It takes two transducins to activate the cGMP-phosphodiesterase 6 in retinal rods

Among cyclic nucleotide phosphodiesterases (PDEs), PDE6 is unique in serving as an effector enzyme in G protein-coupled signal transduction. In retinal rods and cones, PDE6 is membrane-bound and activated to hydrolyse its substrate, cGMP, by binding of two active G protein α-subunits (Gα*). To investigate the activation mechanism of mammalian rod PDE6, we have collected functional and structural data, and analysed them by reaction–diffusion simulations. Gα* titration of membrane-bound PDE6 reveals a strong functional asymmetry of the enzyme with respect to the affinity of Gα* for its two binding sites on membrane-bound PDE6 and the enzymatic activity of the intermediary 1 : 1 Gα* · PDE6 complex. Employing cGMP and its 8-bromo analogue as substrates, we find that Gα* · PDE6 forms with high affinity but has virtually no cGMP hydrolytic activity. To fully activate PDE6, it takes a second copy of Gα* which binds with lower affinity, forming Gα* · PDE6 · Gα*. Reaction–diffusion simulations show that the functional asymmetry of membrane-bound PDE6 constitutes a coincidence switch and explains the lack of G protein-related noise in visual signal transduction. The high local concentration of Gα* generated by a light-activated rhodopsin molecule efficiently activates PDE6, whereas the low density of spontaneously activated Gα* fails to activate the effector enzyme.

BMQ, 0000-0002-0153-7729; TDL, 0000-0003-0299-6115; MH, 0000-0003-0847-5038 Among cyclic nucleotide phosphodiesterases (PDEs), PDE6 is unique in serving as an effector enzyme in G protein-coupled signal transduction. In retinal rods and cones, PDE6 is membrane-bound and activated to hydrolyse its substrate, cGMP, by binding of two active G protein a-subunits (Ga*). To investigate the activation mechanism of mammalian rod PDE6, we have collected functional and structural data, and analysed them by reaction-diffusion simulations. Ga* titration of membrane-bound PDE6 reveals a strong functional asymmetry of the enzyme with respect to the affinity of Ga* for its two binding sites on membrane-bound PDE6 and the enzymatic activity of the intermediary 1 : 1 Ga* . PDE6 complex. Employing cGMP and its 8-bromo analogue as substrates, we find that Ga* . PDE6 forms with high affinity but has virtually no cGMP hydrolytic activity. To fully activate PDE6, it takes a second copy of Ga* which binds with lower affinity, forming Ga* . PDE6 . Ga*. Reaction-diffusion simulations show that the functional asymmetry of membrane-bound PDE6 constitutes a coincidence switch and explains the lack of G protein-related noise in visual signal transduction. The high local concentration of Ga* generated by a lightactivated rhodopsin molecule efficiently activates PDE6, whereas the low density of spontaneously activated Ga* fails to activate the effector enzyme.

Introduction
Cyclic nucleotide phosphodiesterase enzymes (PDEs) play important regulatory roles in diverse signal transduction cascades by degrading the second messenger cyclic nucleotides cAMP and cGMP [1][2][3]. The PDE superfamily comprises 11 families with 21 genes in mammals [4]. Commonly, PDEs have a role in the recovery phase of signal transduction cascades [5], but phosphodiesterase 6 (PDE6) acts as the activating effector of visual signal transduction in retinal rods and cones.
Vision starts with the absorption of a photon by the photosensitive molecule rhodopsin. The active form of rhodopsin (R*) catalyses the exchange of bound GDP for GTP in many copies of the heterotrimeric G-protein transducin (G). The activated GTP-bound a-subunit of G (Ga*) binds and thereby activates PDE6. The rapid degradation of cGMP by active PDE6 causes the closure of cGMP-gated channels, membrane hyperpolarization and neuronal response [6,7] of flat disc vesicles (in rods) or evaginations (in cones) that are stacked in the outer segments of the photoreceptor cells [8]. Membrane binding of PDE6 is mediated by C-terminal isoprenylation [9].
All PDEs comprise N-terminal regulatory/targeting domains and conserved C-terminal catalytic domains. Most PDEs are homodimeric and are activated by interaction with partner proteins and/or cofactors through their N-terminal regulatory domains [2]. Five of the 11 PDE families feature cGMP-binding tandem GAF (cGMP-specific PDEs, adenylyl cyclases and FhlA) domains at their N-terminus and are directly activated by binding of cyclic nucleotides [10], as is well characterized for PDE2 and PDE5 [11]. Again, retinal rod PDE6 is an exception in that it is heterodimeric and features N-terminal tandem GAF domains that are likely to be permanently occupied by cGMP in mammalian rod cells [12]. Another difference from other PDEs is that the PDE6 holoenzyme (holo-PDE6) comprises two additional inhibitory PDE6g subunits (approx. 10 kDa each). The PDE6g subunits span the two PDE6 catalytic subunits (approx. 100 kDa each) from N-to C-terminus [13,14] and maintain inhibition of the holoenzyme by blocking access of cGMP to the C-terminal catalytic pockets [15,16]. Upon binding to membrane-associated holo-PDE6, Ga* displaces the C-termini of the PDE6g subunits from the catalytic cGMP-binding sites, thereby releasing their inhibitory constraint on PDE6ab [17,18].
While the catalytic domains of all PDEs, except PDE6, have been structurally characterized [4], no high-resolution description of a PDE holoenzyme is available. However, a crystal structure for a truncated PDE2A comprising GAFa, GAFb and the catalytic domain was solved [19]. For PDE6, several low-resolution negative-stain electron microscopy (EM) structures have been published [20][21][22]. A recent cryo-EM study confirmed the overall structural organization of PDE6 [23], but a conclusive model of the PDE6 activation mechanism is still lacking. It is well accepted that disc membraneassociated PDE6 is fully activated when two copies of Ga* are bound. However, the enzymatic activity of the membrane-bound intermediary 1 : 1 Ga* . PDE6 complex and the affinity of Ga* for the two binding sites on PDE6, and possible allosteric and/or cooperative effects, remain elusive. Here, we present the results of a combined enzymatic, computational and structural investigation of bovine rod PDE6. Our results reveal that the first Ga* interacts with membrane-bound PDE6 with high affinity, followed by the second Ga* binding with low affinity. The low level of cGMP hydrolytic activity with only a single Ga* bound establishes a functional asymmetry of mammalian rod PDE6 in the presence of membranes, which allows sequestering of spontaneously activated G proteins in a functionally inactive form. We thereby provide an explanation for the previously suggested difference in activity between spontaneously and light-activated PDE6 [24]. The identified properties of the PDE6 effector enzyme have the capacity to keep the noise of the rod cell low enough to allow the reliable detection of single quanta of light.

Protein and membrane preparations
Rod outer segments were prepared from frozen bovine retinas as described [25]. Isolated disc membranes were prepared from rod outer segments by two consecutive extractions with low salt buffer as described [26]. Rhodopsin concentration was determined from its absorption spectrum using 1 500 ¼ 40 000 M 21 cm 21 .

Quantification of phosphodiesterase 6 membrane association
A centrifugal pull-down assay was carried out to separate and quantify membrane association of PDE6 in parallel with the activity measurements. Samples (50 ml) containing PDE6, Ga*, isolated disc membranes and 2.5 mM cGMP were subjected to centrifugation at 14 000g for 5 min at 228C. After removing the supernatant, the pellet was washed once with 50 ml of buffer. Supernatant and pellet fractions were subjected to SDS-PAGE analysis. PDE6 was densitometrically quantified in Coomassie-stained gels (GelAnalyzer). The results described below show that, on rsob.royalsocietypublishing.org Open Biol. 8: 180075 average, 66 + 3% of PDE6 is membrane-bound in the Ga* titration experiments.

Phosphodiesterase 6 activity measurements
PDE6 catalysed hydrolysis of cGMP (or 8-Br-cGMP) generates GMP (or 8-Br-GMP) and a proton. The rate of hydrolysis was monitored in real time using a fast-response micro-pH electrode (Radiometer PHC3359-8, Hach Lange GmbH, Dü sseldorf, Germany) as described [31]. All measurements were performed in 120 ml final volume at 228C in buffer ( pH 7.5) containing 130 mM NaCl, 1 mM MgCl 2 , 1 mM TCEP and 4 mM BTP (for 8-Br-cGMP) or 20 mM BTP (for cGMP). PDE6, Ga* and disc membranes were added as indicated in the figure legends. All samples were incubated with 50 mM cGMP for 10 min prior to the measurements to saturate the non-catalytic cGMP-binding sites of PDE6. Reactions were then initiated by the addition of 2.5 mM cGMP (or 8-Br-cGMP) and the change in pH of the sample was monitored over time (50-

Analysis of titration curves
The rate of PDE6 catalysed cGMP hydrolysis (v) resulting from titration of soluble PDE6 (PDE6 s ) with Ga* (figure 1a; electronic supplementary material, figure S1a) was fitted with a Michaelis-Menten kinetics hyperbolic function: where [PDE6 s ] represents the overall concentration of individual catalytic subunits of PDE6 s and K d the apparent dissociation constant of the Ga*/PDE6 complex in solution, reflecting the finding that the apparent affinity of Ga* for the two Ga* binding sites on soluble PDE6 is identical. In the fit, the maximum reaction rate ðk cG cat Þ of soluble PDE6 was fixed to the value obtained for membrane-associated PDE6 (see below and electronic supplementary material, table S2).
The rate of PDE6-catalysed cGMP hydrolysis resulting from titration of PDE6 with Ga* in the presence of membranes (figure 1a,b) was numerically fitted using SCIENTIST software (MicroMath). Two different activation models were applied (scheme 1). In model 1 (independent activation), membrane-associated PDE6 (PDE6 m ) is assumed to comprise two independent and non-identical Ga*-binding sites (sites 1 and 2; scheme 1a) with different affinities for Ga* (K d1 and K d2 ). Occupancy of each site on PDE6 m by Ga* leads to formation of Ga* . PDE6 m (site 1) and PDE6 m . Ga* (site 2), respectively, and induces the cGMP hydrolytic activity of the respective PDE6 catalytic subunit (k cat1 or k cat2 ). Because only 66% of PDE6 is bound to the membranes under the experimental conditions (figure 2b), activation of PDE6 s is also taken into account.
The concentrations of Ga* . PDE6 m , PDE6 m . Ga* and active PDE6 s (PDE6 s *) as a function of added Ga* were numerically calculated in the fitting procedure (see electronic  was membrane bound on average. Note that, due to the high membrane concentration used in these experiments, the amount of PDE6 bound to the membrane did not depend significantly on the Ga* concentration, which is consistent with a previous study [33]. (c) Coomassie-stained gels of a representative set of samples used in the PDE6 activity measurements (figure 1c). Titration of Ga* (0.25 mM) with PDE6 in the presence of disc membranes (10 mM rhodopsin; R). Samples were partitioned into soluble (s) and pellet ( p) fractions by centrifugation.
Scheme 1. Reaction models of PDE6 activation. In model 1 (a, independent activation), membrane-bound PDE6 is assumed to comprise two independent but nonidentical Ga*-binding sites (see the text and table 1 for details). In model 2 (b, interdependent activation), the two Ga*-binding sites on membrane-bound PDE6 are initially identical. Binding of Ga* to either of these two sites induces a conformational change in the PDE6 that results in altered affinity for the second Ga*. Note that in all our enzymatic measurements, PDE6 was incubated with a permanently activated Ga-subunit (GTPgS-activated Ga; Ga*), i.e. the two equilibrium models are well suited for analysis of the titration curves depicted in figure 1a,b. rsob.royalsocietypublishing.org Open Biol. 8: 180075 supplementary material, appendix S1). The rate of PDE6-catalysed hydrolysis of cGMP (v cG ) was then calculated by the following equation: Because the PDE6 activity measured with 8-Br-cGMP reflects the binding of only one Ga* to PDE6 (see §3.2), the rate of 8-Br-cGMP hydrolysis (v BrcG ) was calculated by the following equation: The data points for the Ga* titration experiments performed with cGMP (figure 1a) and with 8-Br-cGMP (figure 1b) were simultaneously fitted with equations (2.2) and (2.3) using the same set of protein concentrations and dissociation constants but with individual turnover numbers (k cat ). The fit yields the enzymatic parameters summarized in the electronic supplementary material, table S1, though with undefined errors.
To estimate the errors in the parameters, a factor g (0 , g , 1) was introduced, which relates k cG cat1 and k cG cat2 to the overall hydrolytic activity ðk cG cat ¼ k cG cat1 þ k cG cat2 Þ of PDE6: To reduce the number of variables, the data were fitted again with equations (2.6) and (2.3) and with fixed values of g to yield the enzymatic parameters summarized in the electronic supplementary material, table S2. The resulting titration curves are plotted in the electronic supplementary material, figure S1b,c. In model 2 (interdependent activation; scheme 1b), the affinities of the two Ga*-binding sites on PDE6 m for the first Ga* (K d1 ) are assumed to be identical. Formation of Ga* . PDE6 m is accompanied by conformational changes that lead to partial cGMP hydrolytic activity ðk cG cat1 Þ and altered affinity for the second Ga* (K d2 ). Binding of the second Ga* to Ga* . PDE6 m induces full PDE6 cGMP catalytic activity ðk cG cat2 Þ. With 8-Br-cGMP as a substrate, we assume that Ga* . PDE6 m and Ga* . PDE6 m . Ga* have identical hydrolytic activities ðk BrcG cat Þ. The concentrations of Ga* . PDE6 m , Ga* . PDE6 m . Ga* and active PDE6 s (PDE6 s *) as a function of added Ga* were numerically calculated in the fitting procedure (see electronic supplementary material, appendix S1) and the rate of PDE6catalysed hydrolysis of cGMP (v cG ) and 8-Br-cGMP (v BrcG ) was then calculated by the following equations: The data points for the Ga* titration experiments performed with cGMP (figure 1a) and with 8-Br-cGMP (figure 1b) were simultaneously fitted with equations (2.7) and (2.8).

Particle-based reaction -diffusion and ordinary differential equation simulations
Particle-based reaction-diffusion (PBRD) simulations were performed with READDY software [34]. R*, Ga*, PDE6, Ga* . PDE6 and Ga* . PDE6 . Ga* were simulated as explicit space-excluding spherical particles that diffuse on a two-dimensional (2D) disc membrane of area A ¼ 1 mm 2 . Initial particle numbers were 250 PDE6, 0 Ga* . PDE6, 0 Ga* . PDE6 . Ga*, 2500 inactive G proteins and 0 Ga*. Inactive G protein particles switched into their active form Ga* with a rate of 1000/s either at random times (noise scenario), or a single R* sequentially created Ga* (signal scenario). No shut-off reactions were included, i.e. R* and Ga* remained active during the 100 ms reaction -diffusion simulation. All particles were uniformly distributed initially and underwent Brownian motion with diffusion constants derived from their size. Physiological particle radii were taken from crystal structures and our cryo-EM data for PDE6 (see electronic supplementary material, appendix S3 for detailed parameter derivation). If particles collided, they were able to undergo reactions based on scheme 2. Reaction rates were parametrized based on the measured kinetic parameters (electronic supplementary material, table S3). Ordinary differential equation (ODE) simulations were conducted with MATHEMA-TICA 9.0.1.0 and used the same kinetic parameters as in the PBRD signal scenario (see electronic supplementary material, appendix S3 and table S2 for details).

Electron microscopy and image processing
Negative stain EM was performed essentially as described previously [35]. In brief, PDE6 samples were adsorbed onto freshly glow-discharged holey grids (Quantifoil, Germany) covered with an additional thin continuous carbon layer. After negative staining with 2% uranyl acetate, transmission electron microscopic images were collected on a Tecnai G2 Spirit microscope (FEI) operated at 120 kV, which was equipped with a 2 k Â 2 k Eagle CCD camera. Micrographs were acquired at a nominal defocus of 1.0-3.5 mm at a nominal magnification of 42 000Â using the Leginon system for automated data collection [36]. Particle images were either manually identified or detected semi-automatically. Reference-free class averages were generated using SPIDER [37] or ISAC [38]. Class-averages were then used to generate template three-dimensional (3D) structures in EMAN2 [39]. For cryo-electron microscopy, tPDE6 supplemented with 1% CHAPS was applied to freshly glow-discharged holey Scheme 2. Reactions used in the PBRD and ODE simulations.
rsob.royalsocietypublishing.org Open Biol. 8: 180075 grids with an additional thin continuous carbon layer and flash-frozen in liquid ethane using a semi-automated Vitrobot plunger (FEI). Micrographs were collected under the same conditions as for the negative stained samples, but using a cryo-capable holder (Gatan, model 626) and a defocus range of 1.0-5.0 mm. Manually identified particle images were subjected to multiple rounds of multi-reference template matching and 3D K-means-like clustering [40] using the negative stain structure as the seeding template. The final cryo-EM density map has been deposited with the EMDB (accession no. EMD-0102). The resulting PDE6 atomic model is based on rigid-body docking of individual domains of the initial homology model obtained by Zeng-Elmore et al. [41] into our electron density map (for details see electronic supplementary material, appendix S2).

Experimental strategy for the enzymatic analysis
The holo-PDE6 (PDE6abgg) comprises two catalytic cGMP-binding sites that are activated by Ga* binding to two regulatory sites. This complex architecture of the enzyme allows for a variety of possible activation mechanisms: the two Ga* binding sites could potentially be functionally identical, non-identical or cooperative, and in addition, the two catalytic sites might be identical or non-identical. Furthermore, it is well accepted that the activation mechanism of PDE6 in solution differs from that of the membrane-associated enzyme (see Discussion). We therefore analysed activation of the physiologically relevant membrane-associated PDE6 by using the following experimental strategy: (i) A classical real-time pH change assay [31] was employed to titrate PDE6 activity with permanently activated Ga-subunits (GaGTPgS, Ga*), i.e. without the normal physiological inactivation of Ga* by its intrinsic GTPase activity ( figure 1a,b). (ii) The measurements were conducted at high concentrations of PDE6 and membranes to enhance membrane association of PDE6. (iii) The fraction of soluble and membrane-bound PDE6 in the samples used for enzymatic measurements was quantified by centrifugal pull-down analysis (figure 2). In the numerical analysis of the Ga*-titration curves, the activity of both membrane-associated and soluble PDE6 was taken into account. (iv) In addition to the native substrate cGMP, we applied 8-bromo-cGMP (8-Br-cGMP), which has been reported to be slowly hydrolysed by toad PDE6 [32]. The striking difference between the two resulting Ga*-titration curves allowed us to discriminate between partially (Ga* . PDE6) and fully activated PDE6 (Ga* . PDE6 . Ga*) in the numerical analysis (see below). (v) To quantify the enzymatic parameters of membranebound PDE6, the two Ga* titration curves obtained with cGMP and 8-Br-cGMP, under otherwise identical experimental conditions, were simultaneously analysed by a numerical fitting procedure using the same set of protein concentrations and dissociation constants but with different activities for cGMP and 8-Br-cGMP.

3.2.
Binding of the first Ga* to membrane-bound phosphodiesterase 6 induces negligible cGMP hydrolytic activity In agreement with the literature (see [42,43]), the Ga*stimulated activation of PDE6 in solution is very inefficient. Under these conditions, titration of PDE6 activity with Ga* resulted in a hyperbolic saturation curve (figure 1a; electronic supplementary material, figure S1a) with an apparent K d of about 20 mM. The shape of the titration curve and the low affinity of Ga* for soluble PDE6 are consistent with an activation mechanism in which interaction between Ga* and soluble PDE6 is only transient, because the two Ga*s, each in complex with a PDE6g subunit, dissociate from the active catalytic PDE6ab dimer (see Discussion for details). By contrast, in the presence of disc membranes, the Ga* titration assay ( figure 1a) showed a saturation curve of quite different form, with an initial sigmoidal rise that is clearly apparent in the inset, though difficult to see on the scale of the main panel (see also electronic supplementary material, figure S1b). We interpret the sigmoidal shape to indicate that the activation of PDE6 occurs either by cooperative Ga* binding or by successive occupation of two non-identical but independent Ga*-binding sites. Ga* titration of PDE6 activity in the presence of membranes, using 8-Br-cGMP instead of cGMP as a substrate, resulted in a fundamentally different saturation curve (figure 1b). The curve for hydrolysis of 8-Br-cGMP by PDE6 did not exhibit a sigmoidal shape and saturated at about 10 times lower Ga* concentrations. The shallow increase at higher Ga* concentrations (greater than 0.5 mM) can be attributed to the small fraction of soluble PDE6 present in the samples (figure 2) that is activated with low affinity (figure 1a). The striking difference in the shape of the Ga* titration curve obtained for 8-Br-cGMP (figure 2b) compared with that for cGMP (figure 2a) allows us to conclude, firstly, that the hydrolytic activity of the PDE6 is determined not solely by the binding of Ga*, but that the activity is additionally determined in an important manner by the nature of the substrate being hydrolysed. Secondly, the finding that PDE6 activity saturates at 10 times lower Ga* concentration with 8-Br-cGMP as a substrate compared with cGMP strongly suggests that (i) the activity measured with 8-Br-cGMP reflects the binding of only the first Ga* to PDE6, (ii) the activity measured with cGMP reflects binding of both the first and the second Ga*s to PDE6 and (iii) the interaction of PDE6 with the first Ga* occurs with higher affinity than its interaction with the second Ga*.
These concepts can potentially be described by two alternate models of activation (scheme 1): either an 'independent activation model' that assumes independent activation of two intrinsically different PDE6a and PDE6b subunits, or an 'interdependent activation model' which invokes cooperative activation of two initially equivalent Ga*-binding sites on PDE6. To quantify the affinities of Ga* for the two binding sites on PDE6, as well as the enzymatic activities of PDE6 evoked by binding of one and two Ga*s, we applied a simultaneous fit of the data points obtained with cGMP and 8-Br-cGMP, respectively, using the two models. Importantly, the quantification of PDE6 membrane association by pulldown analysis of all samples used for the activity measurements (figure 2) allowed us to account for the enzymatic activity of soluble and membrane-associated PDE6 within rsob.royalsocietypublishing.org Open Biol. 8: 180075 the fitting procedure (see Material and methods, and electronic supplementary material, appendix S1 for details). The two models yielded fits (solid curves) that are indistinguishable on the scale of figure 1a,b, and that describe the data extremely well. The resulting enzymatic parameters are summarized in table 1. Taken together, the results show that occupancy of the high-affinity Ga*-binding site (model 1) or binding of the first Ga* (model 2) on membrane-associated PDE6 by Ga* (K d1 , 20 nM) induces full 8-Br-cGMP hydrolysis but very low cGMP hydrolysis (less than 2.5% of maximum). In striking contrast, occupancy of the low-affinity Ga*-binding site (model 1) or binding of the second Ga* (model 2) to membrane-associated PDE6 (K d2 ¼ 600 nM) induces full cGMP hydrolysis but no further 8-Br-cGMP hydrolysis (table 1).
The validity of the model was further assessed by measuring cGMP hydrolysis with increasing PDE6 concentration but at a fixed Ga* concentration in the presence of membranes. At low PDE6 concentrations, the resulting hydrolytic activity increased with increasing PDE6, but at higher PDE6 concentration it dramatically decreased (figure 1c). The observed shape of the curve, with its decline at high PDE6 concentrations, provides strong qualitative support for our proposed activation mechanism, as follows. At low PDE6 concentrations, Ga* is in excess and occupies both binding sites on PDE6, thereby efficiently activating the enzyme. But when there is substantial excess of PDE6 over Ga*, it is primarily the high-affinity sites that are occupied, which leads to formation of the 1 : 1 Ga* . PDE6 complex at the expense of Ga* . PDE6 . Ga*. In our view, the observed pronounced drop of enzymatic PDE6 activity under these conditions can only be explained by a considerably lower hydrolytic activity of Ga* . PDE6 when compared with Ga* . PDE6 . Ga*. Although it would be interesting to undertake a quantitative evaluation of the effect, this is not currently possible, because the membrane association of PDE6 depends strongly on its concentration (figure 2c).

Reaction-diffusion simulation of phosphodiesterase 6 activation
To model the spatio-temporal activation pattern on a native disc membrane resulting from sequential PDE6 activation, we conducted PBRD simulations, similar to Schö neberg et al. [44], using READDY software [34]. We evaluated PDE6 activation by Ga* in response to two system inputs: (i) a 'noise'-like activation scenario, in which Ga* is spontaneously produced and thus is uniformly distributed on the disc membrane, and (ii) a 'signal' scenario, in which Ga* is produced locally by a single active R* molecule (figure 3a). Both scenarios were simulated with the same initial disc membrane topology, consisting of a 2D disc membrane (A ¼ 1 mm 2 ) that was uniformly populated with 250 PDE6 particles. R*, PDE6 and Ga* were simulated as explicit particles that undergo 2D diffusional motion on the disc membrane. For the signal scenario, we used a Ga* production rate of 1000/s/R*, which is roughly the speed of the reaction under assumed physiological conditions of the rod cell [29]. The Ga*/PDE6 binding affinities determined above (table 1) result in the constraints K d1 ¼ k 21 /k 1 and K d2 ¼ k 22 /k 2 (see electronic supplementary material, appendix S3). Other parameters such as diffusion coefficients were determined as described in the Material and methods, and electronic supplementary material, appendix S3. Six PBRD runs of 100 ms were performed independently in order to compute means and standard deviations of their activation kinetics. We also conducted ODE simulations (see Material and methods and electronic supplementary material, appendix S3 for details) with the same kinetic parameters, for comparison with the PBRD signal scenario. When Ga* production occurs in a delocalized way, by spontaneous activation (low Ga* density, PBRD noise scenario), the form of PDE6 that is created is predominantly the singly bound Ga* . PDE6 (rather than the doubly bound Ga* . PDE6 . Ga*) across the entire disc during the time course of the simulation (100 ms; figure 3b and electronic supplementary material, figure S4). High-affinity binding of Ga* to PDE6 acts here to sequester Ga* and thereby prevent the activation of PDE6 by low-affinity binding of a second Ga* to Ga* . PDE6. Note that the rate of spontaneous Ga* production that we have adopted in the noise scenario is very high, and presumably far exceeds the rate of spontaneous Ga* formation in vivo. We chose this high rate in order to obtain the same overall rate of Ga* production as in the signal scenario and thus to have a rigorous test of the influence of uniform (noise scenario) versus local (signal scenario) Ga* production on PDE6 activation. Even with a spontaneous Ga* activation rate as high as 1000/s (i.e. by a factor 10 4 faster than in the physiological context; see Discussion), the level of fully active Ga* . PDE6 . Ga* does not rise above 0.5 molecules mm 22 on average during the first 100 ms. It is notable that the results of the ODE simulations, in which Ga* is activated by R*, are very similar to PBRD simulations of the noise scenario (figure 3b; electronic supplementary material, figure S4). This is because the ODE method is inherently spatially indifferent, i.e. it simulates a well-mixed and equilibrated system (see [44] for a thorough discussion). However, when the same amount of Ga* is not uniformly distributed but instead produced locally by a single active rhodopsin (high local Ga* density and PBRD signal scenario), the active Ga* . PDE6 . Ga* form dominates 10-fold over Ga* . PDE6 throughout the first 100 ms. Table 1. Enzymatic parameters (dissociation constants for Ga* (K d ) and maximum rate (turnover number, k cat )) of membrane-bound PDE6 (see Material and methods, and electronic supplementary material, tables S1 and S2 for details).  [20][21][22] and the recent cryo-EM structure [23] agree on a general side-by-side, elongated arrangement of the PDE6 a and b chains. Similarly, our initial common line-based negative-stain structure of bovine holo-PDE6 (PDE6abgg, electronic supplementary material, figure S3a-c) resembles the flat, bell-shaped structures published earlier [20,21,23]. As in the published structures, we observe two regions of low electron density that have the appearance of cavities. Based on the mass distribution in the structure, the larger cavity appears to be separating the catalytic domains from the GAF domains, while the smaller cavity appears to be situated between the four GAF domains. Since the negative-stain procedure is known to be prone to structural artefacts [35], we strived to validate the structure of PDE6 by cryo-EM. To overcome the preferential orientation of holo-PDE6 on the carrier grid surface, we generated a truncated PDE6 by limited trypsination. Proteolysis removes approximately 1 kDa of the C-termini of both PDE6 catalytic subunits with their lipid moieties and also the two inhibitory PDE6g subunits [9]. The resulting catalytic core (tPDE6) has been demonstrated to be an active and soluble enzyme [9]. Our results differed from those of Zhang et al. [23], but agree with Kajimura et al. [21] in showing the PDE6g-free tPDE6 to retain the bell-shaped overall structure of the holoenzyme (see electronic supplementary material, appendix S2 for discussion). Consistent with a recent cross-linking study [41], the cryo-EM structure shows the functional sites of the PDE6 situated on opposing faces of the enzyme ( figure 4b).
Intriguingly, during our reconstruction, we observed strong 3D variability [45] for the catalytic domains ( figure 4c). This implies a flexibility of the catalytic domain with respect to the N-terminal half of tPDE6, which is different to the case of the Fab-bound catalytic domains that were found by Zhang et al. [23] to be in a fixed orientation relative to GAFa. Based on atomic models of a nearly full-length PDE2 crystal structure [19] and a recent homology model of PDE6 [41], we derived a new PDE6 model, by sequential rigidbody fitting (see electronic supplementary material, appendix S2 for details), that agrees well with our experimental electron density map ( figure 4a,b).

Asymmetric activation of membrane-associated phosphodiesterase 6
The classical way to study PDE6 activation in vitro is the titration of enzymatic activity with Ga*. When performed in solution, the resulting dose-response curves consistently reveal that Ga* has a very low affinity for soluble PDE6 (figure 1a; electronic supplementary material, figure S1a). This finding is readily explained by the fact that activation of PDE6 in solution involves successive Ga*-mediated dissociation of the two inhibitory PDE6g subunits from the catalytic PDE6ab dimer and thus formation of partially active PDE6abg and fully active PDE6ab (reviewed in [42,43]). Together with results obtained by a reverse titration, i.e. inhibition of a fully active, truncated PDE6ab (tPDE6; obtained by limited proteolysis of PDE6abgg) with exogenous PDE6g, it was concluded that partially activated PDE6abg has 50% of the hydrolytic cGMP activity of the fully activated PDE6ab in solution (see [17]).
In the presence of membranes, however, the affinity of Ga* for PDE6 is dramatically enhanced, as it forms membraneassociated Ga* . PDE6 and Ga* . PDE6 . Ga* complexes (reviewed in [42,43]). Under these conditions, and with mammalian PDE6, the Ga* titration curves are biphasic or sigmoidal, which has led to conflicting interpretations. Proposed activation mechanisms include inhomogeneous populations of Ga* or PDE6, non-identical Ga*-binding sites [27,[46][47][48] and cooperative binding [49,50]. There is also substantial  Figure 3. Comparison of the delocalized noise-like and localized signal scenarios by PBRD simulations. (a) Two scenarios are compared: a 'noise'-like scenario (i), in which Ga* arises randomly in time and with uniform spatial distribution across the disc, and a 'signal' scenario (ii), in which Ga* is produced locally by one activated rhodopsin molecule (thick arrow indicates initial rhodopsin location). A disc membrane (1 mm 2 ) with PDE6 (green), Ga* . PDE6 (red) and Ga* . PDE6 . Ga* (black) is depicted after a 100 ms reaction -diffusion simulation of Ga* production and PDE6 activation (inactive rhodopsins and inactive G proteins are omitted for clarity). (b,c) PBRD simulations were conducted to compare the kinetics of noise (grey) and signal (blue) scenarios. For each scenario, the time evolution of Ga* . PDE6 (b) and Ga* . PDE6 . Ga* (c) was computed for six independent simulations (averages are enveloped by standard deviation). The solutions of an ODE model that is spatially indifferent and hence represents the noise scenario are depicted in red. The dotted line indicates the maximum values that could be produced for each quantity, being limited by the supply of Ga*. Note the opposite behaviour of the two scenarios: the noise scenario predominantly produces Ga* . PDE6, while the signal scenario predominantly produces Ga* . PDE6 . Ga* (see electronic supplementary material, movie S1).
rsob.royalsocietypublishing.org Open Biol. 8: 180075 disagreement regarding the relative hydrolytic activity of the intermediary 1 : 1 Ga* . PDE6 complex; estimates range from less than 20% [27,46,51,52] up to greater than 80% [49] of maximum PDE6 activity. Our finding that the PDE6 activity measured with the cGMP analogue 8-Br-cGMP monitors formation of Ga* . PDE6 allows us to dissect the activation mechanism. By employing 8-Br-cGMP in parallel to the native substrate, cGMP, we can now quantify the affinity of Ga* for the two binding sites on the membrane-bound PDE6, as well as the enzymatic activity of the membrane-associated, intermediary 1 : 1 Ga* . PDE6 complex. The results show that the activation of PDE6 by Ga* in the presence of membranes is a sequential two-step process: the first Ga* interacts with PDE6 with high affinity but induces only negligible cGMP hydrolytic activity, and this is followed by the binding of a second Ga* to a low-affinity site, which leads to full cGMP hydrolytic activity. It is noteworthy that the titration curve of a kinetic lightscattering signal, which was assigned to be a monitor of the interaction of the first Ga* with membrane-bound PDE6 and that was shown to saturate at approximately 10% of the maximal hydrolytic activity [27], can now be seen to reflect the high-affinity binding measured in our biochemical assay using 8-Br-cGMP (figure 1b).
In the following, we will first discuss the implications of the asymmetric PDE6 activation mechanism on visual signal transduction and later the mechanistic basis of asymmetric PDE6 activation.

Role of phosphodiesterase 6 functional asymmetry in phototransduction
The data of this study shine new light on the intriguing capacity of rod photoreceptor cells to detect single quanta of light. A high amount and high density of the signalling proteins (rhodopsin, G protein and PDE6) is required to detect and rapidly transmit the light signal. But all these proteins are prone to produce background noise originating from spontaneous activation events, and the dominant source of such noise will determine the threshold for detection of a photon [53]. Thermal activation of rhodopsin is observed in rare spontaneous bumps of membrane current [54,55]. In addition, electrophysiological recordings show a continuous component of noise that is attributed to spontaneous PDE6 activation, but no detectable component of the continuous noise could be attributed to the spontaneous activation of G protein [56]. The intrinsic nucleotide exchange rate of rod G protein is about 10 24 s 21 in vitro at 378C [57]. Given the slow GTPase activity of free Ga* (reviewed in [42]), each spontaneously activated copy of Ga* would eventually bind to PDE6. If each such Ga* activated one subunit of the PDE6, then this would generate a large and easily detectable noise component (see [58]). Why is such noise not observed?
We believe that the reason lies in the activation mechanism of the membrane-bound, mammalian rod PDE6, whose hydrolytic activity is only appreciably triggered when two copies of Ga* are simultaneously bound to the same PDE6 molecule. The reaction-diffusion simulations have shown that at the low Ga* density that prevails in the absence of activated rhodopsin (noise scenario in figure 4), the high-affinity binding of Ga* to PDE6 acts to sequester Ga* in a functionally inactive form. Thus, Ga* . PDE6 with no significant hydrolytic activity is exclusively formed under physiological conditions in the dark. However, at the high local concentration of Ga* generated by an active rhodopsin molecule (signal scenario in figure 4), the simultaneous occupancy of two sites on the PDE6 by Ga* is a frequent event, leading to the rapid activation of the enzyme and thereby to sufficient cGMP hydrolysis to trigger neuronal signalling. Such a coincidence mechanism [59] of PDE6 activation makes the G protein/effector pair noiseresistant, but allows a fast response to the light signal. A significant PDE6 activity is only achieved with a high local density of Ga*, as is produced by the local activation originating from active rhodopsin. Consistent with such a coincidence or density switch, electrophysiological recordings of mammalian rod photoreceptor cells have recently suggested a significantly lower hydrolytic activity for spontaneously activated PDE6 when compared to the light activated enzyme [24]. Interestingly, in retinal cone cells, the catalytic subunits of PDE6 are identical and thus likely symmetric in their activation, which would be consistent with the higher noise observed in cones compared with rods [60]. We note that activation density switches are also found in other biological systems such as the highly cooperative Ca 2þ -sensor synaptotagmin in  rsob.royalsocietypublishing.org Open Biol. 8: 180075 neurotransmission. In that case, the crucial factor is a high activation density of Ca 2þ flowing through Ca 2þ -channels localized around active zones in presynaptic neurons [61]. The PDE6 activation mechanism described here may also have consequences for the termination of rod phototransduction. It is well accepted that the falling phase of the rod photocurrent is limited by the lifetime of active PDE6 [62]. If the interdependent model of PDE6 activation applies (figure 5c; see Discussion below) deactivation of only one Ga* by its GTPase activity and subsequent release of Ga from a given fully activated PDE6 enzyme would suffice to deactivate its enzymatic activity. This mechanism would thus translate into an accelerated termination the photoresponse in rod cells. For a more thorough analysis of the implications of an asymmetric PDE6 activation for rod phototransduction, see Lamb et al. [58].

Mechanistic basis of asymmetric phosphodiesterase 6 activation
Pandit et al. [19] suggested an activation mechanism of PDE2 in which both catalytic subunits rotate outwards upon cGMP binding to the GAFb domains (figure 5a). We suggest that our cryo-EM structure of pre-activated tPDE6ab is analogous to this putative active, 'open' conformation of PDE2 [19] (figure 5a). Notably, our active tPDE6ab structure is essentially identical to the inactive PDE6abgg structure obtained by Zhang et al. [23]. We thus conclude that in PDE6, the catalytic core is always in an open, intrinsically active conformation that is kept inactive by tight binding of the two PDE6-specific inhibitory PDE6g subunits (see electronic supplementary material, appendix for a detailed discussion). It is known that activation of membrane-bound PDE6 by Ga* involves displacement of the two PDE6g subunit C-termini from the catalytic cGMP sites on PDE6ab [17,18]. However, a conclusive model of the PDE6 activation mechanism is still lacking. Two different classes of model can be envisaged to explain the functional asymmetry of PDE6 described above. Model 1 (independent activation; figure 5b) assumes that the two catalytic PDE6 subunits are intrinsically different with respect to substrate specificity and affinity for Ga*, respectively, and that both subunits are independently activated by Ga* binding. According to this model, one catalytic PDE6 subunit binds Ga* with high affinity and is able to hydrolyse only 8-Br-cGMP, and at a low rate, while the other catalytic PDE6 subunit binds Ga* with low affinity and is able to hydrolyse only cGMP, but at a high rate. Although in this model rod PDE6 would retain only half of its potential hydrolytic power, it is, in principle, possible due to the heterodimeric composition of PDE6ab. Indeed, it has previously been suggested that the two PDE6g binding sites on PDE6ab in solution are not identical [63,64] and that only one of the two sites mediates PDE6 inhibition [63]. On the other hand, such asymmetry has not been detected in the majority of studies on proteolytically activated PDE6ab (tPDE6) (for example, [17]). Furthermore, a study on chimeric homodimeric PDE6 enzymes indicates that the catalytic domains of PDE6a and PDE6b are enzymatically equivalent in solution [65]. An intrinsic functional difference between the two catalytic subunits is thus unlikely, and if it occurred would need to be confined to the membrane-bound and Ga*-activated enzyme.
Although both models fit the data equally well ( figure 1a,b), we thus favour model 2 (interdependent activation, figure 5c). According to this model, the two Ga* binding sites of PDE6 are initially equivalent. High-affinity binding of the first Ga* to either one of the two binding sites induces a conformational change that leads to a 'primed' Ga* . PDE6 state. This first transition is not enough to uncover the catalytic sites for access by cGMP, but is likely to be accompanied by significant structural rearrangements as indicated by light-scattering changes evoked by interaction of the first Ga* with membrane-bound PDE6 [27] (see below). Full activation of both catalytic subunits requires the low-affinity binding of a second copy of Ga*. To explain the results obtained with 8-Br-cGMP, we hypothesize that this substrate has access to both catalytic sites even in the 'primed' Ga* . PDE6 state. Likewise, 8-Br-cGMP has access in the fully active state, and in both configurations the rate of 8-Br-cGMP hydrolysis is equally low. Accordingly, in this model, the two catalytic sites themselves are functionally identical (although differences are not ruled out), yet this mechanism still provides a huge difference in activity towards cGMP between the states with one and two Ga*s bound.
Given the symmetric activation of soluble PDE6, the question arises as to how membrane binding imposes cooperativity in the activation of PDE6 by Ga*. In this regard, a key result of our structural analysis is the strong 3D variability of the catalytic domains (figure 4c), implying a flexibility of these C-terminal domains in the active tPDE6. Furthermore, both C-termini of the catalytic subunits with their prenyl membrane anchors are highly flexible, as has directly been visualized in a recent electron microscopy study of native PDE6 by the highly variable location of a prenyl-binding protein (PrBP; that had originally been termed the PDE6d subunit) [28]. It is thus likely that PDE6 is able to adopt multiple orientations on the disc membrane surface. In a tentative model that is consistent with the proposed activation mechanism, we assume that PDE6 preferentially lies flat on the membrane in the inactive resting state. Because the cryo-EM structure shows the functional sites of PDE6 located on opposing faces of the enzyme (figure 4b), it is tempting to speculate that this resting orientation of PDE6 only allows initial coupling of Ga* to one binding site. Binding of the first Ga* triggers PDE6 to adopt a more (or even fully) upright orientation without full exposure of either catalytic site. Importantly, such a reorientation of PDE6 would correspond to a mass movement orthogonal to the membrane and would thus nicely explain the increase in light scattering of disc membranes upon binding of the first Ga* to membrane-bound PDE6 [27]. The reorientation on the membrane is proposed to allow binding of the second Ga* with lower affinity under conditions with high local Ga* density, which results in conformational changes that fully expose both catalytic sites, thereby unleashing the full catalytic activity of the enzyme. We emphasize that other structural interpretations such as a Ga*-induced bending of membrane-bound PDE6 are possible. However, the key finding of this study, namely that hydrolytic PDE6 activity is only appreciably triggered when two Ga* molecules are bound to PDE6, is model independent. Irrespective of how the asymmetric activation mechanism is achieved by the membrane-bound PDE6, it provides the rod cell with a coincidence switch that allows for noise filtering at the effector stage in phototransduction. Further implications of this new understanding of PDE6 activation on the predicted rsob.royalsocietypublishing.org Open Biol. 8: 180075  [19]: in the closed, inactive PDE2 conformation, access of the substrate to the catalytic cGMP-binding sites (red) is blocked by mutual inhibition of the catalytic domains. Cooperative binding of cGMP to the GAFb domains induces outward rotation of the catalytic domains and hence formation of the open, active PDE2 conformation. (b,c) Activation of membrane-associated rod PDE6: the PDE6ab-dimer adopts an open conformation, which is inhibited by tight interaction with two PDE6g subunits (dark-grey rods) in the resting state. Activation of membrane-associated PDE6 is due to removal of inhibition following the successive binding of two Ga*s (membrane is omitted for clarity). The catalytic cGMP-binding sites are either fully inhibited (red), or have a very low (less than 2.5% of maximum; orange) or high hydrolytic cGMP activity (green). In model 1 (b), the two catalytic PDE6 subunits are intrinsically different with respect to their affinities for Ga* and their catalytic activity, respectively, and are independently activated by Ga*. Occupancy of the high-affinity Ga*-binding site induces very low cGMP hydrolytic activity, whereas occupancy of the low-affinity Ga*-binding site induces full cGMP hydrolytic activity. In model 2 (c), the two catalytic PDE6 subunits are functionally equal. High-affinity binding of the first Ga* to either of the two binding sites on the PDE6 induces a conformational change that confers very low activity to both catalytic sites. Full activation of both catalytic subunits requires low-affinity binding of a second copy of Ga*.