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Phototransduction in Vertebrate Rods: The Electrophysiological Approach to the cGMP Cascade Theory EDWARD N. PUGH, JR., W.H. CORES, AND ].W. TANNER This paper reviews recent developments in the field of phototransduc- tion, with a special focus on electrophysiological work that constrains and informs the transduction theory now called the cyclic GMP cascade theory (for other recent reviews, see Lamb, 1986; Pugh and Cobbs, 1986; Stryer, 1986; Yau et al., 1986; Pugh and Miller, 1987~. INTrRODUCTION The Nature of Phototransduction Phototransduction may be defined as the sequence of events that tran- spire in a photoreceptor from the absorption of a photon to the production of a physiologically significant electrical signal. The latter ideally would be specified as a light-induced membrane polarization at the synaptic region sufficient to alter transmitter release to a degree detectable by a subjacent bipolar cell, but practically can be equally well specified as a light-induced change in cell membrane potential or even in outer-segment membrane current. Research in phototransduction took an exciting turn in 1970 with the publication of Hagins et al.'s (1970) landmark paper on the dark currents and photocurrents of rat rods. Figure 1 summarizes their finding, overlaying the theoretical interpretation of their data on a scanning electron micrograph of a frog retina. In the dark there is a continually flowing, net outer-segment-inward membrane current, whose spatially integrated magnitude is about 50 to 70 pA in the 25-pm outer-segment rat rod at 37C (rat rods are essentially identical to human rods) and is about 40 to 50 pA in the 50-pm frog or toad rod. A little appreciation of the magnitude 59

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EN PUGH' JR., W.H. CORES, ID ID. TONER FIGURE 1 A scanning electron micrograph of the photoreceptor layer of the frog retina on which has been overlaid a schematic of the "dark" or "circulating" current of a rod and the ionic species that carry the current. SOURCE: Courtesy of W.H. Miller. Of the dark current can be had from considering some numbers: since 1 pA of current corresponds to 6.25 x 106 monovalent charges/second, a 50-pA dark current flowing into a human rod outer segment with a water volume of c. 100 fl demands a complete turnover of the ions carrying the current every 5 seconds (50 pC of monovalent charge into 100 fl corresponds to 5 mM of the charge carrier; we can assume that the internal c[Na] is no higher than 50 mM). For the rod membrane potential to be at steady state in the face of the inward current, there must be a balancing outward current in the inner segment. General principles of cellular physiology, ion substitution experiments, and other work lead to the conclusions that 60

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PHOTOTRANSDUCTION IN VERTEBRATE RODS 61 (1) the outer-segment inward current is carried primarily by Na+, (2) the balancing inner-segment outward current is carried primarily by K+, and (3) there exists a potent ATP-requiring Na/K exchange that maintains the dark ionic balance. The latter exchange mechanism has been localized by Stirling and Lee (1980) to be primarily in the ellipsoid region and on the calices of inner-segment membrane that climb up the inner part of the outer segment. Hagins et al. (1970) showed that transverse flashes of light delivered to the outer-segment layer produce local membrane currents photocur- rentsand hypothesized that the photocurrent was merely the suppression of the dark current. Penn and Hagins (1972) showed that the maximal photocurrent was in fact the complete suppression of the dark current. That the rod should hyperpolarize to light follows immediately from the fact that light suppresses the outer-segment dark current: since that latter current is a depolarizing current, its suppression (in the absence of compensatory reaction) must necessarily drive the membrane potential toward the reversal potential of any K+ conductance. Thus, by 1970 the nature of the initial electrophysiological event in phototransduction was made crystal clear: it is the local suppression in the outer segment of inward membrane current. Two Fundamental Constraints We would now like to emphasize two additional hard inferences drawn in the early 1970s, inferences that drove research on the theory of photo- transduction through much of the 1970s and early 1980s. The first was that there must exist a specific conductance in the outer-segment membrane that carries the dark current and that is closed by light the light-sensitive conductance, or go. Hagins et al.'s (1970) work and subsequent work with the suction electrode (Baylor et al., 1979; Lamb et al., 1981) showed ghu to be distributed more or less uniformly throughout the outer-segment membrane and also showed that the effect of a single photon on the conductance was highly localized, perhaps to 2 to 3 ~m. A second hard inference that propelled transduction research was that there must exist an internal messenger in rods. Light-Sensitive Conductance The inference that there must be a specific light-sensitive conductance motivated many "fingerprint" analyses: experiments for characterizing this entity operationally. Chief among these are currentholtage relations, noise power spectra, and ionic permeation experiments. Biophysical character- ~zation might be said to have begun with Bader et al.'s (1979) effort to

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62 E.N PUGH, JR, W.~. CORES, AND ID. TONER determine the currentivoltage (I/V) relation of the conductance; the re- lation was definitively determined in the elegant triple electrode study of Baylor and Nunn (1986~. One striking feature of this I/V relation is its near-zero slope over the entire physiological range of voltages, - 25 mV to 75 mV. As Baylor has pointed out, this unusual I/V relation is ideal for producing virtually no cable losses in the outer segment, thus allowing the full effect of a local dark-current suppression to be converted into a voltage change in the inner-segment membrane. Another basic characterization of gin, was carried out by Bodoia and Detwiler (1984), who measured noise power spectra that could be attributed to noise produced by the conductance per se. Baylor et al. (1980) had previously characterized two other forms of outer-segment noise that manifest themselves through the light-sensitive conductance: (1) "shot noise" events that can, with virtual certainty, be attributed to the thermal isomerization of rhodopsin and (2) a broader band noise that corresponds to some as yet unspecified transducer process. Internal Messenger Hypothesis The second inference that drove much transduction work was the need for an internal messenger, required because of several different kinds of evidence that the rod disks (which one could presume are the site of most photon adsorptions, based on the action spectrum of night vision) are physically separated from the outer-segment plasma membrane by about the distance of a synaptic cleft. In 1970 Yoshikami and Hagins, in analogy with other systems such as muscle, proposed the divalent cation Ca2+ to be the transmitter. About the same time Bitensky et al. (1971), in analogy with Sutherland's fundamental insight, proposed that a cyclic nucleotide was the messenger. It is not our goal to review the incredible burgeoning field of cyclic nucleotide research that followed the Miller and Bitensky hypothesis, nor even a fraction of the elegant work that went into developing tests of the calcium hypothesis (for recent reviews, see Physiological Reviews, 1987~. Rather, we would like simply to underscore the essence of the messenger hypothesis: light-driven changes in its concentration were hypothesized to cause gh,, to close rapidly. Calcium as Internal Messenger One line of evidence that strongly argued against Ca2+ playing the role of internal messenger was developed by Lamb and colleagues (Matthews et al., 1985; Lamb et al., 1986~. Using a combined suction electrode and whole-cell gigaseal electrode (such as illustrated in Figure 2), they infused the calcium buffer/chelator BAPTA into rods and demonstrated that the

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PHOTOTRANSDUCTION IN YERTEBRATE RODS 63 FIGURE 2 A pair of photographs of a salamander rod whose outer segment is held in a suction pipette and whose inner segment has been impaled with a gigaseal electrode; a cone was fortuitously attached to the rod in the inner-segment region. The top picture was taken with transmitted light, the bottom picture with epifluorescence. The cell was intially drawn into the suction pipette under deep infrared illumination. It was then recorded from for approximately 1 min after intracellular access was gained with the gigaseal electrode (as in Figure 3), which contained, in addition to an intracellular medium, 5 mM 5~6~-carboxyfluorescein. The epifluorescence light was then turned on, and the picture on the right was taken; finally, the transmission photograph was made. This experiment demonstrates that substance infused into the inner segment penetrates to the outer segment. The relative differences in intensity of fluorescence of the outer and inner segments probably reflect the differences in the water spacein the outer segment more than half of the volume is occupied by the disks.

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64 E.N PUGH, JR, W.H. CORES, AND ID. TONER initial phase of the photocurrent was not altered by the chelator (as required by the calcium hypothesis), even though internal evidence was strong that much of the chelator did not have calcium bound to it. The Ca2+ messenger hypothesis was mortally wounded when Yau and Nakatani (1984) showed that the outer-segment, light-sensitive membrane current could be carried by pure Ca2+, and that even in the absence of voltage control an inward calcium current of 300 pA, through the light- sensitive conductance, could be sustained for several seconds. The 300 pA of calcium current corresponds to an influx of about 109 Ca2+/second, yet even so required about 5 see to completely shut down the light-sensitive conductance. In contrast, a 200-msec flash delivering about 1000 isomer- izations during the calcium influx shut down the current in about 100 msec. A simple calculation shows that, to produce more calcium than has al- ready come in through the dark current, the flash would have had to cause the release of more than 106 C82+ ions per isomerization in about 200 msec, a much greater release stoichiometry than anyone ever postulated; indeed, the maximal reliable releases by light ever obtained from disk mem- brane suspensions were on the order of a few calcium ions per isomerized rhodopsin! Yau and Nakatani's (1984) experiments also demonstrated the existence of an Na/Ca exchange in the outer-segment plasma membrane, a mechanism that uses the energy in the Na gradient to evict Ca2+. In a subsequent experiment, Yau and Nakatani (1985) showed that about 5 percent of the normal dark current is carried by calcium moving together with sodium; thus, Ca2+ in the outer segment actually declines during the light response. This interpretation was directly confirmed by McNaughton et al. (1986), who administered the coup to the hypothesis that an elevation in internal calcium in the outer segment carries the message of excitation between disk and plasma membrane. Cyclic GMP as Internal Messenger Bill Miller and Grant Nicol (Nicol and Miller, 1978; Miller and Nicol, 1979) were responsible for the beginnings of the electrophysiological testing of the cGMP-transmitter hypothesis: they discovered that injection of cGMP into outer segments depolarizes rods in a magnitude and with a duration that is dose dependent and that light antagonizes the depolarizing effect of cGMP. Miller (1982) extended the work with microelectrode potentiometric recording and presented a series of detailed phenomena consistent with the hypothesis that cGMP acts to open an outer-segment conductance that is shut by light. Consistent with the Miller-Bitenskr hypothesis, MacLeish et al. (1984) showed that cGMP infused into rods induced an increased inward current that was reversed by light. At about the same time, we (Cobbs and Pugh, 1985; Matthews et al., 1985) developed

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PHOTOTRANSDUCTION IN VERTEBRATE RODS Effect of cGMP on Rod Dark Current and Photocurrent A W a' ~ ,=~200i _ O a a a a a a a a b a a c a 65 1 1 1 _ 1 1 1 1 1 1 1 1 1 1 1 1 1 ~ 1 1 1 7~ 1 ~ 0 20 40 60 80 100 120 140 160 180 300 Seconds FIGURE 3 An experiment like that illustrated in Figure 2 in which the gigaseal pipette contained 5 mM garlic GMP. The suction electrode records only outer-segment membrane current. At AP an attached patch (having a resistance greater than a gigohm) was formed; at WC the patch was reptured By slight negative pressure and whole-cell recording mode commenced. A large inward current developed rapidly, which was entirely light suppressible. At W the whole-cell electrode was withdrawn and the membrane patch resealed; over the next 5 min the cell recovered completely to baseline. Positions marked with arrows indicate 20-msec flashes: a, 1000 isomenzations; b, 100; c, 10. The inset b is a tracing from the infrared video record of the expenment. SOURCE: Cobbs and Pugh (1985~. a combined suction electrode and intracellular electrode salamander rod preparation like that used by Bavlor and Nunn fl9861, incorporating a ~ ~ ~ ~ ~ ~ . . ~ glgaseal electrode rather than a mlcroelectrode, as illustrated in blgure i. Some of our results are shown in Figure 3. Since the suction electrode in Figure 3 records only from the outer- segment membrane, this experiment and similar ones by Matthews et al. (1985) demonstrated that the current induced by cGMP is located in the outer segment. In another set of experiments with the same technique (Cobbs et al., 1985), it was demonstrated that cGMP has the same effect on conesthat is, it increases an outer-segment inward current that light suppresses. The cyclic GMP messenger hypothesis came into full flower with the exciting discovery by Fesenko et al. (1985) of a cGMP-gated cation conduc- tance in excised patches of frog outer-segment membrane, as illustrated in Figure 4. Fesenko et al. presented several arguments for identifying the cGMP- gated conductance with the light-sensitive conductance, including I/V rela- tion, noise spectrum, and ion specificity, although all these fingerprints were somewhat discrepant from what was expected. Soon thereafter, however, identification of the cGMP-activated conductance, ROMP, with the light- sensitive conductance, go, was made firm by Yau and Nakatani (1985) and

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66 4 - o o o ~ E ~ 4- o ,` ._ ~ .~ an CL C: Cal +\ ~ X \ o At _W O\+ O O O O [(I - ~ )/i] 6l I O? ~ C 0~/ in ~ ( _ U) o o. o \ O \ X O ' - , o ye` o O O Lo O . Cam C: O ~ LO ~ _ O O O O E ~ =_? o o ~ L' ~ 1 _1 m ~ ~ s 0 ~ ~ ~ a Z ~ ~ ~ ~ ~ O ~ ~ Cal 0~ o .= 8 c, it ~ 0 (U S ='>~= ~ ~ c_ 0 ~ 0 au ~ ~ c~ ~ ~ ~- 11 - =l ~ % o ~ :; 3 ~ s ~ s ~ 3 ~ ~ ~ ~ _ ,,, + ,= _, _ C) L~ ~ ~ h7.o s ~ s ~ ~ 3 o ~ o ~ _ ~ E ~ ~ ~ ~o S ~ ,c =' ~ > _ Ct ~,) ~ ~ =~ '~D ~ S .0 - ' =" _ ~ ~ ~ ~ ~ o ~ a C Zc = a ~ 0 ~ ca 0 ~ _ a ~ ~ , , =~ m ,ps, _ a~ O ~ ~ ~ c., ~ ~ ~ ~ ct ~ S c~ ~ a ~ ;: C ~ 11 c o c~ - - cO - - s' oo ~ - . 3 ~ ~o

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PHOTOTRANSDUCTION IN VERTEBRATE RODS 67 by Matthews (1986, 1987~. Matthews, for example, demonstrated conclu- sively that the light-suppressible channel noise recorded from cell-attached, outer-segment membrane patches had a spectrum identical to that recorded when the identical membrane patch was pulled and perfused with cGMP. The cGMP Cascade: A Biochemical Sketch Figure 5 shows a sketch of the so-called cGMP cascade of the outer segment. This diagram summarizes not only the electrophysiological work cursorily reviewed above but also a virtual flood of biochemistry that followed in the wake of Bitensky et al.'s (1971) hypothesis (space does not even permit even a cursory review of the relevant biochemical literature; for extensive reviews, see Miller, 1981; Stryer, 1986; Pugh and Cobbs, 1986; Liebman et al., 1987~. According to the canonical version of the cascade theory, the sequence of events is as follows: light does only one thing isomerize the rhodopsin chromophore, causing it to undergo a conformation change that converts it into an enzyme. As an enzyme, R* catalyzes the binding of GTP to a protein, GTP-binding protein, which is present in an amount of about one copy for every 10 rhodopsins. Several lines of evidence say that one R* In the absence of the inactivation process can activate several hundred G- proteins/second (Liebman and Pugh, 1979, 1982; Vuong et al., 1984~. Under normal intracellular conditions, however, R* is inactivated fairly rapidly, apparently by phosphorylation and the binding of "48K protein." G* is not an enzyme but rather a general messenger with its own limited lifetime. While active, G* in turn activates, by direct binding, the third protein in the cascade, phosphodiesterase (PDE). PDE is a powerful enzyme capable of catalyzing the breakdown or hydrolysis of about 2000 cGMPs per second. One should keep in mind, however, when describing the "power" of PDE that it is likely that the pee cGMP in the rod outer segment is fat lower than the km of the enzyme, as guessed in 1985 (Cobbs and Pugh, 1985), and that the hydrolysis rate is always scaled by the km. According to the theory, PDE* next reduces the local free cGMP; as the cGMP unbinds from the conductance, it is not replaced, causing ghu to close. This canonical cGMP cascade theory requires fleshing out, even to be a complete qualitative ("what does what") theory and, indeed, is well known to contain several unresolved problems. Most of these problems have to do with the kinetics of the restorative reactions, which are shown in the open arrows in Figure 5. A key problem that remained unresolved after calcium was rejected as the excitational messenger was the nature of its role, if any, in transduction. This problem now appears near resolution. Having been rejected as the excitational message, intracellular calcium concentration has now made a major comeback as a restorative feedback signal and likely

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68 4, ~n D: ~ ~, a, ~ ~ c5 ~ x a) 0 on ,~ i~ c ~ - ~ o ~ c c) E _ o s ~ C ~ C o s ~ C ~ ~ c tC C o ~ C C t,, C S ~ ~,, Q ) Q X O Q ~ ~ O Y S ~ CI) (D S Co ~ ~ Z G) C ~ _ ;;.,;.,; ;; ;;; ;:;:::::; ::::::::::::::::::::::::::::::::::::::::::::: E ~ ........ : : ..................... . ,,, ~ : . :.: :.:.:. :.:.:.: :.: : CG ~ E ~ ~Y/9 ~^.W ' . ~: o y ~r A - D: , ~ L Ul *, 11 : I _ 1 ~ _ C] + ,- , - ~! ,~ 1~) 1 1 o 1 V, o 1 o 1 , mC? 1 1 . z ~ I c a) 1, o ~ 1 . 1 n5 \~ C) + . , i+~m , - A Ir ~n C~ Ct - a) x t.~3 Q C) C) ~ =-- ~ ~ O ~ ~o -- Cc ~ ~ ,lC a, >- ~ 3 ~ ~ C~ .. C: ~ ~ ~ ~ Ct _ ~ ~ o o P ~ a, ~ ~ ._ _ _ r, . ~ ~ ~ 3 ~ c . C ~ Ct ~ _ . ~ ~ ~ ~ ~ b ~ c D t~ C;: ~ C-~ ~ .= C,0 .= ~ ~ `', t.~a ~,, _ c ~ ~ ._ ~ =. .= ~ ~ .o ~ =~_ ~ O ~ .= 3 = Ct ._ _ ~ ~ ~ . o 3 .<= C ~ ~ C ~ C.~ [I) ~ Ct ~ -~= C ~ ~ o -

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PHOTOTRANSDUCTION IN VERTEBRATE RODS R R* k1 G+GTP G*+D . D* k3 69 5'GMP cGMP + (9hv)c ~ (NcGMP.9hv)o - 5 FIGURE 6 A formal chemical schematic of the "activation" steps in the cascade. R*, G*, and D* represent the activated forms of the proteins rhodopsin, G-protein, and phosphodiesterase, respectively; gin, represents the cGMP-activated conductance, which is opened by the cooperative binding of N = 2 to 3 cGMP molecules. A differential equation representation of this reaction sequence is presented in Cobbs and Pugh (1987b). as the internal adaptational message (Matthews et al., 1988; Nakatani and Yau, 1988~. The primary way by which dynamic changes in internal Ca2+ affect the cascade appears to be via the guanylate cyclase reaction (Koch and Stryer, 1988; Hodgkin and Nunn, 1988~. The figure reflects thinking and experimentation up to about early 1989. FORMAL THEORY The remainder of this paper sketches our recent efforts to develop a formal representation of the reactions that lead to the closure of ghU (reactions represented by the filled arrows in Figure 5) and to test this representation against responses of voltage-clamped rods to intense, brief flashes isomerizing up to 20 percent of the rhodopsin. The strategy em- ployed is diametrically opposite those pioneered by Penn and Hagins (1972) and Baylor et al. (1974), both of whom developed formal analyses of the dim flash or linear response and then attempted to incorporate appropriate saturating nonlinearities to extend the analysis. Rather, we build the theory to handle the responses to the most intense flashes first and then change one critical parameter to see if it can explain the responses to less intense flashes. A priori testing of a theory against the most nonlinear range of the response of the rod seems a poor strategy. Nonetheless, we hope to show that this strategy not only makes a great deal of sense but also actually yields rich insight into the system. Figure 6 shows a chemical representation of the relevant cascade reactions. A differential equation representation of this chemical model can be found in Cobbs and Pugh (1987~. One of the interesting formal features of the cGMP theory is that it relies on a "negative" messenger; that is, the signal or photocurrent is produced by the messenger's removal. This feature is no doubt shared by messengers in other systems but is nonetheless remarkable. Because

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70 E.N PUGH, JR, W.~. CORES, AD ID. TONER of this feature, the maximum speed of the photocurrent can in principle be rate limited by any of several steps up to and including the rate of unbinding of the cGMP from the conductance and its attendant closure. In contrast, as pointed out by Penn and Hagins (1972), a transduction theory that employs a positive messenger whose release rate is a monotonic function of the number of Rotas produced by a brief flash predicts that the photocurrent should not reach velocity saturation over the whole range of bleach intensities. This absence of rate limitation is predicted because the more intense the flash the faster the messenger should be released, and thus the second-order binding reaction of the positive messenger to the conductance (which closes it) should proceed at a speed ever increasing with flash intensity. Photocurrent Velocity and Delay Saturation Figure 7 shows the voltage-clamp photocurrents of two rods stimulated with a series of intense 21) psec flashes. Note that the velocity of the voltage- clamp photocurrent appears to saturate at a relatively modest fractional isomerization, about 0.001. By virtue of the voltage-clamp technique it can be confidently asserted that this velocity limitation is not due to capacitative loading the membrane potential could be shown to have changed less that a millivolt during the response. Above 0.001 fractional isomerization, the velocity-saturated photocurrent seems to translate laterally to the left with increasing bleach fraction, and this translatory behavior itself saturates, reaching its left-most position at about 0.1 fractional isomerization. This latter saturation phenomenon we call delay saturation. The average appar- ent latency of the velocity- and delay-saturated voltage-clamp photocurrent is about 7 msec (Cobbs and Pugh, 1987~. Theoretical Account of Velocity Saturation Can a formal representation of the cGMP cascade theory account for these phenomena, and is the account quantitatively consistent with the biochemical data on the reactions? Theory suggests two ways in which the approximately exponential velocity-saturated photocurrent could arise: one is simply by virtue of the rate of cGMP unbinding from the channel and its closure; the second is by virtue of the limitation posed by the maximal PDE activity on the rate at which cGMP may be removed from the cytoplasm. Employing numerical values taken from the biochemical literature Able 3 and 4 in Cobbs and Pugh, 1987) for most of the theory parameters, we found that a velocity limitation imposed either by the intrinsic rate of cGMP unbinding and channel closure (derived from noise power spectra) of the conductance or by the maximal PDE activity (or a combination

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PHOTOTRANSDUCTION IN VERTEBRATE RODS Time from flash (msec) A 0 10 , 20 30 40 50 60 70 I r I 1 1 1 a) Q Ct - a) - > Q a) - > E a) - ~ ~-,~ C - 'l~1 o~3 V B 0 10 1 1 \1, ~ o- 4 \ 1 o- 5 ~ ~ ;~ ~ _ 20 30 40 50 60 70 I I _ _ ~ - p~ A ~r~ ~\ ~ ~ ' W. ~ 71 ~ _ ~ 10-45 v\ V: ~_~~ 10-55 Nit ~ _: ~ it, ;~ = ~_~0 FIGURE 7 Voltage-clamp photocurrents of two rods stimulated with a series of intense Parsec flashes, which isomers the fraction of rhodopsin given by the parameter near each curve. In part A note that there is almost no change in photocurrent velocity for the three most intense flashes, even though the left-most current was produced with a stimulus 1000 times more intense (10-1 vs. 10 4~: this is the phenomenon of velocity saturation. In part A note that the 10-fold increase from 10 4 to 10 3 produces about the same ^~^ aria ~ ~ ~ a^` late rat translation as the 100-fold increase from 10 3 to 10 1 and that in part B the Refold change from 10 1 7 to 10-0 7 produces virtually no change in the lateral position of the photocurrent: this is the phenomenon of delay saturation. Reprinted from Cobbs and Pugh (1987) with permission.

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72 E.N PUGH, JR, W.H. CORES, AND ~D. TONER of both) produced solutions of the equations consistent with our data. These two hypotheses about velocity saturation appear to be resolvable by testing the theory against the photocurrents of rods infused with cGMP or its weakly hodroyzable analog, 8-Bromo-cGMP (Zimmerman and Baylor, 1986; Barkdoll et al., 1988~. The extension of the theory must deal with two serious complications: (1) the diffusion of the nucleotide is relatively slow; (2) the rod outer segment has such a high longitudinal resistance (1 to 3 megohm/pm) that its cable properties must be taken into consideration when modeling the cGMP-induced currents (Cameron and Pugh, 1988~. Our work on extensions of the theory to incorporate diffusion and cable properties is nearly complete, and we should know shortly which feature of the cascade imposes the photocurrent velocity limitations. Theoretical Account of Delay Saturation and Translation Formal theory also provides interesting insight into the translatory behavior that is seen at fractional isomerizations of about 0.001, and the c. 7 msec saturation limit of the translation that occurs at about 0.1 fractional isomerization. It is interesting that the delay saturation occurs at about 0.1 fractional isomerization, at which intensity there is one photolyzed rhodopsin for every G-protein (the ratio of the two proteins being about 10/1~. One would thus expect delay saturation to set in at this flash intensity, given that the time that it takes an isomerized rhodopsin to encounter a G-protein is short. And indeed the time must be short; otherwise one isomerized rhodopsin could not activate 500 to 1000 G-proteins/second (Fung and Stryer, 1980; Liebman and Pugh, 1982~. Further insight can be had by detailed comparison of theory and data. Figure Sa compares average velocity- and delay-saturated photocur- rents of a population of 11 rods (thicker, noisy trace) with a family of theoretical curves (thinner traces). The left-most theoretical curve is a particular parameterization of the theory, optimized to fit the data trace. All the other theoretical curves are generated by changing a single pa- rameter, the only rate constant in the theory expected to depend on light intensity. This rate constant can be expressed as the pseudo-first-order rate at which each rhodopsin activates the pool of G-protein to which it has access before the entire G-protein pool is activated (at these flash levels all the G-protein is predicted to become activated). To produce the series of theoretical curves this one rate constant has been decremented in a geometric series, each decrement approximately twofold. Clearly, the the- ory provides a natural account of the translatory behavior. The underlying cause of translation lies in the very nature of cascaded reactions followed bv a rate-limiting step, not in any details of the parameters.

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PHOTOTRANSDUCTION IN VERTEBRATE RODS A ,:4 ~ ;~ ,,, t ~ \ ~ ~ At - _ it\ _ \ \ \. ~ \ \ ~ \. . _ _ 1 ~ 30 40 0 10 20 Time from flash (msec) B ~ ~ 10-s ~ ~ An fo4 t1o-3 10-1 ~ ~ I ~ 0 10 i, 1 1 1 20 30 40 Time from flash (msec) 73 FIGURE 8 (A) The thickened noisy trace is the mean velocity- and delay-saturated photocurrent of 11 rods stimulated with 20-ysec flashes that isomerized at least 2 percent of the rhodopsin. The thinner traces are solutions of the differential equation representation of the cascade equations in Figure 6, as given in Cobbs and Pugh (1987b), while the parameters are those used in Figure 15A-C of the same paper. Only a single rate parameter, k20, the effective rate with which each rhodopsin activates its respective pool of G-protein, was varied to produce the theoretical traces. From far left to far right 1/k20 = 1.5, 6.0, 12.5, 25, 50, 100, 200, 400, 800, and 1600 msec. (B) Voltage-clamp photocurrents (noisy traces) of a single rod stimulated with 20-psec flashes isomerizing the fraction rhodopsin indicated. The smooth traces are generated by a representation of the cGMP-cascade theory: only one parameter varies between the curves: k20, the pseudo-first-order rate with which rhodopsin activates G-protein. From left to right, 1/k20 = 2.07, 167, 1225, and 13,038 msec.

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74 E.N PUGH, JR, W.H. CORES, AND ID. TONER An approximate functional dependence of the pseudo-first-order rate of G-protein activation on light intensity can be derived from first-passage theory (Szabo et al., 1980), if one assumes that the rate-limiting step in activation of G-protein by rhodopsin is intramembrane lateral diffusion of rhodopsin (Liebman and Pugh, 1981, 1982~; this in turn can be used to predict the delay (fit in Figure &~. The agreement of predicted delay with observation is quite good (see Cobbs and Pugh, 1987, Figure 12C). 1b test the functional dependence in more detail, however, we need to be able to estimate from photocurrents produced by different intensities on individual cells the rate constant itself, not just the delay. Figure 8B shows how this can be done. A family of responses from a single rod is simultaneously fit with an instantiation of the theory by a parameter search routine; the only parameter that is allowed to vary between curves is the rate constant in question. Since we have independent knowledge of the fraction isomerized, we can thus infer the dependence of the rate constant on isomerization. We are in the process of confronting the theory in this fashion with the individual records of many cells, in effect using the theory as a measuring tool for estimating dependence of the rate on fractional isomerization and thus testing the lateral diffusion hypothesis. Efforts to build a formal representation of the cascade that could ac- count for the voltage-clamp responses could not account for the magnitude (7 msec) of the saturated delay unless one were to postulate that about 3 or 4 first-order delay steps of order 2 msec intervened between the binding of rhodopsin to G-protein and the velocity-saturation mechanism (see Cobbs and Pugh, 1987b, Appendix, for details). A natural mechanism for such additional minor delay components would be in the binding of GTP, the conformation change of the G-protein, the binding of G-protein to PDE, and the latter conformational change as it becomes an active enzyme. Here again, theory, applied to the photocurrents, allows us to "see" a biochemical process that might otherwise escape attention. SUMMARY lithe hypothesis that there is an internal messenger in vertebrate pho- totransduction has offered a rich challenge to scientists in many fields and has brought together a wide array of tools and insights. With most of the fundamental qualitative features of phototransduction now understood (i.e., the identity of the molecular entities involved and the roles they play), the field of phototransduction is entering a phase in which formal theo- ries linking photoreceptor biochemistry and electrophysiology can play an important role, permitting deeper understanding of this wonderful process.

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