Maximal rate and nucleotide dependence of rhodopsin-catalyzed transducin activation: initial rate analysis based on a double displacement mechanism.

Despite the growing structural information on receptors and G proteins, the information on affinities and kinetics of protein-protein and protein-nucleotide interactions is still not complete. In this study on photoactivated rhodopsin (R*) and the rod G protein, G(t), we have used kinetic light scattering, backed by direct biochemical assays, to follow G protein activation. Our protocol includes the following: (i) to measure initial rates on the background of rapid depletion of the G(t)GDP substrate; (ii) to titrate G(t)GDP, GTP, and GDP; and (iii) to apply a double displacement reaction scheme to describe the results. All data are simultaneously fitted by one and the same set of parameters. We obtain values of K(m) = 2200 G(t)/microm(2) for G(t)GDP and K(m) = 230 microm for GTP; dissociation constants are K(d) = 530 G(t)/microm(2) for R*-G(t)GDP dissociation and K(d) = 270 microm for GDP release from R*G(t)GDP, once formed. Maximal catalytic rates per photoexcited rhodopsin are 600 G(t)/s at 22 degrees C and 1300 G(t)/s at 34 degrees C. The analysis provides a tool to allocate and quantify better the effects of chemical or mutational protein modifications to individual steps in signal transduction.

In retinal rod cells, absorption of a photon by the visual pigment rhodopsin initiates a cascade of biochemical reactions that eventually generates an electrical signal (1). Much of the tremendous overall gain (10 5 -10 6 ) of the visual cascade depends on two enzymatic amplification stages, namely the receptor-catalyzed nucleotide exchange in the rod G protein, transducin, and the hydrolysis of the second messenger cGMP by the effector, cGMP phosphodiesterase.
Rhodopsin (R) and transducin (G t ) display fundamental sim-ilarities to other receptors and G proteins. However, the function of the rod as a single photon sensory cell requires both low basal activities of R and G t and high speed of catalytic nucleotide exchange in the G protein. Any catalytic activity of rhodopsin is effectively blocked in the dark by the covalently bound inverse agonist 11-cis-retinal. Although a mammalian rod cell contains ϳ10 7 rhodopsin molecules, thus providing the necessary target for efficient light absorption, spontaneous single photon-like activity originates only every 100 s from one of the many dormant receptors (2). On absorption of a photon, lightinduced isomerization converts the chromophore to the agonist all-trans-retinal, thereby triggering conformational changes in the receptor protein that result within milliseconds in the formation of the enzymatically active intermediate metarhodopsin II (for review, see Refs. 3 and 4). Once activated, rhodopsin finds by diffusion its substrate G t . In its inactive, GDPbound state (G t GDP), the heterotrimeric G t holoprotein is peripherally bound to the disc membrane by weak hydrophobic and ionic interactions (5)(6)(7). The activation of the G protein proceeds through a sequence of two mutual displacements (R* for GDP and GTP for R*; so-called double displacement mechanism). Collisional interaction between light-activated rhodopsin (R*) and G t GDP (Fig. 1A, step 1) triggers a conformational change that opens the G t ␣ nucleotide-binding site. Upon GDP release, a stable R*G t complex with an empty nucleotide-binding site on the G t ␣-subunit is formed (step 2). Binding of GTP to the G t ␣-subunit within the R*G t complex enables a second conformational change (step 3) that eventually induces the dissociation of active G t GTP (G t *) from the receptor (step 4) and the (simultaneous or unmeasurably delayed) separation of the ␣and ␤␥-subunits (G t ␣GTP and G t ␤␥). At least in vitro, activation is further accompanied by immediate (delay Ͻ1 ms (8)) dissociation of both G t ␣GTP and G t ␤␥ from the disc membrane. The high rate of R*-catalyzed nucleotide exchange leads to the rapid (transient) accumulation of G t *. Active G t ␣GTP in turn binds to the cGMP phosphodiesterase (PDE) within less than 5 ms (8). The noncatalytic, stoichiometric interaction keeps the PDE active, and hydrolysis of cGMP leads to the closure of cGMP-dependent ion channels in the plasma membrane of the rod outer segment (for review, see Refs. 9 and 10). Despite the detailed knowledge of the reaction mechanisms and despite the growing information about the underlying structures (11,12), sufficiently accurate estimates for the affinities and rates of the protein-protein and protein-nucleotide interactions are still not available. In this study we focus on the crucial activation reaction of the G protein, its rate of catalytic activation, and its dependence on GTP and GDP. Together with the kinetic parameters of PDE activation and cGMP turnover, this is the key parameter for any quantification of the gain of phototransduction in the rod cell (see Refs. 13 and 14). Efforts to measure the actual rate of the catalytic power of rhodopsin date back to the late 70s. To account for the rapid cGMP hydrolysis, Liebman and co-workers (15) concluded that light activation of a single molecule of rhodopsin results in the activation of several hundred molecules of PDE. After identification of transducin (16 -18), direct GDP release and GTP binding studies yielded lower G t activation rates (see Refs. 13 and 14). However, data obtained with low time resolution underestimate the actual rate, when not accounting for rapid depletion of the substrate, and are contaminated by both the onset of deactivation reactions and by slow activation of soluble G t .
Complementary to the biochemical assays are the light-scattering (LS) techniques, which follow flash-induced changes in the scattering of near infrared light as an endogenous probe of specific molecular changes (see Ref. 19). The LS monitor allows one to measure G t activation continuously and in real time, so that the decisive 500 ms after flash excitation are obtained. Following the classical approach of Kü hn and co-workers (5,20), we combine it with biochemical tools to quantify the amount of membrane-bound G t and to calibrate the LS signals. The experimental data can then be used to extract initial rates of G t activation, thereby separating them from slower, associated reactions, such as membrane interaction, rhodopsin kinase interference (21), and the decay of the active receptor. To account for the influence of nucleotide concentration, we titrate G t GDP, GDP, and GTP. The double displacement reaction scheme that takes into account of all these components (22) is then applied to the experimental data.

EXPERIMENTAL PROCEDURES
Membrane and Transducin Preparations-Rod outer segments were prepared from frozen bovine retinas using a sucrose gradient procedure as described (23). Hypotonically stripped disc membranes were prepared from rod outer segments either by two consecutive extractions with low salt buffer as described (24) or by the Ficoll floating procedure similar to the procedure described (25) except that 2% w/v Ficoll instead of 5% was used. Both methods yield osmotically intact disc vesicles with a vesicle size Ͼ400 nm. No significant difference was found between the two types of preparations. Contamination by vesicle aggregates was removed by a 2-m filter (Nucleopore). Membranes were kept on ice and used within 4 days without any loss of activity. Rhodopsin concentration was determined from its absorption spectrum using ⑀ 500 ϭ 40,000 M Ϫ1 cm Ϫ1 . Transducin was purified as described (8). Subunits were further purified on Blue-Sepharose (1 ml of HiTrap Blue, Amersham Pharmacia Biotech) at a flow rate of 1.2 ml/h. Proteins eluted with starting buffer (20 mM BTP, pH 7.5, 1 mM MgCl 2 , 2 mM dithiothreitol) contain inactive G t ␤␥ (26). Active G t ␤␥ was eluted with a linear gradient of 0 -0.3 M NaCl (15 ml). G t ␣ was eluted with 1 M NaCl. The subunits were dialyzed against measuring buffer (20 mM BTP, pH 7.4, 130 mM NaCl, 5 mM MgCl 2 and 2 mM dithiothreitol), concentrated (Amicon, YM-10), and stored at Ϫ40°C. G t ␤␥ concentration was determined by the method of Bradford (27) using bovine serum albumin as the standard. The amount of intact, activable G t ␣ was determined precisely by fluorometric titration with GTP␥S (28).
Because it is known that GDP is slowly converted to GTP by guanylate kinase present in preparations of disc membranes (29,30), the incubation time of GDP prior to the recording of the dissociation signal was minimized to less than 3 min.
Centrifugation Assay-The relative amount of soluble and membranous G t was determined using the centrifugation assay (18,19,21). Aliquots (100 l) of the samples used for recording of LS signals were pelleted by centrifugation (2 min, 21,000 ϫ g, 22°C). After removal of the supernatant, the pellet was washed once (without resuspending, to avoid loss membrane-bound G t ) with buffer and then resuspended in 100 l of buffer. The amount of G t either bound to the membrane pellet or present in the supernatant was analyzed by densitometry on Coomassie Blue-stained sodium dodecyl sulfate-polyacrylamide gel electrophoresis.
All samples were heated to 95°C for 10 min in the presence of SDS, to aggregate most of rhodopsin, which would otherwise mask the G t ␤␥subunit. Background staining by residual rhodopsin was subtracted using a sample without G t (see Fig. 2A, lanes 1 and 2). To ensure reproducible quantification, arrestin was added to the sample buffer as an internal standard.
Kinetic Light Scattering-Light-scattering changes were measured in a set-up described in detail in Heck et al. (19). All measurements were performed in 10-mm path cuvettes with 300-l volumes in isotonic buffer (20 mM BTP, pH 7.4, 130 mM NaCl and 5 mM MgCl 2 ) and at 22°C unless specified otherwise. Reactions are triggered by flash photolysis of rhodopsin with a green (500 Ϯ 20 nm) flash, attenuated by appropriate neutral density filters. The flash intensity is quantified photometrically by the amount of rhodopsin bleached and expressed either in terms of the mole fraction of photoexcited rhodopsin (R*/R) or in the surface density of R* (R*/m 2 ).
Dissociation signals were recorded with a 0.5-5-ms dwell time of the A/D converter (Nicolet 400, Madison, WI). To suppress base-line activation, NH 2 OH was added to the membrane stock at a concentration of 5 mM. The final concentration of NH 2 OH in the samples never exceeded 300 M NH 2 OH, to keep the decay of the flash-induced R* small. For calibration of the LS monitor, dissociation signals were induced by saturating flashes (R*/R ϭ 0.5%). For the kinetic steady state analysis dissociation signals were routinely measured at R*/R ϭ 2.3⅐10 Ϫ4 (5.7 R*/m 2 ), i.e. in the linear range of the light titration curve (Fig. 3). Binding signals (R*/R ϭ 32%) were corrected by a reference signal (N signal) measured on a sample without added G t as described (19). All data were taken at pH 7.4, i.e. in the maximum of the bell-shaped pH/rate profile (31); at this pH, membrane binding of G t GDP (in the dark) is also near its maximum. 2 Amplitudes of the signals are expressed as relative scattering intensity changes (⌬I/I, where I represents the intensity measured before the flash). Calibration of the amplitudes was routinely performed prior to each set of experiments by measuring dissociation and binding signals induced by saturating flashes on aliquots of disc membranes (3 M R) supplemented with 0.5 M G t (see Fig. 2B). As described below (see under "Results"), the dissociation signal exclusively monitors activation 2 M. Heck and K. P. Hofmann, unpublished observations. The formation of the R*G t GDP complex by successful collision of R* and G t GDP (step 1). Release of GDP and formation of the stable R*G t complex with empty nucleotide-binding site (step 2). GTP uptake forms the transient R*G t GTP complex (step 3), which in turn dissociates into R* and active G t GTP (step 4). B, R*-catalyzed nucleotide exchange on G t , using the Cleland notation (horizontal line symbolizes the reaction coordinate (33)). The double displacement mechanism centers around the stable R*G t complex with empty nucleotide-binding site and involves two successive mutual displacements on the G protein, namely R* for GDP and GTP for R*. The initially formed encounter complex (R*⅐G t GDP) converts into a complex with open G t ␣ nucleotide-binding site (R*G t ⅐GDP). GTP uptake leads to the release of active G t via analogous intermediates.
of the membrane-bound pool of G t GDP (G t mb), whereas the binding signal exclusively measures transition of the soluble fraction of G t GDP (G t sol) to the membranes. Thus, the (absolute values of the) maximum scattering change of the signals are proportional to the concentration of G t mb and G t sol, respectively. Together with the known amount of total G t added to the samples, the amplitude of the signals can be converted to concentration units by the scaling factor (F) as shown in Equations 1-3.
Once determined for a given preparation, the scaling factor was used to transform the maximum amplitude of individual dissociation signals where [G t mb] 2D is given in units of molecules per m 2 (see Equation 7 under "Appendix"). Analogously, the maximum slope of the dissociation signal (⌬I/I s Ϫ1 ) was transformed to the surface concentration of G t mb activated per s (G t mb m Ϫ2 s Ϫ1 ).
Reaction Scheme and Mathematical Analysis-The R*-catalyzed steady state G t mb activation rate depends on the G t mb surface concentration as well as on the volume concentrations of both GDP and GTP (Fig. 4C). The multifactorial dependence is well described by the double displacement scheme (formally equivalent to the ping-pong scheme; see By using the steady state approach, the following rate Equation 5 can be derived for the initial rate of G t mb activation (v RG ) in absence of the product G t GTP (see e.g. Ref. 34), where G t mb is the initial surface density of membrane-bound G t GDP, and GDP and GTP denote the volume concentrations of the respective nucleotide. The kinetic parameters are defined as K m(G) for the Michaelis constant for G t mb, K m(GTP) for the Michaelis constant for GTP, K d(GDP) for the dissociation constant of GDP release from R*G t GDP, K d(G) for the dissociation constant of G t mb dissociation from R*G t GDP, and V max for the maximum value of v RG . The definition of the parameters in terms of microscopic rate constants is given in Table I. The factor f A is the fraction of active receptor (without G protein), relative to the total amount of light-activated rhodopsin (see under "Appendix"). Each set of experiments comprises the titration of the dissociation signal with exogenous G t in the presence of fixed concentrations of GTP and GDP. Both the initial activation rate of G t mb (v RG ) and the initial G t mb surface concentration were determined from the maximum slope and the maximum amplitude of the dissociation signal, respectively (see above and "Results"). The G t titrations were repeated (i) at different concentrations of GTP (10 -3000 M) and (ii) at 200 M GTP with different concentrations of GDP (75-2000 M). In this way the dependence of v RG on the three variables (G t mb, GTP, and GDP) was obtained (Fig. 4).
The data points of 23 independent sets of titration experiments (232 data points overall) were numerically fitted with Equation 5, using a , and each of the five kinetic parameters was allowed to vary. The turnover number (V max /R*) was then calculated with the known surface density of R* (5.7 R*/m 2 ).
Note that Equation 5 is converted into a simple Michaelis-Menten type of hyperbolic function for any given (fixed) set of nucleotide concentrations to yield Equation 6, where VЈ max and KЈ m denote the apparent maximum G t activation rate and the apparent Michaelis constant for G t mb, respectively. In Equation 6, both the apparent values depend on the nucleotide concentration.
The validity of the steady state approach is essentially based on the following: (i) the initial G t mb concentration is high as compared with R* even at the lowest G t mb concentrations investigated, and (ii) at the time the maximum slope was obtained, less than 5% of G t mb is activated, thus rendering depletion of the substrate negligible. We have also found that neither lowering the membrane concentration (1.8 M instead of 3 M R) nor addition of excess G t ␤␥ leads to a significant change of the observations (a putative persistent G t ␤␥-receptor interaction may be integrated in the reaction scheme and the respective rate equations derived (22)). Note that both K m(GTP) and K d(GDP) do not depend on the correct determination of G t mb (in contrast to V max , K d(G) , and K m(G) , which linearly depend on any error in the G t mb concentration). Fig. 2A shows the typical, variable membrane binding of G t and its dependence on light and nucleotides as analyzed by the centrifugation assay (18,19,21) (see "Experimental Procedures"). Upon dilution of the membranes, G t GDP (unlike other G proteins) is in equilibrium between a membrane-bound (G t mb) and a soluble form (G t sol) in the dark ( Fig. 2A, lanes 3 and 4). The extent of this "dark binding" depends on several factors, including overall protein and membrane concentration, temperature, pH, ionic strength, and divalent cations (see Refs. 32 and 35). Photoactivation of excess rhodopsin in the absence of GTP or GDP locks G t in its nucleotide-free, receptor-bound conformation (R*G t ), which is seen in a complete shift of G t to the membrane ( Fig. 2A, lanes 5 and 6). Conversely, light activation of rhodopsin in the presence of GTP leads to a complete dissociation of G t from the membranes ( Fig. 2A, lanes 7 and 8). Due  Table I (see text and "Experimental Procedures" for details).

Quantification of Membrane-bound Transducin-
to the low membrane concentration used in the experiments (equivalent to 3 M R), both G t ␣and G t ␤␥-subunits almost quantitatively dissociate from the membrane upon activation ( Fig. 2A), even at high G t concentration (data not shown).
The gain of mass of a membrane, when G t is bound from the solution, and the loss of mass with its dissociation produces large and readily measurable changes in near-infrared light scattering (LS signals; see Ref. 19). Representative light-induced LS signals (measured on the samples used for the centrifugation assay shown in Fig. 2A) are shown in Fig. 2B. Transition of all G t sol to the membrane induced by bleaching excess rhodopsin in the absence of GTP gives rise to an increase of the scattered light ("binding signal" (20,36) ; Fig. 2B, trace a). Accordingly, dissociation of G t mb from the membrane upon activation is seen as decrease of LS ("dissociation signal" (20,36); Fig. 2B, trace b). Since the dissociation step itself is not rate-limiting (see below), the rising phase of the dissociation signal is a real time monitor of G t activation. Notably, binding signals are generally slow as compared with dissociation signals. Previous work resolved this apparent conflict by the finding that, although binding of G t mb to R* is fast, interaction of G t sol with the membrane is slow (36). Consequently, the activation rate of G t sol is limited by its membrane binding, thereby leading to artificially slowed activation rates when total active G t * formation is assayed under conditions where a significant fraction of G t GDP is solubilized.
As indicated in Fig. 2B, the dissociation signal exclusively monitors fast activation of G t mb. Its maximum amplitude is not contaminated by a contribution of G t sol, since the slow mass gain of the membrane upon its binding is just canceled by the fast subsequent dissociation of G t *. Accordingly, the maximum amplitude of the dissociation signal is proportional to the G t mb pool. On the other hand, the maximum amplitude of binding signals induced by saturating flashes is proportional to G t sol, since binding of G t mb to R* does not lead to any LS changes of the membrane suspension (note that this is in contrast to LS measurement on rod outer segment preparations (37,38)). Consequently, comparison of the amplitudes of the dissociation and binding signals allows determination of the sizes of the G t mb and G t sol pools (Fig. 2, B and C). The relative fraction of G t mb varied with different membrane and G t preparations between 40 and 60% of the total G t added. Densitometry on gels as shown in Fig. 2A was used to independently quantify dark binding of G t under the conditions of the LS experiments. Comparison of the results obtained by the two methods (Fig. 2C) shows good agreement, which further confirms the interpretation of the LS signals.
The sum of the maximum amplitudes (absolute values) of the dissociation and binding signals is proportional to the known amount of G t added (i.e. G t mb ϩ G t sol), thereby allowing the calibration of the LS monitor. A calibration factor (F) was calculated for every set of experiments, which relates the relative scattering intensity change to G t concentration units (see Titration of the amplitude of the dissociation signal with G t yields the dependence of G t mb on added G t (Fig. 2D). The slight but reproducible sigmoidal dependence of G t mb on added G t may be explained by a relatively weak G t ␣-G t ␤␥-subunit inter-action in solution and a negligible interaction (relative to the G t -holoprotein) of the isolated subunits with the membrane, which is in agreement with gel filtration and centrifugation experiments. 2 Dependence of G t mb Activation Rate on the Concentration of R*-G t mb activation is accelerated with increasing concentration of R*. Accordingly, the rise time of the dissociation signal depends on the mole fraction of photoexcited rhodopsin (Fig. 3). The light titration curve saturates at high bleaching levels due to the local depletion of G t on the disc membrane (and possibly rate limitation by dissociation of G t * from the membranes). At low bleaching levels (R*/R Ͻ 10 Ϫ3 ) the maximum slope of the dissociation signal depend linear on the R* concentration (dashed line in Fig. 3), which proves that the dissociation of G t * from the membrane is not rate-limiting under these conditions and establishes the rising phase of the dissociation signal as a real time monitor of G t * formation.
Furthermore, the linearity is an important criterion for the analysis of the activation rates since it allows us to normalize the activation rates to R*, i.e. to calculate the turnover number (V max /R*) of R*-catalyzed G t activation. Consequently, we routinely measured the dissociation signal at R*/R ϭ 2.3⅐10 Ϫ4 (5.7 R*/m 2 ).
With decreasing R* the amplitude of the dissociation signal decreases (Fig. 3, inset), since it is proportional to the number of individual vesicles hit by at least one photon (the slow activation of G t mb initially bound to vesicles that do not contain an R* is not detected on the time scale of the experiments). It is seen that under the experimental standard conditions (R*/R ϭ 2.3⅐10 Ϫ4 ) more than 80% of the maximum amplitude is evoked. Fit of the data points to a Poisson sum (solid line in inset of Fig. 3) yield 15.000 R per domain (i.e. vesicle). With the known rhodopsin surface density of 25,000/m 2 , a vesicle size of 440 nm (diameter) is calculated (see Ref. 39 for details), which is in good agreement with the size as estimated from electron micrographs of our preparations (not shown). The slight systematic deviation of the data points from the best fitting Poisson sum is most likely due to slightly nonuniform vesicle size (and contamination by slow GTPase reaction, significant at very low R*).
Steady State Analysis of G t Activation Rate- Fig. 4A shows a typical set of dissociation signals, each evoked by a small flash producing 5.7 R*/m 2 (i.e. in average about 3.4 R* per disc membrane vesicle) with increasing amounts of purified G t added. As expected, both the maximum amplitude (Fig. 2D) and the maximum slope of the signal (Figs. 4 and 5) increase with G t concentration. Expansion of the scales (Fig. 4B) shows that the maximum slope is not immediately reached after light activation of the receptor but is delayed by a short, R*-depending period (8). It is the time it takes all the individual reactions, R* formation, nucleotide exchange, and dissociation of G t * from the membrane, to reach a steady state. The maximal rate of G t * production is reached 40 -100 ms after the flash under the condition of the experiments; despite of this delay, we will refer to it as "initial" rate of G t activation. After the short linear period, the slope of the dissociation signal slows due to depletion of G t mb and increasing activation of G t sol. Because membrane binding of G t sol is slow, distortion of the maximum slope by this effect was neglected. Rapid substrate depletion is a consequence of the membrane-bound state of the proteins, which limits the "reservoir" of the substrate as compared with reactions in solution. As calculated from the dependence of [G t mb] on [G t ] added (Fig. 2D), G t membrane binding saturates at about 7500 G t /m 2 (0.3 G t mb per R), which is in good agreement with previous estimates (40,41).
The maximum slope of the signals (dashed lines in Fig. 4B) was taken from the linear period, which lasts 100 -300 ms, depending on G t concentration (Fig. 4B). It was then converted to the steady state G t * formation rate by the calibration procedure described above (see . Importantly, the initial G t mb concentration was calculated from the maximum amplitude of each signal (see above and under "Experimental Procedures"), thus avoiding errors inferred from variations of total G t added (see Fig. 2D). The titration of the dissociation signal with exogenous G t (Fig. 4A) Fig. 4C, lower panel). The resulting dependence of the initial rate of G t mb activation (v RG ) on the three variables (G t mb, GTP, and GDP) was then fitted by a simultaneous fit to the data, using Equation 5 and 23 sets of dissociation signals; different colors in Fig. 4C identify different concentrations of nucleotide, and different symbols identify different preparations. The kinetic parameters thereby obtained are summarized in Table I.
Dependence of G t mb Activation Rate on Temperature-The temperature dependence of G t mb activation was studied by varying G t mb at each temperature in the presence of 3 mM GTP (no GDP added; Fig. 5A). Because the experiments were done at a single, fixed nucleotide concentration, the data were fit to a simple hyperbolic function (Equation 6). The apparent turnover number of R*-catalyzed G t mb activation (V max Ј /R*) and the apparent Michaelis constant (K m Ј ) for R*-G t interaction as a function of temperature are summarized in Table II. Assuming K m(GTP) as temperature-independent, the true values of V max /R* would be about 8% larger as compared with the apparent ones.
The temperature dependence of the apparent turnover number of R* catalyzed G t activation (V max Ј /R*) is shown in Fig. 5B in Arrhenius coordinates. Below 22°C the data points are well described by a linear relation, yielding an apparent activation energy of the G t activation of 111 kJ/mol. At higher temperatures a pronounced nonlinearity of the Arrhenius plot is observed, indicating an activation energy Ͻ30 kJ/mol above 28°C. DISCUSSION We have studied the receptor-catalyzed nucleotide exchange of a heterotrimeric G protein with the aim to quantify both the maximal catalytic activity of the activated receptor (turnover number) and the influence of GTP and GDP on the velocity of G protein activation. For such analysis, the visual system is well suited because (i) neither the receptor nor the G protein show any measurable basal activity; (ii) the G protein (G t ) is easily isolated and available in the quantities required for titration; and (iii) the light trigger allows us to load the system with defined doses of active receptor.
Initial Rate Analysis-Enzyme-catalyzed reactions are commonly assayed by steady state product formation with a high initial substrate concentration (S 0 Ͼ Ͼ E t ). In the case of G protein-coupled systems, the membrane localization of the substrate (the G protein) limits its initial concentration. Bovine rod disc membranes operate at a G t /R* (S 0 /E t ) ratio of 3000:1 (single photon detection). The low amount of membrane-bound G t GDP (G t mb) leads to rapid depletion of the substrate and causes a very short steady state period. It is obvious that the rapid depletion of the G protein substrate cannot be overcome by overloading the membranes with G protein. Even if, as in the visual system, the G protein is in vitro in equilibrium between a membrane-bound and soluble form, the problem is not solved by a large excess of G protein in solution. The transition of soluble G t GDP (G t sol) to the membrane is far too slow to maintain a high concentration of membrane-bound G t GDP. In other words, the rate of activation of soluble G t GDP is limited by the slow membrane binding step, which is particularly evident when G t activation is assayed at low membrane concentrations. As a consequence, true activation rates are only obtained when the initial rate of G t activation is assayed in the presence of sufficiently high membrane concentrations. The initial rate approach kinetically separates the rapid activation of membrane-bound G t GDP from the slower activation of the soluble G t GDP pool (and from other slow reactions that influence the rate, such as R* deactivation and GTPase reaction). The keys to reliable activation rates are thus a millisecond time resolution and an accurate quantification of the membranebound fraction of the G protein.
Unfortunately, biochemical assays so far applied to this system lack the necessary time resolution. Stopped-flow techniques, which were successfully applied to the study of nucleotide uptake or GTPase reaction of various systems, including small G proteins (see e.g. Refs. 42 and 43) and EF-Tu (see e.g. Ref. 44), are hard to apply to the visual system with its light sensitivity. We thus used the kinetic light-scattering technique to obtain initial rates of G t mb activation. Previous work established the dissociation signal as a real time monitor of the fast activation of the membrane-bound fraction of G t GDP (20,36,37). A precise calibration can be obtained from the dependence on [R*] (37, 38) and/or from classical biochemical assays (this work). Both the initial surface concentration of G t mb and the FIG. 5. Temperature dependence of R*-catalyzed G t mb activation. A, steady state G t activation rate as a function of initial G t mb concentration (both obtained from dissociation signals as described in

Initial Rate Analysis of Transducin Activation
initial G t mb activation rate can be obtained (Figs. 2 and 4).
Double Displacement Scheme-The dependence of the G t activation rate on nucleotide or initial G t GDP concentration is commonly analyzed employing a Michaelis-Menten type of hyperbolic function (e.g. Equation 6). For example, each titration with G t (Figs. 4 and 5) can be fitted with Equation 6. The resulting parameters (KЈ m and VЈ max ), however, are only apparent values when multiple substrates are involved. The K m Ј for one particular substrate (e.g. G t GDP) measured at one fixed set of cofactor (e.g. GTP) concentration changes as the cofactor concentration varies. Analogously, apparent values are obtained when the K m for GTP is evaluated from the dependence of G t activation rate on [GTP] at a fixed (sub-saturating) G t -GDP concentration (see below and Fig. 6A). Generally, the true K m for a particular substrate is the one observed when all other substrates are saturating. Similarly, the true V max is seen when all substrates are present at saturating concentrations and in the absence of any product (for a detailed description, see Ref. 34).
We have used the classical double displacement reaction scheme to describe adequately the receptor-catalyzed activation of a G protein ( Fig. 1 (22)). By using the steady state approach, rate equations can be derived (e.g. Equation 5) that explicitly account for the concentrations of all components involved (R*, G t GDP, GTP, GDP) and allow us to extract the true kinetic parameters for the individual steps.
We note that the inclusion of the transitory complex (R*G t GDP) in the reaction scheme is justified by the experimental data: as seen in Fig. 4C, V max is not approached in the presence of GDP even at infinite G t GDP concentrations. This shows that GDP is not a competitive inhibitor implying that binding of G t GDP to R* and the release of GDP are separated by a transitory R*G t GDP complex with finite lifetime.
Affinity of G t GDP for Photoactivated Rhodopsin-The affinity of G t GDP for R* depends on the equilibrium of the active  Table I (corrected values) and with the estimated native G t concentration (3000 G t /m 2 ) yields curve c (thick line). Varying the relative collisional efficiency of R*-G t interaction via K m(G) and K d(G) by a factor as indicated (right panel) yield curves a, b, and d. This family of curves is also obtained when varying the initial G t concentration at fixed collisional coupling. Altered collisional efficiency results in the respective values of the apparent K m (KЈ m ) for GTP and apparent V max (VЈ max ). B, competition between GTP and GDP under conditions of optimized R*-G t coupling (curve a in A). Family of curves for the dependence of G t activation rate on GTP, with GDP as parameter (left panel) and dependence of G t activation rate on GDP, with GTP as parameter (right panel). C, surface plots of Equation 5, using either kinetic parameters in Table I (   receptor conformation with its tautomeric forms (see under "Appendix"). For the following discussion, we use the corrected parameters K m(G) and K d (G) to characterize the interaction of G t mb with R* (Table I). As compared with the native surface concentration of G t (3000 m Ϫ2 ) the value of K d(G) (530 Ϯ 260 m Ϫ2 ) reflects a surprisingly weak interaction of the proteins. However, this does not contradict the experimentally confirmed stability of the R*G t complex (i.e. the complex without bound nucleotide (45,46)), because formation of the latter is composed of two reactions, namely the initial interaction of G t GDP with R* (step 1 in Fig. 1A) and the succeeding GDP release (step 2 in Fig. 1A). Consequently, the formation of the complex depends on both K d(G) and K d(GDP) (see under "Appendix"). Despite the low affinity of G t GDP to R* (high value of K d(G) ), the reaction is almost quantitatively shifted toward formation of the R*G t complex under typical experimental conditions (i.e. low membrane concentration, no added GDP) because the concentration of the endogenous GDP released is too low to dissociate the complex (K d(GDP) ϭ 270 M; see Table I). At high membrane concentrations, however, the endogenous GDP can significantly affect R*G t formation. When volume concentrations are used and/or the influence of the endogenous GDP is omitted (see e.g. Refs. 47 and 48), the resulting G t -R* affinity depends on all the concentrations used in the experiment. Thus the proper definition and separation of the individual reaction steps is not an academic problem but has an immediate impact on the reaction mechanism.
Dependence on Nucleotides-An important result of this study is the high K d (low affinity) of GDP to R*G t , once formed (K d(GDP) ), and the high K m of GTP (K m(GTP) ). This may seem surprising in view of the higher apparent affinities of the nucleotides obtained 1) by G t activation assays performed at low concentration of G t and/or membrane, or 2) under equilibrium conditions. Reasons for these apparent discrepancies are as follows. 1) As described above, low [G t ] (as compared with K m(G) ) necessarily leads to lower apparent K m Ј for GTP, because R*-G t GDP association becomes rate-limiting (see Fig. 6A). When even slower reactions limit the reaction rate (e.g. membrane binding of soluble G t GDP or association of the detergentsolubilized proteins), the apparent VЈ max can even saturate at micromolar GTP (Ref. 28 and for review see Ref. 49). 2) Equilibrium measurements (e.g. binding studies employing labeled nucleotides) are not suited to quantify the affinity of GTP or GDP to the R*G t complex. The reason is that the dissociation of G t GTP (or G t GDP) from the active receptor, the G t -membrane and G t -subunit interactions, the metarhodopsin equilibrium, and quasi-irreversible reactions such as R* decay and the GTPase reaction all affect the equilibrium. As a consequence equilibrium studies generally overestimate affinities (i.e. underestimate K d ).
The low affinity of GDP to R*G t obtained in this study (K d(GDP) ϭ 270 M) is necessary to explain the essentially quantitative formation of the R*G t complex at low overall concentrations and in the absence of added GDP (see above). The low Michaelis constant for GTP (K m(GTP) ϭ 230 M) is in agreement with conclusions drawn from independent analyses of GTP-induced dissociation of the R*G t complex (50).
G t Activation Rate-Published estimates of the G t activation rate vary from about 10 to Ͼ3000 G t */s per R* formed (for review see Ref. 13). The extreme variation is at least partially due to differences with respect to the method, preparation, and measuring conditions used. For example, when aliquots for a filter assay of GTP uptake are taken in seconds intervals (see e.g. Ref. 51), not only the depletion of membrane-bound G t GDP but also slow reactions may severely affect the results. Activation of soluble G t GDP will be the predominant artifact in bro-ken rod outer segment preparations or reconstituted systems, whereas deactivation of R* may interfere in more intact systems. Evidently, measurements of G t activation on rod outer segments require a sufficiently fast assay that measures the rising phase of G t activation before these influences cut in (Ͻ100 ms for mammalian rods). With such approaches, initial rates in the order of 1000 G t */R*s are obtained (38,52,53).
In the present study on isolated membranes, measuring initial rates of G t mb activation with known G t mb surface concentrations, the steady state approach yields a turnover number of 600 and 1300 G t */R*s at 22 and 34°C, respectively. With the kinetic parameters obtained at 22°C (Table I), the activation rate can be plotted as a function of GTP and GDP (Fig. 6).
The maximal rate is in good agreement with a previous study on whole rod outer segments (800 G t */R*s at 21°C (38)). However, there is a discrepancy because with the isolated membranes and the assumed native G t concentration, V max , is not approached (see Fig. 6A). This is due to an increased K m(G) and K d(G) for R*-G t GDP interaction in the reconstituted preparation. The intact membranes may reserve more quantitative formation of active metarhodopsin II and/or more efficient collisional coupling. The latter is likely to depend on the reversible carboxymethylation of the G␥-subunit (26).
What Is the Rate-limiting Step?-Given the complexity of the reaction scheme (Fig. 1), the question arises whether the maximum rate of receptor-catalyzed G protein activation is limited by the rate of diffusion of the G protein or GTP or by protein conformation changes.
In the Arrhenius representation, the dependence of VЈ max /R* on temperature (Fig. 5B) yields a low temperature (Ͻ22°C) branch with an activation energy of 111 kJ/mol. This value is significantly lower than the one determined for G t activation between Ϫ2 and 12°C and at very low [GTP] (175 kJ/mol (50)). Although the reasons for the difference remain unknown, the high activation energy indicates that a protein conformational change within the reaction sequence is likely to be rate-limiting in this range (54). At sufficiently high temperature, a process with smaller activation energy (E a Ͻ30 kJ/mol) takes over, possibly a diffusion limited process (54). However, it is difficult to extract an individual step when the kinetic parameters are composed of various individual rate constants (see Table I), each of which may have its own temperature dependence.
The lower limit of the R*-G t GDP encounter rate obtained from our analysis (see under "Appendix") is 820 s Ϫ1 at 22°C, i.e. well below its theoretical limit of 7000 s Ϫ1 (13). The lower limit for the bimolecular rate constant of formation of the encounter complex R*G t GTP is 2.6⅐10 6 M Ϫ1 s Ϫ1 (see under "Appendix"), which is much smaller than the diffusional limit of about 10 8 -10 9 M Ϫ1 s Ϫ1 . Thus, at least in the reconstituted system, neither binding of the G protein nor GTP uptake is diffusion-controlled.
Application to Other Receptors-We have shown that the four-step analysis adequately describes the experimental data obtained with the visual system. Modifications of the analysis, to account for ligand binding (22), should make it applicable to other receptor systems, thus providing a basis for the assignment and quantification of chemical and mutational probing.
Acknowledgments-We are indebted to Ulrike Laitko for helpful suggestions. We thank Ingrid Semjonow for excellent technical assistance.

APPENDIX
Membrane Localization of the Proteins-It is obvious that the density of rhodopsin in the disc membrane does not change upon dilution of the disc membrane suspension. As a consequence, neither the equilibrium of the R*-G t GDP interaction nor the rate of the R*G t GDP complex formation depends on the