protein standard for absolute quantification (PSAQ; Brun et al., 2007), full-length GC labeled with 13C/15N during heterologous expression in Sf21 cells was used. The purified PSAQ-GC was analyzed for the fraction of isotope incorporation. The absolute amount of protein was determined by quantitative amino acid analysis. A. punctulata sperm (5 × 107 cells) were dissolved in SDS sample buffer, and then, the PSAQ-GC was added. After in-gel digestion, the peptides were eluted from the gel and analyzed by MS. We obtained a value of 179,020 ± 32,550 GC molecules/sperm cell (mean ± SD; n = 33, 6 animals). Second, we measured the GC density by densitometric analysis of Coomassie-stained sperm proteins separated by SDS-PAGE (Fig. S1). The intensity of the GC band was compared with that of two standard proteins and purified recombinant GC. The mean number of GC molecules per cell determined by densitometry was 295,760 ± 18,870 (mean ± SD of mean values from the three standards; Table 1). The copy numbers derived from these independent approaches agree reasonably well. Previous accounts reported ≤20× lower GC densities (Shimomura and Garbers, 1986; Shimomura et al., 1986; Nishigaki and Darszon, 2000). Although we do not know the reason for this discrepancy, we emphasize that the two methods consistently yield high receptor densities.

The GC is localized to the flagellum (Bönigk et al., 2009). Assuming a flagellar surface area of 35 µm2 (length of 45 µm and radius of 0.125 µm), the density ranges between 5,100 and 8,500 GC molecules/micrometer squared. Considering a diameter of 5.3 nm for the globular extracellular domain (molecular mass of ∼60 kD), the GC covers 11–19% of the flagellar surface. Thus, the GC rivals with rhodopsin in photoreceptors (20,000 rhodopsin molecules/micrometer squared) as one of the most densely packed membrane receptors.

Many ion channels and receptors form supramolecular complexes (signalosome) to enhance signaling efficacy (Huber et al., 1996; Tsunoda et al., 1997; Scott and Zuker, 1998). For signaling complexes to be effective, its components, e.g., the source and target of a cellular messenger, such as cGMP, must exist in equal molar quantities. Therefore, we determined the ratio between the GC and the K+-selective cyclic nucleotide-gated (CNG) channel (CNGK; Strünker et al., 2006; Bönigk et al., 2009), the downstream target of cGMP signaling. We used isotope-labeled AQUA (absolute quantification) peptides for quantification of protein ratios (Gerber et al., 2003). Before tryptic digestion, the sample was spiked with three different AQUA peptides each for GC and CNGK. AQUA peptides often report lower copy numbers of proteins (Brun et al., 2007), because not all of the target peptides are quantitatively recovered during various preparation steps. For example, protein digestion may be incomplete, and digested peptides may not be fully eluted from the gel. Indeed, the recovery rate of GC peptides during the preparation was low (15–25%). We determined a ratio of 24 ± 5 GC copies per CNGK (n = 19, 5 animals). Assuming that peptide recovery was similar for the receptor and the channel, we obtained a density of 355 CNGK molecules/micrometer, i.e., similar to the density of the CNG channel in rod photoreceptors (Haynes et al., 1986; Zimmerman and Baylor, 1986; Cook et al., 1989). This result argues that GC and CNGK do not assemble in a signalosome.

### Chemoattractant binding spans six orders of magnitude

Instead of using a classical receptor–ligand binding assay, we developed a bioassay that allowed measuring ligand binding over six orders of magnitude of resact concentrations. Intact sperm were incubated with various concentrations of the chemoattractant resact. Free and sperm-bound resact was separated by centrifugation. Free resact in the supernatant was used to evoke Ca2+ signals in sperm that had been loaded with the Ca2+ indicator Fluo-4 (Kaupp et al., 2003). The free resact concentration was determined by comparing the slope of Ca2+ signals evoked by the supernatant with signals evoked by defined resact concentrations. Using this assay, a binding isotherm was determined for concentrations ranging from 1 pM to 1 µM. The binding isotherm was shallow and saturates at ∼1 µM resact (126 experiments; Fig. 1 A). A fit of the Hill equation to the binding data yielded a constant of half-maximal binding K1/2 of 0.65 ± 0.08 nM and a Hill coefficient of n = 0.49 ± 0.03 (mean ± standard error of the regression).

Members of the GC family form homodimers or trimers (Wilson and Chinkers, 1995; Yu et al., 1999; Vaandrager, 2002; Ogawa et al., 2004). Therefore, the low Hill coefficient might reflect negative cooperativity among binding sites, i.e., the level of receptor occupancy regulates binding affinity. Alternatively, the receptor population might be composed of a mixture of receptors with a range of different K1/2 values; such a mixture will give rise to shallow binding curves with anomalously low Hill coefficients. Both mechanisms predict that the binding affinity is higher when only one GC subunit in the dimer/trimer is occupied. We tested this prediction at low levels of receptor occupancy (≤25%). A fit of the data with a simple binding isotherm yielded a Kd value of 90 ± 84 pM (24 experiments; range of 1.6–301.2 pM; Fig. 1 B). Whatever the mechanism might be, this result shows that K1/2 values change with receptor occupancy, which extends the operational range and, thereby, prevents premature receptor saturation.

### The receptor GC rapidly inactivates after ligand binding

Generating a single-molecule response not only requires that a single resact molecule binds and activates a receptor but also that activation of a single receptor generates sufficient cGMP molecules, which is ∼25 cGMP molecules (Bönigk et al., 2009). Previous accounts using classical steady-state enzyme assays with broken cells or solubilized receptors reported GC activities that varied by more than four orders of magnitude between experiments (Table S1), and the signaling gain was far too small for single-molecule sensitivity. To revisit this issue, we kinetically followed GC activity by measuring cGMP synthesis in intact sperm with the quenched-flow technique (Kaupp et al., 2003). Resact stimulates a steep rise of cGMP followed by a rapid decline, reflecting synthesis and hydrolysis of cGMP, respectively (Kaupp et al., 2003). To study the rate of cGMP synthesis on its own, hydrolysis was prevented by 3-isobutyl-1-methylxanthine (IBMX), a phosphodiesterase inhibitor. Under these conditions, the cGMP concentration rapidly reached a stable plateau (Fig. 2 A; Kaupp et al., 2003), showing that cGMP synthesis ceased within ∼0.4 s. The cGMP synthesis might be terminated by depletion of the substrate GTP, by GC inactivation, or both. Two observations argue for GC inactivation: the cGMP increase tapers off even at low resact concentrations, and the amount of cGMP synthesized (Kaupp et al., 2003) is much less than the cellular GTP concentration (≳1 mM).

From the time course of cGMP increase (Fig. 2 B), two functionally important parameters can be derived: the turnover number T, i.e., the number of cGMP molecules synthesized by an active GC (GC*) per second, and the rate constant of inactivation ki. Both measures set the signaling gain. The turnover number T was derived according to Eqs. 1–4 (Materials and methods), assuming a bimolecular reaction between ligand and GC. The mean value of T was 72.2 ± 28.7 cGMP molecules/second (seven concentrations with 3–10 experiments; Fig. 2 C). The GC activity rapidly declined (Fig. 2 B) with a rate constant ki of 6.4 ± 2.4 s−1 (Fig. 2 D), corresponding to an inactivation time τi of 157 ms. Thus, during the GC* lifetime, on average, 11 cGMP molecules are produced. The turnover number is similar to that reported for GC-E and GC-F in retinal photoreceptors (74–116 cGMP molecules/second; Peshenko et al., 2011) but many orders of magnitude larger than that determined by steady-state assays (Table S1), which grossly underestimate the turnover caused by rapid GC inactivation.

### Inactivation of GC is caused by dephosphorylation

The GC is phosphorylated at rest and becomes dephosphorylated upon resact binding (Ward and Vacquier, 1983; Suzuki et al., 1984; Ward et al., 1986), suggesting that the GC inactivates by dephosphorylation. We identified by tandem MS the amino acid residues that are phosphorylated at rest and become dephosphorylated after resact stimulation. Curiously, the published sequence of the A. punctulata GC (Singh et al., 1988), the founding member of the GC family (Wedel and Garbers, 2001), lacks the canonical sequence motif of the catalytic domain. We reexamined the primary structure of the GC by cloning of cDNA from an A. punctulata testis library. The derived amino acid sequence differs from the published sequence by 203 residues in the C-terminal region that carries the catalytic domain. MS analysis identified 14 peptides of the new C-terminal region present in native GC (Fig. S2 A). We identified six phosphorylated serine residues in the unstimulated GC (S558, S562, S569, S572, S575, and S1106; Fig. S2 A and Table S2), five of which are located in the kinase homology domain (KHD). After resact stimulation, four phosphorylated residues became completely dephosphorylated: for S562, S569, and S572 in the KHD and S1106 in the C-terminal region, we only identified dephosphorylated peptides. For S558 and S575, we estimated that ∼10% and 1% of these residues remained phosphorylated, respectively (Table S3). A loss of ≤15 phosphate groups has been reported (Vacquier and Moy, 1986). We do not know the reason for this discrepancy; however, we note that previous studies on other GCs revealed less than eight phosphate groups per GC (Potter and Hunter, 1998a,b; Potter, 2011).

Next, we studied whether dephosphorylation of GC could be the mechanism of inactivation. First, we compared the kinetics of inactivation and dephosphorylation. Upon stimulation, the GC undergoes a shift in electrophoretic mobility that is associated with a loss of phosphate groups on serine residues (Ward and Vacquier, 1983; Suzuki et al., 1984; Vacquier and Moy, 1986). We used the shift of ∼4 kD to follow kinetically the dephosphorylation by Western blotting of protein samples from sperm that had been rapidly quenched at various times after mixing with resact (Fig. 3 A). Of note, only a single shift in electrophoretic mobility was observed, although several phosphate groups are removed. We do not know in quantitative terms the phosphorylation status of the upper and lower band. They may consist of a mixed population of GC molecules with different phosphorylation patterns. Moreover, the mobility shift might come along with the removal of a single phosphate only. In fact, a similar observation is known for the Dictyostelium discoideum cAMP receptor; it also exhibits a single mobility shift upon phosphorylation of a specific amino acid residue in a sequence of five phosphorylation steps (Klein et al., 1987; Caterina et al., 1995). We used the motility shift as an indicator for dephosphorylation by itself and refer to the unstimulated population as GCphos and to the shifted population as GCdephos.

The changes in GCphos and GCdephos species were stoichiometric and followed a similar time course (Fig. 3 B). Of note, a change in GC phosphorylation was apparent as early as 25 ms after stimulation. Dephosphorylation started instantaneously with no latency: linear extrapolation of the initial slope of the dephosphorylation rate intercepted with the amount of dephosphorylated GC at t = 0 (Fig. 3 B, inset). Thus, dephosphorylation precedes changes in membrane voltage (Vm), intracellular pH (pHi), and intracellular Ca2+ ([Ca2+]i) that display latencies of several tens to hundreds of milliseconds (Kaupp et al., 2003; Strünker et al., 2006).

The inactivation rate was largely independent of ligand concentration over more than three orders of magnitude (Fig. 2 D). The invariant ki is remarkable, considering that the GC is the most abundant protein. This result suggests that inactivation is an intrinsic property of the GC rather than the result of an extrinsic enzymatic reaction. We further analyzed the time constant τdephos of the dephosphorylation reaction. The following model described the time course of dephosphorylation:

$[GCphos]+[L]⇄k−1k1[GCphosL]→k2[GCdephosL]⇄k−3k3[GCdephos]+[L],$

wherein L denotes the ligand, k1 and k−1 denote the on and off rate constants of binding to GCphos, respectively, k2 is the rate constant of dephosphorylation, and k3 and k−3 are the respective rate constants of binding to GCdephos. A global fit of the data to this model yielded a k2 of 7.53 ± 4.6 s−1 or a τ2 of 133 ms (Fig. 3 C). Thus, the mean τi = 157 ms and τdephos = 133 ms match. This match is also evident when comparing the time course of GC inactivation and GC dephosphorylation (Fig. 3 D). Although we do not know which step in the dephosphorylation reaction reflects the mobility shift, the similar time course suggests that dephosphorylation terminates GC activity.

At low occupancy, dephosphorylation was superstoichiometric. For example, when ≤25% of the GC monomers were occupied, about twice as many GC molecules were dephosphorylated (Fig. 3 E). This finding suggests that the stoichiometry for the resact-to-receptor binding is 1:2, similar to the stoichiometry of atrial natriuretic peptide binding to GC-A (Ogawa et al., 2004). Alternatively, if the stoichiometry of resact binding were 1:1, this would imply that an occupied receptor could dephosphorylate an empty receptor by a trans-mechanism.

### Does alkaline-induced dephosphorylation terminate GC signaling?

Resact initiates a rapid alkalinization by stimulating the activity of an Na+/H+ exchanger (Johnson et al., 1983), and artificial alkalinization of the cytosol by weak bases causes dephosphorylation of the GC, suggesting that resact-induced alkalinization terminates GC activity via dephosphorylation (Ramarao and Garbers, 1985; Ward et al., 1986; Darszon et al., 2008). However, direct proof of this mechanism is lacking. Using the pHi indicator BCECF, we compared resact-induced changes in pHi (Fig. S3 A) with the changes produced by mixing sperm with the weak bases NH4Cl and trimethylamine (TMA; Fig. S3, B and C). The maximal ΔpHi of 0.2 evoked by resact was similar to the ΔpHi evoked by mixing of sperm with 1 mM NH4Cl or 3 mM TMA (Fig. S3, B and C). However, alkalization by 1 mM NH4Cl or 3 mM TMA did not cause GC dephosphorylation (Fig. 4, A and B). Higher concentrations of NH4Cl or TMA produced a stronger alkalization (Fig. S3, B and C) and, indeed, induced a slow GC dephosphorylation that required ≥5 min to become noticeable (Fig. 4, A and B). We conclude that physiological changes in pHi do not produce GC dephosphorylation; moreover, dephosphorylation evoked by strong, nonphysiological alkalization proceeds too slowly to account for the rapid inactivation and dephosphorylation caused by resact.

Nevertheless, we took advantage of the alkaline-induced dephosphorylation to independently test whether dephosphorylated GC, in fact, is inactive and cannot be activated by resact. After a 15-min incubation of sperm with 122 mM TMA, the mobility shift was complete, indicating dephosphorylation (Fig. 4 C), and the cGMP synthesis induced by 250 nM resact was abolished (Fig. 4 D). In untreated control sperm, which contained only phosphorylated GC, 250 nM resact induced both a substantial dephosphorylation within 1.6 s (Fig. 4 C, left) and a rapid cGMP increase that leveled off after 0.4 s (Fig. 4 D). In conclusion, dephosphorylation is the principle mechanism of receptor inactivation, and the dephosphorylated GC cannot be activated by resact.

### Recombinant GC is inactive

The originally cloned GC was inactive (Singh et al., 1988), not surprising considering that the catalytic domain was lacking. We tested whether the full-length GC is active when heterologously expressed. To this end, we coexpressed the GC with a cGMP-sensitive CNG channel (Altenhofen et al., 1991; Schröder-Lang et al., 2007) in HEK293 cells to monitor the cGMP synthesis via Ca2+ influx. Immunohistochemistry on intact HEK293 cells and membrane sheets demonstrated that the GC was targeted to the plasma membrane (Fig. 5 A). However, even high resact concentrations failed to evoke a Ca2+ response, whereas superfusion of cells with 8-bromo (Br)-cGMP, a membrane-permeable cGMP analogue, produced a large Ca2+ signal (Fig. 5, B and C). We next examined, whether heterologously expressed GC was properly glycosylated and phosphorylated. The apparent molecular mass of native dephosphorylated GC was larger than that of recombinant GC. Upon treatment with PNGase, the molecular mass of native GC became smaller, whereas the molecular mass of recombinant GC was largely unchanged (Fig. 5 D). After deglycosylation, the native dephosphorylated GC and the recombinant GC run almost at the same apparent molecular mass. These results show that recombinant GC is differently glycosylated and also dephosphorylated. Alterations of these posttranslational modifications may be the reason why the recombinant protein is nonfunctional (Koller et al., 1993; Müller et al., 2010).

### Dephosphorylation is independent of signaling events downstream of GC

GC activation by resact first evokes a rapid, transient hyperpolarization (Fig. 6 A; Babcock et al., 1992; Strünker et al., 2006) that triggers all other downstream signaling events. In the presence of 58 mM extracellular K+ concentration ([K+]ex), the resact-evoked hyperpolarization was abolished along with changes in pHi and Ca2+ (Fig. 6, A–C), yet the extent of dephosphorylation was largely unaffected (Fig. 6 D). At 100 mM [K+]ex, resact evoked a slight depolarization (15 mV; Fig. 6 A), and voltage-dependent Ca2+ channels opened, which caused a moderate [Ca2+]i increase (Fig. 6 C). At [K+]ex ≥ 58 mM, dephosphorylation proceeded two to three times slower (Fig. 6 E), and consequently, cGMP synthesis lasted longer; thereby, cGMP levels were enhanced two- to threefold (Fig. 6 F; Harumi et al., 1992). However, higher cGMP levels did not affect the extent of dephosphorylation (Fig. 6 D). Thus, the rapid dephosphorylation is independent of resact-induced ΔVm, ΔpHi, Δ[Ca2+]i, and ΔcGMP.

Finally, three powerful inhibitors of generic phosphatases—calyculin A, okadaic acid (Ishihara et al., 1989), and sanguinarine chloride (Aburai et al., 2010)—did not affect the extent and speed of dephosphorylation (Fig. 6, G and H). Moreover, the resact-induced cGMP increase was not altered by calyculin A (Fig. S4). Thus, inhibitors of PP1, PP2A, and PP2C, which account for the majority of conventional serine/threonine phosphatases, have little or no effect. Collectively, these results suggest that activated GC undergoes autodephosphorylation rather than dephosphorylation by an exogenous phosphatase.

Here, we identify several features of a chemoreceptor that enable sperm to count chemoattractant molecules with a precision at the physical limit and a sampling rate of ∼1 Hz. Key to this remarkable skill is (a) a high receptor GC density, (b) a high ligand affinity combined with a wide operational range, (c) a relatively long-lived receptor–ligand complex, and (d) rapid inactivation by multiple autodephosphorylation. We will discuss the functional significance of each feature.

### Why is the receptor density so high?

Chemoattractants randomly impinging on the cell surface cause “molecule noise” that limits the precision of chemical sensing. A measure of the precision of sensing is the uncertainty δc/c, i.e., the incremental increase δc of a concentration c; only if δc/c is sufficiently high, a new binding event can be distinguished from molecule noise. If we consider a sperm cell as an absorbing sphere covered with surface receptors, the uncertainty δc/c of measuring a concentration c is given by δc/c = (NR s D c τ)−1/2, wherein NR is the number of the receptors, s is the effective radius of the binding site, D is the diffusion constant of the chemoattractant, and τ is the sampling time (Berg and Purcell, 1977). We calculated δc/c for different resact concentrations from 0.1 pM to 10 nM (Fig. 7 A) using the following parameters: NR = 3 × 105 receptors (Table 1), Dresact = 2.4 × 10−6 cm2/s (Kashikar et al., 2012), and τ = 0.5 s (Kaupp et al., 2003; Kashikar et al., 2012). The dimension s of the binding site is not known. Therefore, we used as upper and lower limits the radius of the extracellular GC domain (2.65 nm) or the radius of the resact peptide (0.65 nm; Fig. 7 B), respectively. At 1 pM resact, the uncertainty δc/c to count molecules is 0.13–0.27 or 13–27%. For an ellipsoid-shaped flagellum (half-axis a = 25 µm and b = 0.125 µm; Berg, 1993), at 1 pM, on average, 3.5 resact molecules are impinging during the sampling time of 0.5 s. This exercise illustrates that, at very low resact concentrations, A. punctulata sperm in fact can count individual binding events, i.e., operate at the physical limit. In comparison, bacteria and amoebae operate at nano- to micromolar chemoattractant concentrations; therefore, these cells get by with ∼15,000 receptors per cell (Li and Hazelbauer, 2004; Cannistraro et al., 2011; Sourjik and Wingreen, 2012).

The high GC density is beneficial for a second reason. In the Berg–Purcell model, receptors can be reused within a few milliseconds after clearance of the binding site from ligands. Clearance occurs by dissociation of the ligand from the binding site. This assumption is well reasoned for bacterial receptors with micro- to millimolar affinities and, therefore, dwell times of the ligand on the receptor in the micro- to millisecond range. However, the high ligand affinity of the GC in the subnanomolar range prevents receptors from becoming cleared quickly; consequently, on their voyage to the egg, sperm would suffer a continuous loss of vacant or functional receptors. A high receptor density combined with an extended binding range ensures that a sufficient number of vacant receptors are available even at high ligand concentrations prevailing near the egg. For example, when only 3% of vacant receptors are left (NR = 9,000), a resact concentration of 10 nM near the egg (Kashikar et al., 2012) can be sensed with an uncertainty of only 5% (Fig. 7 A). As much as sperm are single-use machines, the GC is a single-use chemoreceptor.

### Receptor occupancy controls ligand affinity

The binding curve of resact is much shallower than a normal binding isotherm and spans six orders of magnitude; thereby, sperm escape premature saturation at higher ligand concentrations. We also provide evidence that ligand affinity is higher at low compared with high chemoattractant concentrations. The subnanomolar affinity at very low concentrations is advantageous in two respects. It provides a ligand–receptor complex that is relatively long-lived to produce sufficient cGMP molecules, and it prevents overcounting by multiple rebinding of ligand to the same or neighboring receptors, which adds noise without providing new information on the gradient (Endres and Wingreen, 2009).

Negative cooperativity between binding sites might be a mechanism that gradually lowers binding affinity as more receptors become occupied. In fact, a Hill coefficient of n = 0.5 is consistent with negative cooperativity between subunits in a dimeric or trimeric GC complex. However, other mechanisms cannot be excluded. A set of low- to high-affinity receptors would also extend the operational range. An example of shallow binding isotherms as a result of mixed receptor populations has been provided for CNG channel activation by cGMP (Ruiz et al., 1999). Alternatively, one of the resact-induced cellular responses could serve as negative feedback that lowers receptor affinity. Any of these mechanisms reconciles a wide dynamic range with the need for high affinity and long signaling lifetime at very low chemoattractant concentrations.

### The GC inactivates by autodephosphorylation

The GC is a moonlighting enzyme, whose multiple catalytic functions are not yet fully appreciated. In fact, members of the GC family in plants have long been known as kinases, whereas their ability to synthesize cGMP was revealed only recently (Irving et al., 2012). Moreover, the GC in rod photoreceptors can undergo autophosphorylation and sustains phosphorylation of standard substrates (Aparicio and Applebury, 1996; Bereta et al., 2010).

Here, we add a new twist. Several lines of evidence suggest that the GC inactivates by autodephosphorylation. First, inactivation kinetics is largely independent of the number of occupied GC molecules. This finding is difficult to reconcile with exogenous phosphatase activity: the GC is the most abundant protein in the flagellum, and the availability of a phosphatase should become rate limiting at high stimulation levels. Second, dephosphorylation along with cGMP synthesis is the first detectable cellular event and does not require changes in cGMP, Vm, pHi, and [Ca2+]i. Finally, several inhibitors that abolish the activity of most generic serine/threonine phosphatases are unable to prevent dephosphorylation. However, we cannot exclude the possibility that the GC also displays intrinsic kinase activity in the resting state. Upon resact binding, kinase activity might be diminished and might result in dephosphorylation, i.e., the balance between autokinase and autophosphatase activity determines the phosphorylation status.

Quite generally, phosphorylation/dephosphorylation represents a reversible chemical reaction. Several bifunctional proteins, e.g., the isocitrate dehydrogenase kinase/phosphatase, support both phosphorylation and dephosphorylation (Zheng and Jia, 2010). Most likely, phosphatase and kinase activity of the GC are located in the KHD. Three amino acid motifs (VAIK, HRD, and DFG) are essential for the alignment of ATP and substrate in the active center of classic kinases to facilitate transfer of a phosphogroup (Hanks and Hunter, 1995). In the GC of sea urchin sperm, 26 of 31 amino acid residues that constitute the core structure in kinases are conserved, among them the invariant K597 of the VAIK motif and D710 of the DFG motif. However, the catalytic aspartate in the HRD motif, which initiates phosphotransfer by nucleophilic attack of a hydroxyl group in the substrate, is replaced by a histidine (H691). Pseudokinases lacking one of these key residues have been considered as catalytically inactive, although some pseudokinases developed alternative mechanism for catalysis (Boudeau et al., 2006; Mukherjee et al., 2008). One such example is GC-E of photoreceptors, which displays kinase activity, although it lacks the catalytic aspartate in the HRD motif (Aparicio and Applebury, 1996).

The activity of mammalian receptors GC-A and GC-B is also regulated by phosphorylation; dephosphorylation of five to six serine or threonine residues in the KHD terminates GC activity (Fig. S2 B; Potter and Hunter, 1998a,b; Potter, 2011). Moreover, substitution of serine with glutamate residues, which mimic phosphorylated sites but cannot be dephosphorylated, produces mutants that do not desensitize (Potter and Hunter, 1999; Yoder et al., 2010, 2012). The kinases and phosphatases acting on GC-A and GC-B are not known. We suggest that autophosphorylation/dephosphorylation should also be considered for other members of the GC family.

### Why autodephosphorylation in multiple steps?

Sperm navigation relies on the timing and waveform of Ca2+ signals that control steering responses (Friedrich and Jülicher, 2007; Alvarez et al., 2012, 2014). Sperm periodically sample chemoattractant concentrations for 0.2–0.6 s about once every second (Kashikar et al., 2012). Thus, the GC inactivation time of 150 ms is perfectly tuned to the sampling time and frequency. Autodephosphorylation could provide a mechanism for inherently precise timing of inactivation and endows sperm with the ability to track periodic signals with a frequency of ∼1 Hz.

However, in the single-molecule regimen, an exponential probability distribution of the GC* lifetime would produce highly variable Ca2+ responses. This source of molecule noise compromises the precision of chemoattractant measurement at low chemoattractant concentrations. Sequential multistage dephosphorylation could tightly control the GC* lifetime and, thereby, produce uniform Ca2+ responses. A precedent for stepwise receptor inactivation has been proposed for rod photoreceptors (Burns and Pugh, 2010): two phosphorylation steps of rhodopsin and final “capping” of phosphorylated rhodopsin by arrestin are sufficient to control the lifetime of active rhodopsin and, thereby, reduce photon noise (Whitlock and Lamb, 1999; Doan et al., 2006; Burns and Pugh, 2010). However, other mechanisms, such as spatiotemporal filtering by longitudinal diffusion of cGMP, also can produce uniform single-photon responses (Bisegna et al., 2008; Caruso et al., 2011).

### Comparison with other signaling systems—commonalities and differences

Several mechanisms have been proposed that explain cellular ultrasensitivity. These concepts largely originate from the study of signaling in photoreceptors, olfactory neurons, and bacteria. Mechanisms include (a) lattices of highly cooperative chemoreceptors in bacteria (Maddock and Shapiro, 1993; Bray et al., 1998; Duke and Bray, 1999; Gestwicki and Kiessling, 2002; Sourjik and Berg, 2004), (b) high multistage gain provided by a cascade of enzymatic reactions in photoreceptors (Pugh and Lamb, 2000; Yau and Hardie, 2009; Kaupp, 2010), (c) local signaling by supramolecular complexes (transducisome or signalosome; Huber et al., 1996; Tsunoda et al., 1997; Scott and Zuker, 1998), and (d) restricted diffusion of chemical messengers in confined cellular subcompartments (Rich et al., 2000, 2001).

Sperm use different principles to achieve single-molecule sensitivity. First, sperm do not rely on arrays of receptor clusters that display positive cooperativity. Second, amplification at the receptor level is orders of magnitude lower in sperm compared with rod photoreceptors. Capture of a single photon initiates the hydrolysis of ∼6,600 cGMP molecules by two-stage amplification (Pugh and Lamb, 2000; Burns and Pugh, 2010), whereas binding of a single resact molecule produces ∼11 cGMP molecules; thus, cGMP amplification in rods is ∼600-fold larger. Nonetheless, rod and sperm operate at a similar level of sensitivity: Binding of a molecule to sperm or capture of a photon by rods each evokes a ΔVm of 1–2 mV (Pugh and Lamb, 2000; Strünker et al., 2006). Taking into account a volume ratio Vrod/Vflagellum of 80/2 fl = 40:1, the change in cGMP concentration per unit volume is only 15× larger in rods compared with sperm. Finally, the input resistance of sperm (≳5 GΩ; Navarro et al., 2007; Zeng et al., 2013) is at least fivefold higher than that of mammalian rod photoreceptors (1–2 GΩ; Schneeweis and Schnapf, 1995); thus, by changing the open probability of only a few CNGK channels, sperm can produce a single-molecule response.

Third, it has been argued that second-messenger concentrations steeply decay from the site of synthesis (Rich et al., 2000, 2001), which calls either for a signaling complex between receptors and downstream targets or for restricted diffusion in subcellular compartments that channel the messenger to the target. In order for a GC–CNGK complex to be effective, receptor (GC) and target (CNGK channel) ought to be present stoichiometrically, whereas, in fact, the GC is ∼20-fold more abundant than the CNGK.

To examine the impact of diffusion, we analytically solved unrestricted diffusion of cGMP from a point source of synthesis at the membrane for a cylindrical geometry (see Materials and methods). Within ∼15 µs, the cGMP concentration equilibrates across the flagellar diameter, and within ∼100 ms, it equilibrates along the length of the flagellum (Video 1). In a 155-nm-long segment of the flagellum, neglecting cGMP binding to high-affinity buffers or hydrolysis by phosphodiesterase, the cGMP transiently rises to micromolar concentrations that saturate any nearby CNGK channels (K1/2 = 25 nM; Video 1; Bönigk et al., 2009). For a regular arrangement of ∼100 GC dimers in a 155 × 155–nm membrane patch, an active GC* would be girded by nine CNGK channels at a distance not farther than ∼100 nm (Fig. 7 C); these next neighbors would be first served with cGMP molecules. Because of the high input resistance of sperm, opening a few CNGK channels is sufficient to hyperpolarize sperm by 2 mV (Strünker et al., 2006). Thus, there is no need to invoke signaling complexes or restricted diffusion to account for single-molecule sensitivity of sperm. The exquisite cGMP sensitivity of CNGK channels, the miniscule flagellar volume, and the high input resistance are key. The hallmarks of this signaling mechanism provide a blueprint for chemical sensing in small compartments, such as olfactory cilia, insect antennae, or even synaptic boutons.

### Materials and reagents

We obtained dry sperm by injecting 0.5 M KCl into the body cavity of A. punctulata or stimulating the animal electrically. Dry sperm was diluted in artificial sea water (ASW), which contained 423 mM NaCl, 9.27 mM CaCl2, 9 mM KCl, 22.94 mM MgCl2, 25.5 mM MgSO4, 0.1 mM EDTA, and 10 mM Hepes, pH 7.8, adjusted with NaOH. All reagents were purchased from Sigma-Aldrich if not otherwise stated.

### Sperm counting

The number of sperm cells in a sample is critical for the determination of the GC density. Sperm cells in a suspension were counted with a Neubauer cell counter and a CASY Cell Counter system (Roche). Cell counts obtained by either method were not statistically different. The sperm number ranged from 0.7 × 1010 to 8.7 × 1010 sperm cells/milliliter dry sperm; the mean was 3.4 ± 1.8 × 1010 cells/milliliter (19 animals; Fig. S5).

### Cloning of the GC

An oligo-dT–primed cDNA library was constructed in a phage λ ZAP II vector (Agilent Technologies) using poly(A)+ RNA from A. punctulata testis. Approximately 500,000 independent recombinants were screened with a PCR fragment encoding a portion of the KHD of the GC (Singh et al., 1988). A full-length clone of ∼4,000 bp was completely sequenced on both strands. The largest open reading frame codes for a protein of 1,122 amino acid residues with a calculated molecular mass of 126 kD. The sequence was analyzed with PROSITE for potential sites of posttranslational modification. For GC expression, the sequence has been cloned into the pcDNA3.1(+)-hygromycin vector (Invitrogen). To ensure proper membrane targeting, the GC signal peptide (amino acids 1–24) has been replaced with the signal peptide of the human epidermal growth factor receptor (MRPSGTAGAALLALLAALCPA).

### Antibodies

Rat monoclonal antibody GCN-3D12 was directed against aa 86–197 in the N-terminal domain of the GC from A. punctulata. A fusion protein comprising an N-terminal maltose-binding protein and aa 86–197 of the GC was generated and heterologously expressed in Escherichia coli. After purification with an amylose affinity column (New England Biolabs, Inc.), rats were immunized subcutaneously and intraperitoneally with the fusion protein in the presence of Freund’s adjuvant. A boost without adjuvant was given 6 wk after the primary injection. Fusion was performed using standard procedures. Supernatants were tested by differential ELISA with the GC–maltose-binding protein fusion protein and with unrelated proteins coupled to the same carrier. Monoclonal antibodies that reacted specifically with GC were further analyzed by Western blotting. Tissue culture supernatant of clone 3D12, rat IgG1 subclass, was used in this study. The antibody recognized the recombinant and the native protein both in the phosphorylated and unphosphorylated states. Mouse monoclonal antibody CRO/CBL 3B10-121 directed against aa 482–664 of the rat CNGA2 channel was generated following the same procedure (Meyer et al., 2000).

### Stable expression of the recombinant GC

To functionally study the recombinant GC, a HEK293 cell line expressing a mutated olfactory CNGA2 channel was used. The T537S mutation renders the CNG channel more sensitive for cGMP; the mutant channel is suitable as a cGMP sensor in functional assays (Altenhofen et al., 1991). Cells were transfected using the Neon Transfection System (Life Technologies) according to the manufacturer’s instructions. For the selection of HEK293 cells stably expressing the CNGA2 mutant and GC, 0.8 mg/ml antibiotic G418 (Invitrogen) and 0.5 mg/ml hygromycin B were used. Monoclonal cell lines were identified by Western blotting and immunocytochemistry using CNGA2- and GC-specific antibodies.

### Immunocytochemistry and membrane sheets

Double-stable HEK293 cells were placed on 13-mm coverslips coated with 0.1 mg/ml poly-l-lysine. Cells were cultured at 29°C overnight to enhance membrane insertion of the GC. Membrane sheets were produced according to Heuser (2000), applying a 0.1-s ultrasound pulse to cells bathed in 1 ml stabilization buffer (70 mM KCl, 5 mM MgCl2, 3 mM EGTA, 1 mM DTT, and 30 mM Hepes, pH 7.4). Cells or membrane sheets were fixed for 5 min with 4% paraformaldehyde. After permeabilization with 0.5% Triton X-100 and 5% ChemiBLOCKER (EMD Millipore), cells or membrane sheets were incubated with primary antibodies CRO/CBL 3B10-121 (1:100) and GCN-3D12 (1:10) for 1 h. For visualization, goat anti–mouse Alexa Fluor 488 (Life Technologies)– and donkey anti–rat Cy3 (Jackson ImmunoResearch Laboratories, Inc.)– conjugated secondary antibodies were used.

### Ca2+ imaging of a double-stable HEK293 cell line

HEK293 cells stably expressing the recombinant GC and the cGMP sensor were placed in poly-l-lysine–coated 96-well plates. After culturing at 29°C overnight, the medium was replaced by extracellular solution (140 mM NaCl, 5.4 mM KCl, 1 mM MgCl2, 1.8 mM CaCl2, and 5 mM Hepes, pH 7.4). Cells were loaded with Fluo-4 acetoxymethylester (AM) in the presence of 0.01% Pluronic F127 for 1 h. After replacing the loading solution with extracellular solution, changes in fluorescence upon stimulation with 200 µM resact or 3 mM 8-Br-cGMP were recorded with a cell^R imaging system (Olympus).

### Deglycosylation of membrane proteins

For deglycosylation, membrane proteins were denatured by incubation in 0.5% SDS and 40 mM DTT at 95°C for 10 min. Deglycosylation was performed by 500 U PNGase F (New England Biolabs, Inc.) for 2 h at 37°C in the presence of 1% Nonidet P-40 in 50 mM phosphate buffer, pH 7.5.

### Purification of recombinant GC

As a standard for absolute quantification of the GC, the isotope-labeled protein was heterologously produced in Spodoptera frugiperda (Sf21) cells that were adapted to an IML406 medium supplemented with 13C6-lysine, 15N4-arginine, and 5% FCS (Brüggert et al., 2003). Cells were infected with a baculovirus containing the GC sequence (Bac-to-Bac Baculovirus Expression System; Life Technologies) and harvested after 72 h by centrifugation (700 g for 5 min at 4°C). The cell pellet was suspended into SDS sample buffer (50 mM Tris-HCl, pH 6.8, 2% SDS, 10% glycerol, 1% β-mercaptoethanol, and 0.02% bromophenol blue). Proteins were separated by a 6% SDS-PAGE. The gel band corresponding to the recombinant GC was excised and eluted by overnight incubation at 4°C in a buffer containing 150 mM NaCl, 0.1% SDS, 2 mM EDTA, and 10 mM Tris-HCl, pH 8.0. Protein purity was checked on a Coomassie-stained gel. Protein concentration was determined at 280 nm (ε280 = 161,810 M−1cm−1) and by amino acid analysis (Protagen Protein Services). Incorporation of the label into the recombinant GC was analyzed by selected reaction-monitoring (SRM) MS. The incorporation rate was calculated based on the relative intensity of the unlabeled compared with the fully labeled protein. The purified, labeled GC was used as a PSAQ by MS (Brun et al., 2007).

### Mass spectrometric identification of receptor GC

We analyzed membrane proteins of sperm flagella with MudPIT (Multidimensional Protein Identification Technology). Membrane pellets (300 µg protein) were washed twice with 100 mM (NH4)2CO3, pH 11; proteins were digested by sequencing-grade modified trypsin (Promega) in a methanol and NH4HCO3 buffer (Blonder et al., 2004). After removal of membranes by centrifugation (100,000 g for 30 min at 4°C), supernatants were desalted using solid-phase extraction pipette tips (Spec PT C18 AR; Varian). For the MudPIT analysis (Fränzel et al., 2010), a mass spectrometer (LTQ Orbitrap Velos; Thermo Fisher Scientific) was used. All database searches were performed using the SEQUEST algorithm, embedded in Proteome Discoverer (version 1.2.0.208; Thermo Fisher Scientific), with an NCBI protein database for Strongylocentrotus purpuratus proteins. The S. purpuratus protein sequences for the GC and the potassium-selective channel CNGK were replaced by the respective sequences from A. punctulata. Only tryptic peptides with a maximum of two missed cleavage sites were considered. Oxidized methionine was also accepted as modification. The mass tolerance for precursor ions was set to 6 ppm; the mass tolerance for peptide fragments was set to 0.8 amu. For search result filtering, the false discovery rate was set to <1%; at least two unique peptides per protein with search result rank 1 were required for identification.

### Determination of GC phosphorylation sites

Phosphorylated amino acid residues of GC were identified by MS. To prepare GCphos, dry sperm was solubilized for 30 min at 4°C in a buffer containing 25 mM MES, pH 6.2, 38% (vol/vol) glycerol, 10 mM NaF, 10 mM benzamidine, phosphatase inhibitor cocktails I and II (Sigma-Aldrich), and 1% (vol/vol) Triton X-100. After centrifugation (16,000 g for 30 min at 4°C), solubilized proteins were subjected to SDS-PAGE. To prepare GCdephos, dry sperm was diluted 1:6 in ASW and incubated with 4 µM resact for 10 min at room temperature. Sperm were solubilized in a buffer containing 25 mM MES, pH 6.2, protease inhibitor cocktail (Roche), and 1% (vol/vol) Triton X-100. Coomassie-stained protein bands of GCphos and GCdephos were excised from the gel and further investigated by MS. In-gel digestion with trypsin, chymotrypsin, AspN, and elastase was performed overnight as described in Czupalla et al. (2003) and Schlosser et al. (2005). Titanium dioxide-based enrichment of phosphorylated sequences followed by nano–liquid chromatography (LC)-MS/MS was performed on a mass spectrometer (quadrupole time-of-flight [Q-TOF] Ultima; Micromass) as described in Klemm et al. (2006). Peptides were separated using a capillary column (3 µm, 100 Å, and 150-mm × 75-µm inner diameter; PepMap C18; Dionex) and a flow rate of 200 nl/min. Mobile phase A was 0.1% formic acid in acetonitrile–water (3:97, vol/vol), and B was 0.1% formic acid in acetonitrile–water (8:2, vol/vol). Runs were performed using a gradient of 10–65% B in 60 min. To perform MS/MS experiments, automatic function switching (survey scanning) was used.

To identify phosphorylated and nonphosphorylated peptides after resact stimulation in semiquantitative terms, we performed additional MS analyses without titanium dioxide-based enrichment of phosphorylated sequences (hybrid mass spectrometer [Orbitrap Elite; Thermo Fisher Scientific] equipped with a liquid chromatography system [UltiMate 3000 LC; Dionex]). MS data were acquired in a data-dependent strategy, selecting MS/MS fragmentation events based on the precursor abundance in the MS scan. LTQ Orbitrap Velos MS/MS spectra were acquired with a target value of 10,000 ions. The maximum injection time for MS/MS was 80 ms, and the dynamic exclusion time was 60 s. Mascot Server 1.9 and 2.2.2 (Matrix Science) were used for database searching of the Q-TOF Ultima and Orbitrap Elite measurements, respectively. For Q-TOF data, mass tolerance was set to ±150 ppm and ±0.15 D for precursor mass and fragment ion mass, respectively. For Orbitrap Elite data, mass tolerance was set to ±10 ppm and ±0.35 D for precursor mass and fragment ion mass, respectively. The site-specific percentage of phosphorylation after stimulation by resact was estimated by evaluation of ion intensity ratios of the corresponding peptide/phosphopeptide pairs as previously described (Boehm et al., 2012).

Searches were performed only on the GC sequence, allowing for either up to three missed cleavages for the tryptic digest or up to four missed cleavages for the digestion with AspN and chymotrypsin. For all searches, the following variable modifications were considered: carboxyamidomethyl for cysteine, propionamide for cysteine, oxidation of methionine, and phosphorylation of serine, threonine, and tyrosine. The search provided a peak list that contained all potentially phosphorylated peptides matching the GC sequence. The processed MS/MS spectra were compared with the theoretical fragment mass of GC peptides.

### Quantification of GC density by SRM MS

14 suitable peptides were identified from MudPIT data with Skyline software (version 1.3.0.3871; MacCoss Lab, University of Washington; MacLean et al., 2010). Based on SRM measurements, the three best peptides (SVLIVTGEPVLR, QQIFATIGTYR, and LGGYELEER) were selected for absolute GC quantification; the corresponding isotope-labeled AQUA peptides (SpikeTides_TQL) were purchased from JPT Peptide Technologies. As internal standards, both the GC-PSAQ and the respective AQUA peptides were used. For quantification of the CNGK channel, the following peptides were used: GIDQSNLFR, AQIYTVAEER, and FVLNPDSPVVR. An aliquot of 5 × 107 sperm was spiked with GC-PSAQ (1.2 µg or 9.53 pmol) and subjected to 12.5% SDS-PAGE. The sample was allowed to migrate into the separation gel by ∼1 cm. The Coomassie-stained gel band was excised and digested overnight at 37°C with 6.25 ng/µl trypsin in 25 mM NH4HCO3, pH 8.6 (Schluesener et al., 2005). For quantification with AQUA peptides, samples were spiked with 4,000 fmol of each GC and 200 fmol of each CNGK AQUA peptide before tryptic digestion. SRM measurements on a mass spectrometer (TSQ Vantage; Thermo Fisher Scientific) and data analysis with Skyline software were as previously described with some modifications (Wolff et al., 2013). TSQ Vantage was operated by instrument method files of Xcalibur (version 2.1.0.1139; Thermo Fisher Scientific), and for compound optimization, the TSQ Tune software was used (Thermo Fisher Scientific). The SRM instrument method consisted of a list of timed SRM scan events over a 66-min run time, whereby a measuring time window of ±1.5 min from each peak maximum was set. Fixed parameters were a resolution of 0.2 full width at half-maximum quadrupole 1 and 0.7 full width at half-maximum quadrupole 3, 2 s cycle time, 1.5 mTorr collision gas pressure, and 270°C capillary temperature. Chromatography was performed via a trap column (5-µm particle, 180 µm × 20 mm; 2G-V/M Symmetry C18; Waters) and an analytical column (1.8-µm particle; 75 µm × 150 mm; HSS T3; Waters). Flow rate was 0.4 µl/min, and spray voltage was set to 1.6–1.8 kV. The multistep gradient of buffer A (0.1% vol/vol formic acid) and buffer B (0.1% vol/vol formic acid in acetonitrile) was established as follows: for 0–6 min, 99% buffer A and 1% buffer B; for 6–10 min, 99–95% A; for 10–45 min, 95–70% A; for 45–51 min; 70–15% A; and for 51–66 min, 99% A.

### Densitometric quantification of GC content

Sperm number in a sample was adjusted to 107, 5 × 106, and 2.5 × 106. Sperm samples were dissolved in SDS sample buffer. Proteins were separated by 6% SDS-PAGE. For calibration, two standard proteins (α-macroglobulin and phosphorylase b) and recombinant GC were run on the same gel at different amounts (100–500 ng). The gel was stained with blue silver (Candiano et al., 2004) overnight and scanned using an imaging system (LAS-3000 Luminescent Image Analyzer; Fujifilm). Intensity of protein bands was densitometrically analyzed with ImageJ software (National Institutes of Health).

### Assay of resact binding

The binding of resact to intact sperm was determined by a bioassay. As described in Kashikar et al. (2012), sperm were incubated for 5 min at room temperature in LoBind Eppendorf tubes with various concentrations of total resact (Rt); for low concentrations of GC and resact, the incubation time was ≤30 min. Nonbound (free) and bound resact (Rf and Rb, respectively) were separated by centrifugation (2 min at 16,000 g). The concentration of free resact Rf in the supernatant was determined by stopped-flow experiments using sperm that had been loaded with the Ca2+ indicator Fluo-4 as the Ca2+ sensor. The initial slope of a Ca2+ signal, evoked by the unknown concentration of free resact (Rf), was measured and compared with the resact standards. Resact standards and samples were appropriately diluted such that standards and samples contained similar resact concentrations around 10 pM; calibration is most accurate at ≤20 pM resact. This calibration assay was performed for each binding experiment. The bound resact concentration was calculated according to Rb = RtRf. Total resact concentrations ranged from ∼3 pM to 1 µM. The amount of GC was adjusted accordingly by using different sperm dilutions (1.5 × 104 to 1.8 × 108 sperm/ml).

### Determination of dephosphorylation kinetics

The time course of GC dephosphorylation was analyzed by quenched-flow measurements as described in Kaupp et al. (2003). Sperm density was adjusted to a GC content of 120 nM. After stimulation of sperm with different resact concentrations, the reaction was rapidly stopped by mixing with 1.5 M HClO4 in a ratio of 1:3. The solution was neutralized by adding fivefold volume of neutralization buffer (125 mM sodium citrate, 175 mM sodium phosphate, and 250 mM Hepes, pH 7.6). The phosphorylated (GCphos) and dephosphorylated forms of GC (GCdephos) were resolved on a 7.5% dirty SDS-PAGE with 0.13% bis-acrylamide content and low purity SDS (Sigma-Aldrich; Ward and Vacquier, 1983; Suzuki et al., 1984). GC was visualized by Western blotting using a GC-specific antibody and an HRP-coupled secondary antibody. Western blots were scanned using LAS-3000 Luminescent Image Analyzer. The ratio between GCphos and GCdephos was densitometrically determined with ImageJ software.

### Determination of cGMP synthesis

Samples obtained by the quenched-flow technique were used for the analysis of cGMP synthesis as well. The solution was neutralized by adding 1 M K3PO4. KClO4 precipitate and cell debris were removed by centrifugation (15 min at 20,000 g and 4°C). The cGMP concentration in 40 µl of the supernatant was determined using an assay (CatchPoint Cyclic-AMP Fluorescent Assay Kit; Molecular Devices) according to the manufacturer’s instructions. To improve the sensitivity of the assay, the supernatant was acetylated with 120 µM acetic anhydride and 200 µM triethylamine. Alternatively, cGMP content was determined by radioimmune assay (Kaupp et al., 2003).

### Determination of GC activity and inactivation

GC activity was investigated in situ in intact motile sperm. Quenched-flow experiments were performed to obtain dose–response curves of the time course of cGMP levels in sperm stimulated with various resact concentrations. Experiments were performed in the presence of IBMX (final concentration of 1 mM) to prevent hydrolysis of cGMP by phosphodiesterases. The increase in cGMP was plotted versus stimulation time. The cGMP increase corresponded to the cGMP level of stimulated sperm (mean of triplicates) subtracted by the cGMP level of unstimulated sperm (mean of triplicates). To determine the GC turnover, we had to consider that at short quenching times, the bimolecular binding reaction of resact to GC is not completed. Therefore, we calculated the number of activated GC molecules (GC*) versus time by using the analytical solution of the bimolecular binding reaction:

$GC*(t)=−λ1(e(λ1−λ2)t−1)kon(e(λ1−λ2)t−λ1λ2), with$
(1)
$λ1,2=−12(kon[GC0]+kon[R0]+koff)±12(kon[GC0]+kon[R0]+koff)2−4kon2[GC0][R0].$

[GC0] is the total GC concentration; [R0] is the total resact concentration; kon and koff are the forward and backward rates of the binding reaction, respectively. We assumed kon = 5 × 107 M−1s−1; because of the high affinity of the GC for resact, koff is very small and was neglected for the calculations performed. To determine the mean number of activated GC molecules from the time course of GC production we used

$GC*−(t)=1t∫0tGC*(t)dt.$
(2)

The apparent turnover number of GC (Tapp) is determined by

$Tapp=[cGMP](t)GC*−(t).$
(3)

An inactivation model is fitted to the time course of Tapp:

$Tapp=Texp(−kit)+y0,$
(4)

with T, the turnover number, and ki, the inactivation rate.

Values of T and ki were determined for each resact concentration independently (3–10 experiments; Fig. 3 D and E). We calculated the arithmetic mean of these values to obtain T and ki as given in the Results.

### Numerical analysis of kinetic data

Numerical analysis was performed using the program DynaFit (3.28.064; BioKin, Ltd.). DynaFit derives the equations for the numerical analysis directly from reaction schemes. The following reaction scheme was used:

$[GCphos]+[L]⇄k−1k1[GCphosL]→k2[GCdephosL]⇄k−3k3[GCdephos]+[L].$

Input data were the mean values of the time course of dephosphorylation (mean of 6–12 experiments for each concentration). We used k1 = k3 = 2 × 108 M−1s−1 as a fixed parameter. The following results were obtained: k−1 = 294 ± 220 s−1, k2 = 7.53 ± 4.6 s−1, and k−3 = 2.5 ± 1.9 s−1. An offset of 9.4 ± 1.1 nM was obtained, indicating that the reaction ceases.

### Diffusion of cGMP in the flagellum

Diffusion of cGMP along the flagellum is modeled by solving the diffusion equation:

$∂c(r,t)∂t=DΔc(r,t)$
(5)

for a closed cylinder of radius a and length L. In Eq. 5, c(r,t) is the cGMP concentration as a function of the position r and time t, D is the diffusion coefficient, and Δ denotes the three-dimensional Laplace operator. The GC is located at the cell surface. It is furthermore assumed that at time 0, a single cGMP molecule exists at the position of the GC. Eq. 5 can be solved in cylindrical coordinates by an expansion into orthogonal functions (Morse and Feshbach, 1953), and the final solution reads

$c(ρ,ϕ,z,t)=πDt∑n=−∞∞∑α=1∞cn,αJn(kn,αρ)exp[in ϕ−Dkn,α2t−z24Dt],$
(6)

in which (ρ, φ, z) are cylindrical coordinates. The site of cGMP production (GC position) is located at (ρ = a, φ = 0, z = 0), and the flagellum extends between z = −L/2 and z = L/2. The functions Jn denote Bessel functions of the first kind (Abramowitz and Stegum, 1984). The kn are the roots of the transcendental equation

$J′n(kn,αa)=0,$
(7)

in which a prime denotes the first derivative, and α indexes the different roots. The constants cn are given by

$cn,α(q)=[2π2(a2−n2kn,α2)Jn(kn,αa)]−1.$
(8)

The equilibration of the cGMP concentration across the flagellum is governed by the smallest nonzero root kn, which has the value k0,2 = ∼3.8317/α (k0,1 being 0). The characteristic relaxation time connected with this root is $(k0,22D)−1,$ and for a flagellar radius a of 150 nm and a cGMP diffusion coefficient of ∼10−6 cm2/s, a characteristic time of ∼15 µs is obtained. Thus, any inhomogeneity of cGMP concentration across the flagellum is rapidly equilibrated.

### Measurement of changes in Vm, Ca2+i, and pH in sperm

We studied resact-induced changes in Vm, [Ca2+]i, and pHi with a rapid-mixing device (SFM-400; BioLogic) in the stopped-flow mode. The changes in Vm, [Ca2+]i, and pHi were measured with the fluorescent dyes di-8-ANEPPS, Fluo-4-AM, and BCECF-AM (Molecular Probes), respectively (Kaupp et al., 2003; Strünker et al., 2006).

### Statistics

Values are given as means ± SD unless otherwise stated. Goodness of regressions is given as ±standard error of the regression.

### Online supplemental material

Fig. S1 shows the densitometric analysis of a representative Coomassie-stained SDS polyacrylamide gel to estimate the GC density per sperm cell. Fig. S2 shows the primary structure of the GC. Fig. S3 shows changes in pHi of sperm stimulated with either resact, NH4Cl, or TMA. Fig. S4 shows that the resact-induced cGMP increase is not altered by the phosphatase inhibitor calyculin. Fig. S5 shows the statistics of sperm counting. Table S1 shows turnover values of the GC reported in the literature. Table S2 shows phosphopeptides of the phosphorylated GC identified by nano-LC–MS/MS. Table S3 shows tryptic peptides of the dephosphorylated GC. Video 1 shows the simulated cGMP diffusion along the sperm flagellum.

We thank Heike Krause for preparing the manuscript, Dr. René Pascal for graphical work, and Dr. Luis Alvarez for careful reading.

This work was supported by the German Research Foundation and the Fonds der Chemischen Industrie.

The authors declare no competing financial interests.

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Abbreviations used in this paper:

• AM

acetoxymethylester

•
• ASW

artificial sea water

•
• [Ca2+]i

intracellular Ca2+

•
• cGMP

cyclic guanosine 3′,5′-monophosphate

•
• CNG

cyclic nucleotide gated

•
• CNGK

K+-selective CNG channel

•
• GC

guanylyl cyclase

•
• IBMX

3-isobutyl-1-methylxanthine

•
• KHD

kinase homology domain

•
• LC

liquid chromatography

•
• MS

mass spectrometry

•
• pHi

intracellular pH

•
• PSAQ

protein standard for absolute quantification

•
• Q-TOF

•
• SRM

selected reaction monitoring

•
• TMA

trimethylamine

•
• Vm

membrane voltage

## Author notes

M. Pichlo, S. Bungert-Plümke, and I. Weyand contributed equally to this paper.