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.
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Abstract |
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We investigated the kinetics and sensitivity of photocurrent responses of salamander rods, both in darkness and during adaptation to steady backgrounds producing 203,000 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
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INTRODUCTION |
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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,
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
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MATERIALS AND METHODS |
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Suction Pipet Recordings
Our methods for preparing isolated salamander rods and for recording and analyzing their electrical responses have been reported previously (
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 (
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.)
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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 (
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
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 (
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.
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To begin with, the values of all parameters were set to those of the standard rod (see Appendix A). The value of ßDark 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
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THEORY |
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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.
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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(tpeak)/, in the limit of dim flashes (where, by convention, r is measured at the peak); hence, the fractional sensitivity is defined as S = R(tpeak)/
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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 Jrel(I) = j(I)/jDark, whereas the relative sensitivity is srel = s/sDark, and the relative fractional sensitivity is Srel = S/SDark.
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
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(1) |
where f(t) is the absolute proportion of cGMP-activated channels open, cG(t) is the free concentration of cGMP, ncG is the Hill coefficient, and KcG(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
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(2) |
We have adopted the symbol F for this variable for consistency with our previous notation (
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 KcG(t) in Equation 2 as unchanged from the steady value KcG(I), even though KcG(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
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(3) |
Now, provided that the cGMP-activated current jcG is directly proportional to the number of channels open (i.e., independent of membrane voltage) then JcG(t) = F(t), and we can write
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(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 KcG(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 RcG(t) to provide a measure of cG(t)/cG(I).
In practice, a complication arises in calculating the cGMP-activated component of current jcG because we can only measure the total outer segment current jtot, which is the sum of jcG and the electrogenic exchange current jex. 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 jex(t), and simply approximate it as constant; i.e., jex(t) jex(I). Thus, at early times, we can approximate the fractional response RcG(t) required in Equation 4 as
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(5) |
A graphical illustration of this normalization is shown in Fig 2 B, where a scale for RcG 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 jex(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 jex(t) is expected to change substantially, we will simply determine R(t) with respect to the total current by calculating Rtot(t) = rtot(t)/jtot(I).
Relation between PDE Activity and Circulating Current
By considering the differential equation for the synthesis and hydrolysis of cGMP, ß(t), in the rate constant of cGMP hydrolysis, from its dark-adapted level ßDark, 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
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(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- RcG(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 RcG(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 Frel(I) = f(I)/fDark. If we again assume that the circulating current j(I) is directly proportional to channel opening f(I), then we have
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(7) |
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 srel = s/sDark (in the past, this has often been denoted as SF/SFD, 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 Srel = S/SDark simply by dividing it by the relative circulating current Jrel(I), because of the following relations:
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(8) |
The crucial insight is that use of the relative fractional sensitivity (Srel) 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.
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RESULTS |
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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,
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, RcG(t) = jcG(t)/jcG(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 (AI) 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 (
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.
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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
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 SDark = 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 Srel 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, Jrel(I) = j(I)/jDark. Fig 6 (B and C) present the relative measures of sensitivity, s/sDark and S/SDark, 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
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 (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
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(9) |
One difference between this formulation and that of
As assumed by jtot), and we take the maximum value of the derivative, which occurs
100200 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).
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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, ncG = 2 (left) and ncG = 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, ncG. 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 ncG = 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 (150200 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 ncG = 2, and to a good approximation the equivalent values for ncG = 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 ncG = 2, the estimate of ß(I) increases from 1 s-1 in darkness to 1020 s-1 for steady illumination of 1,0002,000 photoisomerizations per second, which (as shown by Fig 6) suppresses 6070% of the circulating current. We have intentionally not normalized ß(I) to its dark level, for reasons that will become apparent later.
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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 (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.
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Measurement of the Effective R* Lifetime during Light Adaptation
Fig 10 illustrates an experiment of a type introduced by
As reported by T50 = 2.3, 2.9, and 3.7 s, where the symbol
T50 denotes the shortening of recovery time measured at the 50% criterion level.
By examining the other test flash intensities, and other criterion levels of recovery, we found that the measurements of step/flash acceleration were quite robust. For the intermediate flash intensity (b), the corresponding shifts for the three levels of adaptation were T50 = 2.1, 2.5, and 3.0 s, broadly comparable to (but 1018% shorter than) the values obtained with the strongest flash. Similarly, at a criterion level of 20% recovery, the shifts were
T20 = 2.0, 2.6, and 3.1 s for flash b, and 2.3, 3.0 and 4.0 s for flash c. The relatively small size of the variations indicates that the shape of the recovery phase is similar at different intensities of saturating flash, but simply shifted in time, and that the dominant time constant of recovery is at most only weakly affected by background illumination. In the following analysis we will neglect such variations. Fig 10 B presents the shift
T50 as a function of adapting intensity, for six rods from this study and for the rod in
By making several assumptions, it is possible to convert the shifts obtained in the step/flash experiments into changes in the effective lifetime of R*. The first two assumptions are expressed in Equation A1 and Equation A2 of Appendix A A, which specify that the activities of R* and E* each decline as first-order processes, with time constants R and
E at a given level of adaptation. The third assumption is that
E is independent of background intensity, a matter that we examine in Fig 11. The final assumption is that
E >
R. This last assumption restates our view, set out in the previous section, that
E represents the dominant time constant of recovery, and can therefore be estimated from the slope of the plot of recovery time versus logarithm of flash intensity, of the kind illustrated in Fig 5.
The practical meaning of these assumptions is that, when measured at times much greater than R, the state of activation underlying the saturating flash response declines as an exponential with time constant
E, from an initial level that is directly proportional to the time constant
R. Hence, if
R changes from its dark-adapted value of
R, Dark then the induced shift in recovery time
T is given to a good approximation by the exponential relation
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(10) |
Analysis of the exact form of the solution to Equation A1 and Equation A2, given by E is much greater than
R, Dark, as is the case in the salamander rod, where
E = 1.52.7 s and
R, Dark
0.4 s, and we therefore adopt Equation 10 in the estimation of
R. The extracted values are presented in the next section along with those of the other two time constants of recovery.
It is worth mentioning that, even if the assumption of first-order decline in R* activity is not correct, the ratio calculated in Equation 10 (and plotted in Fig 11 A) remains useful. Provided that the R* activity declines much more rapidly than the PDE time constant E, the factor exp(-
T/
E) will represent the light- to dark-adapted ratio of the integrated R* activity,
R*(t) dt.
To compare the shifts measured in the step/flash experiments with theory, we include in Fig 10 B two traces generated with our model of recoverin's interaction with RK. The traces were generated by solving the steady state, including the equations of Appendix A C, and then substituting the values of R(I)/
R,Dark from Equation A12 into Equation 10 above to obtain
T. We used two values of
E corresponding roughly to the upper and lower range of estimates obtained in Table 2:
E = 2.4 s (Fig 10 A, top trace) and 1.6 s (Fig 10 A, bottom trace). Comparison of these traces with the symbols in Fig 10 B shows a general correspondence between the predicted shifts and the estimates of
E (Table 2). Thus, rod f (
,
E = 2.7 s) exhibited the largest shifts, whereas rod b (
,
E = 1.5 s) exhibited the smallest.
Dependence of the Three Principal Time Constants of Recovery on Adaptation Level
In Fig 11, we present our collected measurements of the three principal time constants governing the recovery phase of salamander rod phototransduction as functions of the intensity I of steady background illumination. The estimated lifetimes of R* and E* have been plotted relative to their dark-adapted levels, as R/
R, Dark (A) and
E/
E, Dark (B). But, for the lifetime of cGMP (C), we plotted 1/ß without normalization to the dark-adapted level. Our reason for not doing so is that ßDark appeared to vary from cell to cell in a manner unrelated to the light-activated PDE activity. Thus, in Fig 9, ßDark exhibited a range of nearly fourfold, whereas at backgrounds in the neighborhood of I = 1,000 photoisomerizations per second, the range of ß(I) was only slightly greater than twofold.
Fig 11 B shows that the E* lifetime E is at most only weakly dependent on background intensity, with the estimates for most rods decreasing by 2040% for backgrounds producing >500 photoisomerizations per second (see also Fig 5 B). We are uncertain whether this apparent decline in
E is a true reflection of an underlying mechanism or whether it is due in some way to the limitations of the method of analysis.
In contrast to the modest and somewhat irregular decline in the estimate of E, all rods exhibited a systematic decline in the estimate of
R beginning at the lowest backgrounds and reaching three- to fivefold at the highest backgrounds. One of the assumptions underlying the calculation of
R/
R, Dark is that
E is independent of background intensity, and, as discussed above in relation to Fig 11 B, this assumption may not be strictly correct. If the time constant
E does decrease with increasing background intensity then the values of
R/
R, Dark that we have extracted will be underestimates; i.e., the true reduction in
R will not be as pronounced as suggested by Fig 11 A. The curve in Fig 11 A plots the predictions of a model of recoverin's calcium-dependent inhibition of rhodopsin kinase that will be considered in the DISCUSSION and Appendix AC.
In comparison with the modest changes shown in Fig 11 (A and B), the reduction in the time constant of cGMP turnover, 1/ß that is plotted in Fig 11 C is much greater, declining by 20-fold at backgrounds of 2,000 photoisomerizations per second. Hence, for the three inactivation reactions of phototransduction, the crucial message of Fig 11 is that, in the transition from dark- to light-adapted conditions, the change in the mean lifetime is modest for R*, small for E*, and major for cGMP.
Significance of the Altered Time Constants
To assess the effects of the changes in the time constant on response kinetics and flash sensitivity, Fig 12 presents the responses of the rod of Fig 2 (Table 2, rod a), along with theoretical traces computed using the model set out in the Appendix A. The responses have been normalized in the manner of Fig 3. Thus, we plotted the fractional cGMP-activated current JcG(t) = jcG(t)/jcG(I) according to Equation 5, which assumes that the component jex of Na+/Ca2+-K+ exchange current does not change appreciably over this time scale (Fig 2). To concentrate on the steady-state effects induced by the backgrounds, rather than on any dynamic changes elicited by the test flashes, we have restricted examination to the first 250 ms after the flash. And likewise, to concentrate on the steady state rather than dynamic predictions of the model, the theoretical traces have been computed under calcium-clamp conditions. Thus, the steady state of the model has been computed as described in Appendix A B, to generate the parameters Ca(I), R(I), ß(I), etc., and thereafter the simulated flash response has been computed with Ca(t) held at Ca(I). This is equivalent to an experiment in which the rod first adapts to a background in Ringer's, and is then exposed to a calcium-clamping solution, during which period it is tested with flashes.
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Comparison of the experimental and theoretical traces in Fig 12 (AD) shows that, on the whole, the model provides a good account of the early phase of each family of flash responses. To assist in evaluating the significance of the steady-state changes, we present two additional panels (Fig 12E and Fig F). Fig 12 E superimposes all the traces presented in AD, reconfirming that (irrespective of background intensity) the fractional responses to each flash intensity do indeed begin rising along a common trajectory; however, they peel off earlier as the background intensity increases. Likewise, Fig 12 F superimposes the theoretical traces from A and D, emphasizing the extent of change in predicted kinetics between the two extreme states of adaptation: dark-adapted (continuous traces), and on a background of 2,600 photoisomerizations per second (dashed traces). Since we have eliminated any dynamic (i.e., flash-induced) change in parameters from these simulations, and since the steady-state changes in cyclase activity are accounted for in the procedure of normalization to fractional cGMP-activated current, we conclude that the peeling-off behavior observed in the simulations on this time scale is mediated entirely by steady-state changes in ß(I) and R(I).
To further assess the effects of altered ß(I) and R(I) on response kinetics and sensitivity, we reexamined previous experimental work in which Ca2+i was clamped after adaptation to background illumination. The results from Figure 10 B of
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We think it impressive that the general form of agreement between simulation and experiment is so close under these conditions of calcium clamp. In considering this behavior, it is important to note that the pronounced acceleration of response kinetics in the presence of the background occurs in spite of the prevention of dynamic (i.e., response-induced) changes in Ca2+i, both in experiment and simulation. Thus, the time to the peak of the experimental responses decreases from 2.4 s in darkness (Fig 13 A) to 1.2 s on the dimmer background (Fig 13 B) and to 0.7 s on the brighter background (Fig 13 C), purely as a result of steady-state changes in transduction parameters. Less obvious in Fig 13, but equally important, is the fact that the fractional sensitivity of the response also declines, despite the clamping of Ca2+i to its steady level. To appreciate this desensitization, it is necessary to note that the test flash intensity increased in the ratio 1:4:25 in the three panels of Fig 13; measurement of the peak amplitudes indicates that the relative fractional sensitivity Srel(I) (defined in Equation 8) declined in the ratio 1:0.23:0.027.
The effects of the decline in the time constants R(I) and 1/ß(I) on fractional sensitivity and kinetics can be approximated by the convolution of three first-order decay reactions, where two of the time constants change with adaptation while
E remains constant. This corresponds closely to one formulation of the effects of adaptation considered by
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DISCUSSION |
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Photoreceptor light adaptation encompasses a complex set of molecular changes by which the cell adjusts to the ambient level of illumination. One manifestation of light adaptation is an extension of the range of intensities over which the cell is able to operate (
Light Adaptation Does Not Alter the Gain of the Amplifying Steps of Phototransduction
Our results strongly support the conclusion that there is no change in the gain of any of the amplifying steps in phototransduction at the intensities and durations of light adaptation used in our experiments. The theoretical basis for this assertion comes from the analysis underlying Equation 6, which shows that, if the fractional response is invariant at early times, then the initial time course of flash-activated PDE activity must be common. Hence, the empirical test is provided by experiments in which flash responses are scaled as the fractional change in cGMP-activated current. These experiments show that all the scaled responses to a flash of any given intensity initially follow a common trajectory, independent of background illumination (Fig 3 and Fig 12 E), and, more generally, that the scaled responses to all flashes begin rising along a single trajectory when they are further divided by the test flash intensity (Fig 4). Thus, the results of Fig 4 place on a solid foundation the suggestion made previously by
Our conclusion that the amplification of phototransduction is unaltered by adaptation is at variance with conclusions drawn by several other investigators, who have reported that the early rising phase of the response is reduced by adaptation (R and 1/ß(I), will each have declined to
150 ms, so that deviations from a common early rise will be expected to occur by
100 ms. Hence, the observation of a lowered slope of the rising phase at times later than this does not indicate a reduced amplification constant.
An additional factor that may explain the apparent difference between our interpretations and those of 120 nM. At such a concentration, the mechanism they describe would be expected to reduce the gain by only a small amount (<10%).
Elevated Phosphodiesterase Activity Evoked by Steady Light
We have made new measurements, and provided further understanding, of the light-evoked increase in steady PDE activity, which we have quantified through the steady-state rate constant ß(I) of cGMP hydrolysis. First, we have been able to estimate ß(I) at higher intensities than previously (up to 2,600 photoisomerizations per second) by comparing the predictions of our mathematical model with the results of experiments performed using the IBMX-jump method of , elicited by the massive rise in cytoplasmic Ca2+ concentration that inevitably accompanies the IBMX-induced opening of cGMP-gated channels. Second, we have provided (in Eq. B7) a formulation for the dependence of ß(I) on fundamental parameters of the cascade, as
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(11) |
where R(I) is the effective lifetime of R* in the presence of the background,
E is the effective lifetime of G*-E*, A is the amplification constant of transduction, ncG is the Hill coefficient of channel activation, and I is the intensity of steady light. Third, we have shown that this relatively simple expression provides a good account of the experimentally measured dependence of ß(I) on steady light (Fig 9). Fourth, we have shown that the dark-adapted rate constant of cGMP hydrolysis (ßDark) appears to exhibit greater variability from cell to cell than does the light-stimulated increase in ß(I). Therefore, we suggest that ßDark is determined by factors other than, or additional to, the four that scale the intensity in Equation 11. Fifth, we have extended the analysis of
Our Equation 11 above is closely analogous to the expression for PDE activation used by R(I)
E /ncG, which comprises four parameters, each of which has a defined physical meaning and can be estimated independently. Since we have provided evidence that A is constant and that
E is, at most, weakly dependent on adaptation, and since we have no reason to suspect a change in ncG, the calcium dependence of ß* expressed in their (
R in our formulation; this is specified in Equation A12 and Appendix A C.
Inspection of Fig 9 shows that there is an approximately fourfold difference between our description and that of 50 photons µm-2 s-1), the
2.5 s-1, whereas our description gives ß(I)
10 s-1. In addition, there is a smaller discrepancy in the dark-adapted value in the two cases:
0.3 s-1, whereas our experiments gave 0.81.6 s-1. These differences are illustrated by the lower curves in Fig 9: the dotted traces plot the predictions of Equation 2 from
Contribution of Individual Molecular Mechanisms to Overall Adaptational Behavior
The effect of increasing background intensity is to increase the steady rate constant of cGMP hydrolysis, ß(I), thereby lowering the cGMP concentration, and driving the photoreceptor towards saturation. In our view, the primary function of "adaptation" is to prevent the rod from being driven into saturation, thereby preventing the massive reduction in sensitivity that would otherwise occur. Three molecular mechanisms are known to help the rod evade saturation, and each is calcium-dependent: (1) the GCAP-dependent activation of guanylyl cyclase ("GCAP mechanism"); (2) the recoverin-dependent increase in rhodopsin kinase activity ("Rec mechanism"); and (3) the calmodulin-dependent decrease in the K1/2 of the cGMP-activated channels ("CaM mechanism").
In an attempt to evaluate the relative importance of these mechanisms in the maintenance of circulating current and sensitivity, we provide in Fig 14 a series of calculations for the model rod in which the three mechanisms are either present or absent in all combinations. In considering the following analysis, it is important to bear in mind that we are not performing direct experimental manipulations, but that we are instead investigating the performance of our model when we manipulate it in ways designed to simulate alterations in the presumed molecular mechanisms. Nevertheless, we think that important lessons can be learned.
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A, B, and C (Fig 14) present the predictions for steady-state current, sensitivity, and fractional sensitivity, respectively, in the format of Fig 6, with the following color coding. In each case, blue denotes the CaM mechanism alone; green denotes the Rec mechanism alone; and red denotes the GCAP mechanism alone. The other three colors denote paired combinations of these mechanisms: CaM + Rec (cyan); CaM + GCAP (magenta); and Rec + GCAP (yellow). Black denotes the case with none of the mechanisms enabled, whereas dark gray denotes the normal case with all three mechanisms active. In accordance with the conclusions of
In Fig 14 A, an additional ordinate scale is provided for Ca(I), since the steady-state calcium concentration is uniquely determined by the steady circulating current. At any fixed level of calcium, one can think of the rightward shift of each curve relative to the leftmost curve as the predicted effect of that mechanism (or combination of mechanisms) in extending the intensity range over which the cell can operate at that particular calcium level.
Contributions to Absolute Sensitivity and Fractional Sensitivity
Since light adaptation leads to reduced flash sensitivity, one might naively hope to determine the contribution of the individual molecular mechanisms to the overall desensitization that is observed, but such a division is fraught with difficulty. The problem arises because the feedback loop underlying photoreceptor light adaptation leads to the prevention of sensitivity loss, rather than to desensitization per se. Hence, as illustrated in Fig 14, the role of each of the calcium-modulated feedback mechanisms is to sensitize rather than desensitize the cell. To appreciate this, one needs to consider a vertical line drawn on Fig 14B at any arbitrary intensity: the vertical spacing between the traces then gives the predicted effect of that mechanism (or those mechanisms) on sensitivity at the particular background level.
For example, imagine a steady background of 1,000 photoisomerizations per second in Fig 14 B, and consider the predicted effect of separately disabling the three individual mechanisms. With all mechanisms functional, the relative sensitivity of the model rod is calculated as 0.032 (gray trace); with the CaM mechanism disabled, it should be indistinguishable from this, at 0.032 (yellow trace); with the Rec mechanism disabled, it should be down to 0.0136 (magenta trace); and with the GCAP mechanism disabled, it should be greatly depressed, to 0.0031 (cyan trace). Hence, the model predicts that, at this intensity, the CaM mechanism has negligible effect on sensitivity, whereas the Rec and GCAP mechanisms sensitize the rod by factors of 2.3-fold and 10-fold, respectively (in each case with respect to the situation where the mechanism is disabled).
In a similar manner, one can assess the predicted contributions of the different mechanisms to the fractional sensitivity plotted in Fig 14 C. In comparing B and C in Fig 14, perhaps the most prominent feature is the tight grouping of the traces in C compared with the wide spacing in B. For a line drawn at 1,000 photoisomerizations per second in Fig 14 C, the solid curves are separated vertically by a factor of <2. This tight grouping means that our model predicts the "biochemical sensitivity" of the cascade at this fixed intensity to be barely affected by the presence or absence of the different molecular mechanisms. How might mechanistic insensitivity of this type come about?
Desensitization of the Biochemical Cascade: Kinetic Roles of ß(I) and R(I)
The decline in fractional sensitivity in Fig 14 C must be caused by changes in the kinetics of inactivation of the biochemical response, i.e., by the shortening of the time constants of the signal integrating steps of the cascade (with possible contributions by dynamic feedback through the flash-induced change in Ca2+i). That this is so, may be seen from the fact that the rising phase of the fractional response R(t), and hence of cG(t)/cG(I), is unaffected by the presence of background illumination (Fig 3, Fig 4, and Fig 12). Hence, the decline in S, which is measured at the peak of the response, occurs because the time to peak becomes shorter. In the same way, the theoretical traces in Fig 14 C reflect the reductions in biochemical sensitivity predicted to result from accelerated recovery kinetics, whereas the traces in Fig 14 A reflect the time-invariant reductions in sensitivity predicted to result from response compression, and the two sets of traces multiply together to yield the overall reductions in sensitivity predicted in Fig 14 B.
Our simulations further support the conclusion that dynamic calcium feedback contributes little to the decline in relative fractional sensitivity. Thus, the dotted curve in Fig 14 C computed for a rod with Ca2+i clamped (to the level set by a background presented in Ringer's) lies very close to the gray curve obtained for a rod operating normally in Ringer's, with Ca2+i free to change dynamically. Thus, we are led to the conclusion that the primary factors contributing to the decline in fractional sensitivity are the declines in the two time constants, R and 1/ß(I) (Fig 11 and Fig 13). The tight "bunching" in Fig 14 C indicates that, in the presence of the normal drop in steady-state Ca2+i, the combined effect of the reductions in these two time constants in the model rod is computed to be roughly the same, irrespective of the combination of mechanisms enabled. Thus, in a case where a greater reduction in
R occurs, there is a smaller increase in ß, and, hence, a smaller reduction in 1/ß, so that the resulting time course is quite similar.
A slight exception to this trend occurs for the green trace (Rec mechanism alone), which differs significantly from the other traces at relatively dim backgrounds. This occurs because, when both the other feedback mechanisms are disabled in our model, the Rec mechanism is brought into play at relatively low intensities, and the shortening of R* lifetime causes a more pronounced reduction in biochemical sensitivity than occurs in the full model.
Relative Importance of ß(I) and R(I) in the Normal Case
To assess the relative importance of the increased PDE rate constant of cGMP hydrolysis (ß) and the Rec-mediated shortening of R* lifetime (R) in mediating the observed reduction in fractional sensitivity in the normal case, we now consider the effect of the altered time constants in a cascaded chain of integrating stages. Thus, we consider the dim-flash approximation derived by
R(I),
E, and 1/ß(I).
The two dashed traces in Fig 14 C investigate the predicted contributions to the normal case of changes in 1/ß alone and in R alone. For these two traces, one of the time constants has been held at its dark-adapted level, while the other has been varied according to the predictions of the full model. Clearly, neither of these situations can occur in reality, and we present them purely in the context of attempting to separate the contributions of the two time constants to the normal behavior. These traces show that the contribution of 1/ß(I) (dashed) is predicted to significantly outweigh that of
R(I) (dot-dashed), especially at higher background intensities where the decrease in R* time constant saturates.
We reiterate the proviso stated earlier, that the interpretations we have reached above have been obtained from analysis of the predictions of our model, rather than from direct experimental manipulation.
Bathtub Analogy of Reactions Governing cGMP Concentration
In an attempt to provide a more intuitive understanding of the role of the increased rate constant of cGMP hydrolysis in desensitizing the fractional response and accelerating the recovery, we now present an informal description, which we call the "bathtub analogy" of the reactions governing cGMP.
Imagine a bathtub, in which the depth of water represents the cGMP concentration. The rate at which water runs into the tub from a tap represents the activity of guanylyl cyclase (), and the rate at which water drains out of the tub is proportional both to the depth of the water and also to the size of the drain, which represents the PDE activity, ß. When a steady state is reached, the depth of water will equal the rate of influx divided by the rate constant of efflux; i.e., cG(I) =
(I)/ß(I). Now imagine that the size of the drain is briefly enlarged, before returning to its previous size, causing a transient increment in the rate of efflux,
ß(t). This will elicit a transient drop in water level,
cG(t), followed by eventual recovery to the original steady level. The question is: with what time course does the water level recover, once the drain has returned to its original size? The answer is that it recovers exponentially, according to a rate constant ß(I), or time constant 1/ß(I).
Next, imagine that the size of the drain is permanently enlarged, thus increasing ß(I) and, in addition, that the tap is correspondingly opened up to increase the steady influx of water, thus increasing (I). If the two parameters are increased in the same ratio then the steady-state depth of water, cG(I), will remain unchanged. Suppose now that the same incremental stimulus is given as previouslya transient additional opening of the drain,
ß(t). If this stimulus is delivered instantaneously, it will cause the same initial drop in water level as previously. But, very importantly, the recovery will occur more rapidly. Thus, the water level will begin rising more rapidly than previously, because the influx of water through the tap is faster, yet it will reach the same steady level as before; therefore, it must reach that level sooner.
In general terms, the effect of enlarging the drain will be to accelerate the rate at which the water level reequilibrates whenever it is perturbed, whereas the effect of a steady opening-up of the tap will simply be to scale-up the depth of water in the tub. Importantly, if one expresses the depth during the response as a fraction of its level before the stimulus, (i.e., as cG(t)/cG(I)), then the response will be independent of the rate of influx through the tap, provided that the rate is constant; i.e., that (t) =
(I).
Flux of cGMP
The existence of the powerful Ca2+-mediated feedback loop results in relatively small changes in concentration of cGMP and Ca2+ during light adaptation, but quite large changes in the flux of cGMP, corresponding to large increases in and ß. The flux of cGMP in the model rod increases from 3.5 µM s-1 in darkness to
27 µM s-1 in the presence of a background producing I = 3,000 photoisomerizations per second, whereas ß increases from 1.0 to 21 s-1, and cG only declines from 3.5 to 1.1 µM. Experimental measurements with the 18O method (applied to toad rods in the intact retina) have yielded even larger changes in the flux of cGMP (
2 µM s-1 in darkness to
100 µM s-1 during exposure to a steady light of I = 3,000 photoisomerization per second.
Some years ago, it was proposed that the light-induced changes in cGMP flux, per se, might underlie the photoreceptor's electrical response (27 µM s-1 requires an equal rate of GTP utilization by guanylyl cyclase, and ultimately of ATP utilization. For comparison, maintenance of the 16 pA circulating current at the same intensity requires ATP utilization at a rate of
50 µM s-1.
Relative Robustness of Conclusions
The reader may rightfully inquire as to the relative certainty (or robustness) of our conclusions, in particular, of those involving calculations with the model rod presented in the Appendix A. We think that our conclusions fall into the following several categories of certainty: (a) robust, conclusions obtained through analysis of the experimental results with the "activation-only" form of the model; (b) reasonably robust, conclusions obtained by analysis using the full model under conditions of fixed Ca2+ concentration; and (c) less robust, conclusions dependent on the full model when the Ca2+ concentration is changing dynamically.
Thus, at the highest level of certainty is our conclusion that the amplification constant of phototransduction is unaltered by adaptation, since this was obtained by analysis of experimental traces simply scaled according to the steady circulating current (Fig 3, Fig 4, and Fig 9). Next in degree of robustness, we consider to be the calculated dependence of ß on I (Fig 8 and Fig 9), because this depends primarily on the Hill relation for channel activation, in conjunction with steady synthesis and hydrolysis of cGMP. Although our correction of the estimates at high background intensities, by analysis with the model rod, introduces some model dependence into the estimated values of ß, this has little effect on the overall shape of the relation (Fig 9).
We also consider the characterization of the step/flash effect as a calcium-dependent shortening of a "nondominant time constant" (Fig 10 and Fig 11) to be a robust conclusion, especially in light of our evidence that the amplification constant is not affected by adaptation. However, our identification of this nondominant time constant as the effective lifetime of R* (and specifically our description of this lifetime as being determined by the calcium-dependent inhibition of rhodopsin kinase by recoverin) clearly depends on our model and on the values adopted for the parameters of the recoverin binding reactions (Appendix A C). Although these values have been taken from the biochemical literature, they have not been obtained for salamander rod proteins, and there are substantial differences in the estimates from different laboratories and for different species.
Next in robustness are our conclusions concerning the contributions of the different calcium-dependent mechanisms to the cell's operating range, i.e., its response versus intensity relation (Fig 14 A). Although we feel confident that the relative contributions predicted for the three mechanisms are broadly correct, we acknowledge that the model utilizes a number of calcium-dependent parameters whose exact values remain somewhat uncertain.
Finally, we consider our predictions of response kinetics, and of parameters derived from the response kinetics, to be the least robust aspects of our conclusions, since the underlying calculations involve dynamic changes in Ca2+i and, therefore, dynamic changes in all Ca-dependent processes in the rod. Accordingly, the predicted form of sensitivity as a function of background intensity (Fig 6B and Fig C, and Fig 14B and Fig C) cannot be considered as particularly robust; i.e., the shape of the relation is likely to be model-dependent. Despite this qualification, we think our conclusion that the increase in ß(I) represents the dominant factor in desensitizing the rod's biochemical cascade remains robust, since the effect is present in calcium-clamped rods (Fig 13).
Limitations of Our Present Description of Transduction
Our present model of the salamander rod achieves a good description of the steady-state dependence of circulating current (Fig 6 A) and sensitivity (Fig 6B and Fig C) on background intensity, and a good description of the kinetics of responses obtained under constant calcium conditions (Fig 12 and Fig 13). Where it falls down is in its prediction of the exact form of the response kinetics under conditions where Ca2+i is free to change; i.e., in normal Ringer's solution (traces not shown). Thus, the numerical solutions do not yet provide a satisfactory description of the overall family of flash responses in Ringer's, or even of just the dim-flash response when tested over the full range of adapting intensities. We emphasize that what we seek is a model with a single set of parameters that are consistent with all relevant measurements in the literature, including measurements of Ca2+i, the concentrations and binding parameters of the calcium binding proteins, etc. We think that the key features remaining to be resolved relate to the dynamics of shut-off of the various proteins, and entwined with these issues are kinetic aspects of the calcium buffering provided by the various calcium binding proteins, including recoverin, guanylyl cyclase activating proteins, and calmodulin.
We do not underestimate the problems that remain in obtaining a complete molecular description of the rod's response to flashes on backgrounds. But at this stage, we are confident, first, that the conventional description of activation is accurate and, second, that the main factors underlying light adaptation have been described adequately in steady-state terms. However, we think that further information will be needed about dynamic changes in these inactivation steps, before a definitive molecular description of the rod's electrical response can be provided.
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Footnotes |
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1 Abbreviations used in this paper: IBMX, isobutyl methylxanthine; PDE, phosphodiesterase.
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Acknowledgements |
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This work was supported by National Institutes of Health grant EY-02660 and a Jules and Doris Stein Research to Prevent Blindness Professorship (to E.N. Pugh Jr.), and by Wellcome Trust grant 034792 (to T.D. Lamb).
Submitted: 8 August 2000
Revised: 13 September 2000
Accepted: 15 September 2000
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Appendix A |
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THE EQUATIONS OF PHOTOTRANSDUCTION
We, and other groups, have previously presented equations describing the G-protein cascade of phototransduction that embody insights and formalisms from numerous biochemical and physiological investigations. In this Appendix Awe summarize those equations, and we acknowledge their first use (even when in slightly different form) using the following abbreviations: FKL (
In general, each of the variables is a function both of the steady background intensity (I) and the time (t) after a flash, e.g., j(I, t), but for simplicity, we will usually drop one or both of these independent variables. Thus, we will usually denote the time-dependent form as j(t), or often simply as j where this is unambiguous, whereas we will denote its steady state value j(I,) simply as j(I), with its dark-adapted steady value denoted as jDark. Although many of the variables are calcium-dependent, in general, this will not be denoted explicitly. For brevity, the definitions of all the variables and constants are given in Table 3 and Table 4, respectively.
Differential Equations
The rates of supply and removal of the active species R*, E*, cG, and Ca can be expressed in terms of the four differential equations.
Activated rhodopsin:
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(A1) |
Activated PDE:
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(A2) |
Free cGMP concentration [KM (4)]:
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(A3) |
Free Ca2+ concentration [NEP (12)]:
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(A4) |
In each case, the first term on the right represents generation, whereas the second term represents removal. In the first three equations, the rate constants of turnover of the active substance are the following: kR (= 1/R) for R*, kE (= 1/
E) for E*, and ß for cG. As a simplification in writing Equation A2, any depletion in the pools of activatable G-protein and PDE, which may occur with intense flashes, has been ignored. In addition, a short delay teff contributed cumulatively by several of the activation steps has also been ignored, but can readily be accounted for by a simple time shift.
Equations Relevant to the Rising Phase
Two variables describing the rising phase, which do not depend explicitly on Ca2+ concentration, are specified by the following equations.
Rate constant of cGMP hydrolysis [LP (4.3)]:
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(A5) |
cGMP-activated channel current [FKL]:
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(A6) |
Nevertheless, it should, be borne in mind that KcG in Equation A6 is a function of Ca; see Equation A11.
From the equations above, it is possible to solve for the rising phase of the rod's response to illumination, and the solution is characterized by an amplification constant defined as follows:
Amplification constant [LP (6.9)]:
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(A7) |
where
Rate constant of cGMP hydrolysis per E* [LP (4.4)]:
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(A8) |
Equations Related to Recovery and Adaptation
The remaining equations relate primarily to the recovery phase and to adaptation, and the parameters are explicitly dependent on Ca2+ concentration. Two of these parameters, describing the electrogenic exchange current and the guanylyl cyclase activity, are well established in the literature.
Exchange current [LCM (1)]:
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(A9) |
Guanylyl cyclase [FMRT (16)]:
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(A10) |
In addition, we present three new equations, the first being for the Ca2+/calmodulin modulation of channel activation, and the next two characterizing the Ca2+/recoverin/RK system. Whereas
Channel activation constant,
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(A11) |
In Appendix C, we analyze the recoverin/RK system, and we develop equations specifying the free concentration of recoverin and of RK, and recoverin's Ca2+-buffering power, in terms of the Ca2+ concentration. Here, we simply take the resulting variables, RK (from Eq. C1 with C3) and BCa, Rec (from Eq. C5), and use these to specify the rate constant of R* decay, and the total Ca2+-buffering power of the cytoplasm.
Rate constant of R* decay:
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(A12) |
Ca2+-buffering power:
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(A13) |
Finally, the total circulating current of the outer segment is the sum of the current through the cGMP-activated channels and the electrogenic exchange current:
Total outer segment current:
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(A14) |
except that, when the membrane capacitive time constant (m) is taken into account, a filtered version of this equation must be used.
Exposure to IBMX
To deal with exposure of the outer segment to IBMX, we assume that the PDE rate constant of cGMP hydrolysis (ß) that occurs in Equation A3 and is defined in Equation A5, is inhibited (divided) by the following factor.
PDE inhibition factor:
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(A15) |
where IBMX is the concentration of IBMX in the perfusate, t is time after the solution change, I
100 ms is the time constant of equilibration, and KI = 10 µM is the competitive inhibition constant.
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Appendix B |
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THE STEADY STATE
The steady state of the system described in Appendix A may be determined by setting the derivatives in Equation A4 equal to zero, and solving the resulting equations simultaneously with the other equations. Although it is not possible to obtain an analytical solution in terms of the steady background intensity (I), it is instead possible to adopt an inverse approach, because all the variables can be specified as functions of Ca2+concentration. Hence, one may perform the following sequence of operations.
(a) Select a wide range of steady state values of Ca(I).
(b) Calculate the steady-state Ca2+-dependent variables: jex(I), (I), KcG(I), RK(I), and kR(I).
(c) Substitute these values into Equation A4 with the derivatives set to zero, and into Equation A5 and Equation A6, to obtain respectively:
from Equation A4,
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(B1) |
from Equation A6,
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(B2) |
from Equation A3,
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(B3) |
from Equation A5,
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(B4) |
from Equation A2,
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(B5) |
from Equation A1,
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(B6) |
By substitution of the definition of the amplification constant (A), from Equation A7, the last three equations above may be combined to yield
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(B7) |
which relates I to ß(I) without the need for assumptions about the values of RE and ßsub.
Any of the steady variables determined above, including Ca(I), may readily be plotted as a function of intensity, e.g., Ca(I) versus I, or as a function of any of the other steady variables.
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Appendix C |
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A QUANTITATIVE MODEL OF RECOVERIN'S INTERACTIONS
Recoverin's Interactions with Calcium and with Rhodopsin Kinase
The calcium binding protein recoverin has been reported to be present in amphibian rods at a concentration of at least 30 µM (
In addition to its role as a calcium buffer, recoverin with two Ca2+ bound (Rec · 2 Ca) has been found to inhibit the phosphorylation of rhodopsin (
We believe that these two actions of recoverin, its calcium buffering and its inhibition of RK, are critical in describing certain calcium-dependent features of light-adaptation. Accordingly, we have developed a model of the binding interactions of recoverin, which is expressed in the chemical Scheme 1, which is similar to that in
Analysis of the Model of Recoverin's Binding: Free Concentrations of Recoverin and RK
The experimental evidence supports the view that the binding of Rec to Ca2+ equilibrates very rapidly, as does the binding of myristoylated Rec · 2 Ca to disc membranes (
To analyze the system in Scheme 1, one first writes the equations defining the five equilibrium constants, K1K5, and then the two conservation equations specifying the total quantities of recoverin and rhodopsin kinase, Rectot and RKtot, respectively. In addition, from the thermodynamic principle that there can be no net movement around the reaction loop in Scheme 1, one obtains the interrelation that K5 = (K2/M)(K4/K3). The concentrations of free recoverin and rhodopsin kinase, expressed in fractional form Rec/Rectot and RK/RKtot are then found to be related by the equation
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(C1) |
where the parameter C1 is given by
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(C2) |
After some tedious algebra, one obtains the following quadratic equation for the fraction of free recoverin:
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(C3) |
where the parameter C2 is given by
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(C4) |
Hence, one first evaluates the parameters C1 and C2, then solves the quadratic in Eq. C3 to obtain the fractional recoverin concentration, and finally substitutes this into Eq. C1 to obtain the fractional rhodopsin kinase concentration. The rate constant of R* inactivation is obtained by substitution in Equation A12.
Recoverin's Calcium Buffering Power
Once the dependence of free recoverin concentration on free calcium concentration has been determined, the calcium buffering power contributed by recoverin can be calculated. Since recoverin has been assumed always to bind two Ca2+ ions, then its Ca2+-buffering power (defined in terms of the total quantity of calcium, Catot), can be expressed as
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(C5) |
The right-hand side of Eq. C5 may be evaluated most simply by numerical differentiation of the relationship between Rec and Ca. Alternatively, it is possible to differentiate the quadratic expression in Eq. C3, taking care to note that C1 and C2 are not constants, but instead are functions of Ca. After some excruciating algebra, one obtains a very complicated analytical expression for BCa, Rec that will not be presented here, but which agrees exactly with the numerical solution.
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