Original Article

The Role of Steady Phosphodiesterase Activity in the Kinetics and Sensitivity of the Light-adapted Salamander Rod Photoresponse

Correspondence to: E.N. Pugh, Jr., University of Pennsylvania, Department of Ophthalmology, Stellar-Chance Building, 422 Curie Boulevard, Philadelphia, PA 19104-6069. Fax:(215) 573-7155 E-mail:pugh{at}mail.med.upenn.edu.

	Abstract

Top Abstract INTRODUCTION MATERIALS AND METHODS THEORY RESULTS DISCUSSION Acknowledgements Appendix A Appendix B Appendix C References

We investigated the kinetics and sensitivity of photocurrent responses of salamander rods, both in darkness and during adaptation to steady backgrounds producing 20–3,000 photoisomerizations per second, using suction pipet recordings. The most intense backgrounds suppressed 80% of the circulating dark current and decreased the flash sensitivity 30-fold. To investigate the underlying transduction mechanism, we expressed the responses as a fraction of the steady level of cGMP-activated current recorded in the background. The fractional responses to flashes of any fixed intensity began rising along a common trajectory, regardless of background intensity. We interpret these invariant initial trajectories to indicate that, at these background intensities, light adaptation does not alter the gain of any of the amplifying steps of phototransduction. For subsaturating flashes of fixed intensity, the fractional responses obtained on backgrounds of different intensity were found to "peel off" from their common initial trajectory in a background-dependent manner: the more intense the background, the earlier the time of peeling off. This behavior is consistent with a background-induced reduction in the effective lifetime of at least one of the three major integrating steps in phototransduction; i.e., an acceleration of one or more of the following: (1) the inactivation of activated rhodopsin (R*); (2) the inactivation of activated phosphodiesterase (E*, representing the complex G–PDE of phosphodiesterase with the transducin -subunit); or (3) the hydrolysis of cGMP, with rate constant ß. Our measurements show that, over the range of background intensities we used, ß increased on average to 20 times its dark-adapted value; and our theoretical analysis indicates that this increase in ß is the primary mechanism underlying the measured shortening of time-to-peak of the dim-flash response and the decrease in sensitivity of the fractional response.

Key Words: photoreceptors, G-protein cascade, sensory transduction, light adaptation, cGMP hydrolysis

	INTRODUCTION

Top Abstract INTRODUCTION MATERIALS AND METHODS THEORY RESULTS DISCUSSION Acknowledgements Appendix A Appendix B Appendix C References

In the presence of background illumination, rod photoreceptors adjust their sensitivity and response kinetics over an intensity range of several decades, and cone photoreceptors do so over an even greater range of intensities. Over the years, a number of investigators have studied the dependence of the rod's steady photocurrent and flash sensitivity on the intensity of background illumination. Other investigators have measured a shortening of the effective lifetime of cGMP (using an "IBMX-jump" protocol), and a shortening of the apparent lifetime of activated rhodopsin (monitored with bright flashes) during steady illumination. In other studies, it has been reported that the amplification of phototransduction is reduced during light adaptation.

In the present work the aim of our experiments has been to investigate all of these properties in the same population of rod photoreceptors. Thus, in an ideal experiment we have attempted: (1) to measure the steady state response versus intensity relation; (2) to measure families of flash responses on a range of backgrounds, from very dim flashes (to determine flash sensitivity) up to very bright flashes (to determine the dominant time constant of recovery); (3) to measure responses to steps of isobutyl methylxanthine (IBMX),¹ both in darkness and on backgrounds (to determine the steady-state rate constant of cGMP hydrolysis); and (4) to measure "step/flash" behavior, which permits estimation of the lifetime of activated rhodopsin. In practice, it has not been feasible to perform all these experiments on an individual rod, but, in a population of about a dozen rods recorded for up to 4 h, we were able to perform several of the procedures on each.

In a recent quantitative study of light adaptation using truncated salamander rods, Koutalos et al. 1995a , Koutalos et al. 1995b investigated the contributions of guanylyl cyclase activity and phosphodiesterase activity to the overall light adaptation behavior of the cells. One of our goals has been to extend their analysis of the steady state by focusing on the role of the phosphodiesterase activity, which we have measured using the "IBMX-jump" method. Another goal has been to characterize the effects of adaptation-dependent changes in the principal integrating steps of phototransduction, which include the following: the lifetime of R*; the lifetime of the active phosphodiesterase complex (PDE*); and the lifetime of cGMP, which is the reciprocal of the instantaneous rate constant of cGMP hydrolysis. As an aid to achieving these goals, we developed a molecular model of the complete set of reactions mediating transduction and adaptation, and solved the equations to obtain the steady state response versus intensity relation. In addition, we have integrated the equations numerically, so as to predict the kinetic responses and to examine the dependence of the solutions on the time constants of the principal integrating steps.

Our main conclusions are, first, that the gain of the activation steps in transduction is unaltered during light adaptation; and, second, that much of the acceleration in kinetics and desensitization of the biochemical cascade arises from the increased rate constant of cGMP hydrolysis resulting from light-stimulated PDE activity. The negative feedback loop mediated by Ca²⁺ concentration acts to prevent the suppression of circulating current that would otherwise occur and, in this way, the drop in Ca²⁺ concentration rescues the cell from the saturation that would occur in the absence of adaptational mechanisms. A preliminary and qualitative description of some of these results has been presented by Pugh et al. 1999 .

	MATERIALS AND METHODS

Top Abstract INTRODUCTION MATERIALS AND METHODS THEORY RESULTS DISCUSSION Acknowledgements Appendix A Appendix B Appendix C References

Suction Pipet Recordings
Our methods for preparing isolated salamander rods and for recording and analyzing their electrical responses have been reported previously (Lyubarsky et al. 1996 ; Nikonov et al. 1998 ). The photocurrents were low pass–filtered at 150 Hz (4-pole Butterworth) and sampled at 300 Hz; the delay introduced by this filtering was measured as 5.5 ms at the 50% response to a step input, and as 5.4 ms for a ramp input. All records were analyzed at full bandwidth, and are presented in the figures at full bandwidth, unless otherwise specified.

For all the experiments reported here, the rod's inner segment was drawn into a suction pipet, which recorded the circulating current, while the protruding outer segment was continually superfused with a standard amphibian Ringer's solution (Lyubarsky et al. 1996 ). In "IBMX-jump" experiments, the outer segment was briefly exposed to a test solution containing 500 µM IBMX (a competitive inhibitor of phosphodiesterase), by rapid translation of a laminar-flow boundary across the cell. This procedure was used to estimate the activity of guanylyl cyclase (and, thereby, the phosphodiesterase activity in the steady state before the jump) in the manner developed by Hodgkin and Nunn 1988 .

To obtain enough information to make the required quantitative calculations for an individual rod, we found it necessary to hold the cell for at least an hour, and in the best experiments, we achieved stable recordings for >4 h. A summary of the stability of our recordings is presented in Fig 1, which plots the amplitudes of saturating responses obtained under dark-adapted conditions over the entire recording duration, for each of the nine rods that provided the core observations presented in this paper. (Data from five additional rods recorded for 1 h are also included in some summary figures.)

View larger version (19K): [in this window] [in a new window]   Figure 1. History of the responses of the principal rods of the experiments. Each point represents the response to a saturating flash presented to a rod after two or more minutes of dark adaptation. (A) Histories of rods a and c of Table 2 presented separately from those of the other rods (B) for clarity. The gaps in the response histories represent periods when the rods were exposed to background lights or to IBMX. (B) Histories of the seven additional principal rods.

Light Stimuli
Light stimuli were monochromatic (500 nm, bandwidth 8 nm), circularly polarized, and generated via one of two optical channels: (1) a tungsten halogen lamp illuminating a grating monochromator, followed by a shutter; and (2) a xenon flash lamp (flash duration, 20 µs) filtered by an interference filter. In all experiments using backgrounds, the steady illumination was provided by the shuttered incandescent beam, and the flashes came from the xenon flash lamp. For some experiments in dark-adapted conditions, the flashes were delivered using the shuttered beam, and the flash duration was 22 ms. Flash intensities () are given in estimated numbers of photoisomerizations per outer segment, calculated by multiplying the measured flux density of the flash at the image plane (in photons per square micrometer) by the estimated outer segment collecting area of 18 µm² for salamander rods (Baylor et al. 1979 ; Lyubarsky et al. 1996 ). Steady intensities (I) are similarly given in photoisomerizations per second. For results taken from other investigations, we have adopted a collecting area of 20 µm² for circularly polarized (or unpolarized) light, and 40 µm² for linearly polarized light, as was generally used in those studies.

Light Adaptation Protocol
Dark-adapted rods were exposed to steps of light of calibrated intensity for periods of 2 min. Beginning at least 20 s after the onset of the background, a number of test flashes were delivered at separations sufficient to allow full recovery. These were followed by a saturating flash, to determine the circulating current remaining in the presence of the background, and after recovery from this bright flash, the background was extinguished. The cycle was repeated for a series of test flash intensities, and the entire procedure was repeated for a range of background intensities. Control experiments established that the time course of the response to the saturating flash was unchanged over the epoch of the background from 20 s to 2 min. In some experiments (the step/flash protocol), a saturating flash was delivered at the instant the background was extinguished, as in Fain et al. 1989 .

Numerical Integration of Equations
A complete set of equations describing transduction in the G-protein cascade is set out in the Appendix A. To solve these equations numerically, we coded the equations independently in our two laboratories, using Matlab (The Mathworks), and the programs are available at http://www.physiol.cam.ac.uk/staff/Lamb/RodSim and upon request. The solutions to both steady state and time-varying equations obtained with the two programs agreed very closely.

Simulated Responses to Steps of IBMX
To simulate responses to steps of IBMX in darkness or during steady backgrounds (for the analysis in Fig 7), we adopted the following procedures. The value of ß was reduced according to the competitive inhibition factor given in Equation A15, which specifies a time constant (_I) for equilibration of the concentration of IBMX in the outer segment with that in the perfusate. Previous experiments had shown that the time for completion of the movement of the laminar boundary across the rod is 100 ms (Lyubarsky et al. 1996 ). Therefore, we initially set _I to this value, and varied it to obtain the best fit to the earliest onset of increased current over the family of background intensities; we found that the best fit was obtained with _I = 100 ms, and so we maintained this value throughout.

View larger version (22K): [in this window] [in a new window]   Figure 1. History of the responses of the principal rods of the experiments. Each point represents the response to a saturating flash presented to a rod after two or more minutes of dark adaptation. (A) Histories of rods a and c of Table 2 presented separately from those of the other rods (B) for clarity. The gaps in the response histories represent periods when the rods were exposed to background lights or to IBMX. (B) Histories of the seven additional principal rods.

View larger version (22K): [in this window] [in a new window]   Figure 2. Photocurrent response families of a salamander rod, obtained under four conditions of adaptation: in darkness (A) and in the presence of steady background lights of the indicated intensities (I) in photoisomerizations per second (B–D). Each of the four families presents averaged responses r(t) to the same sequence of flashes, estimated to produce = 260, 830, 2,600, 8,300, 26,000, 83,000, and 260,000 photoisomerizations per flash. Each trace is averaged from at least 5 responses, but up to 30 responses were averaged to produce the responses with smallest amplitudes. Rod a of Table 2. The additional scales at the right of B provide graphical definitions of the fractional cGMP-activated current JcG(t) and response RcG(t), according to Equation 4 and Equation 5.

View larger version (35K): [in this window] [in a new window]   Figure 3. Fractional responses of a rod under six conditions of adaptation: dark adapted, and in the presence of steady backgrounds producing I = 19, 60, 190, 600, and 1,900 photoisomerizations per second. The responses are expressed as a fraction of the maximal cGMP-activated current in each adaptational condition; i.e., as RcG(t) rtot(t) / jcG(I), estimated according to Equation 5 and the scale in Fig 2 B. Each panel illustrates responses to flashes of a single intensity, at the indicated value of , in photoisomerizations; responses to the more intense flashes (right column) are presented on a shorter time scale, and the responses to = 830 photoisomerizations are repeated on both scales (E and E'). Each trace shown is the average from at least 5 trials, with up to 30 trials being averaged for the smallest amplitude traces. Rod b of Table 2.

View larger version (27K): [in this window] [in a new window]   Figure 4. Fractional response per photoisomerization, R(t)/, for dim flashes presented in darkness and on five backgrounds, for the rod of Fig 3 (Table 2, rod b). In each adaptational state, the mean dim flash response per photoisomerization has been calculated, using only those flash intensities that elicited a relatively small signal; i.e., those with R(tpeak) 30%. The traces have broadly the same form as those in Fig 3 B, but have been averaged from a larger number of trials, and from test flashes of >1 intensity. The background intensities were I = 0, 19, 60, 190, 600, and 1,900 photoisomerizations per second, and the respective numbers of flash responses averaged were 51, 37, 30, 30, 43, and 20. The smooth trace (gray) was computed with the pure activation model (Lamb and Pugh 1992 , modified to include the membrane time constant, m according to Equation 5 of Smith and Lamb 1997 ), with A = 0.063 s-2, m = 20 ms, and teff = 20 ms.

View larger version (27K): [in this window] [in a new window]   Figure 5. Effects of light adaptation on fractional response amplitude and recovery time for saturating flashes. (A) The cell of Fig 2 (Table 2, rod a); and (B) the cell of Fig 3 (Table 2, rod b). For each cell, a family of responses was obtained for flash intensities ranging from 10 to at least 10,000 photoisomerizations, presented in darkness or on backgrounds of at least three intensities. From these families, two parameters were measured and plotted: (1) the fractional response amplitude, R(tpeak) = r(tpeak)/j(I), measured at the peak, is plotted in the top left of both panels, using the left ordinate scale; and (2) the time to 50% recovery, T50, (for each flash sufficiently bright to saturate the response) is plotted in the bottom right of both panels, using the right ordinate. Each symbol shape represents a different background intensity; closed symbols are for 20 µs xenon flashes; open symbols are for 22 ms flashes from the shuttered beam. (A) •, , darkness; , , and , I = 260, 810, and 2,600 photoisomerizations per second, respectively; (B) , darkness; , , , , and , I = 19, 60, 190, 600, and 1,900 photoisomerizations per second, respectively, from the top down. All points in the four plots represent averages derived from 2–15 individual responses; error bars have been omitted for clarity. For the points in the recovery half-time plots, the average SDs for the four adaptation conditions of A are 0.15, 0.28, 0.09, and 0.13 s; for the six adaptation conditions of B, they are 0.18, 0.17, 0.13, 0.12, and 0.08 s.

View larger version (20K): [in this window] [in a new window]   Figure 6. Dependence of steady circulating current and flash sensitivity of salamander rods on background intensity. (A) Relative circulating current in the steady state, Jrel(I) = j(I)/jDark, where j(I) is the steady current and jDark is the dark current. (B) Relative sensitivity, defined as srel(I) = s(I)/sDark, where s(I) is the absolute sensitivity and sDark is its dark-adapted value. (C) Relative fractional sensitivity, defined as Srel(I) = (s(I)/sDark)/Jrel(I); see Equation 8. Symbols from the present investigation are identified in Table 2. Symbols from three previous studies are: , Hodgkin and Nunn, 1988; , Matthews et al. 1988 , average of seven cells; , Koutalos et al. 1995b , average of six cells. The curves are the predictions of the model set out in the Appendix A, using the parameters of the "standard" rod listed in Table 4. The curve in A was obtained from Eq. B7 in Appendix B. The curves in B and C were obtained by simulating (at a range of background intensities) the response to a dim flash, and determining its peak amplitude.

View larger version (16K): [in this window] [in a new window]   Figure 7. Method of estimation of the steady-state PDE rate constant of cGMP hydrolysis. (A) Exposure to 500 µM IBMX, on a slow time-base, showing seven repeated trials under dark-adapted conditions. In A and B, the fractional circulating current, J(t) = j(t)/j(I), has been plotted, determined by the following protocol. The steady circulating current j(I) was measured, by delivering an intense flash ( = 8,600 photoisomerizations) at the first arrow. For this rod, we obtained jDark = 34 pA under the dark-adapted conditions of A. After a delay of 90 s, to allow complete recovery, a rapid translation of the chamber moved the laminar boundary of the flowing solutions across the rod (defined as time zero), exposing the outer segment to Ringer's solution containing 500 µM IBMX, and eliciting a rapid increase in circulating current because of inhibition of phosphodiesterase activity. A flash of the same intensity as before was then delivered under manual control (arrows), and 1 s later the rod was returned to control Ringer's solution. The rod was allowed to recover for several minutes, and the IBMX exposure and flash were repeated for a total of seven times. After the series of jumps, the response amplitude was again measured, and found to be 32.5 pA. Two of the seven records were obtained in the absence of infrared illumination, and are indistinguishable from the other five. The small "bumps" in the response tails occur at the time of return to control Ringer's solution, and are due to the extrusion of Ca2+ by the Na+/Ca2+-K+ exchanger. (B) Fractional circulating current J(t) on a faster time-base, for jumps into IBMX in the dark, or in the presence of steady illumination producing I = 15, 48, or 480 photoisomerizations per second, that reduced the relative circulating current to Jrel(I) = 0.90, 0.79, and 0.42 (n = 7, 3, 3, and 2 traces, respectively). The traces in darkness are the same as in A. (C) Derivatives of J(t)1/2, estimated by fitting each trace with a running 61-point parabola, and evaluating the derivative at the midpoint. At the sampling rate of 300 Hz, this parabola covered 0.10 s before and after the midpoint; the apparent rise of the derivatives before time zero is an artifact of using this finite width. Derivatives estimated with narrower windows gave similar maxima, but greater noise. Rod d of Table 2.

To begin with, the values of all parameters were set to those of the standard rod (see Appendix A). The value of ß_Dark for the particular rod was determined as that which provided the best fitting simulation to the IBMX step in darkness; this value invariably agreed to within 10% of that obtained using the Hodgkin and Nunn 1988 method of analysis (which is described in RESULTS). The amplification constant (A) of the rod was extracted by analysis of the rising phase of the flash response family obtained in the dark-adapted state; this analysis differed from that of Lamb and Pugh 1992 , in that the activation model incorporating the membrane time constant (Smith and Lamb 1997 ) was used. Finally, for each IBMX step in light-adapted conditions, the value of I was found that minimized the sum-of-squares error between experiment and prediction over the first 200 ms of the response. From this value of I, the value of ß(I) was found by substitution in Eq. B7. From the steepness of the variation in the sum-of-squares error with variation in ß (see Fig 8 E), we think that our extracted estimates of ß are reliable to within about ±10%.

View larger version (25K): [in this window] [in a new window]   Figure 8. Estimation of the steady rate constant ß(I) of cGMP turnover, by the fitting of simulated responses to the IBMX-jump experiments. The top row (A and B) presents the averaged traces from Fig 7 B (Table 2, rod d); the middle row (C and D) presents equivalent results from the rod of Fig 2 (Table 2, rod a). The left and right columns show simulations for ncG = 2 and 3, respectively. The procedure for fitting is described in the MATERIALS AND METHODS. In brief, the response of the model in the Appendix A was evaluated, in response to a sudden reduction in PDE activity from its initial steady level. This calculation was repeated over a range of values of steady intensity (I) to find the intensity and, hence, the value of ß(I), that minimized the sum-of-squares error from each experimental trace over the time window 0–200 ms. The parameters of the model were set to those measured for the respective cells (Table 2, rods d and a), together with the remaining parameters for the "standard" rod in Table 4 (except that Rectot was set to 20 µM for rod a, in C and D). The value of ßDark in each panel was determined by applying the above fitting to the IBMX-jump data obtained under dark-adapted conditions. The dotted curves show the predictions of the model when the Ca2+ concentration was clamped at the level predicted by the model for the respective light-adapted state; these curves are well approximated by J@t(1+It)ncG. (E) Dependence of the RMS error on ß(I), for the two cells, calculated with ncG = 2, denoted with the same symbols as in Table 2: •, for A; , for C. This plot gives an indication of the precision with which ß(I) is determined by this method.

	THEORY

Top Abstract INTRODUCTION MATERIALS AND METHODS THEORY RESULTS DISCUSSION Acknowledgements Appendix A Appendix B Appendix C References

In this section, we examine ways of quantifying the PDE activity that underlies the rod's electrical response. We show that a fundamentally important parameter that must be extracted is the fractional opening of cGMP-activated channels, which we denote as F. To estimate this parameter, we need to express the rod's response (and/or circulating current) in fractional terms. Similarly, we have found it important to express the rod's sensitivity in terms of the fractional response; as we shall show, we thereby avoid the effects of "response compression" and obtain a measure of the intrinsic biochemical adaptation.

Symbols and Terminology
The three independent variables of our analysis are t, , and I, where t is the time after a stimulus delivering photoisomerizations to the rod, in the presence of a steady background intensity of I photoisomerizations per second. Four important dependent variables that we will use in this section are as follows: f(t), the proportion of cGMP-activated channels open; j(t), the circulating current; r(t), the response expressed as the change in this current; and s, the sensitivity. Note that we use lowercase symbols to denote the absolute values of these dependent variables. We will now distinguish two ways of normalizing these variables, and in an effort to avoid ambiguity, we will adopt two different terms to refer to these different types of normalization, which are summarized in Table 1.

First, we will use the term "fractional" to indicate that the circulating current has been divided by its steady state value, and that the response and sensitivity have been calculated from this fractional current. We will denote these fractional parameters using the corresponding uppercase symbols J(t), R(t), and S. Furthermore, we will denote steady state values obtained on a background of intensity (I) by writing them in the form j(I), ß(I), etc. Thus, the fractional circulating current is defined as J(t) = j(t)/j(I), and the fractional response as R(t) = r(t)/j(I), where r(t) = j(I) - j(t). Hence, R(t) is the complement of J(t); i.e., R(t) = 1 - J(t). The absolute sensitivity is defined as s = r(t_peak)/, in the limit of dim flashes (where, by convention, r is measured at the peak); hence, the fractional sensitivity is defined as S = R(t_peak)/.

To distinguish our second way of normalizing, we will use the term "relative" to indicate that a steady value is expressed relative to its value in darkness. Thus, the relative circulating current is J_rel(I) = j(I)/j_Dark, whereas the relative sensitivity is s_rel = s/s_Dark, and the relative fractional sensitivity is S_rel = S/S_Dark.

Fractional cGMP-activated Current and Response
The importance of expressing the circulating current (and/or the response) in fractional terms is that this immediately provides us with an estimate of the fractional level of channel opening, which in turn gives us the cGMP concentration, and (as we will show) thereby provides information about the underlying PDE activity.

The cGMP-activated opening of channels is described by the Hill relation, Equation A6, as

(1)

where f(t) is the absolute proportion of cGMP-activated channels open, cG(t) is the free concentration of cGMP, n_cG is the Hill coefficient, and K_cG(t) is the half-activation concentration. The approximation on the right applies because the cGMP concentration is always much smaller than the half-activation concentration. Hence, the fractional opening of cGMP-gated channels (i.e., expressed as a fraction of the steady-state level) is defined as

(2)

We have adopted the symbol F for this variable for consistency with our previous notation (Lamb and Pugh 1992 ).

At sufficiently early times in the response to any stimulus, the Ca²⁺ concentration Ca(t) will have changed negligibly from the steady-state level Ca(I), and, therefore, it will be acceptable to regard K_cG(t) in Equation 2 as unchanged from the steady value K_cG(I), even though K_cG(t) will change at later times through modulation of the channels by Ca²⁺-calmodulin (see Equation A11). Accordingly, at early times in any response, the fractional opening of channels F(t) will approximate to

(3)

Now, provided that the cGMP-activated current j_cG is directly proportional to the number of channels open (i.e., independent of membrane voltage) then J_cG(t) = F(t), and we can write

(4)

where the subscript "_cG" has been introduced to denote the cGMP-activated component of J or R.

Equation 4 shows that, even in the presence of steady background illumination, and in the face of changes in the steady magnitude of K_cG(I) in different adaptational states, the fractional cGMP concentration at early times can be extracted simply by measuring the fractional cGMP-activated current; i.e., we can use R_cG(t) to provide a measure of cG(t)/cG(I).

In practice, a complication arises in calculating the cGMP-activated component of current j_cG because we can only measure the total outer segment current j_tot, which is the sum of j_cG and the electrogenic exchange current j_ex. Unfortunately, we do not have a direct measure of the time course of the latter (small) component, except for the special case of a strongly saturating flash. However numerical simulations (not presented) indicate that over the early rising phase of the flash response, it is adequate to ignore the time dependence of j_ex(t), and simply approximate it as constant; i.e., j_ex(t) j_ex(I). Thus, at early times, we can approximate the fractional response R_cG(t) required in Equation 4 as

(5)

A graphical illustration of this normalization is shown in Fig 2 B, where a scale for R_cG is plotted at the right, running from zero at the steady-state level of measured current to a value of unity at the level of current reached shortly after an extremely bright flash (i.e., at the initial level of the exchange current). One needs to be aware that the approximation in Equation 5 breaks down at later times, when j_ex(t) changes. In view of this limitation, we will use Equation 5 to evaluate the response R(t) in Equation 4 only when we are examining the early phase of light responses. In other cases, on a slower time base, when j_ex(t) is expected to change substantially, we will simply determine R(t) with respect to the total current by calculating R_tot(t) = r_tot(t)/j_tot(I).

Relation between PDE Activity and Circulating Current
By considering the differential equation for the synthesis and hydrolysis of cGMP, Lamb and Pugh 1992 derived an expression for the flash-induced increase, ß(t), in the rate constant of cGMP hydrolysis, from its dark-adapted level ß_Dark, in terms of the current scaled to the dark level. Since we have now shown that a comparable scaling is applicable for steady backgrounds, rather than just in darkness, Lamb and Pugh's Equation 6.18 can be extended to the general form

(6)

At sufficiently early times, when F(t) 1, the final term in this expression approaches zero, so that ß(t) is given by the first term, in which the only variable is the fractional opening of cGMP-activated channels, F(t), which we have shown is given by 1- R_cG(t) (Equation 4).

The important conclusion from this equation is that, if, at sufficiently early times, it can be shown experimentally that the fractional response R_cG(t) has a common initial phase in the presence of different backgrounds then the initial time course of PDE activation underlying the responses must also be the same on the different backgrounds.

Relative Steady-state Current
Since F(t) expresses the channel activation as a fraction of its steady-state level, it must always start from unity. But another parameter of considerable interest is the steady-state level of channel activation in a steady background, relative to its dark-adapted level, which we denote as F_rel(I) = f(I)/f_Dark. If we again assume that the circulating current j(I) is directly proportional to channel opening f(I), then we have

(7)

Koutalos et al. 1995b have shown that, in the steady state, the exchange current j_ex(I) is directly proportional to the cGMP-activated current j_cG(I) (see Equation A4), so that the relative steady-state current F_rel(I) will be the same whether Equation 7 is evaluated using j_cG or using j_tot.

Fractional Sensitivity of the Flash Response
According to our analysis above, the transduction process may be probed at the level of PDE activity by first converting the absolute response (r) to fractional response (R), and in the same way the rod's sensitivity may be corrected for "response compression" by measuring the fractional sensitivity, S = R/. The sensitivity parameter that is conventionally plotted is the relative sensitivity s_rel = s/s_Dark (in the past, this has often been denoted as S_F/S_F^D, but we avoid that terminology here since F denotes fractional opening of channels). This measure of raw sensitivity may be converted to the fractional form S_rel = S/S_Dark simply by dividing it by the relative circulating current J_rel(I), because of the following relations:

(8)

The crucial insight is that use of the relative fractional sensitivity (S_rel) in Equation 8 removes the response compression that results from a reduced steady-state level of circulating current. The application of this concept will be illustrated in Fig 5.

	RESULTS

Top Abstract INTRODUCTION MATERIALS AND METHODS THEORY RESULTS DISCUSSION Acknowledgements Appendix A Appendix B Appendix C References

Flash Response Families in Dark-adapted and Light-adapted Conditions
Fig 2 presents families of flash responses from one rod under four adaptation conditions: darkness, and in the presence of steady illumination estimated to produce I = 260, 810, and 2,600 photoisomerizations per second. An identical series of seven flashes was delivered in each panel, and the traces of raw response r(t) clearly show the hallmarks of light adaptation: progressive reduction in sensitivity; a decrease in time to peak of the dim-flash response; and earlier recovery from a bright flash, in the presence of successively brighter backgrounds. For example, under the four conditions of adaptation, the dimmest flash suppressed 20, 4.7, 3, and 1.1 pA of circulating current, and the peak response occurred at 0.6, 0.38, 0.34, and 0.30 s, respectively. For the most intense flash, the time taken to reach 50% recovery was 12.3, 9.1, 7.8, and 6.6 s in the four conditions.

There are conflicting reports in the literature as to whether part of photoreceptor desensitization during light adaptation is brought about by a reduction in the gain of any of the "amplification" steps underlying activation of the G-protein cascade. This has been investigated through examination of the early rising phase of light-adapted responses. On the one hand, Torre et al. 1986 and Fain et al. 1989 have reported that this early rising phase is unaltered by adaptation to weak backgrounds, even though the recovery phase occurs earlier. On the other hand, both Gray-Keller and Detwiler 1994 and Jones 1995 have reported that the early rising phase of the response is attenuated, and that their results indicate a reduction in the amplification constant of transduction. Likewise, Lagnado and Baylor 1994 have reported that, in the presence of lowered intracellular Ca²⁺ concentration, the gain of activation is reduced. In view of these differences, one of the principal aims of our experiments has been to test thoroughly whether the gain of transduction is altered during light adaptation.

Invariance of the Initial Activation Phase of Phototransduction
To examine this question, it is essential (as explained in THEORY) to express the cGMP-activated currents (and/or responses) in fractional form. Accordingly, Fig 3 presents results similar to those in Fig 2, from a rod tested under six different states of adaptation, after transformation in three ways. First, we plotted the fractional cGMP-activated response, R_cG(t) = j_cG(t)/j_cG(I); second, we expanded the time scale by factors of 10- and 20-fold; and third, we grouped the responses according to flash intensity rather than background. The individual panels in Fig 3 (A–I) paint a highly consistent picture: for every flash intensity the fractional response R(t) began rising along a common trajectory independent of the state of adaptation.

It might be thought that the common initial rate of rise in Fig 3 could be limited by the membrane time constant. However, even at the highest flash intensity (Fig 3 I) the slope was only 12 s^-1, well short of the maximal slope (60 s^-1) previously reported for responses of nonvoltage-clamped salamander rods stimulated with much more intense flashes, which has been shown to be set by the membrane time constant (Cobbs and Pugh 1987 ). Hence, the membrane capacitive time constant will only become limiting at even higher flash intensities than illustrated in Fig 3.

In the THEORY, we drew the important conclusion from Equation 6 that the occurrence of a common rising phase for the fractional response R(t) in the presence of different backgrounds could only occur if the initial time course of the underlying PDE activation was common. Applying that insight, we conclude from the analysis of Fig 3 that a flash of fixed intensity elicits an increment in PDE activity, ß(t), which initially is independent of the state of steady adaptation. We applied the same analysis to the responses of the 11 rods for which extensively averaged records were available (Table 2), and for two additional rods with less extensive data, for backgrounds suppressing up to 75% of the dark current. In all cases, behavior very similar to that in Fig 3 was observed, with close coincidence of the early phase of the fractional response R(t) to a given flash presented on different backgrounds.

As a final point in relation to the traces in Fig 3, it is interesting to note that the more intense the background, the earlier in time the peeling-off occurs; i.e., the earlier the deviation of the fractional response from the common initial trajectory. In a subsequent section, we show that behavior of this kind is, in fact, expected as a consequence of the increased steady rate constant of cGMP hydrolysis, ß(I), whose measurement we describe shortly.

From the results for the rod in Fig 3, we calculated the average dim-flash response per photoisomerization, R(t)/, in each of the six adaptational states, and we have plotted these traces in Fig 4. For each background intensity (or darkness), we considered only those test flash intensities that elicited a fractional response R(t) of less than 30% at its peak, and we calculated the weighted average response per isomerization. Hence, the composite plot in Fig 4 is broadly analogous to any of the individual panels for a fixed flash intensity in Fig 3 (e.g., Fig 3 D), except that it is constructed only from dim-flash responses and has been scaled according to flash intensity. It is also similar to the plot in Figure 3 of Baylor and Hodgkin 1974 for turtle cones, except that the traces in that plot were not scaled according to the maximal response in each adaptation condition.

Fig 4 extends our finding of an invariant early rise at any fixed intensity, by showing that the initial time course of the fractional response per photoisomerization R(t)/ is invariant. Furthermore, this figure shows that the parabolic approximation of the "activation only" model provides a remarkably accurate prediction of the response in each adaptational state, up until the time of peeling off (which is shorter in the presence of brighter backgrounds), at which point each individual experimental trace suddenly deviates from the parabola.

Absolute Sensitivity and Fractional Sensitivity during Light Adaptation
We now illustrate the method described in the THEORY for extracting a measure of flash sensitivity that is "corrected for response compression." Fig 5A and Fig B, illustrates data from the rods of Fig 2 and Fig 3, respectively. The top left section of each panel (left ordinate) plots the amplitude of the rod's fractional response, R (measured at the peak), as a function of flash intensity ; the circles were obtained under dark-adapted conditions, while the other sets of symbols correspond to different background intensities. The fractional sensitivity, S = R/ in the limit of dim flashes (see THEORY), is given by the horizontal position of the curves that have been fitted; for the dark-adapted measurements in Fig 5 A, the horizontal position gives the fractional sensitivity as S_Dark = 0.0036 photoisomerization^-1. (The fitted curves on the leftside of Fig 5 are exponential saturation functions, but the chosen form of equation is not critical since all that is relevant to sensitivity is the horizontal positioning at dim flash intensities.) For the three backgrounds tested in Fig 5 A, the rightward shifts of the other fitted curves from the dark-adapted one give the relative fractional sensitivity S_rel as 0.24, 0.18, and 0.08. These rightward shifts reflect the extent of desensitization of transduction because of factors other than response compression. We shall return later to the results plotted in the lower right of each panel in Fig 5.

Collected Measurements of Circulating Current and Sensitivity
In Fig 6, we summarize our steady-state measurements of circulating current and sensitivity for all the rods of this study as well as for selected results from salamander rods in other investigations; in each panel, the values are given relative to the dark-adapted level. Fig 6. A presents the relative circulating current in the steady state, J_rel(I) = j(I)/j_Dark. Fig 6 (B and C) present the relative measures of sensitivity, s/s_Dark and S/S_Dark, where s = r/ is the absolute sensitivity, and S = R/ is the fractional sensitivity, as defined in the THEORY. The relative sensitivity in Fig 6 B is the parameter that usually has been plotted in previous studies, and the relative fractional sensitivity in Fig 6 C is obtained by dividing the results in B by those in A (Equation 8). The values in Fig 6 C are completely equivalent to the lateral shifts shown for the two illustrative cells on the left of Fig 5, and represent the reduction in flash sensitivity after correction for response compression. Also shown in Fig 6 are theoretical traces (continuous curves), which we will describe later.

Measurement of the Steady-state Rate Constant of cGMP Hydrolysis, ß(I)
An unavoidable consequence of increasing the intensity of the steady illumination is that the steady rate constant of cGMP hydrolysis ß(I) will increase, and it is our goal both to measure this increase and to show how it contributes to desensitization. To measure the steady rate constant ß(I), we used the IBMX-jump method of Hodgkin and Nunn 1988 with modified analysis. (We retain the conventional term rate constant to describe ß, even though the value of ß is not constant, but varies as a function of steady intensity and can also change dynamically during the light response.)

Fig 7 A superimposes the fractional current recorded in response to seven repetitions of exposure of a dark-adapted rod outer segment to Ringer's solution containing 500 µM IBMX. Once the current had increased appreciably, a saturating flash was delivered (with manual triggering; timing indicated by arrows), and shortly thereafter, the rod was returned to normal Ringer's solution. The responses to IBMX exposure were highly reproducible. Furthermore, no differences were observable between two traces obtained in total darkness and five traces obtained in the presence of the normal dim infrared illumination. These seven responses are shown again in Fig 7 B on a faster time base (lowest set of traces), along with similar results collected when the rod had adapted to steady backgrounds of three intensities. In each case, the current was expressed as the fraction J(t) of the steady-state level before IBMX exposure.

Our first method of estimating ß(I), which is closely similar to that of Hodgkin and Nunn 1988 , is illustrated in Fig 7 C. It is based on the assumption that a few hundred milliseconds after the solution change, the IBMX concentration within the outer segment will have risen enough to totally inhibit all the PDE activity, yet the cyclase rate (t) will not have changed from its initial steady rate (I). On the basis of the first of these assumptions, the term ß in Equation A3 disappears, so that dcG/dt (t), whereas on the basis of the second assumption, (t) (I) = ß(I) cG(I), so that in conjunction with Equation 4 we can write

(9)

One difference between this formulation and that of Hodgkin and Nunn 1988 is that we use normalization with respect to the steady current present before the IBMX exposure, rather than with respect to the dark current.

As assumed by Hodgkin and Nunn 1988 , we ignore the exchange current (i.e., we assume that j_cG j_tot), and we take the maximum value of the derivative, which occurs 100–200 ms after the solution change, to represent ß(I). Thus, an implicit assumption of this method is that the time of occurrence of the maximal slope is late enough that the IBMX will have equilibrated, but early enough that the cyclase rate will not have changed. Accordingly, the peaks of the traces plotted in Fig 7 C provide estimates of the steady rate constant of cGMP hydrolysis applicable in darkness and in the presence of steady adapting backgrounds. We hypothesize that the main limitation in this approach is that is not constant after the solution change and, instead, that the increase in Ca²⁺ concentration that occurs within 200 ms can cause appreciable inhibition of guanylyl cyclase before maximal inhibition of PDE occurs, thus, leading to underestimation of the rate constant, ß(I).

In an attempt to investigate this hypothesis, we numerically integrated the entire set of equations for phototransduction presented in Appendix A, as described in detail in MATERIALS AND METHODS (see Table 3 and Table 4).

Fig 8 compares the recorded responses to IBMX steps with the predictions of the model, for two cells: the top row (Fig 8A and Fig B) shows the averaged traces from Fig 7 B, whereas the bottom row (Fig 8C and Fig D) shows similar averaged traces from the rod of Fig 2. The left and right columns show the predictions obtained using two assumptions for the value of the Hill coefficient of the cGMP-activated channels, n_cG = 2 (left) and n_cG = 3 (right). Inspection of Fig 8 shows that the quality of fit of the simulated traces to the experimental traces was very good over the initial 200 ms, for each adaptational state, and this finding lends credence to the general adequacy of the theoretical framework laid out in the Appendix A. Comparison of the left and right columns of Fig 8 shows that the quality of fit was essentially unaffected by the assumed value of channel cooperativity, n_cG. Between the different traces, we kept all the parameters of the model (i.e., those listed in Table 4 [see Appendix A]) constant, and we varied only the intensity (I) of steady illumination to find the best fit over the initial 200 ms. Even though the fitting has been constrained only over this early phase, the theory traces generated with the model provide a reasonably good general description of the whole family of responses out to 1 s.

The estimates of ß(I) obtained by the approach illustrated in Fig 8 coincided closely with those obtained by the derivative method of Fig 7, for IBMX jumps in darkness and in the presence of relatively dim backgrounds. However, at brighter backgrounds, the estimates from the derivative method were smaller, as would be expected if that method was compromised by a rapid change in . Thus, for the cell illustrated in Fig 8 A, the derivative method gave values of ß(I) = 1.3, 2.0, 3.2, and 6.6 s^-1 (in darkness and on the three backgrounds), whereas the simulation approach gave ß(I) = 1.4, 1.8, 3.2, and 8.5 s^-1 (in both cases using n_cG = 2). Similarly, for the rod of Fig 8 B, the derivative method gave 0.92, 3.5, 6.6, and 11.5 s^-1, whereas the simulation approach gave 1.0, 3.5, 7.5, and 16.6 s^-1. We would emphasize that the discrepancy between the pairs of estimates of ß(I) at higher intensities was not caused by failure of the theory curves to describe the experimental recordings. Indeed, the maximum slopes of the respective experimental and simulated traces agreed closely with each other. Instead, the simulations indicated that, by the time that the maximal slope was attained (150–200 ms), (t) had declined to 70% of its initial steady level (I), so that the approximation underlying Equation 9 was compromised. Hence, we conclude that the derivative method underestimates ß(I) at higher intensities, and that for these backgrounds, the method of fitting simulated responses is more accurate.

It is possible to investigate this conclusion, and the underlying basis of the effect, by considering the predicted behavior of our model rod to a step of IBMX when changes in Ca²⁺ concentration are prevented. These simulations gave predicted responses (dotted traces in Fig 8) that followed purely accelerating trajectories. When we compared the maximal slope predicted by the full model with the slope at the corresponding time predicted by the calcium-clamped model, we found only a slight difference in darkness or with a dim background, but a considerable discrepancy when the background was bright. On the assumption that such differences in the model calculations genuinely reflect the behavior of real rods, we conclude that the primary shortcoming in the derivative approach stems from the dynamic change in Ca²⁺ concentration that accompanies exposure to IBMX.

A more intuitive (and less model-dependent) way to arrive at the same conclusion can be obtained by considering a straightforward approximation. If we take the cyclase activity under calcium-clamped conditions to be constant at the steady-state level determined by the background, and then integrate both sides of Equation 9, we obtain an analytical prediction for the IBMX-jump response as t[1+It]^ncG. This is a continually accelerating function of time that closely approximates each of the dotted traces in Fig 8. Importantly, it is the trajectory that the response of the real rod would need to follow, if the derivative method of Equation 9 were to give the correct value for ß(I). And since the slope of the real rod's response is considerably smaller than the slope of this trajectory for brighter backgrounds, we again conclude that the derivative method underestimates ß(I).

Collected Measurements of the Rate Constant of cGMP Hydrolysis, ß(I)
We now summarize in Fig 9 the estimates of ß(I) obtained with the derivative method (Equation 9), both from this study (closed symbols) and from previous investigations (open symbols). All estimates were obtained with an assumed Hill coefficient of n_cG = 2, and to a good approximation the equivalent values for n_cG = 3 can be obtained simply by scaling all the points down to two thirds of their plotted values. In addition, at the higher intensities, we have also shown the estimates of ß(I) determined by the fitting method of Fig 8. Each of these estimates is shown at the upper end of a vertical arrow from the corresponding point obtained with the derivative method, which, as explained above, is expected to provide an underestimate of the true value of ß(I). The results in Fig 9 show that, for an assumed channel cooperativity of n_cG = 2, the estimate of ß(I) increases from 1 s^-1 in darkness to 10–20 s^-1 for steady illumination of 1,000–2,000 photoisomerizations per second, which (as shown by Fig 6) suppresses 60–70% of the circulating current. We have intentionally not normalized ß(I) to its dark level, for reasons that will become apparent later.

View larger version (24K): [in this window] [in a new window]   Figure 9. Steady-state rate constant, ß(I), of cGMP hydrolysis as a function of background intensity. (A) Estimates of ß(I) obtained using the derivative method of Fig 7 and Equation 9 are plotted (mean ± SD of repeated measurements). In addition, estimates obtained by the "fitting" method of Fig 8 are also shown at intensities of I > 800 photoisomerizations per second, linked by vertical arrows to the corresponding points obtained with the derivative method. In all cases, it has been assumed that ncG = 2. Closed symbols are from our own experiments and are identified in Table 2. Open symbols are from two other studies that used the IBMX-jump or Li+-jump methods. , Hodgkin and Nunn 1988 Li+-jump experiments: single cell from their Figure 2, plus ßDark from Table 1, with mean ± SD for n = 17 rods. , Cornwall and Fain 1994 IBMX-jump for a single cell, their Figure 6. , Cornwall and Fain 1994 Li+-jump for a single rod, their Figure 2. Cornwall and Fain assumed ncG = 3 in their analysis, and we have adjusted their data for ncG = 2. The solid curve plots the steady-state expression for ß(I) as a function of I given by Eq. B7, with ßDark = 1.0 s-1, A = 0.08 s-2, ncG = 2, E = 1.6 s, and kR,max = 12 s-1 (which yields R, Dark = 0.35 s). The two dashed curves are the same, except for ßDark = 0.5 and 1.5 s-1. The two dotted curves were derived with Equation 2Equation 3Equation 4Equation 5Equation 6 of Koutalos et al. 1995b for Ca2+i, Dark = 200 nM (bottom dotted trace) and 500 nM (top dotted trace).

In subsequent sections, we will investigate the contribution of this increase in ß(I) to the desensitization of the flash response observed during light adaptation, and we will also investigate the role that it plays in the earlier "peeling away" of the flash responses from the common initial trajectory, which is observed with more intense backgrounds. But before doing so, we need to quantify any adaptational changes that occur in the other two major recovery processes: the mean lifetime of activated rhodopsin (_R) and the mean lifetime of activated PDE (_E).

The Mean Effective Lifetime of Activated PDE during Light Adaptation
Previous investigations have shown that the "dominant" time constant in recovery of the bright-flash response (i.e., the slowest time constant) is virtually unaffected by light adaptation or by cytoplasmic Ca²⁺ concentration (Pepperberg et al. 1992 , Pepperberg et al. 1996 ; Lyubarsky et al. 1996 ; Murnick and Lamb 1996 ; Nikonov et al. 1998 ). Nikonov et al. 1998 have reviewed the evidence and concluded that this time constant corresponds to the mean lifetime of activated PDE, denoted as _E.

The method for estimating the magnitude of the dominant time constant is illustrated by the points in the bottom right section of the two panels in Fig 5. The measurements plot the time taken for recovery to a criterion level of circulating current (of 50% in Fig 5) after saturating flashes of different intensity, which were presented either in dark- or light-adapted conditions. When the flash intensity is plotted on a logarithmic scale, as in Fig 5, then a straight line relationship is consistent with first-order removal of a substance that is produced in proportion to light, and the slope of this line is directly proportional to the time constant of removal. Hence, the straight, and broadly parallel, results in Fig 5 A are consistent with first-order removal, with a time constant that appears independent of adapting intensity (1.6 ± 0.2 s, mean ± SD). In Fig 5 B, the points at each background fall along a straight line, but the slope of the line appears to decline as the background intensity increases, indicating a reduction in the size of the dominant time constant at higher levels of adaptation. Our collected measurements are presented in Fig 11, and will be described shortly.

View larger version (18K): [in this window] [in a new window]   Figure 10. Step/flash experiment used as the basis for determining the decrease in R* lifetime. (A) Responses of rod f of Table 2, stimulated with flashes producing = 5,100 (a), 16,000 (b), or 51,000 (c) photoisomerizations, either in darkness (top set), or synchronously with the termination of a step of light delivering I = 370, 1,200, or 3,700 photoisomerizations per second, that had been applied for 20 s. The effect of the backgrounds in shortening the duration of the response is indicated diagrammatically for flash c by the leftward pointing arrows, which originate from a line coinciding with the time of 50% recovery for the flash delivered in darkness; the magnitude of this leftward shift in time to 50% recovery is denoted T50. (The traces were digitally filtered at 50 Hz with the MatlabTM routine "filtfilt".) (B) Dependence of T50 on step intensity for six rods from this study (closed symbols, identified in Table 2), and for the rod in Figure 8 of Fain et al. 1989 , , which was exposed to steps lasting 7 s. When more than 1 flash intensity was used (as in A), T50 was determined as the mean shift for the different intensities, and the bars indicate ± SD. The two curves plot predictions of the model in the Appendix A using the parameters of the standard rod, except for E, which is 2.4 s for the top curve and 1.6 s for the bottom curve.

View larger version (17K): [in this window] [in a new window]   Figure 11. Dependence of the three main time constants of rod phototransduction on the intensity of steady adapting light. (A) R/R, Dark, the effective lifetime of R* relative to its dark-adapted lifetime, inferred as described in the text (Equation 10) from the step/flash experiments of Fig 10. (B) E/E, Dark, the effective lifetime of activated PDE, E*, relative to its dark-adapted lifetime, extracted by measuring the dominant time constant of recovery for saturating flashes (Fig 5). (C) Time constant of cGMP hydrolysis, 1/ß(I), determined as the reciprocal of the steady-state rate constant of hydrolysis as measured by the methods of Fig 7 and Fig 8, and summarized in Fig 9. The error bars (Fig 9) have been removed for simplicity, and only the estimates obtained with the fitting method (Fig 8) have been shown in cases in which the two methods yielded different estimates of ß.

Measurement of the Effective R* Lifetime during Light Adaptation
Fig 10 illustrates an experiment of a type introduced by Fain et al. 1989 that has been hypothesized to measure the change in effective lifetime of R* elicited by adaptation to backgrounds (Matthews 1996 , Matthews 1997 ; Murnick and Lamb 1996 ). The protocol, which we refer to as a "step/flash" experiment, is illustrated in Fig 10 A. The rod was exposed to a saturating flas