INTRODUCTION

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This work examines the mechanism that enables retinal rod cells to register single photon absorptions with macroscopic signals of constant size and shape. Constancy of the elementary response is essential if the number and timing of photon absorptions are to be accurately represented. The classic frequency of seeing experiments of Hecht et al. (1942) and van der Velden (1946) established that the human visual system can detect the absorption of a few photons and that individual rods can successfully detect single photons. More recent work by Sakitt (1972) suggests that the visual system can literally count photon absorptions beginning at one or two, requiring the rods to encode accurate information about the number of absorbed photons. Photon counting would not be possible if the rod's elementary response fluctuated widely, as small responses would not be sensed by central neurons and large responses would mimic the effect of multiple photon absorptions. Variations in the shape of the elementary response would also degrade information about the timing of photon absorption and thus impair the temporal precision of rod vision. As photon absorptions occur rarely in each rod over much of the intensity range of rod vision, accurate registration of the number and timing of photon absorptions is important for normal rod vision.

It is well known that reliable photon detection requires amplification and low dark noise. The amplification is achieved by the cascade diagrammed in Fig. 1 (reviewed by Pugh and Lamb, 1993). An effective photon absorption photoisomerizes a rhodopsin molecule, which becomes catalytically active. A photoisomerized rhodopsin activates thousands of copies of the G-protein transducin (T), each of which can activate a catalytic subunit of phosphodiesterase (PDE). An activated PDE subunit typically hydrolyzes at least 50 cyclic guanosine monophosphate (cGMP) molecules (Pugh and Lamb, 1993; Rieke and Baylor, 1996). The resulting reduction in the cGMP concentration allows hundreds of cationic channels in the surface membrane to close, preventing more than 10⁶ cations from entering the outer segment. This macroscopic decrease in inward current hyperpolarizes the cell membrane and slows transmitter release from the synaptic terminal. Dark noise in the transduction current arises primarily from thermal isomerization of rhodopsin and from spontaneous activation of PDE (Baylor et al., 1980; Rieke and Baylor, 1996). Although the dark noise is relatively low, it appears to limit the absolute sensitivity of vision (Aho et al., 1988).

View larger version (10K): [in this window] [in a new window]   FIGURE 1   Diagram of phototransduction cascade. Effective absorption of a photon activates the photopigment rhodopsin (Rh); the cascade amplifies rhodopsin's activity to create a macroscopic electrical response. Active rhodopsin catalyzes the activation of the G protein transducin (T), which in turn activates phosphodiesterase (PDE). Activated PDE hydrolyzes cGMP, causing its concentration to fall, channels in the surface membrane to close, and the current flowing into the outer segment to decrease. The cGMP concentration and dark current are restored by cGMP synthesis by guanylate cyclase (GC). The recovery of the flash response is accelerated by Ca2+ feedback. Ca2+ enters the cell through the cGMP-gated channels and is extruded by Na+/K+, Ca2+ exchange. Influx of Ca2+ slows during the light response while efflux continues, causing the internal Ca2+ concentration to drop. The fall in Ca2+ concentration increases the rate of cGMP synthesis and thus speeds the return of the cGMP concentration and current to their respective dark values.

The first evidence for the reproducibility of the rod's elementary electrical response came from statistical analysis of the photocurrents evoked by dim flashes (Baylor et al., 1979b, 1984), which revealed that the standard deviation of the response amplitude was only ~20% of the mean and that the time course was nearly fixed. The molecular mechanism of this reproducibility is intriguing because the signals generated by many types of single particles show large intertrial fluctuations. Familiar examples are the amount of charge transferred during an ion channel's open time and the time required for the decay of a radioactive atom. Such fluctuations arise from stochastic variations in the active lifetime of the particle. The rod's elementary response should reflect variability in the timing of rhodopsin deactivation because rhodopsin drives the amplifying cascade while it remains active. Yet the fluctuations in the elementary response are remarkably small. This might be explained in either of two ways: 1) the elementary response might be insensitive to variations in rhodopsin's active lifetime, or 2) the active lifetime might have low variability. We present evidence favoring the second possibility and explore the contributions of several mechanisms.

	MATERIALS AND METHODS

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The experiments were carried out on isolated rods from the dark-adapted retina of the toad Bufo marinus, as described by Rieke and Baylor (1996). Single rods were isolated by shredding a small piece of retina, and their membrane current was recorded with a suction electrode (Baylor et al., 1979a). Experiments were performed on intact cells or on truncated, internally dialyzed outer segments. In either case, membrane current collected by the suction electrode was amplified, low-pass filtered at 20 Hz (3 dB point; 8-pole Bessel low-pass), and digitized at 100 Hz. Light responses were elicited by 10-ms flashes of 500-nm light; the flash strength was controlled with calibrated neutral density filters. The cell was usually positioned in the suction electrode to collect as much dark current as possible. In some experiments the contribution of cellular dark noise to the measured current was minimized by drawing only the tip of the outer segment into the suction electrode and applying the stimulating flash as a transverse slit 10 µm wide. The transverse slit was also used in experiments on truncated outer segments because the shape of the response depended on the longitudinal distance from the site of truncation; in these experiments the center of the slit was positioned ~20 µm from the cut end of the outer segment. In all experiments a half-saturating response was measured periodically to check the stability of the cell, and the experiment was terminated if the response changed significantly.

Table 1 gives the compositions of the solutions. Solution changes were usually achieved with a series of electronically controlled pinch valves (Biochem Valves, Boonton, NJ) whose outlets were connected to a common perfusion pipe ~100 µm in diameter. Solution changes with this system were completed in 200-300 ms, as judged by junction potential measurements. In measurements of rhodopsin's catalytic activity (Fig. 7), faster solution changes were achieved by moving the interface between two continuously flowing solutions across the outer segment. Solutions were driven by positive pressure through a pair of glass pipes with openings ~50 µm in diameter; the pipes were mounted on a piezoelectric translation stage (Burleigh Instruments, Fishers, NY). Solution changes at the cut end of the outer segment were completed in less than 10 ms with this system.

One set of experiments (those of Fig. 16) required a complete change of the nucleotide concentrations within the outer segment during the flash response. This was difficult at room temperature, as the time required for diffusion into the outer segment was comparable to the duration of the flash response. At 5-8°C, however, the duration of the flash response was much longer than the diffusion time. Low temperatures were achieved by cooling the solutions entering the chamber with a Peltier device (Ferrotec America, Chelmsford, MA) and blowing cold, dry air from a vortex tube (Illinois Tool Works, Glenview, IL) over the chamber. The temperature near the outer segment was monitored with a small thermocouple (Harvard Apparatus, Holliston, MA). All solutions flowed continuously to ensure that the temperature was uniform and steady; solution changes were made with the pipes mounted on the piezoelectric translation stage as described above.

In some experiments changes in the outer segment's free internal Ca²⁺ concentration were suppressed by inhibiting Ca²⁺ influx and efflux. Ca²⁺ efflux was inhibited by removing internal K⁺ or external Na⁺, both of which are required for Na⁺/K⁺, Ca²⁺ exchange (Cervetto et al., 1989); Ca²⁺ influx was inhibited by lowering the external Ca²⁺ concentration to reduce or eliminate the driving force on Ca²⁺ ions. For truncated outer segments (Yau and Nakatani, 1985), K⁺ was omitted from the dialyzing solution and the solution in the suction electrode; the free Ca²⁺ concentration was buffered to 500-600 nM in the dialyzing solution and to a few nM inside the suction electrode. For intact cells, the inner segment was held in the suction electrode while the outer segment was superfused with a solution lacking Na⁺ and Mg²⁺ and containing 10-20 nM free Ca²⁺ (Nakatani and Yau, 1988a; Matthews et al., 1988). Under these conditions the dark current was carried by outward movement of K⁺ and remained relatively stable (<10% change) for periods of 30-60 s, after which the outer segment was superfused with Ringer's for at least 30 s.

The experiment illustrated in Fig. 2 tested for residual light-induced changes in the free Ca²⁺ concentration in intact cells whose outer segments were superfused with a solution lacking Na⁺ and containing low Ca²⁺. Dim flash responses were recorded from an intact rod with the Ca²⁺ changing freely (thin trace in Fig. 2 A) or with changes in Ca²⁺ suppressed (thin trace in Fig. 2 B). The rod was then superfused for 15 min with a solution containing 10 µM BAPTA-AM, a membrane-permeable Ca²⁺ buffer. Responses to the flash were recorded again with the Ca²⁺ changing freely or held constant (thick traces in Fig. 2, A and B). Increasing the Ca²⁺ buffering capacity of the outer segment should slow changes in free Ca²⁺ and thus render Ca²⁺ feedback less effective in accelerating the flash response. Indeed, exposure to BAPTA slowed the control flash response and made it biphasic (Fig. 2 A), as observed previously (Torre et al., 1986). If changes in the internal Ca²⁺ alter the flash response when the outer segment is superfused with the 0 Na⁺, low Ca²⁺ solution, the addition of BAPTA would alter the flash response under these conditions as well. In this case, however, the flash response changed little (Fig. 2 B). In three experiments of this type, changes in the time to peak and amplitude after the addition of BAPTA were at least fivefold smaller with the Ca²⁺ held constant than with it changing freely. The relative insensitivity of the flash response to exogenous buffer indicates that superfusion with the 0 Na⁺, low Ca²⁺ solution effectively suppressed light-induced changes in Ca²⁺ within the outer segment.

View larger version (14K): [in this window] [in a new window]   FIGURE 2   Test for residual light-induced changes in the internal Ca2+ concentration when the outer segment was superfused with a 0 Na+, low Ca2+ solution (see Materials and Methods). Flash strength was 1.3 photons µm2. (A) Dim flash responses measured in an intact rod with the inner segment in the suction electrode and the outer segment superfused with Ringer's, allowing the Ca2+ concentration to change freely. The response shown by the thin trace was measured before exposure to BAPTA-AM; the response shown by the thick trace was measured after the cell was superfused with 10 µM BAPTA-AM for 15 min and returned to Ringer's. Increasing the Ca2+ buffering capacity of the outer segment by exposure to BAPTA-AM clearly altered the dim flash response. The dark current with the Ca2+ changing freely was 13 pA. (B) Dim flash responses measured from the same cell as in A, but with light-induced changes in the internal Ca2+ concentration suppressed by superfusing the outer segment with a solution lacking Na+ and containing low Ca2+. The response shown by the thin trace was measured before BAPTA exposure, the response shown by the thick trace after. The addition of Ca2+ buffer to the outer segment had only a small effect on the dim flash response, indicating that residual light-induced changes in Ca2+ were small on the time scale of the response. The dark current was +16 pA.

	THEORY

This section presents a model that relates the statistics of rhodopsin shutoff to the time-dependent mean and variance of the elementary response. We use this model in two ways. In the Results, the calculated mean and variance are compared to the quantities measured when rhodopsin shutoff was slowed and presumably made more variable (see Figs. 12 and 17). In the Discussion, the model is used to explore how the low variability of the elementary response constrains possible mechanisms of reproducibility (Fig. 18). The parameters of the model were held fixed for all calculations, as the aim was to explore classes of models for reproducibility rather than to provide accurate fits to individual measurements.

Relation between rhodopsin activity and change in current

We begin by relating the time course of rhodopsin's catalytic activity to changes in PDE activity, cGMP concentration, and membrane current. The model for the transduction cascade is similar to that of Pugh and Lamb (1993) and Nikonov et al. (1998). A more complete description can be found in Rieke and Baylor (1996).

Active rhodopsin decreases the cGMP concentration by catalyzing the activation of transducin, which in turn activates a cGMP phosphodiesterase (PDE) (Fig. 1). As this latter step occurs quickly (reviewed by Pugh and Lamb, 1993), we ignore any delay introduced by transducin activation and approximate the time derivative of the PDE activity P(t) as

(1)

where R is the rate of PDE activation for a rhodopsin activity R,  is the rate constant for PDE deactivation, and P_D is the dark PDE activity. Equation 1 describes the light-induced change in PDE activity as the output of a low-pass filter with time constant ¹ applied to rhodopsin's catalytic activity.

The time derivative of the cGMP concentration G(t) depends on the difference between the rates of cGMP synthesis and hydrolysis (Fig. 1),

(2)

where  is the rate of cGMP synthesis. Pugh and Lamb (1993) applied Eq. 2 at short times after a flash, assuming that the synthesis rate was constant, that the PDE activity could be approximated by a delayed ramp, and that P(t)  P_D. In this case the change in cGMP concentration is proportional to exp(at²), where a is a constant proportional to the flash strength. Their analysis accurately describes the initial rise of the flash response.

In intact rods, a light-induced fall in the free Ca²⁺ concentration affects several elements of the transduction cascade (reviewed by Koutalos and Yau, 1996). The most pronounced of these effects is an increase in the rate of cGMP synthesis and a consequent speeding of response recovery, and for simplicity we will include only this effect of Ca²⁺ in the model. The free Ca²⁺ concentration depends on the rates of Ca²⁺ influx through the cGMP-gated channels and Ca²⁺ efflux by Na⁺/K⁺, Ca²⁺ exchange (Nakatani and Yau, 1988b; Cervetto et al., 1989). Although a complete description of the exchange rate requires several time constants (Rispoli et al., 1993; Gray-Keller and Detwiler, 1994; McCarthy et al., 1996; Murnick and Lamb, 1996), the fastest component should dominate during the flash response. Thus the time derivative of the free Ca²⁺ concentration C can be approximated by

(3)

where q is a constant relating changes in the free Ca²⁺ concentration to the membrane current I (Nakatani and Yau, 1988b), and  is the rate constant for Ca²⁺ efflux.  depends on the activity of both the exchange proteins and intracellular Ca²⁺ buffers. The dependence of the rate of cGMP synthesis on the free Ca²⁺ concentration can be described by the Hill curve (Koch and Stryer, 1988; Koutalos et al., 1995a):

(4)

where _max is the maximum synthesis rate, K_GC and m are affinity and cooperativity constants, and the approximation is valid for C  K_GC. This approximation should hold for small changes in the current, as the free Ca²⁺ concentration in darkness is two to three times greater than K_GC.

We write the change in cGMP concentration as g(t) = G(t)  G_D, where G_D is the dark cGMP concentration. g(t) can be approximated from Eqs. 1-5 as a filtered version of the rhodopsin activity R(t), assuming that the changes in the PDE activity, cGMP concentration, and free Ca²⁺ concentration are small relative to the dark values (see Rieke and Baylor, 1996):

(5)

When the free Ca²⁺ concentration and hence the synthesis rate  are constant, the Fourier transform of the filter F is given by

(6)

where  = 2f is the angular frequency in radians per second and () = exp(it)F(t)dt. When the Ca²⁺ concentration changes freely, the Fourier transform of the filter takes the form

(7)

The changes in cGMP concentration described by Eqs. 5-7 depend on two time scales: 1) that for the decay of the light-activated PDE activity, determined by the time course of rhodopsin's catalytic activity and the decay rate  of PDE; and 2) that for the restoration of the cGMP concentration, determined by the dark cGMP synthesis rate (equal to P_DG_D) and the rate constant  for the fall in Ca²⁺. For all calculations we assumed m = 2, P_D = 0.1 s¹,  = 2 s¹, and  = 2 s¹ (see Koutalos et al., 1995a,b; Rieke and Baylor, 1996).

Equation 5 describes the change in the internal cGMP concentration produced by rhodopsin activity. The membrane current rapidly tracks this change (Karpen et al., 1988), and for cGMP concentrations at which less than half the channels are open, the current can be approximated as (Zimmerman and Baylor, 1986)

(8)

where k  8 × 10³ pA/µM³ in toad rods (Rieke and Baylor, 1996). The approximation in Eq. 8 should be valid for the experiments described here; in intact cells ~5% of the channels were open in the dark, whereas in experiments on truncated outer segments 10-20% of the channels were open in darkness. Assuming g(t) G_D, Eq. 8 can be expanded and approximated by the linear term. The result is that the change in current i(t) is approximately

(9)

Equation 9 should provide a good description of the single photon current response, as the change in cGMP is thought to be small compared to the dark value at all points along the outer segment (Pugh and Lamb, 1993). Equations 5 and 9 can be combined to estimate the current change produced by rhodopsin activity R(t),

(10)

where the Fourier transform of the filter F() is given by Eq. 6 or 7.

The model described above treats the cGMP and Ca²⁺ concentrations as spatially homogeneous, ignoring diffusion. If the current change in an intact rod is linearly related to rhodopsin activity, then the time course and amplitude of the current response depend only on the total changes in cGMP and Ca²⁺ and not on their spatial extent. In this case diffusion can be ignored. In truncated outer segments, diffusion causes the cGMP concentration to depend on longitudinal position, and in outer segments without cGMP synthesis, diffusion restores the cGMP concentration and dark current. To test the effect of diffusion on the single photon response in truncated outer segments with cGMP synthesis proceeding normally, we compared the behavior of the model described above with that of a model including cGMP diffusion (see Rieke and Baylor, 1996). Calculated flash responses with and without diffusion were nearly identical, and thus for simplicity we neglected diffusion. Dim flash responses in truncated outer segments without cGMP synthesis were fitted assuming that restoration of the cGMP concentration by diffusion occurred at a constant rate _eff. This simplified treatment again provided calculated responses in close agreement with those calculated when diffusion was included.

Stochastic model for rhodopsin shutoff

Equation 10 provides an estimate of the elementary current response given the time course of the activity of a single photoisomerized rhodopsin molecule. Intertrial fluctuations in the response could arise either from variations in the time course of rhodopsin's activity or from fluctuations in the transduction cascade. Because a single active rhodopsin rapidly generates hundreds or thousands of active transducin molecules (reviewed by Pugh and Lamb, 1993), stochastic fluctuations in the transducin activity or transducin's activation products should be small compared to fluctuations in the rhodopsin activity. In this case the filter F is effectively deterministic, and variability in the elementary response can be attributed to rhodopsin. To investigate how the measured response fluctuations constrain fluctuations in the rhodopsin activity, we considered two stochastic models for rhodopsin shutoff. In each model the time course of the catalytic activity of a single rhodopsin molecule was calculated and the corresponding elementary response was generated from Eq. 10, which assumes that the cascade responds linearly and deterministically to rhodopsin activity. This procedure was repeated for several hundred trials, and the time-dependent ensemble mean and variance were calculated and compared with experiment (Fig. 18).

The effect of feedback control of rhodopsin shutoff on the mean and variance of the elementary response was investigated assuming that the putative feedback signal accumulated linearly with time and accelerated rhodopsin shutoff with a cooperativity h. Thus the feedback caused the probability density for rhodopsin shutoff to increase proportionally with t^h, where t is the time after photoisomerization. Shutoff was assumed to occur as a single step.

The effect of multiple transitions in rhodopsin shutoff on the mean and variance of the elementary response was investigated assuming that each transition was memoryless and first-order. Transitions were assumed to occur sequentially with rate constants proportional to the catalytic activity of the state preceding the transition; thus states with low catalytic activity decayed more slowly than states with high activity. This choice of rate constants and activities was made for two reasons. First, this model distributes rhodopsin's cumulative activity equally among the states and produces the maximum reduction in the variance of the elementary response for a given number of states. Second, a gradual decline in rhodopsin activity is consistent with the approximately exponential time course of rhodopsin's activity measured in Fig. 7.

	RESULTS

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Reproducibility of the single photon response

Variability in the amplitude and time course of the elementary response constrains the mechanisms responsible for reproducibility. Thus we analyzed the statistics of the responses to a fixed dim flash, producing an average of less than one photoisomerization per trial; a short section of one such experiment is shown in Fig. 3 A. Each flash generated zero, one, or two photoisomerizations and a quantized change in current. The intertrial variability in the response is consistent with the Poisson statistics that govern the probability of photoisomerization (Baylor et al., 1979b; see below). Each elementary response had a similar amplitude and shape. This reproducibility allows responses to zero, one, or two photoisomerizations to be clearly distinguished, as shown in Fig. 3 B, where 50 individual responses are superimposed. The largest response presumably resulted from two or three photoisomerizations. Thus the rod is an accurate photon counter that reliably detects a single photoisomerization and differentiates between one and two photoisomerizations.

View larger version (25K): [in this window] [in a new window]   FIGURE 3   Single photon responses. (A) Photocurrents from an intact rod stimulated by a series of dim flashes delivered at the times indicated by the flash monitor. The flashes produced an average of 0.7 photoisomerizations per trial. Two events from spontaneous rhodopsin isomerization are marked by arrows. The outer segment was in the suction electrode, and the cell was superfused with a bicarbonate-based Ringer's. Flash stimuli were applied over a transverse slit 10 µm wide positioned near the middle of the outer segment. Bandwidth: 0-3 Hz. The dark current was 25 pA. (B) Superimposed responses to 50 flashes, including those in A. The responses were recorded sequentially, except for the removal of responses clearly contaminated by thermal events (such as those marked by arrows in A). The mean current in a 1 s interval before the flash has been set to zero in each case to correct for baseline drift and to facilitate comparison of the response shapes. Responses to zero, one, and two photoisomerizations can be clearly distinguished, as each elementary response had an amplitude and time course similar to those of the others. The largest response presumably resulted from two or three photoisomerizations.

Variability of the response amplitude and time course

(11)

View larger version (19K): [in this window] [in a new window]   FIGURE 4   Reproducibility of the single photon response. Recordings were made from an intact rod superfused with bicarbonate-based Ringer's with its outer segment in the suction electrode. Flash stimuli were applied over a transverse slit 10 µm wide positioned near the middle of the outer segment. The dark current was 23 pA. (A) Amplitude histogram constructed from a series of 410 dim flash responses like those in Fig. 3. The inset shows the mean response; the flash was delivered at the beginning of the horizontal scale bar. The amplitude of each response was measured as the average decrease in current between 1.75 and 2.25 s. The smooth curve fitted to the experimental histogram was calculated according to Eq. 11, which assumes that the noise in darkness and the noise in the elementary response amplitude are independent and additive and that the number of photoisomerizations per flash is described by Poisson statistics. The fit was calculated for 0.67 photoisomerizations per flash, a mean elementary response amplitude of 0.66 pA, a standard deviation of the current in darkness of 0.09 pA, and a standard deviation of the elementary response amplitude of 0.14 pA. (B) Histogram measuring reproducibility of the elementary response shape (stepped curve) constructed from the 129 responses from A, with an amplitude between 0.3 and 1.0 pA. Each response was fitted according to Eq. 12 with the output of a cascade of four identical, independent low-pass filters. The free variable in the fit was the low-pass filter time constant, and these time constants form the histogram plotted. The smooth curve is a Gaussian with a mean of 0.58 s and a standard deviation of 0.12 s. (C) Time-dependent variance of responses measured in darkness ("dark") and in the presence of the flash stimulus ("light"). The variance measured in darkness resulted from baseline drift and instrumental and cellular noise. The additional variance with light exposure arose from intertrial variability in the measured responses; this variance contains contributions from Poisson fluctuations in the number of photons absorbed per flash and variability in the elementary response. Same experiment as in A and B. (D) Light-dependent variance increase (thick trace) and square of the mean response (thin trace). The variance increase is the difference (light  dark) between the two traces in C. As described in the text, the variance increase would have the same shape as the square of the mean response if each photoisomerization produced an identical response and the variance increase were solely attributable to variations in the number of photoisomerizations. Significant fluctuations in the shape of the elementary response would cause the variance to have a shape different from that of the square of the mean. The scaling factor between the variance and the square of the mean indicated that the flash produced an average of 0.61 photoisomerizations.

(12)

Time-dependent variance of the elementary response

f

f

View larger version (18K): [in this window] [in a new window]   FIGURE 5   Residual variability of the single photon response. (A) Time-dependent variance of 71 elementary responses ("singles") and 119 traces recorded in darkness ("dark"). Elementary responses were identified from a histogram of the response amplitudes as described in the text. Responses clearly contaminated by discrete noise events were excluded. The variance measured in darkness was caused by instrumental and cellular dark noise. The additional variance of the singles is due to intertrial variability in the elementary response. Current was collected from only the distal third of the outer segment to reduce the cellular dark noise. Light stimuli were applied over a 10 µm wide slit centered on the region from which current was collected. The flash produced an average of 0.56 photoisomerizations. (B) Variance of the elementary response from A (thick trace) and square of the mean response (thin trace). Assuming that the variance of the singles and the dark variance were independent and additive, the variance in the elementary response could be isolated as the difference (singles  dark). Note that the peak of the variance is ~15 times smaller than the square of the mean. (C) Collected results from experiments on 12 cells. In each cell the variance and the square of the mean elementary response were measured as in A and B. Each measure was normalized by the time to peak and the square of the peak amplitude of the mean elementary response. The average of the normalized variance and square of the mean response are plotted. Note that the variance is ~15 times smaller than the square of the mean.

Time course of rhodopsin's catalytic activity

Experiments such as those in Figs. 3-5 quantify the reproducibility of the rod's elementary response. Before exploring possible mechanisms for reproducibility, we examined a general problem that bears upon all potential mechanisms: the time course of rhodopsin's catalytic activity. It has been suggested that rhodopsin deactivation dominates the rate of decline in PDE activity after a flash (Pepperberg et al., 1994; Corson et al., 1994) and, alternatively, that rhodopsin activity decays more quickly (Murnick and Lamb, 1996; Sagoo and Lagnado, 1997; Nikonov et al., 1998). The essential question for reproducibility is whether the amplitude alone or both the amplitude and the shape of the elementary response are sensitive to fluctuations in rhodopsin's catalytic activity. If the catalytic activity is confined to a brief time interval at the beginning of the response, variability in rhodopsin's activity should affect the response amplitude but not its shape. If, instead, the catalytic activity persists through a significant fraction of the elementary response, variability in the activity should affect both the response amplitude and shape. The experiments described below indicate that rhodopsin's activity persists through a significant fraction of the dim flash response in truncated outer segments at constant internal Ca²⁺. We use this result in subsequent experiments to test the mechanisms responsible for reproducibility.

Time course of rhodopsin activity in truncated outer segments

View larger version (12K): [in this window] [in a new window]   FIGURE 6   Procedure for changing rhodopsin-transducin gain. Photo-isomerization promotes the binding of transducin-GDP to isomerized rhodopsin and the dissociation of GDP. This leaves the nucleotide binding site on transducin empty. Binding of GTP causes dissociation of rhodopsin-transducin and transducin activation. Binding of GDP simply returns rhodopsin-transducin to the initial state, from which rhodopsin and transducin-GDP or GDP alone can dissociate. Thus a high GDP concentration causes several futile cycles of GDP binding and unbinding for each transducin that is activated. A high GTP concentration suppresses futile cycling and causes efficient transducin activation. This procedure allows the gain of transducin activation to be lowered without using a very low GTP concentration, which alone could slow rhodopsin phosphorylation or arrestin binding and thus prolong the flash response (see Fig. 13). This procedure assumes that increasing the GTP concentration does not cause significant GDP-GTP exchange on the  subunit of transducin; biochemical experiments (Fung, 1983) support this assumption.

View larger version (16K): [in this window] [in a new window]   FIGURE 7   Time course of rhodopsin's catalytic activity measured by abruptly increasing the gain of transducin activation. (A) Original records from one such experiment. The outer segment was initially dialyzed with a solution containing 10 µM GTP and 90 µM GDP, giving low rhodopsin-transducin gain. At a specific time after a flash was delivered, the dialyzing solution was switched to one containing 1 mM GTP and 90 µM GDP, giving high rhodopsin-transducin gain. In traces 1-3 this solution change was made 1, 2, and 8 s after the flash, as shown in the upper timing trace. Trace 4 is a flash response measured in the low-gain dialyzing solution. Trace 5 is the change in current produced by the solution change in the absence of a flash. Flash stimuli were applied over a 10 µm wide transverse slit and produced ~60 photoisomerizations. The dark current was 75 pA. (B) Linearized difference currents from A. Each of the responses in A was linearized (see text) to yield a proportional measure of rhodopsin activity. The two corrected control responsesthe flash in the low gain solution (trace 4) and the current change produced by the solution change alone (trace 5)were subtracted from the corrected responses to both the flash and solution change (traces 1-3). The initial slope of these corrected difference currents is proportional to rhodopsin's catalytic activity. (C) Collected results from 13 experiments. Results from each experiment have been normalized by the amplitude Rhexp and time constant exp of the best fit exponential, Rh(t) = Rhexpexp(t/exp). The mean time constant was 2.3 ± 0.2 s (mean ± SEM). Measurements from the experiment in A and B are plotted as filled circles.

(13)

t

Comparison of deactivation kinetics in truncated and intact cells

(14)

1

View larger version (16K): [in this window] [in a new window]   FIGURE 8   Time course of PDE activity after a dim flash. (A) Average dim flash response in an intact cell measured at constant internal Ca2+ (see Materials and Methods). The flash produced an average of 1.2 photoisomerizations. The dark current was +9.5 pA. (B) Time course of PDE activity calculated according to Eq. 14 from the flash response in A, assuming a mean dark PDE activity of 0.1 s1. The smooth curve is an exponential with a time constant of 2.1 s fitted to the measured trace between 3 and 15 s.

Summary

Possible mechanisms for reproducibility

Experiments such as those illustrated in Figs. 3-5 indicate that the entire waveform of the elementary response is reproducible. This is unexpected because the response originates from a single rhodopsin molecule whose active lifetime might be expected to fluctuate from trial to trial (see Introduction). Rhodopsin shutoff is thought to result from one or two phosphorylations followed by arrestin binding (Ohguro et al., 1995). If the time required for phosphorylation or arrestin binding were the dominant delay in rhodopsin deactivation, the distribution of catalytic lifetimes would be approximately exponential. If the amplitude of the photocurrent were proportional to rhodopsin's catalytic lifetime, the distribution of photocurrent amplitudes would also be nearly exponential. For the exponential distribution, the ratio of the mean  to the standard deviation _A is 1, substantially less than the measured ratio of 5. The ratio Â/_A would increase only slightly (as the square root of the number of steps) if rhodopsin shutoff involved two or three steps with similar rate constants, and the increase in Â/_A would be less if the rate constants differed significantly. How, then, is such good reproducibility achieved? We tested the three possibilities outlined below.

Feedback control of single photon responses

View larger version (13K): [in this window] [in a new window]   FIGURE 9   Possible mechanisms for reproducibility. The low variability of the elementary response indicates either low intertrial variability in rhodopsin's catalytic activity or suppression of the effects of such variability by the transduction cascade. Three potential mechanisms are shown schematically. (A) A feedback signal x*(t) might control the rate  of rhodopsin shutoff or the rate  of activation of a downstream product of rhodopsin. Feedback control of rhodopsin shutoff could reduce intertrial variability in rhodopsin's activity, whereas feedback to a downstream element of the cascade could make the membrane current insensitive to variability in rhodopsin's activity. (B) A saturation might cause the membrane current to be insensitive to variability in rhodopsin's activity. A saturation acting at the peak of the response such as that depicted here (e.g., local depletion of open cGMP-gated channels) could reduce variability in the response amplitude. (C) Rhodopsin's catalytic activity might deactivate through a series of transitions, each of which reduces the activity by a small amount and occurs after a stochastic, first-order delay. Despite variations in the timing of individual transitions, variability in rhodopsin's cumulative activity could be reduced.

Saturation

Multiple steps in rhodopsin shutoff

Test of molecular mechanisms for reproducibility

Feedback

View larger version (18K): [in this window] [in a new window]   FIGURE 10   Single photon responses at constant internal Ca2+. (A) Comparison of average dim flash responses measured with the Ca2+ allowed to change normally and with the Ca2+ held constant near its normal concentration in darkness (see Materials and Methods). Responses have been normalized by the dark current, which was 26 pA with the Ca2+ changing freely and +10 pA with the Ca2+ held constant. The flash produced an average of 0.6 photoisomerizations. (B) Amplitude histogram from 83 dim flash responses measured at constant internal Ca2+. The amplitudes are negative because responses were inverted when the outer segment was superfused with the 0 Na+, low Ca2+ solution (see Materials and Methods). Peaks corresponding to 0 and 1 photoisomerization can be clearly distinguished. The smooth curve was calculated according to Eq. 11 with  = 1.1 pA, A = 0.25 pA, D = 0.14 pA, and  = 0.61 photoisomerizations per flash. The mean response is shown in A. (C) Time-dependent variance increase (thick trace) and square of the mean response (thin trace) for responses contributing to the amplitude histogram in B. The light-dependent variance increase has been isolated by subtracting the variance measured in darkness from that measured from the flash responses, as in Fig. 4 C. The scaling factor between the variance