|
|
|
|
|
|
|
||
Molecular Mechanisms of Dark Noise in Retinal Cones
Correspondence to Juan I. Korenbrot: juan{at}itsa.ucsf.edu
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
|---|
55 ms. In nonmammalian rods, in contrast, active PDE lifetime is 555 ms. This remarkable difference helps explain why cones are noisier than rods and why cone photocurrents are smaller in peak amplitude and faster in time course than those in rods. Both these features make cones less light sensitive than rods.
Key Words: phototransduction • phosphodiesterase • guanylate cyclase • cGMP • calcium
Abbreviations used in this paper: GC, guanylate cyclase; CNG, cGMP-gated; PDE, phosphodiesterase; VP, visual pigment.
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
|---|
), but detection threshold is higher in cones. The limit of light detection varies among cones in different species, and even between cone subtypes in the same species (Miller and Korenbrot, 1993). Still, in complete darkness, even the most sensitive cones require the coincident absorption of several photons (some four to seven) to generate a detectable signal (Schnapf et al., 1990; Miller and Korenbrot, 1993; Donner et al., 1998). To be detected, light-dependent currents must exceed in amplitude intrinsic fluctuations of the photoreceptor dark membrane current referred to as "dark noise." For example, in single cones of striped bass, the extrapolated single photon peak current amplitude is 0.14 pA (this report) and it is 0.03 pA in macaque cones (Schnapf et al., 1990). These signals are undetectable because they do not exceed the dark current noise variance, 0.28 pA2 in bass and 0.12 pA2 in macaque (0–20 Hz range) (Schnapf et al., 1990). In rods, in contrast, single photon peak photocurrent amplitude is 1 pA in toads (Baylor et al., 1979) and 0.7 pA in macaque (Baylor et al., 1984). These signals are readily detected above dark current noise of variance 0.035 pA2 in toads (Baylor et al., 1980) and 0.030 pA2 in macaque (0–20 Hz range) (Baylor et al., 1984).
To elucidate the molecular mechanisms underlying dark noise in cones and, hence, the limit of their sensitivity, we investigated the properties and molecular mechanisms of membrane current noise in dark-adapted, green-sensitive single cones of the striped bass. Cone dark noise has been previously characterized both as fluctuation in membrane voltage (Lamb and Simon, 1977; Schneeweis and Schnapf, 1999) and in membrane current (Schnapf et al., 1990; Rieke and Baylor, 2000; Sampath and Baylor, 2002). These studies have shown that dark noise consists of light-sensitive and -insensitive components. The light-sensitive component originates from two principal molecular sources: (1) occasional, spontaneous thermal activation of visual pigment (VP) molecules and (2) continuous fluctuations in the cytoplasmic concentration of cGMP and Ca2+, as well as in the activity of cGMP-gated (CNG) ion channels. The two components are readily distinguished from each other because of their distinct kinetics: noise that originates from VP excitation has a time course identical to that of the dim light photocurrent, whereas the continuous noise does not (Rieke and Baylor, 2000).
In an elegant study in toad rods, Rieke and Baylor (1996) demonstrated that the continuous component of dark noise consists of components of distinct frequency. High frequency noise is generated by open to close transitions in the CNG ion channels, while low frequency noise is caused by fluctuating cGMP concentration due to variance in phosphodiesterase (PDE) activity. This enzyme catalyzes cGMP hydrolysis and its activation by excited rhodopsin is at the core of the biochemical mechanisms of phototransduction (for reviews see Pugh and Lamb, 2000; Ebrey and Koutalos, 2001). In an extension of their studies to cone photoreceptors in tiger salamander retina, Rieke and Baylor (2000) found that dark noise characteristics differ among cones depending on their VP. In all cone subtypes, noise lacks discrete, single photon transitions. In tiger salamander retina, the continuous dark noise in red-sensitive, L cones arises from spontaneous VP excitation that occurs at a rate of 1,000 s–1 at 20°C (Sampath and Baylor, 2002), much higher than that of rhodopsin in tiger salamander rods (0.03 s–1 at 20°C) (Vu et al., 1997). In blue-sensitive S cones, on the other hand, dark noise does not appear to arise from VP thermal excitation because its time characteristics differ from those of the dim light photoresponse (Rieke and Baylor, 2000). In cones of other species studied to date (turtle, Lamb and Simon, 1977; macaque, Schneeweis and Schnapf, 1999; and fish, this report), dark current noise does not appear to arise from thermal VP excitation since its power spectrum is different from that of the dim light photoresponse.
We present experimental data to identify the molecular origin of the continuous component of dark noise in green sensitive single cones of the bass retina. We demonstrate that dark noise is not caused by high rate spontaneous visual pigment excitation, but rather by fluctuations in cytoplasmic levels of cGMP and Ca2+ in darkness. Furthermore, in the absence of Ca2+ fluctuations, cGMP fluctuations are caused by spontaneous, thermal activation of PDE. This is the same mechanism known to cause the continuous dark noise in rods (Rieke and Baylor, 1996) and which had been suggested as a source of noise in blue sensitive cones (Rieke and Baylor, 2000).
Mathematical analysis of the features of dark noise allows us to characterize for the first time the kinetics of PDE activation in an intact, functional cone. The time course of the dim light photocurrent is faster in cones than in rods in all species studied to date (for reviews see Korenbrot, 1995; Pugh and Lamb, 2000; Ebrey and Koutalos, 2001). Detailed quantitative models suggest that this acceleration can reflect any one, or any combination, of three principal kinetic events: (1) the rate of deactivation of excited visual pigment, (2) the rate of inactivation of PDE, and (3) the rate of activation of guanylate cyclase (GC) (Sneyd and Tranchina, 1989; Ichikawa, 1994; Hamer and Tyler, 1995; Korenbrot and Rebrik, 2002). With respect to PDE, biochemical studies have demonstrated that the catalytic efficiency of active PDE is essentially the same in rods and cones (Gillespie and Beavo, 1988; Cote et al., 2002). In contrast, our analysis of dark noise indicates that the lifetime of the active state of PDE is 10 times shorter in cones than in rods. This remarkable difference not only helps explain why cones are noisier than rods, but also why cone photocurrents are smaller in peak amplitude and faster in time to peak than those in rods. The limitations of a small signal superimposed on high noise makes the cone less sensitive to light than the rod.
|
MATERIALS AND METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
|---|
). Zaprinast, 8-p-chlorophenylthio-cGMP (8-cpt-cGMP), and nifedipine were obtained from Calbiochem.
Electrical Recording
Isolated cone photoreceptors were firmly attached to a concanavilin-A–coated glass coverslip that formed the bottom of an open electrophysiological recording chamber. The chamber was held on an inverted microscope equipped with DIC contrast enhancement, and the cell-bathing solution was intermittently exchanged. Microscopic observations were conducted under IR illumination (840–880 nm) with the aid of video cameras and monitors. Composition of the cell-bathing Ringer's solution was (in mM) NaCl (126), CsCl (10), KCl (2.4), NaHCO3 (5), NaH2PO4 (1), MgCl2 (1), CaCl2 (1), nifendipine (0.01), minimum essential medium amino acids and vitamins (GIBCO-BRL), glucose (10), BSA (0.1 mg/ml), and HEPES (10). pH was 7.5 and osmotic pressure 310 mOsM.
We measured membrane current at room temperature under voltage clamp using tight-seal electrodes in the whole-cell mode. Electrodes were produced from aluminosilicate glass (Corning 1724, 1.5 x 1.0 mm od x id). Currents were recorded with a patch clamp amplifier (Axopatch 1D; Axon Instruments). The analogue signal was simultaneously low pass filtered (0–100 Hz) through two different 8 pole filters, one a Bessel filter and the other a Butterworth filter (Frequency Devices) and then digitized on line at 300 Hz (Digidata1322A and pClamp software; Axon Instruments).
The composition of the normal tight-seal electrode-filling solution was (in mM) K+ gluconate (115), K+ aspartate (20), KCl (33), MgCl2 (1 free), GTP (1), ATP (3), and MOPS (10). pH was 7.25 and osmotic pressure 305 mOsM. For different experimental purposes, the electrode-filling solution was modified to yield one of three conditions. (1) Ca2+-buffered solution contained normal GTP, ATP, and in addition 10 mM BAPTA titrated with CaCl2 to yield 400 nM free Ca2+ (confirmed using BAPTA absorption spectra as a Ca2+ indicator). Ca2+ buffers were designed using WinMaxC software (www.stanford.edu/~cpatton). (2) Nucleotide-free solution lacked ATP and GTP, either in a normal or a Ca2+-buffered formulation. (3) Triphosphate nucleotide-free, Ca2+-buffered solution containing added cyclic nucleotides.
Light stimuli were delivered with an epiillumination system that used the microscope objective as its final lens (Nikon Fluor 40x/1.3 NA oil). The focused image of an adjustable aperture placed on the optical path limited illumination to a 40 µm diameter circle centered on the cell under study. Light was generated by a DC operated Tungsten source. Narrow band interference (10 nm bandwidth) and calibrated neutral density filters controlled color and intensity, while stimulus duration was controlled with an electronically triggered fast electromechanical shutter (Vincent and Associates, Rochester, NY). Light intensity was measured with a calibrated photodiode placed on the microscope stage at the same position as the cells (UDT Sensors).
Single Cell Superfusion
The tip of a polyimide-coated silica capillary (PT Technologies) 125 µm ID was placed within 100 µm from the cell under study and in the same vertical plane. Solution flowed through the superfusing capillary under positive pressure (50 mm Hg). Flow was controlled with an electronically triggered pinch valve (BPS-4; ALA Scientific). Upon activation of the valve, solution change around the cell was complete within 50 ms.
Hydroxylamine Treatment
A dark-adapted single cone was first positioned in the optical center of the imaging lens and then superfused with the single cell system described above. Superfusing solution consisted of (in mM) hydroxylamineHCl (60), NaCl (63), CsCl (5), KCl (1.2), NaHCO3 (2.5), NaH2PO4 (0.5), MgCl2 (1), CaCl2 (1), and HEPES (20). pH was 7.5 and osmotic pressure 310 mOsM. The selected cone was superfused for exactly 120 s and then washed by continuous bath perfusion with normal Ringer's for 5 min. Tight seal electrodes were applied to the treated cone only after this extensive washout. Thus, hydroxylamine was absent from the cell at the time of electrophysiological measurements.
Data Analysis
Power spectral density of steady currents processed through a Butterworth filter (0–100 Hz) were computed from 13.66-s-long data episodes sampled at 300 Hz (4,098 points per episode) (Clampfit; Axon Instruments). In some datasets, there was a small, but detectable, linear drift over the sampling period; when such drift was apparent, it was removed by subtracting the mean slope of the drift before computing power spectra. To reduce the dataset, each individual power spectrum was processed by computing a box car average over one to three data points between 0 and 10 Hz, five data points between 10 and 40 Hz, 10 data points between 40 and 90 Hz, and 16 data points between 90 and 150 Hz. In data presentation, the mean of the box car average is indicated as a symbol and its standard deviation as an error bar. For graphic convenience, only the positive error bars are drawn in the illustrations. Experimental data were fit with defined mathematical expressions using nonlinear least square minimization algorithms (Origin; Origin Labs). In text and tables, the reported statistical errors are standard deviations.
To determine the power in the current noise (variance) over a specified bandwidth (typically 0–20 Hz), nonaveraged power spectra were integrated and the value of the integral at 20 Hz measured. Light-sensitive noise was computed from the difference in variance of the current measured in complete darkness and that measured in the same cell in the continuous presence of light at intensities that saturated the photocurrent amplitude (typically 1.2 x 105 540 nm photons/µm2 sec). Numerical solutions of systems of simultaneous differential equations were computed using 20Sim modeling software (ControlLab Products B.V.).
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
|---|
). In complete darkness, the voltage-clamped holding current in isolated single cones fluctuates in amplitude about a mean value (Fig. 1). This current noise arises from statistical variance in the activity of light-sensitive, CNG ion channel in the cell's outer segment, as well as in the activity of voltage-gated channels in the inner segment. To characterize the light-sensitive component of dark noise at –40 mV, we measured fluctuations in the holding current of cones bathed in a Ringer's solution containing 100 µm nifedipine and 10 mM Cs+. These chemicals effectively block L-type Ca2+ and Kir channels, the most active voltage-gated channels in cones at –40 mV in bass cones (unpublished data), as they do in cones of other species (Barnes and Hille, 1989; Maricq and Korenbrot, 1990a,b). We conducted experiments at –40 mV holding voltage because this is near the resting voltage in intact, dark-adapted cones.
|
). For a 10-ms flash stimulus, the peak photocurrent amplitude increases with light intensity as described by the Michaelis-Menten equation
 | (1.1) |
is the intensity at half-maximum amplitude. For 11 different cones, we found mean Imax = 24.9 ± 4.6 pA and = 168.6 ± 60 photons/µm2. Given a calculated cross section of absorption of 1.92 µm2 for the bass cone outer segment, = 319 ± 114 photoisomerizations. Amplitude of the bass cone single photon response, extrapolated from responses in the linear range, is 0.14 pA.
Dark Current Noise in Normal Bass Single Cones
Typical holding currents measured in the 0–40 Hz frequency range using a Butterworth filter are illustrated in Fig. 1 A. Shown are currents measured in the same cell in darkness and under continuous illumination sufficient to saturate the photocurrent. For nine cells, the mean dark holding current was –4.2 ± 10.1 pA and fluctuations about the mean had an average variance of 0.28 ± 0.15 pA2 (0–20 Hz). For the same cells in the light, the mean holding current was 15.2 ± 9.5 pA, and the noise average variance was 0.02 ± 0.01 pA2 (0–20 Hz). Variance of the light-sensitive component then was 0.258 ± 0.13. Power spectral-density analysis of the current fluctuations allows additional quantitative characterization of dark–light noise difference. At frequencies <30 Hz, power density in dark current noise increased with frequency along a function illustrated as the continuous line over the data points in Fig. 1 C. The function is discussed below in the theoretical section. Over the same frequency, the power density in the light was not only much smaller in amplitude, but increased inversely with frequency with a relatively shallow slope (Fig. 1 C). At frequencies >30 Hz (and up to the limit of our sampling at 100 Hz), dark and light noises were practically indistinguishable from each other and essentially independent of frequency. Henceforth, we use "dark noise" to mean specifically the difference noise between dark and light currents. Because light-sensitive CNG ion channels are exclusively localized in the outer segment "dark current noise" is synonymous with "outer segment current noise."
In rod photoreceptors, spontaneous thermal rhodopsin activation gives rise to discrete, large transients in the dark current. The time course of these shot events (and the corresponding frequency power spectrum) is identical to that of the dim light photocurrent in the same cell (Yau et al., 1979; Baylor et al., 1980). In bass single cones, we did not observe discrete shot events in the dark current. To analyze the origin of dark current fluctuations, we compared the power spectra S(
) (power spectral–density function) of the dark noise current (Fig. 1 C) and the dim flash photocurrent (Fig. 1 D). The photocurrent power spectrum is well fit by the product of four Lorentzians of identical rate (continuous line in Fig. 1 D).
 | (1.2) |
; Baylor et al., 1980; Schnapf et al., 1990). It does not represent a specific molecular mechanism; it is a useful descriptive equation. Data of quality similar to that in Fig. 1 were collected in 11 different cells and the mean value of 
was 5.72 ± 0.79 Hz. Expression 1.2 with = 5.72 does not fit the power spectra of the dark noise (Fig. 1 C). Our finding in bass single cones is similar to previous results of dark noise analysis in cones of other species (Lamb and Simon, 1977; Schnapf et al., 1990; Schneeweis and Schnapf, 1999). This fact reveals that individual fluctuations whose sum is the observed dark noise have a time course different than that of the dim light photocurrent.
In rods, the power spectra of the discrete components of dark noise and the dim light photocurrent are essentially identical; a finding that indicates that spontaneous VP excitation is the cause of the discrete dark noise (Baylor et al., 1984; Vu et al., 1997). The same finding is true in L-type salamander cones (Rieke and Baylor 2000; Sampath and Baylor 2002) and transgenic rods expressing human red-sensitive cone VP (Kefalov et al., 2003). The dissimilarity between the power spectra of dark noise and of dim light photocurrents indicates that thermal VP excitation is not the dominant molecular source of dark noise in bass single cones. Experimental affirmation of this conclusion is presented below.
Dark Current Noise in Ca2+-buffered Cones
The light-sensitive current in cone photoreceptors is sustained by flux through CNG ion channels in the outer segment membrane. Light-sensitive current fluctuations, hence, must arise either from open-to-close transitions in the active CNG channels or from fluctuations in the cytoplasmic levels of cGMP. Current fluctuations due to channel flicker have been characterized in membrane patches detached from bass cone outer segments (Picones and Korenbrot, 1994). In the 0–1,000 Hz frequency range, the power spectrum of these fluctuations is well described by the sum of two Lorentzians of characteristic frequencies 
1 and 2. 1 = 26 Hz reflects the kinetics of cGMP binding to the channels. 2 = 318 Hz reflects channel flickering kinetics. Because channel flicker is fast, it does not contribute to dark noise in the frequency domain explored in this report, 0–30 Hz.
In cones photoreceptors, cGMP fluctuations can arise indirectly from fluctuations in cytoplasmic Ca2+. Ca2+ regulates both the activity of guanylate cyclase (GC) (Koch and Stryer, 1988; Gorczyca et al., 1995), the enzyme that synthesizes cGMP, and the ligand sensitivity of CNG channels (Rebrik and Korenbrot, 1998; Korenbrot and Rebrik, 2002). To distinguish the effects of fluctuations in cGMP from fluctuations in cytoplasmic Ca2+, we measured current in cells in which potential cytoplasmic Ca2+ fluctuations were attenuated by loading their cytoplasm with 10 mM BAPTA titrated to yield 400 nM free Ca2+, the free Ca2+ concentration measured in dark-adapted cones of the tiger salamander (Sampath et al., 1999). We loaded BAPTA/Ca2+ by waiting for their diffusion from the electrode lumen into the cell cytoplasm, which we have shown elsewhere is complete 150 s after attaining whole cell mode (Holcman and Korenbrot, 2004). In the experiments reported here, we began recording current data 2.5 min after first attaining whole cell mode.
To confirm that bass cones were effectively loaded with BAPTA, we characterized their response to light. Previous studies have demonstrated that effective cytoplasmic Ca2+ buffering slows down the cone photocurrent time course and increases its photosensitivity (Nakatani and Yau, 1988; Matthews et al., 1990). The holding dark current at –40 mV in BAPTA-buffered cells was –13.5 ± 21.6 pA (14 cells), not that different from the value in normal cones –3.2 ± 8.9 (17 cells). Bass cones loaded with BAPTA/Ca2+ exhibited the expected changes in photocurrent kinetics and sensitivity (Fig. 2 B). In seven different cones, we found the following mean values (terms from Eq. 1.1): Imax = 27.4 ± 16 pA and = 42.3 ± 15.3 photons/µm2 (compared with Imax = 24.9 ± 4.6 pA and = 168.6 ± 60 photons/µm2 in normal cells). The mean time to peak for dim light flash photocurrents was 185 ± 32 ms in BAPTA-loaded cones, but 78 ± 5 ms in 11 normal ones. Thus, BAPTA is effectively loaded into the cone outer segment since photocurrents are slower and more sensitive to light. On the other hand, the mean dark holding current and peak photocurrent amplitude are not significantly changed by BAPTA/Ca2+ load. These facts suggest that the dark cytoplasmic free Ca2+ concentration in the patched cone outer segments is not very different from that in unperturbed cells. We will take the dark cytoplasmic level to be 400 nM, the value measured in intact cones (Sampath et al., 1999).
|
1/1.8 x 104. This implies that if the mean Ca2+ level is 400 nM, GC activity does not follow changes of ±0.02 nM or smaller. Also, we only require the 10 mM BAPTA buffering system maintain Ca2+ constant in the DARK, in the presence of what must be small oscillations caused by dark current noise (in balance with the Na/Ca2+,K exchanger). This is a small concentration challenge when compared with the much larger challenge caused by illumination. Thus, Ca2+ buffering by BAPTA in the dark-adapted cone is effective, although its ability to clamp cytoplasmic Ca2+ during intense, prolonged steps of light may be less effective.
The dark current noise in Ca2+-buffered cones is different from that in normal cones both in its amplitude and power spectrum (Fig. 2 A). In eight BAPTA-loaded cones, the mean variance of the current noise was 0.32 ± 0.13 pA2 in the dark and 0.016 pA2 in the light (0–20 Hz). The power density spectrum in the presence of BAPTA is different from that in the absence of the buffer and the difference is analyzed in detail below (continuous line in Fig. 2 C, compare with Fig. 1 C). Importantly, in the presence of BAPTA, the power spectrum of dark noise is different from that of the photocurrent. The photocurrent power spectrum is well fit by the product of three Lorentzians of identical rate (continuous line in Fig. 2 D). In 12 cells, the mean value of was 2.17 ± 0.57 Hz. The power spectrum of dark noise is described by a very different function (discussed below) (continuous line in Fig. 2 C), again, indicating that VP thermal excitation is not the dominant mechanism underlying dark noise.
Dark Noise in Bass Single Cones Does Not Arise from Thermal Excitation of Cone Visual Pigment
We have reasoned, in agreement with others before (Baylor et al., 1984; Rieke and Baylor, 1996), that in both normal and BAPTA/Ca2+-loaded cones, thermal excitation of VP is not the dominant cause of dark current noise because the time course of the VP-initiated events is different from that of the individual events underlying current noise. But this does not mean thermal VP excitation does not occur, simply that its rate is slow compared with the dominant molecular mechanism. We attempted to uncover the relative contribution of VP thermal excitation, if any, to the observed dark noise. To this end, we measured dark current noise in cones containing significantly fewer numbers of dark VP than normal cells. If overall dark noise includes a significant contribution from spontaneous VP excitation, then reducing the number of VP in darkness should change the power of the noise signal. Power (in watts) was measured by integrating the power spectral density between 0 and 20 Hz, a range that includes nearly in full the light-sensitive power (Figs. 1 and 2).
We reduced the number of VP molecules by briefly treating individual cell in the dark with hydroxylamine and washing extensively before starting the electrophysiological recording (see MATERIALS AND METHODS). Hydroxylamine removes 11-cis retinal from dark cone VP (dark-bleaching), but not from rod VP (Johnson et al., 1993; Kawamura and Yokoyama, 1998). Gene sequence data has identified 5 phylogenetically distinct classes of VP (Yokoyama, 1994). Only rod rhodopsin (class RH1) is impervious to hydroxylamine treatment in the dark. In every other class of VP, hydroxylamine causes loss of chromophore in darkness with a time constant of minutes to tens of minutes, depending on the molecular identity of the VP (Johnson et al., 1993; Kawamura and Yokoyama, 1998). The phylogenetic class of single bass VP is either RH2 or MWS/LWS by its wavelength of maximum absorbance (540 nm) and can be reasonably expected to dark-bleach by hydroxylamine.
Individual cones were superfused in the dark for 120 s with 60 mM hydroxylamine, followed by continuous washing for 5 min. After washing, dark current noise and photocurrents were measured in the treated cells with electrodes filled with BAPTA/Ca2+ solution. Hydroxylamine likely enters the cone cytoplasm (and leaves during washout) because it permeates through open CNG ion channels (Hackos and Korenbrot, 1999). The photocurrents recorded in treated cells were of normal time course and their peak amplitude increased with light intensity (Fig. 3 B). We did not find light-unresponsive cells. The cones, however, were substantially less sensitive to light than normal ones. At the brightest flash intensity possible in our instrument (2.5 x 104 540 nm photons/µm2), photocurrents were comparable in peak amplitudes to those generated by 10–20 photons/µm2 flashes in normal cones. That is, dark hydroxylamine treatment resulted in photocurrents of typical time course, but 1/103 as light sensitive as those in untreated cones.
|
; Leibrock and Lamb, 1997). Hydroxylamine-treated cones had a dark current amplitude within the range of that of untreated cells (mean dark current was –1 ± 8.8 pA, n = 5), indicating that dark cGMP and Ca2+ concentrations were unchanged. Also, the photocurrent kinetics of hydroxylamine-treated cells was indistinguishable from that of normal cells. This is qualitatively demonstrated by comparing the time course of data in Fig. 2 B and Fig. 3 B. Quantitatively, the data in Fig. 3 D show that photocurrent power spectra recorded in hydroxylamine dark-treated cones were the same as those measured in untreated cones. Photocurrent power spectra in hydroxylamine-treated cells were well fit by the product of three identical Lorentzians with average characteristic frequency 1.63 Hz ± 0.67 (n = 3). These are the same function and similar characteristic frequencies to those that describe normal photocurrents. In normal cells, the average characteristic frequency was 2.17 ± 0.57 Hz (n = 12). Finally, hydroxylamine treatment did not alter the cone's voltage-gated currents (unpublished data). Thus, there is no evidence of unanticipated pharmacological effects. Brief dark hydroxylamine treatment reduces the number of VP pigment (and thus sensitivity) without evidently affecting the biochemical phototransduction cascade.
Since photoreceptor sensitivity is proportional to VP concentration, loss of photosensitivity indicates our hydroxylamine treatment caused chemical bleaching of 999 out of every 103 VP molecules. The absorption cross section, xs, of a single bass cones illuminated on its side with unpolarized, 540 nm light is given by (Baylor et al., 1979; Miller and Korenbrot, 1993)
 |
). For unpolarized light = 0.5 and quantum efficiency of bleaching Qeff is 0.67. In a normal single cone xs = 1.92 µm2. Our hydroxylamine treatment reduced xs to 0.00195 µm2; since the cell geometry is unchanged this means that only 1 out of every 1,000 dark VP originally present remains available to capture photons.
Jones et al. (1996) suggested that light-bleached VP can cause light adaptation as made evident by a speeding up of the photocurrent kinetics in rods in which a significant fraction of VP had first been bleached by light (>0.1%). Since cone photocurrents we measured following hydroxylamine treatment have essentially the same kinetics as those of normal, dark-adapted photoreceptors, we infer that hydroxylamine-bleached VP molecules do not, themselves, cause light adaptation.
Hydroxylamine treatment did not detectably affect the power spectral density of the dark noise, illustrated in Fig. 3 C. The spectra were well fit by the same mathematical function (continuous line in Fig. 3 B) that describes the noise in untreated cells (detailed below). More important, the time-averaged power of the dark noise in treated and untreated cells was not different. Mean average power in treated cells was 0.32 ± 0.14 pA2 (n = 6) and it was 0.32 ± 0.09 pA2 (n = 5) in treated cells. These values are not statistically different (two-tailed Student's t test). Thus, reducing the number of dark VP molecules does not change the frequency or power characteristics of the dark noise power spectral density. These are the anticipated results that affirm that spontaneous excitation of VP molecules is not the dominant cause of dark current fluctuations in bass single cones.
Dark Current Noise in Ca2+-buffered Cones Originates from Fluctuation in Phosphodiesterase Activity
To demonstrate that dark current variance indeed arises from cGMP fluctuations in Ca2+-buffered cones, we measured current noise in BAPTA-loaded cells in the absence of added GTP and ATP. In the absence of triphosphate nucleotides, there is no cGMP synthesis, and after endogenous cGMP is consumed, CNG ion channels in the outer segment close. This is manifested by a slow change in holding current at –40 mV from its starting value near 0 to a steady positive value, a measure of outward current flow through Kv channels in the inner segment. In striped bass single cones, this stationary condition is reached 150 s after attaining whole cell mode (Rebrik et al., 2000; Holcman and Korenbrot, 2004).
The mean dark holding current at –40 mV in cones loaded with BAPTA/Ca2+ without GTP and ATP and measured 2.5 min after establishing whole cell mode or thereafter was 42.8 ± 21.6 pA (five cells). The mean variance of the current noise was 0.037 ± 0.012 pA2 (0–20 Hz) and, of course, it was light insensitive. This noise variance is essentially the same as that measured under continuous light in BAPTA-loaded cones when endogenous cGMP level is also zero (0.016 ± 0.005 pA2). Moreover, the dark noise power spectra in the absence of cGMP (Fig. 4 A) (five cells) or in the presence of continuous light (Fig. 2 C) (seven cells) are essentially the same. These results demonstrate that light-sensitive dark current noise is strictly dependent on the presence of cGMP.
|
). At –40 mV and in the absence of divalent cations, 8-cpt-cGMP half-maximally activates CNG channels in bass cone detached membrane patches at 5 µM (unpublished data). Cones loaded with BAPTA/Ca2+ and 2 µM 8-cpt-cGMP (without GTP or ATP) exhibited an inward current that slowly and continuously increased over time (mean rate –1.27 pA/s, five cells). A steady state was not reached and, eventually, the current was so large (hundreds of pA) that cells were irreversibly damaged. The inability to reach equilibrium likely reflects the fact that 8-cpt-cGMP is membrane permeable, and, in effect, there is a never ending flow from pipette lumen to cell cytoplasm to the bathing solution across the cell membrane. Experimentally we defined a quasi steady state by continuously monitoring current amplitude and measuring noise when current magnitude was near –100 pA (Fig. 4 B). For five cells analyzed, the mean holding current at –40 mV was –82 ± 16.5 pA and the drift rate –1.27 ± 0.9 pA/s. Calculations indicate that under these conditions, the number of active CNG channels was about three times the number normally active in darkness (when outer segment inward current is about –30 pA).
The power spectrum of dark current activated by 8-cpt-cGMP in BAPTA/Ca2+-loaded cones (Fig. 4 B) appears essentially the same as that measured in the absence of cGMP, achieved either by omitting GTP and ATP (Fig. 4 A) or in a normal cell under continuous, saturating light (Fig. 2 C). Current noise activated by 8-cpt-cGMP exhibits weak 1/f dependence <30 Hz and is frequency independent >30 Hz. It is not fit by the function that describes the noise in normal, BAPTA/Ca2+-loaded cones (Fig. 4 C). The same results were obtained in five different cells. That is, the nonhydrolyzable cGMP analogue activates CNG channels, but its concentration does not fluctuate because it is not hydrolyzed and, hence, cannot reflect PDE dynamics. When cGMP is present, channels are also open, but current noise is much larger, reflecting cGMP hydrolysis and PDE dynamics. These observations demonstrate that cGMP fluctuations caused by PDE activity are the principal source of current dark noise <30 Hz in Ca2+-buffered single cones.
A Theory to Model Dark Current Noise
We present a model that assumes thermal fluctuations in the number of active PDE molecules in darkness and computes the consequent fluctuations in cytoplasmic cGMP concentration and the outer segment membrane current. Details of mathematical derivations and an analysis of the equations are presented in APPENDIX. Here we outline the features of the conceptual model and its mathematical expression.
We assume that the total number of PDE molecules in the cone outer segment, N0, is constant and distributes between active, N*, and inactive states, N, due to thermal activation. Activation events are independent from each other, and the transition between inactive and active states occurs with forward activation rate ka and reverse inactivation rate 
21:
 | (1.3) |
We show in Appendix 1 that the dynamics of the number of active PDE is well described by the following effective stochastic equation:
 | (1.4) |
1 = kaN0 and 2 = (1/ + ka), 0 is variance, and dw is the standard centered Brownian motion of variance 1.
Cytoplasmic free cGMP concentration is controlled by the balanced activity of PDE and GC. The reaction rates of each of these enzymes have been thoroughly investigated (for reviews see Pugh and Lamb, 2000; Ebrey and Koutalos, 2001). The total concentration of cGMP, denoted as C(t), fluctuates according to
 | (1.5) |
max is the GC maximum reaction rate, Ca(t) is the cytoplasmic free Ca2+ concentration, and KaCa is the Ca2+ concentration at half maximal GC activation. At a fixed Ca2+ concentration, Eq. 1.5 becomes
 | (1.6) |
 |
kCAT is divided by two because the active PDE holoenzyme is a dimer (for review see Beavo, 1995).
In Appendix 2, we show that the power spectrum of steady-state fluctuations in cGMP concentration can be computed from Eqs. 1.4 and 1.6 and is given by
 | (1.7) |
This is the product of two Lorentzians each of characteristic frequencies 1 = 2 = ka + 21, and 2 = ksubNd*, where Nd* is the mean number of active PDE molecules in the dark.
From the known dependence of current on cGMP concentrations in bass cones (APPENDIX, Eq. A2.7) (Korenbrot and Rebrik, 2002), the power spectrum of the dark current, S1(), is given by
 | (1.8) |
Mean Dark Activities of PDE and GC in Bass Cones
Eqs. 1.7 and 1.8 state that if thermal fluctuations of PDE are the cause of dark noise, then in BAPTA/Ca2+-loaded cones, the power spectrum of dark current fluctuations should be described by the product of two Lorentzians of characteristic frequencies 1 and 2. The dark noise power spectrum is, indeed, fit by the product of two Lorentzians, but the values 1 and 2 cannot be simply determined by matching experimental and theoretical data because more than one combination of values for these parameters achieves successful match.
To make a more certain determination of PDE chemical kinetics, we first measured directly the value of 2 in bass cones. Recall from Eqs. 1.6 and 1.7 that 2 = ksubNd* = ßdark. ßdark is the steady-state cGMP hydrolysis rate in the dark. In darkness, rates of cGMP synthesis and hydrolysis are equal and opposite each other. If cGMP synthesis or hydrolysis are instantly blocked, the nucleotide concentration (and hence the dark membrane current) will change with a time course determined by the activity of the unblocked enzyme. ßdark was first measured in rods by Hodgkin and Nunn (1988) who demonstrated that blocking GC (by suddenly elevating cytoplasmic Ca2+) or PDE (with the enzyme inhibitor IBMX) yields essentially the same result.
In dark-adapted BAPTA/Ca2+-loaded bass cones, we measured the dark rate of cGMP synthesis. We recorded the change in membrane current caused by the sudden suppression of PDE activity with 200 µM zaprinast, a membrane-permeable PDE blocker (IC50 = 125 nM) (Gillespie and Beavo, 1989). In any given trial, we first established that the cell under study functioned normally by evaluating its dark current noise and flash photocurrents. We then measured the effect of rapidly (
50 ms) changing the solution bathing the cell to Ringer's containing zaprinast. Fig. 5 illustrates typical results observed in every cell studied (n = 4). The cells' photocurrents (Fig. 5 A) and dark current noise (Fig. 5 B) were indistinguishable from those of a larger population of normal cones. For this small set, peak photocurrent amplitude was 28 ± 1.1 pA, time to peak 93 ± 6.9 ms, and photosensitivity 184.2 ± 37 photons/µm2. Upon switching to the zaprinast-containing solution, the inward current increased linearly up to a limiting, steady value (Fig. 5 C). The linear rate of current increase reflects the controlling activity of GC; as cGMP raises, so does the current. As time progresses and the current increases, cytoplasmic free Ca2+ also raises which, in turn, reduces Ca2+-dependent GC activity. A new stationary conditioning is reached with a balance between the new, reduced rate of synthesis and the diffusional loss of cGMP from the outer segment into the patch pipette.
|
dark, can be explicitly computed from the tangent at t = 0. Only near zero is the computation possible since it is based on the presumption that only the initial (linear) rate of current increase is defined by GC activity alone. As time progresses and cytoplasmic Ca2+ rises, the initial conditions change. In the experimental data (Fig. 5 C), there is a brief delay between the addition of zaprinast and the linear change in membrane current, most likely time required for zaprinast to permeate and accumulate within the cell. The slope of the tangent fit to the initial rate of current rise was 21.1 ± 6 pA/s (N = 4, range 16.6–29.6 pA/s) (Fig. 5), from which we calculate a mean cGMP synthesis rate in darkness, dark ± 1.7 µM cGMP/s.
By definition, dark = ßdarkC0, where C0 is the cytoplasmic cGMP concentration in darkness. C0 is 25 µM, calculated from the relationship between dark current amplitude and cGMP concentration (Eq. 1.10; KcG at 400 nM Ca2+ is 135 µM cGMP and n = 2.5), given that mean dark outer segment current is 30 pA and this is 2% of Imax (Cobbs et al., 1985; Rebrik et al., 2000). From the measured dark value we compute mean ßdark = 0.25 ± 0.06 s–1.
The experimental data in Fig. 5 C can also be analyzed to yield the value of ßdark with a simpler algorithm proposed by Hodgkin and Nunn (1988). This algorithm requires independent knowledge of the cooperative dependence of cGMP-dependent current on cGMP concentration (Eq. 1.10), a value = 2.5 in bass cones. Analysis of our data with the Hodgkin and Nunn algorithm yields ßdark = 0.27 ± 0.06 s–1.
Rates of PDE Activation and Inactivation in Bass Cones
From the experimental ßdark value, we assigned 2 
0.248 Hz. We then fit Eq. 1.8 to the dark current power spectra measured in Ca2+-buffered cones with the value of 1 as the sole adjustable parameter (and a scaling coefficient to match the zero frequency power). Panels in Figs. 2, 4, and 6 illustrate the computer-aided, nonlinear least-squares fit of theoretical and experimental data in five different cells and demonstrate the range of the adequacy of the fit. The chi-square minimization in the fitting algorithm yields an estimate of the error in the value of the 1 parameter. In all cells analyzed this error was 10%. To illustrate conservatively the range of the error in the optimum value of the adjustable parameter 1, we plot in Fig. 6 (top panel) the optimal function, as well as two other functions in which the value of 1 is 20% larger and smaller than the optimum. These lines demonstrate the confidence limits of the fit. The error in the fit of any one power spectra is less than the error from differences among the cells in our sample. For 11 cones, the mean value of 1 was 18.53 ± 4.41 Hz.
|
1 and 2, the following computations are possible. From the definition 2 = ksubNd* = 0.25 s–1 and the biochemically determined value of ksub (Table I), we calculate the mean number of active PDE in darkness, Nd* 60 (Table II). In the steady-state, solution of Eq. 1.4 (from Appendix 1) yields
 | (1.9) |
1/70 that of the VP (Zhang et al., 2003), VP concentration in fish cones is 3.3 mM (Harosi, 1976) and the volume of a single bass cone outer segment is 0.1 pL (Holcman and Korenbrot, 2004). From the definition 1 = ka + 21 = 18.53 s–1 and Eq. 1.9, we compute the rates of cone PDE activation and inactivation to be ka = 3.7 x 10–4 s–1 and 21 = 18.5 s–1 (Table II).
|
|
and anywhere between 0.9 and 1.6 s–1 (mean 1.2) by Nikonov et al. (2000). In toad rods, this rate is 1.8 s–1 (Rieke and Baylor, 1996). The total number of active PDE molecules in darkness is higher in toad or salamander rod outer segment than bass cone outer segment, this difference, however, reflects their size difference. In both receptor types, the ratio of dark active PDE over total PDE, Nd*/N0, is not that different. In both cell types, PDE activation is very fast and of essentially identical rate. The inactivation rate, however, is 5–10 times faster in cones than rods. Because the inactivation rate is so much slower than activation, it determines the lifetime of the active PDE state ( = 1/[ka + 21]). These results mean that at room temperature in nonmammalian, intact photoreceptors, the lifetime of dark active PDE is between 0.5 and 1.1 s in rods, but it is only 50 ms in cones.
Dark Current Noise in Normal Cones
To understand dark noise in a normal cone, we extended the theoretical model to include Ca2+ dynamics. Cytoplasmic Ca2+ in the outer segment is regulated by the kinetic balance between Ca2+ influx through the CNG ion channels and its efflux through Na/Ca,K exchangers (Yau and Nakatani, 1985; Miller and Korenbrot, 1987). Free Ca2+ regulates GC activity (Koch and Stryer, 1988; Gorczyca et al., 1995), and in cones, but not rods, it also regulates the ligand sensitivity of the CNG channels (Rebrik and Korenbrot, 1998; Rebrik et al., 2000).
When Ca2+ concentration fluctuates, the dynamics of cGMP concentration is given by Eq. 1.5. The cGMP dependence of outer segment current is Ca2+ dependent and given by (Rebrik et al., 2000)
 | (1.10) |
)
 | (1.11) |
, the ratio of free/total Ca2+ (Miller and Korenbrot, 1987; Sneyd and Tranchina, 1989; Miller and Korenbrot, 1993). If the kinetics of buffering are assumed to be fast compared with the rate of Ca2+ entry, then Ca(t) is given by
 | (1.12) |
 |
), is cytoplasmic Ca2+-buffering power, zF are valence and Faraday's constant, and 
is the time constant of outer segment Ca2+clearance via the Na/Ca,K exchanger (time to reduce free Ca2+ to 1/e of its initial value). The values of these parameters are known from biochemical and biophysical literature and are collected in Table I. The system of Eqs. 1.10–1.13 (referred to as Sc) describes the coupled dynamics of PDE, cGMP, and Ca2+ cytoplasmic concentration in darkness. The system Sc is analyzed in Appendix 4. We show that the power spectrum of the dark noise, computed by linearizing the system around the steady state, is given by
 | (1.13) |
 |
 |
Expression 1.13 defines the power spectrum of dark current noise in normal cones. Although it includes several independent parameters, the values of all but one of these parameters is known from data available in the biochemical and biophysical literature. We assigned the values listed in Table I. We set <
