Middendorf et al. (Middendorf, T.R., R.W. Aldrich, and D.A. Baylor. 2000. J. Gen. Physiol. 116:227–252) showed that ultraviolet light decreases the current through cloned cyclic nucleotide–gated channels from bovine retina activated by high concentrations of cGMP. Here we probe the mechanism of the current reduction. The channels' open probability before irradiation, Po(0), determined the sign of the change in current amplitude that occurred upon irradiation. UV always decreased the current through channels with high initial open probabilities [Po(0) > 0.3]. Manipulations that promoted channel opening antagonized the current reduction by UV. In contrast, UV always increased the current through channels with low initial open probabilities [Po(0) ≤ 0.02], and the magnitude of the current increase varied inversely with Po(0). The dual effects of UV on channel currents and the correlation of both effects with Po(0) suggest that the channels contain two distinct classes of UV target residues whose photochemical modification exerts opposing effects on channel gating. We present a simple model based on this idea that accounts quantitatively for the UV effects on the currents and provides estimates for the photochemical quantum yields and free energy costs of modifying the UV targets. Simulations indicate that UV modification may be used to produce and quantify large changes in channel gating energetics in regimes where the associated changes in open probability are not measurable by existing techniques.
Cyclic nucleotide-gated (CNG) ion channels are activated cooperatively by the binding of multiple cyclic nucleotide ligands to a cytoplasmic COOH-terminal domain of the protein (Kaupp et al. 1989). CNG channels play central roles in vision (Stryer 1986; Yau and Baylor 1989), olfaction (Lancet 1986; Zufall et al. 1994), and possibly other sensory modalities (Coburn and Bargmann 1996; Komatsu et al. 1996; Misaka et al. 1998). Their expression in a host of other tissues, including heart (Biel et al. 1994; Ratcliffe et al. 1995), testis (Biel et al. 1994; Weyand et al. 1994), kidney (Marunaka et al. 1991; Ahmad et al. 1992; Biel et al. 1994; Karlson et al. 1995), and brain (Yao et al. 1995; Kingston et al. 1996; Ding et al. 1997; Zhang et al. 1997; Timpe et al. 1999), suggests that they may participate in nonsensory processes as well. Understanding the molecular mechanism of CNG channel activation is of interest not only due to the channels' important physiological roles, but also because they serve as a model system for studying allostery and cooperativity.
The primary experiment used to test activation models for CNG and other ligand-gated channels is to measure the dependence of their open probability on cyclic nucleotide concentration. The endpoints of this dose–response relation are often difficult to measure accurately because the open probabilities of CNG channels span the enormous range from <10−5 in the absence of ligand (Ruiz and Karpen 1997; Tibbs et al. 1997) to >0.90 in saturating ligand (Goulding et al. 1994; Taylor and Baylor 1995; Varnum and Zagotta 1996). Furthermore, two other defining features of the ligand dose–response relation for these channels, the apparent slope and the concentration of cyclic nucleotide producing half-maximal activation, may vary significantly between experiments (Ruiz et al. 1999). The combined effect of these uncertainties is to limit the usefulness of the dose–response relation in evaluating theories for CNG channel gating.
Combined measurements of gating and ionic currents have greatly assisted the process of discriminating among candidate models for the voltage-dependent activation of Shaker potassium channels (Bezanilla et al. 1994; Zagotta et al. 1994; Schoppa and Sigworth 1998). Likewise, detailed models for the activation of large conductance, Ca+2-activated K+ (mSlo) channels have been developed using measurements of the channels' sensitivity to both membrane voltage and intracellular Ca2+ concentration (Cox et al. 1997; Cui et al. 1997; Horrigan and Aldrich 1999; Horrigan et al. 1999; Rothberg and Magleby 1999). In this spirit, perturbations of gating energetics combined with measurements of the ligand dose–response relation may be useful for studying the activation mechanism of CNG channels and other ligand-gated channels that are relatively insensitive to membrane voltage.
Spectroscopic methods offer a promising approach for supplementing the information obtained from traditional electrical measurements on channels. For example, luminescence signals from voltage-gated channels labeled with fluorescent dyes have revealed new details about the protein motions involved in gating (Mannuzzu et al. 1996; Cha and Bezanilla 1997; Cha et al. 1999; Glauner et al. 1999). We have used a complementary spectroscopic approach that employs UV light to photochemically modify the intrinsic aromatic amino acid chromophores in CNG channels. The preceding paper (Middendorf et al. 2000) showed that UV dramatically reduces the ionic currents through fully liganded CNG channels. The wavelength dependence of the effect was very similar to the absorption spectrum of tryptophan, suggesting that UV decreased the currents by photochemically modifying one or more “target” tryptophan residues in the channels. Here we investigate the mechanism of the UV effect on the currents.
Materials And Methods
Channel expression, electrical recordings, solutions, and UV irradiation apparatus were described in the preceding paper (Middendorf et al. 2000). Briefly, channels were expressed in Xenopus oocytes by microinjection of the appropriate cRNA. Currents through inside-out membrane patches excised from injected oocytes were recorded 3–21 d after injection. Patches were irradiated with light emitted by a 75 W xenon arc lamp and focused on the preparation with a quartz lens. UV wavelengths were selected using 10-nm full-width at half-maximum bandpass interference filters. The cDNA for the rat olfactory (OLF) CNG channel was a generous gift from Prof. R. Reed of Johns Hopkins University (Baltimore, MD).
Effect of UV on Ligand Dose–Response Relation
As shown previously (Middendorf et al. 2000), UV decreased the amplitude of macroscopic currents through bovine retinal CNG (RET) channels activated by a saturating concentration of cGMP (1 mM, Fig. 1 A). Since cyclic nucleotides absorb strongly at the UV wavelengths employed (250–330 nm), the patches were irradiated in the absence of cGMP to avoid possible photochemical modification of the ligand or its cross linking to the channels.
In stark contrast to the current reduction in 1 mM cGMP (Fig. 1 A), the same UV exposures increased the current activated by a low concentration of cGMP (2 μM, B). Each trace was corrected for leak by subtracting the current in the absence of cGMP after the same UV dose. This procedure ruled out the trivial possibilities that the additional current after irradiation flowed through the leakage conductance of the seal or through the UV-activated conductance (Middendorf et al. 2000), since these conductances were insensitive to cGMP (data not shown).
Fig. 1 C displays the combined results for the patch in A and B as a series of pre- and post-UV ligand dose–response relations. These relations plot the fractional current activation I/Imax (defined as the current relative to the maximal current in saturating cGMP before irradiation) as a function of cGMP concentration. The relations crossed at I/Imax ≈ 0.04 due to the opposite effects of UV on the currents activated by high and low concentrations of cGMP. This fractional activation occurred at a cGMP concentration of ∼15 μM, which is 4.7× lower than the initial half-saturating concentration of 70.2 μM. The slopes of the relations and their positions on the abscissa were compared by fitting them with the Hill equation:
where Imax(D) is the maximal current in saturating ligand after a UV dose D, h is the Hill coefficient, and K1/2 is the half-saturating ligand concentration. The Hill coefficient decreased progressively from 1.85 before UV to 0.97 and 0.53 after the first and second UV doses, respectively. Higher UV doses reduced the fractional activation even further in other experiments (Middendorf et al. 2000), suggesting that the Hill coefficient for fully modified channels may be <0.53. Furthermore, the curves may be artificially steepened because the leak correction procedure may have overestimated the leak at low cGMP concentrations due to the increased spontaneous channel openings after UV (see Fig. 15). The Hill coefficients for the post-UV relations are difficult to interpret, however, since the patches likely contained a mixture of channels with different numbers of modified target residues. The reduced slope of the overall relation for such a heterogeneous population could result from UV effects on K1/2 rather than h. UV had similar effects on the cGMP dose–response relations of RET channels from two other patches.
We also investigated the effect of UV on currents through a second type of CNG channel from rat olfactory epithelium (denoted OLF) (Dhallan et al. 1990). The open probability (Gordon and Zagotta 1995b; Varnum and Zagotta 1996) and single channel conductance (Kaupp et al. 1989; Goulding et al. 1992) of OLF channels are larger than those of RET channels. The amino acid sequences of OLF and RET channels are similar, with most of the differences occurring outside of the “core” region that contains the six presumed membrane-spanning domains and the cyclic nucleotide–binding domain. 8 of the 10 tryptophan residues occupy equivalent positions in RET and OLF channel subunits. OLF and RET channels contain nonequivalent tryptophans in the cytoplasmic NH2-terminal domain before the first presumed transmembrane segment (W81 in OLF and W9 in RET). In addition, OLF channels contain a tryptophan in the S1 transmembrane segment, W141, that is not present in RET channels, while RET channels contain a tryptophan in the S3–S4 linker, W263, that is not found in OLF channels.
The effects of UV light on OLF channels (Fig. 2) were similar in several respects to those on RET channels (Fig. 1). UV decreased the current through OLF channels activated by saturating cGMP (1 mM, Fig. 2 A), but increased the current activated by a very low concentration of cGMP (0.2 μM, Fig. 2 B) in the same patch after the identical doses. In addition, UV decreased the slope of the cGMP dose–response relation for OLF channels (Fig. 2 C). The relations before and after UV crossed at I/Imax ≈ 0.03, corresponding to 0.5 μM cGMP (5.6× lower than the initial half-saturating concentration of 2.8 μM).
OLF and RET channels differed in their absolute sensitivity to UV. A dose of 4.91 × 109 photons · μm−2 at 280 nm reduced the amplitude of currents through RET channels in saturating cGMP by a large factor (I/Imax = 0.464 ± 0.003, Fig. 1), but had only a slight effect on the current through OLF channels (I/Imax = 0.944 ± 0.003, Fig. 2). The reason for the difference in UV sensitivities is discussed later (see Fig. 5).
Mechanism of UV Effect
The results in Fig. 1 and Fig. 2 are inconsistent with an “all-or-none” effect of UV on CNG channel currents. Models of this type assume that UV has no effect on a channel until modification of a critical number of target residues renders the channel nonconducting (Middendorf et al. 2000). For such a model, only two functionally distinguishable classes of channels are possible: channels containing less than the critical number (n*) of modified target residues that are functionally identical to unmodified channels, and channels that contain at least n* modified targets that do not conduct current. Thus, photochemical modification simply reduces the number of functional channels in the patch, and UV is predicted to reduce the current by a constant factor at all ligand concentrations. This prediction is inconsistent with the results in Fig. 1 and Fig. 2. The preceding paper (Middendorf et al. 2000) showed that the difference in UV sensitivities of wild-type and W353Y mutant RET channels is also inconsistent with an all-or-none UV effect. We conclude that UV reduces CNG channel currents in a graded fashion, and that some UV-modified channels conduct current, but their ligand dose–response relations differ from those of unmodified channels.
where isc is the current through a single open channel. We assume that UV does not alter N, the total number of channels initially in the patch, and treat “destruction” of channels by UV as a reduction of Po and/or isc to zero (see below). The channels' cyclic nucleotide affinity, Kb, also influences the current amplitude, since Po and isc depend on the number of bound ligands (Ildefonse and Bennett 1991; Taylor and Baylor 1995; Ruiz and Karpen 1997, Ruiz and Karpen 1999; Liu et al. 1998). A priori, UV might alter the channel current by altering any combination of the parameters Po, isc, and Kb. The opposite effects of UV on the currents through channels activated by high versus low concentrations of cGMP (Fig. 1 and Fig. 2) are inconsistent with a single effect of UV on these parameters. We conclude that UV exerts at least two distinct effects on the channels, and consider first the mechanism of the current reduction in saturating cGMP.
Mechanism of Current Reduction by UV
UV might have decreased the currents through CNG channels activated by 1 mM cGMP (Fig. 1 A and 2 A) by reducing the channels' affinity for ligand such that 1 mM cGMP was no longer saturating. However, raising the cGMP concentration from 1 to 3 mM did not increase the current amplitude after irradiation (Fig. 1). In other experiments (data not shown), raising the cGMP concentration from 1 to 20 mM did not increase the post-UV current amplitude. The UV effects on OLF channels (Fig. 2 C) were also inconsistent with this mechanism, since the current amplitude after irradiation saturated at ∼40% of the pre-UV value.
If UV altered the channels' unitary conductance, but not their open probability, then UV should reduce the currents activated by any saturating concentration of ligand by the same fraction. In contrast to this prediction, the UV dose–response relations differed for OLF channels activated by 10, 100, and 1,000 μM cGMP (Fig. 3 A), saturating concentrations before irradiation (Fig. 2 C). Increasing the cGMP concentration over this range shifted the relations to the right on the abscissa and increased their slope (Fig. 3 B). The results in Fig. 3 are thus inconsistent with the idea that UV reduced the currents mainly by decreasing the channels' unitary conductance.
The parameter σ in is the absorption cross section of a UV target, and φ is its photochemical quantum yield (the fraction of absorptions that produce a photoproduct). The slope factor, n*, is a parameter that characterizes the steepness of the UV dose–response relation. No physical significance was attached to the values of these fitting parameters since, as noted above, UV did not alter the currents in an all-or-none manner. Rather, the fits provided a simple means for quantifying the slope of a relation and its D1/2 value. The latter quantity is defined as the UV dose that reduced the current amplitude to half of its initial value. The UV parameters obtained from the fits are compiled in Table.
The results in Fig. 3 are not explained by differential UV effects on the unitary conductances of channel subconductance states. In RET channels, fully liganded channels reside almost exclusively in the level with the largest conductance (Ildefonse and Bennett 1991; Taylor and Baylor 1995; Ruiz and Karpen 1997, Ruiz and Karpen 1999). Also, results from the preceding paper (Middendorf et al. 2000) indicate that UV does not affect other pore properties of the channels, such as their ion selectivity. These results do not completely rule out UV effects on isc; however, results to be presented indicate that possible effects of this type are small. Having ruled out other possibilities, we conclude that UV reduced the currents mainly by lowering the channels' open probability.
It was not possible to measure directly the effect of UV on the unitary conductance and open probability of single CNG channels because of interference by the UV-activated conductances in oocytes (Middendorf et al. 2000). Therefore, we used the alternate approach of modeling the UV effect on macroscopic currents (see below).
Energy Additive Model
Of the various physical models considered in the preceding paper (Middendorf et al. 2000), only the energy additive model is consistent with the graded reduction in channel open probability suggested by the results in Fig. 1,Fig. 2,Fig. 3. This model was described in detail previously (Middendorf et al. 2000) and is briefly summarized here.
Assume that fully liganded channels have a single open and a single closed state, contain n identical and independent UV target residues per subunit, and that modification of each target alters the free energy difference between the channels' open and closed states by an equal and additive amount. Then, due to the statistical nature of light absorption, the various channels in a patch will contain different numbers of modified target residues (denoted by the index k) after exposure to a subsaturating UV dose. The equilibrium constant between the open and closed states of a channel with k modified targets, K(k), is given by:
Here, ΔG 0(0) is the standard free energy difference between channel states before irradiation, and ΔΔG 0(1) is the free energy “cost” of modifying a single target residue. is simplified by expressing these thermodynamic parameters in RT units (R is the gas constant, T is the absolute temperature, and RT = 0.58 kcal/mol). The equilibrium constant is related to the channels' open probability according to
Since irradiation decreases Po, modification of the UV targets favors channel closing (i.e., ΔΔG 0(1) > 0).
The energy additive model is illustrated by the schematic in Fig. 4 A. Before irradiation, the open state O0 has a lower free energy than the closed state C0, consistent with the high initial open probabilities of RET and OLF channels in saturating cGMP (Table). The relative free energies of these states must invert after irradiation, since UV ultimately reduces Po to a value <0.5 (Fig. 1,Fig. 2,Fig. 3). UV may invert the levels by stabilizing or destabilizing either or both states; the observed reduction in Po requires only a net stabilization of the closed state relative to the open state. For simplicity, the entire effect of UV is represented in Fig. 4 A by an increase in the free energy of the open state.
The current varies with dose according to Eq. 40 of Middendorf et al. 2000:
where f(k, D) denotes the fraction of channels containing k modified target residues after a UV dose D:
The UV dose–response relation () depends on five parameters: (a) the absorption cross-section of the target residues, σ; (b) the photochemical quantum yield of the targets, φ; (c) the number of target residues per channel subunit, n; (d) the free energy difference between the channels' open and closed states before irradiation, ΔG 0(0); and (e) the free energy cost of modifying a single target residue, ΔΔG 0(1). Ranges of possible parameter values are estimated in the following. (a) The main target residues in RET channels were identified as tryptophans from the close correspondence between the channels' action spectrum and the absorption spectrum of tryptophan (Middendorf et al. 2000). Since tryptophan's absorption cross section is not very sensitive to environment (McLaren and Shugar 1964), we use the value for tryptophan in free solution, σ = 2.17 × 10−17 cm2 (Middendorf et al. 2000). (b) Typical photochemical quantum yields for tryptophans in proteins are in the range 0.01 ≤ φ ≤ 0.2 (McLaren and Shugar 1964; Vladimirov et al. 1970; Grossweiner 1976). However, since φ depends on the protein environment around the target, these values should be considered only as a starting estimate. (c) Homo-oligomeric RET and OLF channels contain 10 tryptophan residues per subunit (Kaupp et al. 1989; Dhallan et al. 1990); thus, 1 ≤ n ≤ 10. (d) The open probability of RET channels in saturating cGMP is ∼0.95 (see Table), corresponding to ΔG 0(0) = −3.0 RT (see and ). For OLF channels, ΔG 0(0) = −9.9 RT. (e) As noted above, the observed decrease in Po after irradiation implies that ΔΔG 0(1) > 0. A narrower range of possible values for this parameter is obtained by considering the limiting value of I(D)/I(0) for large values of D. If we denote this limit as M, then, from :
Using the estimate M ≤ 0.05 (Middendorf et al. 2000, and Fig. 3 A) and the above values of n and ΔG 0(0) (Middendorf et al. 2000), evaluation of yields ΔΔG 0(1) ≥ +0.15 RT for RET channels and ΔΔG 0(1) ≥ +0.32 RT for OLF channels.
The open probability of CNG channels can be varied by changing the channel sequence (e.g., RET vs. OLF channels; Goulding et al. 1994; Gordon and Zagotta 1995b; Zong et al. 1998; Paoletti et al. 1999), by varying the identity of the activating ligand (e.g., cGMP vs. cAMP vs. no ligand; Goulding et al. 1994; Gordon and Zagotta 1995b; Varnum et al. 1995), by introducing chemical species that bind to the channels (such as the transition metals Ni2+, Zn+2, and Co+2; Ildefonse and Bennett 1991; Ildefonse et al. 1993; Karpen et al. 1993; Gordon and Zagotta 1995a), or by modifying them chemically; e.g., with N-ethyl maleimide (Finn et al. 1995; Gordon et al. 1997; Brown et al. 1998), copper phenanthroline (Gordon et al. 1997), or methanethiosulfonate reagents (Brown et al. 1998). By exploiting these factors, it is possible to vary ΔG 0(0) between −9.9 RT (OLF channels in saturating cGMP) and +11.9 RT (RET channels in the absence of ligand). Over this free energy range, the equilibrium constant for channel opening varies by nine orders of magnitude.
The next section presents theoretical UV dose–response relations calculated using the energy additive model. The curves predict how the UV dose–response relation should vary for channels with different values of ΔG 0(0). The theory is then compared with the observed UV dose–response relations for CNG channels.
Effects of Varying ΔG 0(0) on the UV Dose–Response Relation in Saturating Ligand: Simulations
UV dose–response relations were calculated using , ΔG 0(0) values from Table and values of n and ΔΔG 0(1), consistent with the constraints discussed in the previous section. When the simulated UV dose–response relations are plotted using a logarithmic abscissa, the quantum yield and absorption cross section of the targets affect only the absolute positions of the curves, not their shapes. We eliminated the curves' dependence on σ and φ by transforming the abscissa to the dimensionless coordinate σ·φ·D and comparing only the relative positions of the simulated curves on the dose axis.
The effect on the theoretical relations of varying ΔG 0(0) depended on the relative magnitudes of the free energy parameters ΔΔG 0(1) and ΔG 0(0), and on the number of target residues per subunit, n. Three limiting cases were examined.
If ΔΔG 0(1) is much larger than |ΔG 0(0)| (Fig. 4 B), then reduces to :
In this limit, the simulated UV dose–response relations were independent of ΔG 0(0) and the current approached an asymptote of zero for all possible target numbers. These predictions are consistent with the idea that photochemical modification of a single target residue abolishes the channel current, and that modification of additional targets has no measurable effect.
When ΔΔG 0(1) and |ΔG 0(0)| were comparable in magnitude (Fig. 4 C), decreasing ΔG 0(0) (i.e., making channel opening more favorable) shifted the simulated relations to the right along the abscissa and increased their slope. These trends reflect the larger number of target modifications (and the proportionately higher UV dose) that are needed to offset the increased initial relative stabilization of the channels' open state. Put another way, increasing the channels' initial open probability antagonizes the effect of UV.
If ΔΔG 0(1) was much smaller than |ΔG 0(0)| (Fig. 4 D), then increasing −ΔG 0(0) relative to ΔΔG 0(1) again shifted the simulated curves to the right along the abscissa and increased their slope, but also increased the limiting value of I(D)/I(0). The latter effect occurs when the free energy cost of modifying all of the target residues, equal to 4n·ΔΔG 0(1), is not much larger than |ΔG 0(0)|. In the limit that 4n·ΔΔG 0(1) << |ΔG 0(0)|, reduces to :
and the UV effect on current amplitude disappears (Fig. 4 D, top).
For all three limiting cases, the curves for n = 10 were shifted to the left of those for n = 1 due to increased light collection by a larger number of targets. The slopes of the relations were sensitive to the number of target modifications needed to reduce the current significantly rather than the total number of target residues present in the channels.
Effects of Varying ΔG 0(0) on the UV Dose–Response Relation in Saturating Ligand: Experimental Results
This section compares the simulated curves of Fig. 4B–D, to the observed UV dose–response relations for CNG channels with different initial free energy gaps. Varying the channels' amino acid sequence was the first of three methods used to alter ΔG 0(0). In saturating cGMP, channel opening is much less favorable for RET than for OLF channels [ΔG 0(0) = −3.0 vs. −9.9 RT]. Results from several laboratories (Goulding et al. 1994; Gordon and Zagotta 1995b; Gordon et al. 1997; Varnum and Zagotta 1997) are consistent with the idea that this difference in gating efficacy results from a favorable interaction between an NH2-terminal domain and the COOH-terminal cyclic nucleotide binding domain that occurs only in OLF channels (Varnum and Zagotta 1997).
The UV dose–response relations for RET and OLF channels clustered into well-defined groups (Fig. 5 A), with the OLF channel cluster far to the right on the abscissa. The half-maximal dose, D1/2, for each patch was estimated by fitting the experimental points with a smooth curve using . Each relation for patches expressing a given channel was then shifted along the abscissa so that D1/2 for the shifted points was equal to the average D1/2. Pooling the results in this way removed the variation in absolute UV sensitivity between patches and revealed the highly reproducible shapes of the UV dose–response relations for each channel type (Fig. 5 B). OLF channels were roughly four times less sensitive to UV than RET channels, and their UV dose–response relations were two and a half times steeper (Table). For both channels, UV ultimately reduced the current to <5% of its initial value.
The open probability of CNG channels was also varied by adding low concentrations (∼10 μM) of Ni2+ ions to the cytoplasmic surfaces of the patches. Ni2+ and other divalent transition metals potentiate the responses of CNG channels to cGMP (Ildefonse and Bennett 1991; Ildefonse et al. 1993; Karpen et al. 1993) by binding to a histidine residue located between the S6 putative transmembrane segment and the consensus cGMP binding domain (Gordon and Zagotta 1995a). Ni2+ may promote channel opening by binding more tightly to the open than to the closed state of the channel (Gordon and Zagotta 1995a).
Adding Ni2+ ions reduced the UV sensitivity of RET channels activated by saturating cGMP (Fig. 6 A) approximately twofold, and increased the slope of the UV dose–response relation by ∼70%. UV ultimately reduced the currents in the presence or absence of Ni2+ to <5% of their initial amplitudes. The effects of Ni2+ on the gating of the channels before irradiation (Fig. 6 B) agreed well with those reported previously (Gordon and Zagotta 1995a): Ni2+ increased the channels' apparent affinities for cAMP and cGMP by factors of 4 and 15, respectively, and increased the current amplitude in saturating cAMP 60-fold.
The channels' gating energetics were also varied by changing the identity of the activating ligand. The current through RET channels activated by saturating cAMP is only ∼2% of that activated by saturating cGMP (Kaupp et al. 1989; Goulding et al. 1992; Gordon and Zagotta 1995a; Varnum and Zagotta 1996). This result, coupled with the finding that the unitary conductances of channels bound fully with cAMP and cGMP are the same (Sunderman and Zagotta 1999), indicates that cAMP is a poorer agonist than cGMP. For OLF channels, the current amplitudes in saturating cAMP and cGMP are similar. The lower agonist potency of cAMP is manifested in this case as a decrease in the channels' apparent affinity for cAMP compared with cGMP (Goulding et al. 1994; Gordon and Zagotta 1995b).
Fig. 7 shows UV dose–response relations for RET and OLF channels activated by saturating concentrations of cAMP and cGMP. Separate responses to cAMP and cGMP were measured for most of the patches after each UV dose. This approach eliminated variations in UV sensitivity between patches, enabling us to detect small differences in the UV dose–response relations of channels activated by each ligand. (10 μM Ni2+ was also included in the bath solutions for the experiments on RET channels. UV had an unusual effect on the currents through RET channels activated by cAMP in the absence of Ni2+ (see Fig. 14). Ni2+ was omitted in the experiments on OLF channels.)
For RET channels, substituting cGMP + Ni2+ for cAMP + Ni2+ increased D1/2 by 72% and increased the slope factor of the relation by 70% (Fig. 7 A), basing the comparison on patches for which separate UV dose–response relations were obtained for both ligands. For OLF channels, substituting cGMP for cAMP increased D1/2 by 42% and increased the slope factor of the relation approximately twofold (Fig. 7 B).
The results in Fig. 5,Fig. 6,Fig. 7 are summarized in Table. Varying ΔG 0(0) by the three types of energetic perturbations had similar effects on the channels' UV dose–response relations. Making ΔG 0(0) more negative shifted the UV dose–response relations to the right on the abscissa and increased their slopes. This correlation between shift and slope is explained by the energy additive model. As ΔG 0(0) is made more negative, more targets must be modified to invert the relative free energies of the channels' open and closed states and lower Po. The steepness of the UV dose–response relation increases in proportion to the number of required modifications. It takes a larger photon dose to modify more targets, leading to the parallel increase in D1/2.
The observed effects of varying ΔG 0(0) on the UV dose–response relations (Fig. 5,Fig. 6,Fig. 7) are consistent with Case II (Fig. 4 C), but not Case I (Fig. 4 B) or Case III (Fig. 4 D) of the energy additive model. We conclude that (a) UV reduced the currents in saturating cGMP by lowering the channels' open probability, and (b) ΔΔG 0(1) is comparable in magnitude to |ΔG 0(0)| for RET and OLF channels.
Fig. 5,Fig. 6,Fig. 7 show only 4 of 10 possible pairwise comparisons between the UV dose–response relations for the five channel/ligand/Ni2+ combinations studied. 8 of 10 pairs (including those in Fig. 5,Fig. 6,Fig. 7) exhibited the positive correlation between −ΔG 0(0) and D1/2 that is predicted by Case II of the energy additive model. Two pairs violated the expected trend. First, the half-maximal UV dose was slightly larger for RET channels activated by cAMP + Ni2+ than by cGMP alone, even though −ΔG 0(0) is only about half as large (Fig. 8 A and Table). A more significant deviation from the expected trend is shown in Fig. 8 B. The fit to the UV dose–response relation for RET channels activated by saturating cGMP + Ni2+ from A (reproduced as a dashed line in Fig. 8 B) is shifted leftward on the abscissa from the relation for OLF channels activated by cAMP, even though −ΔG 0(0) is much larger (Table).
The energy additive model also predicts a positive correlation between −ΔG 0(0) and the slope factor for a channel's UV dose–response relation. 9 of 10 channel/ligand/Ni2+ combinations followed this prediction. The lone discrepancy again occurred for the second of two pairs described above: the slope factor was smaller for RET/cGMP/Ni2+ compared with OLF/cAMP, despite its larger initial free energy gap.
Fig. 8C and Fig. D, shows explicitly the relations between the UV and thermodynamic parameters for all of the channel/ligand combinations studied. When plotted as a function of −ΔG 0(0) (Fig. 8 C), the D1/2 values clustered into two groups, with the points for OLF channels displaced above those for RET channels. Assuming that D1/2 for each channel type at any intermediate value of −ΔG 0(0) may be obtained by interpolating between measured values, the results suggest that OLF channels have a lower UV sensitivity than RET channels with the same value of −ΔG 0(0). The slope factors of the UV dose–response relations for OLF channels were also larger than those for RET channels after correcting for differences in ΔG 0(0) (Fig. 8 D).
What factors are responsible for the differences between the UV dose–response relations of RET and OLF channels with the same value of ΔG 0(0) (Fig. 8C and Fig. D)? A difference in the number or quantum yields of the UV targets in the two types of channels could account for the observed variation in D1/2 (Fig. 8 C), but is not expected to cause a difference in the slopes of the channels' UV dose–response relations, as was observed (Fig. 8 D). The results in Fig. 8 D are more consistent with the idea that the free energy cost of target modification is different in RET and OLF channels. To test this hypothesis, we fit the results in Fig. 5,Fig. 6,Fig. 7 simultaneously, using the energy additive model (). As predicted, the ΔΔG 0(1) values obtained from the fits were different for RET and OLF channels. In addition, the free energy costs varied for a given channel activated by different ligands. The smooth curves in Fig. 9A and Fig. B, show the fits for n = 2; excellent fits were obtained for all target numbers greater than one per subunit. The magnitude of ΔΔG 0(1) for each channel/ligand combination (Fig. 9 C) was relatively independent of the number of targets for n ≥ 2, probably because the total free energy cost of modifying two targets per subunit was sufficient to reduce the open probability close to zero. Additional targets, if present, are essentially undetectable because of the negligible incremental effect of their modification on the current amplitude.
The differences in ΔΔG 0(1) for RET and OLF channels activated by a given ligand are not surprising. Some of the tryptophan residues occupy inequivalent positions in RET and OLF channels. The associated ΔΔG 0(1) values would almost certainly differ if any of these tryptophans were UV targets. Furthermore, the ΔΔG 0(1)'s might differ even for homologous target residues in the two channels, since the free energy change associated with mutating equivalent residues in related proteins often depends on the environment of the mutated residue (Creighton 1993).
The differences in ΔΔG 0(1) for the same channel activated by different ligands implies that at least one of the target residues interacts with the cyclic nucleotides, their binding site, or with structures that affect the coupling between ligand binding and channel opening.
The estimated photochemical quantum yields varied inversely with the number of targets per subunit, from ∼2% for n = 1 to 0.2% for n = 10 (Fig. 9 D). The reciprocal relationship between n and φ is expected due to their appearance as a product in the exponent in .
UV Sensitivity of Pore Tryptophan Mutants
In the preceding paper (Middendorf et al. 2000), we described an attempt to identify the target tryptophan residue(s) in RET channels by measuring the UV sensitivities of mutant CNG channels in which 1 of the 10 native tryptophans per subunit was replaced by another amino acid. We expected such mutations to decrease or possibly eliminate the channels' UV sensitivity if the replaced residues were UV targets. To our surprise, the mutant W353Y, which substitutes tyrosine for a highly conserved tryptophan residue in the channel pore, was seven times more UV sensitive than the parent RET channel.
A possible explanation for this result is that the W353Y mutation disrupts channel opening. The energy additive model (Fig. 4 A) predicts that, other factors being equal, a mutation that destabilizes the channels' open state relative to the closed state should decrease the number of target modifications that are needed to reduce the open probability to a small value. Other characteristics of RET/W353Y channels were consistent with this hypothesis. The apparent expression of the mutant channels was poor; cGMP-dependent currents were small and were detected infrequently, and then only in the presence of low concentrations of cytoplasmic Ni2+. Since Ni2+ ions promote channel opening (Gordon and Zagotta 1995a) without affecting the conductance of open channels (Sunderman and Zagotta 1999), it is likely that the open probability of RET/W353Y channels is very low in the absence of Ni2+.
Due to the difficulty in obtaining cyclic nucleotide–dependent currents from RET/W353Y channels, we did not characterize this mutant further. Instead, we prepared the equivalent mutant in the OLF channel background, OLF/W332Y. Assuming that the energetic effect of the mutation is similar in the two backgrounds, we reasoned that the open probability in saturating cGMP may be much higher for OLF/W332Y compared with RET/W353Y channels because the allosteric opening transition is much more energetically favorable for wild-type OLF compared with wild-type RET channels (Goulding et al. 1994; Gordon and Zagotta 1995b; Gordon et al. 1997; Varnum and Zagotta 1997). Consistent with this prediction, large (many nanoampere) currents were detected in oocytes injected with cRNA coding for OLF/W332Y channels. OLF/W332Y channels activated by saturating (1 mM) cGMP were about six times more UV sensitive than the parent OLF channels (Fig. 10 A). The UV dose–response relation of OLF/W332Y channels was also 2.5× shallower than that of wild-type OLF channels. Similar results were obtained for a second OLF channel mutant in which histidine replaced tryptophan 332 (Fig. 10 B). These results are consistent with the hypothesis that replacing the conserved pore tryptophan residue with tyrosine or histidine lowers the channels' open probability. Two additional lines of evidence support this idea. First, the half-saturating cGMP concentration before UV was greater for OLF/W332Y channels (K1/2 = 17.7 μM) than for wild-type OLF channels (K1/2 = 2.5 μM, Fig. 10 C). In potassium channels, which have a similar pore sequence to CNG channels, the tryptophan residue equivalent to W332 is located near the extracellular side of the channel pore (Doyle et al. 1998). If W332 occupies a similar position in OLF channels, it is probably located far from the cytoplasmic COOH-terminal cyclic nucleotide–binding domain. Thus, it is more likely that the effect of the mutation is to disrupt the allosteric channel opening transition, rather than to alter the cGMP binding step. The ratio of the current amplitudes in saturating cAMP and saturating cGMP (Fig. 10 D) was also smaller for OLF/W332Y and OLF/W332H channels than for wild-type OLF channels, providing direct evidence that the pore mutations lowered the channels' open probability.
Since UV light may modify tyrosine residues in proteins (McLaren and Shugar 1964), it was possible that replacing tryptophan 332 with tyrosine in the OLF channel increased the UV sensitivity because tyrosine at position 332 is a “better” target than the original tryptophan. In this context, “better” means that the target is modified more readily and/or that its modification has a higher free energy cost. This hypothesis was easily tested: if photochemical modification of tyrosine 332 dominated the UV effect on OLF/W332Y channels, the wavelength dependence of the mutant channels' UV sensitivity should match the wavelength dependence of tyrosine absorption. The UV sensitivity of OLF/W332Y channels was measured at two wavelengths for which the relative absorption probabilities of tryptophan and tyrosine are very different. Increasing the excitation wavelength from 280 to 300 nm increased D1/2 by a large factor (Fig. 11 A). However, the slopes of the mutant channels' UV dose–response relations were the same at 280 and 300 nm, indicating that the UV wavelength affected the probability of target modification, but not the nature of the modification or the mechanism of the current reduction. This result is a necessary precondition for identifying the target residues from the wavelength dependence of the UV sensitivity.
The ratio of the UV sensitivities of OLF/W332Y channels at 280 and 300 nm (15.9 ± 6.3, Fig. 11 C) was similar to the corresponding ratio of 15.7 for tryptophan absorption in aqueous solution, but was much smaller than the ratio of 111 for tyrosine absorption at these wavelengths. This comparison indicates that the photochemical reaction(s) that reduces the current amplitude in the mutant channels is initiated by absorption in one or more of the remaining tryptophan residues, with little or no contribution from the newly introduced tyrosine residue at position 332. The wavelength dependence of the UV sensitivity of OLF/W332H channels was also consistent with tryptophan absorption (Fig. 11B and Fig. C).
Consistent with the lower agonist efficacy of cAMP (Fig. 10 D), OLF/W332Y channels were more sensitive to UV when activated by saturating cAMP than when activated by saturating cGMP (Fig. 12 A). Similar results were obtained for OLF/W332H channels activated by these two ligands (Fig. 12 B). Although the differences in D1/2 and slope for the channels activated by the two ligands were not large when averaged across all experiments, separate responses to cAMP and cGMP were recorded after each UV dose for most of the patches. The UV dose–response relations in cAMP were always left-shifted and shallower than the relations in cGMP.
Mechanism of Current Increase by UV
UV increased the current through CNG channels activated by low concentrations of cGMP (Fig. 1 B and 2 B). In the following sections, we consider the mechanism of this second effect of UV. We ask: (a) by what mechanism does UV increase the currents? and (b) why does UV increase the current at low concentrations of ligand but decrease the current at higher concentrations of ligand?
The magnitude of the current increase by UV depended on the cGMP concentration (Fig. 1 C and 2 C). This result is not expected if UV increased the conductance of a single open state of the channels or enhanced their cGMP binding affinity, since either effect should alter the current by a constant fraction at all ligand concentrations. However, RET channels have multiple open states with different unitary conductances, and the relative occupancy of these levels depends on the cyclic nucleotide concentration (Ildefonse and Bennett 1991; Taylor and Baylor 1995; Ruiz and Karpen 1997; Ruiz and Karpen 1999). Thus, we cannot rule out the possibility that UV alters the channels' ligand dose–response relation by exerting differential UV effects on the unitary conductances of the various open states. The latter hypothesis is difficult to test because UV-activated conductances in the oocyte membrane preclude analysis by single channel recording (Middendorf et al. 2000). Instead, we investigated the effect at the macroscopic level by asking whether the observed current increase is consistent with UV effects on the channels' open probability or their unitary conductance.
Since the opposing UV effects on channel current were observed in some cases within the same patch (Fig. 1 C and 2 C), it is likely that the channels contain at least two distinct types of target residues. If both UV effects are on the channels' open probability, then modification of the two types of targets must exert opposite effects on the channels' gating energetics. For simplicity, we identify the two types of targets by the symbols (+) and (−), which refer to the sign of the free energy change associated with their modification. As noted earlier, the positive free energy cost associated with modification of a (+) target, ΔΔG 0(1+), has the effect of decreasing Po (Fig. 4 A). The quantity ΔΔG 0(1−) is negative, consistent with the idea that modification of (−) targets stabilizes the channels' open state(s) relative to their closed state(s), and thereby increases Po (Fig. 13 A). For simplicity, it is assumed in Fig. 13 A that the entire effect of modifying the (−) targets is on the free energy of the channels' open state.
We used the energy additive model to test the idea that UV increased the currents by enhancing the channels' open probability. Theoretical UV dose–response relations were calculated for channels with different ΔG 0(0) values using with ΔΔG 0(1) < 0, and then compared with the observed relations for channels with a range of different, but very low, initial open probabilities.
Effect of Varying ΔG 0(0) on the Current Increase by UV: Simulations
The calculated UV dose–response relations were characterized by fitting with a modified version of the all-or-none model (Middendorf et al. 2000). The fits provided quantitative estimates for the curves' horizontal positions, maximal slopes, and maximum fractional current increases. The model assumes that each channel subunit contains n independent and identical (−) targets and no (+) targets, and that UV has no effect on the channel current until modification of a critical number of the targets (denoted n*) increases the current by a factor M. These ideas are described by the relation:
where the index k denotes the number of modified (−) targets. Because UV can increase Po to a value no greater than unity, the maximum fractional current increase is equal to 1/Po(0). ignores the effect of modifying the (+) targets, which will be incorporated at a later stage.
The UV dose–response relation for the modified all-or-none model is obtained by combining of this paper with Eq. 25 of the preceding paper (Middendorf et al. 2000), yielding:
As before (Fig. 4, B–D), the effect of varying ΔG 0(0) on the simulated UV dose–response relations depended on the relative magnitudes of the free energy parameters ΔΔG 0(1−) and ΔG 0(0). Three limiting cases were considered.
Case IV: in the limit that −ΔΔG 0(1−) is much larger than |ΔG 0(0)| (Fig. 13 B), reduces to:
where Po(0) denotes the channels' open probability before irradiation. In this limit, the fractional current increase after UV reached the maximum possible value of M = 1/Po(0), regardless of the number of UV targets in the channels. On the other hand, the positions of the relations on the abscissa and their slopes were not affected by varying ΔG0(0). These effects are consistent with the idea that modification of a single (−) target increases the channels' open probability to a value near unity if the free energy cost of target modification is both negative and much larger in absolute magnitude than ΔG0(0). Due to the reciprocal relation between M and Po(0), the maximum fractional current increase may be quite large for low values of Po(0) (note the logarithmic ordinate in Fig. 13 B), but is negligible for Po(0) ≈ 1.
Case V: if −ΔΔG 0(1−) was comparable to |ΔG 0(0)| (Fig. 13 C), the fractional current increase after UV again depended on ΔG 0(0). For n = 1, the magnitude of the current enhancement by UV increased as ΔG 0(0) was made more positive, but did not reach the maximum possible value of 1/Po(0). For ΔG 0(0) = +7.0 (corresponding to OLF channels in the absence of ligand), I(D)/I(0) reached only 5% of the maximum possible value, but, for ΔG 0(0) = +3.91 (corresponding to RET channels activated by saturating cAMP), the current increased to nearly half the maximum possible value. For a large number of targets, the fractional current increase did approach a value of 1/Po(0). The relations also shifted to the right along the abscissa and became steeper as Po(0) was decreased [i.e., as ΔG 0(0) was made more positive], but these effects were modest compared with those on the current amplitude.
Case VI: in the limit that −ΔΔG 0(1) was much smaller than |ΔG 0(0)| (Fig. 13 D), the simulated curves again shifted to the right along the abscissa and became steeper as ΔG 0(0) was increased. However, the current asymptotes in this limit were much smaller than 1/Po(0), regardless of the number of targets. This latter effect occurred when the total free energy change associated with modifying all of the target residues (equal to 4n · ΔΔG 0(1), was insufficient to offset a large, positive value of ΔG 0(0). In the limit that −4n · ΔΔG 0(1) << |ΔG 0(0)|, reduces to :
and the UV effect on the current amplitude disappears (Fig. 13 D, top). With these predictions in hand, we turn to experimental measurements of UV dose–response relations for two channel/ligand combinations with low open probabilities: (a) RET channels activated by saturating concentrations of the poor agonist cAMP, and (b) OLF channels in the absence of ligand.
Effect of Varying ΔG 0(0) on the Current Increase by UV: Experimental Results
The open probability of RET channels activated by saturating cAMP is only ∼1.5% (Goulding et al. 1994; Varnum and Zagotta 1996). UV increased the currents through RET channels activated by saturating (20 mM) cAMP approximately threefold (Fig. 14 A). Similar results (not shown) were obtained for channels activated by 5 mM cAMP. The same UV dose decreased the current elicited by saturating (1 mM) cGMP nearly fivefold for this same patch (Fig. 14 B). The UV dose–response relations for this patch are shown in Fig. 14C (cAMP) and D (cGMP). Note the 100-fold difference in vertical scales in Fig. 14C and Fig. D. The current increase in cAMP reached a maximum after a dose of 5 × 109 photons · μm−2. Fitting the UV dose–response relation in cAMP with the modified all-or-none model () yielded estimates of 7.7 × 109 photons · μm−2 for D1/2, 0.85 for the slope factor, and 5.7 for the maximum fractional current increase. The value of M was only about one fifth of the maximum possible value [1/Po(0) = 27]. The D1/2 and slope factors for the UV dose–response relation in saturating cGMP were similar to those obtained for other RET channel patches (Table). The opposing effects of UV on RET channel currents activated by saturating concentrations of the two ligands suggest that the channels' initial open probability, rather than the absolute number of bound ligands, determined the sign of the change in current amplitude after irradiation.
We also measured the effect of UV on the spontaneous currents through OLF channels. CNG channels can open in the absence of ligand, although their open probability under these conditions is extremely low (Picones and Korenbrot 1995; Ruiz and Karpen 1997; Tibbs et al. 1997). We used the channels' sensitivity to block by internal divalent ions (Haynes et al. 1986; Stern et al. 1987; Colamartino et al. 1991; Zimmerman and Baylor 1992) to isolate the currents through unliganded CNG channels. Spontaneous OLF channel currents were obtained as the difference between the patch currents in a control solution lacking cGMP and in an otherwise identical solution containing 10 mM Mg2+. This leak subtraction protocol allowed us to measure the currents through unliganded OLF channels without interference from other sources such as the UV-activated conductance (Middendorf et al. 2000). At this concentration, Mg2+ completely blocked the current through OLF channels, but reduced the UV-activated conductance by only ∼15%, and had no detectable effect on the leakage conductance of the seal (data not shown).
Exposure to 9.49 × 109 photons · μm−2 increased the spontaneous currents through OLF channels in one patch by a factor of ∼30 (Fig. 15 A), but decreased the same patch's current at saturating cGMP by 30% (B). UV dose–response relations from similar experiments on five patches are displayed in Fig. 15 C. To facilitate comparison between results from different patches, the spontaneous currents are expressed as a fraction of the patch's current in saturating cGMP before irradiation. On average, a UV dose of 2 × 1010 photons · μm−2 increased the spontaneous current by a factor of 28.9 ± 12.1 (mean ± SEM). The same UV dose typically reduced the current in saturating cGMP by ∼50% (Table). Fitting the combined results in Fig. 15 C with yielded estimates of 2.4 × 1010 photons · μm−2 for D1/2 and 1.29 for the slope factor. The current asymptote estimated from the fit was M = 67, which is only 6% of the maximum possible value [1/Po(0) = 1,087].
The currents activated by saturating cGMP before UV and the spontaneous currents after UV were blocked by similar concentrations of internal Mg2+ ions (Fig. 15 D), providing further verification that the increased currents after irradiation were through unliganded CNG channels.
yielded inhibition constants (Ki) of 201 ± 23 μM for the spontaneous currents after UV and 350 ± 43 μM for the cGMP-activated currents before UV. The small difference in the Ki values may reflect a weak state dependence to the block, or may indicate that the binding site for internal Mg2+ is affected slightly by UV modification of the channels. The latter possibility could be tested by measuring the affinity for Mg2+ block of cGMP-activated currents after irradiation.
In summary, UV increased the currents through four channel/ligand pairs with low initial Po values: RET and OLF channels activated by low concentrations of cGMP (Fig. 1 and Fig. 2, respectively), RET channels activated by saturating cAMP (Fig. 14), and OLF channels in the absence of ligand (Fig. 15). For the first three of these pairs, the channels' average initial open probability was on the order of 1%, and UV increased the current in each case by about a factor of 5. The open probability of unliganded OLF channels is ∼10-fold lower (∼0.1%, see Table), and the fractional increase in current after a saturating UV dose was ∼10-fold higher (∼70). For each of the four channel/ligand combinations, the fractional current increase after a saturating UV dose correlated inversely with the channels' initial open probability, as predicted by the energy additive model, but was significantly less than the maximum possible value of M = 1/Po(0) (Fig. 13C and Fig. D). The UV dose–response relation for unliganded OLF channels was shifted to the right on the abscissa and was steeper than that for RET channels activated by saturating cAMP. The observed changes in the curves' horizontal positions, slopes, and limiting current asymptotes as ΔG 0(0) was varied are most consistent with the simulations for Case V of the energy additive model, with n = 1 (Fig. 13 C) and Case VI, with n = 10 (D). We conclude that (a) UV increased the currents through RET and OLF channels by increasing Po, and (b) the free energy change associated with modification of (−) targets is comparable in magnitude with |ΔG 0(0)| if the channels contain only a few (−) targets, but ΔΔG 0(1−) may be significantly smaller than |ΔG 0(0)| if the number of (−) targets is closer to 10 per subunit. The results are clearly inconsistent with −ΔΔG 0(1) being much larger than |ΔG 0(0)|, regardless of the number of targets.
Modeling the Two Opposing Effects of UV
The net effect of UV light on CNG channel currents depended on the channels' initial open probability. UV always decreased the current when the channels' initial open probability was high (Fig. 1 A, 2 A, 3, 5–7, 10, and 12), and always increased the current when Po(0) was very low (Fig. 1 B, 2 B, 14, and 15). Why does the sign of the change in current after UV vary if all of the channels contain both (+) and (−) targets that are modified randomly by UV? In some cases, the current amplitude in a given patch changed in opposite directions depending on the “readout” conditions employed (compare Fig. 1, Fig. 2, Fig. 14, and Fig. 15). The opposing changes in current occurred after exposure to similar UV doses, arguing against a large difference in the quantum yields for modifying the (+) and (−) targets. The results are not explained by a difference in the state dependence of these quantum yields either, since the channels were always irradiated in the absence of ligand.
To understand this complex behavior, it was necessary to consider the combined effects of modifying both types of targets in the same channels. To this end, we expanded the energy additive model () to include (+) and (−) targets. For simplicity, the two types of targets were assumed to be independent, so that the free energy changes associated with their modification were additive. The UV dose–response relation for the expanded energy additive model is given by:
Fig. 16 shows simultaneous fits of the expanded energy additive model to the results from Fig. 5,Fig. 6,Fig. 7, Fig. 14, and Fig. 15. The quality of the fits is gratifying, given the relative simplicity of the model. Though not correct in all details, the fits reproduce the main features of the experimental results, including the sign of the changes in current amplitude after irradiation, and the approximate relative slopes, horizontal positions, and current asymptotes of the UV dose–response relations for all conditions studied. The model even duplicated the opposite changes in current amplitude that occurred in some cases after the same UV dose when the channels were activated under different conditions (Fig. 16 B). The fitting procedure made the interesting prediction that the UV dose–response relation of RET channels in saturating cAMP is actually biphasic. The current was predicted to reach a maximum after exposure to ∼8 × 109 photons · μm−2, and then to decrease after additional UV (Fig. 16 B). It will be interesting to test this prediction experimentally.
The estimated values of ΔΔG 0 for the (+) targets followed the same trends as those obtained from the fits using (Fig. 9): ΔΔG 0(1+) was about twice as large for RET channels as for OLF channels activated by the same ligand, and was somewhat larger for a given channel activated by cGMP than by cAMP. The magnitude of ΔΔG 0(1+) for each channel/ligand combination was somewhat larger than that estimated using the simpler version of the model (), presumably because modification of the (−) targets partially offsets the free energy deficit caused by modification of the (+) targets. The estimated values of ΔΔG 0(1−) were similar for all channel/ligand combinations studied.
The estimates for ΔΔG 0 and φ were not unique, since they depended on the (unknown) number of (+) and (−) targets in the channels. We assumed (arbitrarily) that RET and OLF channels contain three (+) targets and two (−) targets per subunit. Increasing the number of either type of target had the effect of decreasing the corresponding quantum yield, similar to the effects observed earlier (Fig. 9 D). The values of the fitting parameters are given in the legend to Fig. 16.
The fits in Fig. 16 provide a possible explanation for why UV decreased the current under some activation conditions but increased the current under other conditions. First, consider the effect of UV on channels with a high initial open probability. Modification of the channels' (−) targets may increase the current through such channels by at most a factor of 1/Po(0) (see above), which is a small factor for Po(0) ≈ 1. On the other hand, modification of the channels' (+) targets may reduce the current to a small fraction of its initial value, and therefore dominates the UV effect on the patch current. The situation is very different if the channels' initial open probability is very low. In this case, modification of the channels' (−) targets may increase the current amplitude by a very large factor, since 1/Po(0) represents a 100–1,000-fold enhancement for some of the experimental conditions employed (Table). The current through the channel subpopulations that contain many modified (−) targets, but few modified (+) targets therefore dominates the UV effect, leading to the observed increase in macroscopic current.
The simulations in Fig. 16 confirm these ideas quantitatively. For example, only ∼15% of the RET channels are estimated to carry over 85% of the current activated by saturating cAMP after a dose of 100 × 108 photons · μm−2 (Fig. 16 B). This dominant component of the current was carried by channels with two to six modified (−) targets, but no modified (+) targets. On average, UV increased the current through this subpopulation of channels by a factor of 25. For this same channel/ligand combination in the presence Ni2+, Po(0) is much higher (≈0.8), and the effect of modifying the (−) targets is small [1/Po(0) = 1.25]. Therefore, modification of the (+) targets dominates under these conditions, and UV decreases the macroscopic currents.
Modeling the UV Effect on the Ligand Dose–Response Relation
As shown in Fig. 16, the expanded energy additive model accounted successfully for the disparate effects of UV on the currents through unliganded and fully liganded CNG channels. However, modeling the UV effect on channel currents over the full range of cGMP concentrations tested (Fig. 1 C and 2 C) required a general theory relating channel open probability to ligand concentration and UV dose. This general theory was obtained by combining various models for CNG channel activation gating with the expanded energy additive model ().
We only considered activation models that include unliganded openings, a well-documented phenomenon (Kramer et al. 1994; Picones and Korenbrot 1995; Ruiz and Karpen 1997; Tibbs et al. 1997). Cyclic allosteric models incorporate this feature, yet are conceptually simple and are consistent with many other features of CNG channel gating (Goulding et al. 1994; Varnum and Zagotta 1996; Liu et al. 1998). Although these models do not account for the multiple subconductance states observed in single RET channel patches (Ruiz and Karpen 1997, Ruiz and Karpen 1999), they are consistent with the ligand dose–response relations of single OLF channels (Liu et al. 1998) and the macroscopic behavior of RET channels (Goulding et al. 1994; Varnum and Zagotta 1996).
Cyclic allosteric gating models are built upon three basic assumptions. First, it is assumed that the channels contain “gating units” that interconvert between two conformations in a single, concerted step. We use the generic term “gating units” here because the subunit composition of a gating unit differs for different cyclic allosteric models. The two possible conformations of the gating units are denoted as T (“tense”) and R (“relaxed”), in reference to the conformations of the hemoglobin molecule (Monod et al. 1965). For ion channels, the T and R states correspond to resting and activated conformations of the gating units, respectively. Since CNG channels are tetramers (Liu et al. 1996; Morrill and MacKinnon 1999), symmetry considerations suggest that each gating unit contains either one, two, or four channel subunits. We consider the simplest cyclic allosteric model for each of these possibilities. The Hodgkin-Huxley model (HH model) (Hodgkin and Huxley 1952) assumes that the channels contain four independent gating units, each composed of a single channel subunit (Fig. 17 A). The coupled dimer model (CD model) (Liu et al. 1998) assumes that the channels contain two independent gating units, each consisting of two channel subunits (Fig. 17 B). Finally, the Monod-Wyman-Changeux model (MWC model) (Monod et al. 1965) assumes that the entire channel is a single gating unit composed of four subunits (Fig. 17 C). The second assumption of the cyclic allosteric models is that the gating units interconvert between the T and R conformations in the presence or absence of ligand. Finally, the activating ligand may bind to the T and R conformations of a gating unit with different affinities (denoted KT and KR, respectively). Let L denote the equilibrium constant relating the two conformations of an unliganded gating unit: L = [T]/[R]. Thermodynamic coupling between the different liganded states of each gating unit changes the equilibrium constant for a gating unit that contains m bound ligands to c m · L, where c = KR/K T.
The derives general relations for the combined dependence of CNG channel open probability on UV dose and ligand concentration for three models that combine the HH, CD, or MWC schemes with the expanded energy additive model (). In these hybrid models, UV alters Po by changing the values of the gating parameters c, L, and KR. The UV dose dependences of these parameters are quantified by replacing the phenomenological (+) and (−) targets of the expanded energy additive model with c, L, and KR targets, and associating a quantum yield and a free energy cost with their modification (see Eqs. A3–A5).
Since UV increased the current through unliganded OLF channels (Fig. 15), the free energy cost for modifying an L target must be negative (see ). This finding, coupled with the observation that UV decreased the current through OLF channels in saturating cGMP, implies that the free energy cost for modifying a c target is positive (see ). In other words, UV modification of L targets enhances spontaneous channel opening, while modification of c targets disrupts the coupling between ligand binding and channel opening.
The ligand dose–response relations of RET channels before and after UV were fit using each of the three hybrid UV-cyclic allosteric models (Fig. 17, D–F). The initial value of L for each cyclic allosteric model was estimated from the channels' spontaneous open probability, Psp, using the relation:
In , the parameter a denotes the number of gating units in a channel. The initial value of the gating parameter c for each model was computed from Psp and the open probability in saturating cGMP, Pmax (see Table), using the relation:
and were obtained by considering the limiting behavior of and (see ), and making the simplifying assumption that the channels are open only when all of their gating units are in the activated conformation. The initial value of KR for each model was determined by fitting the cGMP dose–response relation before UV, using and and the initial values of c and L determined from and .
The post-UV ligand dose–response relations were fit simultaneously using and , with the quantum yields and free energy costs of the L and c targets as the only adjustable parameters. The results of Middendorf et al. 2000 did not provide a specific estimate for the number of targets in the channels, but did suggest that the number is small. We assumed (arbitrarily) that the channels contain three c targets and two L targets. The cGMP dose–response relations of OLF channels before and after UV were analyzed by the same procedure.
Fig. 17D–I, shows the fits of the hybrid UV-cyclic allosteric models to the ligand dose–response relations of RET and OLF channels before and after UV. The simulated curves for all three models reproduced the general features of the results, including the magnitude of the current reduction in saturating cGMP, the magnitude of the current increase at very low cGMP concentration, and the shallower slopes of the relations after UV. Due to the complexity of the computations, we did not systematically explore the effects of varying the number of c and L targets. However, since the results could be fit using other target numbers (not shown), the UV parameters obtained from the fits are not unique. The results were fit equally well by the UV-MWC and UV-CD hybrid models, but less well by the UV-HH model. Other simulations (not shown) indicate that a “best” model might be identified from the three hybrid models if independent estimates were available for the number or quantum yields of the UV targets. The values of the fitting parameters are given in the legend to Fig. 17.
Mechanism of Current Alteration by UV
UV light had variable effects on the currents through CNG channels. The channels' initial open probability determined the sign of the change in current after irradiation. UV decreased the current through channels with high initial open probabilities [Po(0) > 0.3; Fig. 1 A, 2 A, 3, 5–7, 10, and 12], but had the opposite effect on channels with low initial open probability values [Po(0) < 0.02; Fig. 1 B, 2 B, 14, and 15]. These effects of UV could not be attributed to variability in the measurements, as the dose dependence of channel current was highly reproducible for each set of experimental conditions (see, for example, Fig. 5). Furthermore, the opposite effects of UV on channel current were observed in many cases within the same patch (Fig. 1, Fig. 2, Fig. 14, and Fig. 15).
The expanded energy additive model () accounted successfully for the UV effects on the channel currents for all conditions studied (Fig. 16). This model assumes that the channels contain two distinct types of target residues whose modification exerts opposite and additive effects on the free energy difference between the channels' open and closed states. The next two sections discuss how the presence of the two types of UV targets complicates both the interpretation of the channels' action spectrum (Middendorf et al. 2000) and the identification of the target residues within the channel sequence.
Interpretation of Action Spectrum in Saturating cGMP
The wavelength dependence of the UV sensitivity (the action spectrum) of RET channels activated by saturating cGMP was very similar to the absorption spectrum of tryptophan (Middendorf et al. 2000). Since the initial open probability of RET channels in saturating cGMP is close to one (Table), and the modification of the (+) targets dominates the UV effect under these conditions (see above), the form of the action spectrum strongly suggests that the (+) targets are tryptophans. It is more difficult to identify the (−) targets from the action spectrum because they make a small contribution to the UV dose–response relation when Po(0) is close to one (see above). We estimated the relative contributions of the (+) and (−) targets to the UV dose–response relation by calculating the relations with and without (−) targets, using the parameters from the fits in Fig. 16 A. Including the (−) targets in the calculation increased the half-saturating UV dose by only 9%. We then computed the action spectrum that is expected if the (−) targets were tyrosine residues by adding normalized tryptophan and tyrosine absorption spectra together in a 10:1 ratio. The calculated action spectrum was not sufficiently different from the absorption spectrum of tryptophan alone to allow identification of the (−) targets by this method. A more sensitive method for identifying the (−) targets may be to measure the action spectrum of channels with low initial open probabilities, since modification of the (−) targets dominates the UV effect under those conditions (see above).
Identification and Characterization of Target Residues
As described in the preceding paper (Middendorf et al. 2000), one approach to locating the UV targets in the channels is to identify tryptophan residues that alter the channels' UV sensitivity when replaced by other amino acids. This approach assumes that mutating a residue in the channel will alter the channels' UV sensitivity if the residue is a UV target, but have no effect on the UV sensitivity if it is not a UV target. The results in the present paper indicate that mutations may also change the channels' UV sensitivity indirectly by altering their initial open probability (see Fig. 10). The indirect effect may occur even if the replaced tryptophan is not a UV target. The converse is also possible: mutations that replace target tryptophans with other residues may have little or no effect on the channels' UV sensitivity. For example, mutating a (+) target tryptophan to another amino acid will tend to reduce the channels' UV sensitivity by lowering the net absorption cross section of the (+) targets. However, this contribution to the UV sensitivity may be offset if the mutation lowers Po(0), since the latter effect would tend to increase the channels' UV sensitivity. These arguments indicate that replacing a tryptophan residue by a different amino acid may either increase, decrease, or have no affect on the channels' UV sensitivity, whether the tryptophan is a target residue or not! Clearly, it is incorrect to identify specific tryptophans in the channel sequence as targets based solely on changes in the UV sensitivities of mutant channels. Rather, it is important to have a detailed physical model for interpreting UV sensitivity results.
Given the many complicated effects possible in a UV modification experiment, and the difficulty of determining a complete model for the UV effect, could other methods be used to identify the UV targets in CNG channels? An approach that eliminates some of the complications outlined above is to examine the UV sensitivity of CNG channels containing only a single tryptophan residue per subunit. The remaining tryptophan in such a mutant could be identified as a UV target with confidence if the channel was sensitive to UV and its action spectrum had the form of a tryptophan absorption spectrum. The sign of the change in current after irradiation would allow further classification of the tryptophan as a (+) or (−) target. A significant potential problem with this approach is the difficulty of expressing channels with multiple tryptophan replacements. We failed to obtain cGMP-dependent currents from many RET channel mutants that replaced more than one of the channels' 10 native tryptophans with other amino acids (Middendorf et al. 2000). However, the apparent lack of expression was likely due in many cases to a very low open probability of the mutant channels. As we demonstrated for the pore tryptophan mutants (Fig. 10), tryptophan replacements may be tolerated better in the OLF channel due to its more favorable activation properties.
Energetic Contribution of the Pore Tryptophan Residue to Channel Gating and Its Relation to Channel Structure
We found that replacing the pore tryptophan residue by other aromatic amino acids reduced the open probability of OLF channels (Fig. 10) and RET channels (Middendorf et al. 2000) significantly. Using and and the results in Fig. 10 D, we estimated the quantitative effect of the pore mutations on the channels' gating energetics. Assuming that the difference between ΔG 0 for the allosteric opening transition in saturating cGMP and cAMP is the same for wild-type OLF and OLF/W332 mutant channels, we estimate that replacing tryptophan 332 by tyrosine (histidine) changed the free energy difference for the allosteric opening transition by approximately +5.4 RT (+4.8 RT). These energetic changes are similar to the difference in the free energy of the allosteric opening transition for OLF channels activated by saturating cAMP compared with saturating cGMP (approximately +5.3 RT, see Table), and to the energetic effect of cytoplasmic Ni2+ ions on the gating of RET channels in saturating ligand (approximately −5 RT; Gordon and Zagotta 1995a).
The pore tryptophan residue is conserved in all known CNG channels, as well as the related voltage-gated potassium channels (Jan and Jan 1990) and a proton-gated channel, KcsA, from the bacterium Streptomyces lividans. KcsA channels contain two hydrophobic transmembrane regions and an intervening pore sequence that likely corresponds to the S5, pore, and S6 regions of CNG and voltage-gated channels. Recent structural results on KcsA (Doyle et al. 1998; Perozo et al. 1998, Perozo et al. 1999) provide a framework for interpreting our results for the pore tryptophan mutants in CNG channels. The conserved tryptophan residue in KcsA channels is located near the COOH-terminal end of the pore helix, a region of the channel that moves during channel opening (Perozo et al. 1999). This residue and the preceding tryptophan residue (which is a tyrosine in CNG channels) form a collar of aromatic amino acids positioned around the channels' selectivity filter (Doyle et al. 1998). The tryptophans in the collar interact with a tyrosine in the selectivity filter via hydrogen bonds, suggesting that the tryptophans may influence its structure. If the structure of KcsA and CNG channels are similar, it is not surprising that altering the sidechain of the pore tryptophan has such a drastic effect on the open probability of CNG channels. Mutation of other residues in the channel pore has also been shown to affect activation gating (Bucossi et al. 1997; Fodor et al. 1997a,Fodor et al. 1997b). Our results are consistent with the idea that the pore tryptophans may influence gating by interacting directly with the channel's selectivity filter. It is worth noting that the tyrosine residue in the selectivity filter of KcsA and voltage-gated channels is missing in CNG channels.
UV Sensitivity of Pore Tryptophan Mutants
An alternative explanation for the increased UV sensitivity of OLF/W332Y and OLF/W332H channels (Fig. 10A and Fig. B) is that the pore tryptophan residues are (−) targets. Photochemical modification of W332 would favor channel opening and therefore antagonize the current reduction due to modification of the channels' (+) targets. Replacing the pore tryptophan with a different amino acid would remove this “protective” effect, making the channels more sensitive to UV. We do not favor this idea. It seems unlikely that tryptophan 332 is a (−) target since replacing this residue by similar amino acids such as tyrosine or histidine reduced the channels' open probability (Fig. 10C and Fig. D). As discussed earlier, we favor instead the idea that the pore mutation increased the UV sensitivity of OLF/W332Y and OLF/W332H channels by reducing the channels' initial open probability (Fig. 4). Because conservative mutations of the pore tryptophans reduced the channels' open probability (Fig. 10C and Fig. D), photochemical modification of those residues will likely reduce Po as well, suggesting that they may actually be (+) targets.
Channel Destruction by UV
Modeling of the UV dose–response relations (Fig. 16) suggests that the free energetic cost of modifying UV targets in CNG channels is comparable in magnitude to the initial free energy difference between the channels' open and closed states. It is possible that some photochemical modifications may exert more drastic effects on the channels, which we will call channel destruction. In those instances, the free energy cost of target modification is much larger than ΔG 0(0), and a single target modification completely eliminates the channel current. This mechanism of channel destruction by UV is formally equivalent to the all-or-none model described in the preceding paper (Middendorf et al. 2000).
We estimated the maximum possible contribution of channel destruction to the UV effect on CNG channels by comparing the UV dose–response relations of OLF/W332Y and OLF/W332H channels to that of wild-type OLF channels. Since wild-type channels contain one more tryptophan per subunit than the pore mutant channels, the amount of UV-induced destruction of OLF channels represents an upper limit to the amount that may occur in OLF/W332Y and OLF/W332H channels. Furthermore, since ΔG 0(0) is more negative for the wild-type compared with the mutant channels, a modification that destroyed an OLF channel would necessarily be sufficient to destroy one of the pore mutant channels. A UV dose containing 8.50 × 109 photons · μm−2 reduced the current through OLF channels by only ∼10%, but reduced the current through the pore mutant channels by 85–90% (Fig. 10A and Fig. B). This comparison suggests that channel destruction accounts for no more than ∼10–20% of the current reduction by UV.
Expected Heterogeneity of Single Channel Records after Irradiation
The idea that UV alters the open probabilities of CNG channels by modifying two distinct types of target residues leads to a number of testable predictions regarding the effect of UV on the currents through single CNG channels. Since UV modification of the targets occurs randomly, the minimal UV dose required to alter the channels' open probability is expected to vary from patch to patch, even for channels containing a single UV target. Analysis of such records for a large number of patches may provide a direct estimate of the targets' photochemical quantum yields.
The expanded energy additive model () predicts that modification of an individual (+) or (−) UV target in a channel should cause a discrete “jump” in the channel's open probability to a lower or higher value, respectively. The magnitude of the changes in open probability associated with such jumps may provide estimates for the free energy cost of modifying each type of target.
The UV-activated conductances present in oocyte membranes (Middendorf et al. 2000) currently prevent us from measuring UV effects at the single channel level. This problem may be circumvented by identifying compounds that block the UV-activated conductances, or by using an expression system where they are not present.
Using UV Modification to Measure Extremes in Channel Energetics
This section describes how UV modification may be used to measure free energy changes in regimes that were previously inaccessible to accurate measurement. For a channel with a single open and a single closed state, the open probability depends on the standard free energy difference between those states as:
where ΔG0(0) is expressed in RT units. indicates that small uncertainties in open probability correspond to huge uncertainties in the associated free energy difference when Po is near unity (Fig. 18 A). Thus, it is difficult in many cases to quantify even large energetic effects on channel gating equilibria because the effect on Po, the observable quantity in most experiments, is negligible (see Colquhoun 1998).
Fig. 18 B shows the UV dose–response relation for wild-type OLF channels in saturating cGMP, along with the fit to these results (1) from Fig. 16. The initial free energy difference, ΔG 0(0), is −9.9 RT for this channel/ligand pair, which corresponds to an open probability close to unity [Po(0) = 0.99995, Table]. Fig. 18 B, 2–4, are calculated for hypothetical channels with even larger ΔG 0(0) values, but the same UV parameters as used for 1. For example, 2–4 might correspond to UV dose–response relations for channels containing mutations that enhance channel opening relative to OLF/cGMP. The hypothetical channels' open probabilities are so close to unity that the energetic effects of the mutations could not be measured by existing methods, such as single channel recording or noise analysis. The simulations indicate that the differences in ΔG 0(0) for the hypothetical channels would be detected easily by the UV modification method, however.
UV modification may also be useful for investigating channels with very low open probabilities. For example, the activation mechanism of unliganded CNG channels is quite difficult to study because the spontaneous currents are very small (Taylor and Baylor 1995; Ruiz and Karpen 1997; Tibbs et al. 1997). Mutant channels that lack (+) targets may provide an ideal system for studying this process. Simulations using predict that UV should increase the spontaneous open probabilities for such mutants into a range where the unliganded openings are easily measured.
Using UV Modification to Test Models for CNG Channel Activation
Studies of channel activation may benefit from the use of multiple methods for simultaneously perturbing gating. For example, quantitative measurements of the combined effects of intracellular Ca2+ and membrane voltage on the gating of Ca-activated K (mSlo) channels provided significant constraints on activation models for those channels (Cox et al. 1997; Cui et al. 1997; Horrigan and Aldrich 1999; Horrigan et al. 1999; Rothberg and Magleby 1999). The UV dose dependence of currents reported here may be useful for investigating the activation mechanism of CNG channels. Like membrane voltage in the example above, UV dose provides a second “axis” for perturbing channel gating that is distinct from changing the ligand concentration. Further characterization of the UV effect will be necessary to understand the combined energetic effects of ligand binding and target modification on channel gating. Since UV modification breaks the symmetry of the channels (see ), it may be particularly useful for studying cooperative effects in channel gating.
Relationship to Other Spectroscopic Experiments
Spectroscopic approaches have provided new insights into the mechanism of ion channel gating. Voltage-dependent changes in the emission from channels labeled with fluorescent dyes measure the structural changes associated with gating charge movement and channel opening directly (Mannuzzu et al. 1996; Cha and Bezanilla 1997; Cha et al. 1999; Glauner et al. 1999). A distinct drawback of this technique is the large size of the fluorescent probe and its maleimide linker, which may alter channel gating and provide a rather poor spatial resolution. Measurements of the emission from the channels' intrinsic tryptophan fluorophores may be useful because they circumvent these limitations. Furthermore, the results in this paper and the preceding paper (Middendorf et al. 2000) indicate that some of the tryptophans in CNG channels are likely located in or near the channels' gating machinery, and thus may report on gating conformational changes.
The relatively high photobleaching quantum yields of protein tryptophans (φ ≈ 10−1–10−3) compared with fluorescent dyes (φ ≈ 10−4–10−6) poses two problems for channel fluorescence measurements. First, very low light levels and large numbers of channels may be required to prevent significant reduction in the fluorescence signals during the course of an experiment. In addition, we have shown here that photochemical modification of tryptophan residues perturbs channel activation. Thus, it will be very important to ensure that the signals in channel fluorescence experiments originate from channels with unmodified UV targets.
Such experiments may also be useful as a direct method for determining the photochemical quantum yield of the UV targets in CNG channels. Direct measurements of the quantum yields will be useful because they reduce the number of variable parameters needed to fit the UV dose–response relations and may provide additional constraints for testing and refining channel activation models (Fig. 17).
The authors thank Denis Baylor and Dan Cox for helpful discussions, Denis Baylor and Laura Mazzola for critical reading of the manuscript, and Robert Schneeveis for excellent technical assistance.
This work was supported by grants from the National Institutes of Health (NS23294), the National Eye Institute (EY01543), and the McKnight Foundation. R.W. Aldrich is an investigator with the Howard Hughes Medical Institute.
This section develops a general theory for the combined dependence of CNG channel open probability on ligand concentration and UV dose. The theory is used in results to analyze the effect of UV light on the cGMP dose–response relations of RET and OLF channels (17).
The general theory uses the cyclic allosteric models described above to characterize CNG channel gating in the absence of UV. The fundamental mechanistic similarity of the HH, CD, and MWC models allows the dependence of channel open probability on ligand concentration for all of these models to be expressed by the single equation:
In , the first term in parentheses is the appropriate binomial coefficient and [A] is the ligand concentration. Factor a is the number of gating units in the channel, which is equal to 4 for the HH model, 2 for the CD model, and 1 for the MWC model. b is the minimum number of gating units that must activate to open the channel, and may assume values of 1, 2, 3, or 4 for the HH model, 1 or 2 for the CD model, and 1 for the MWC model. PR([A]) is the probability that a channel gating unit is in the activated (R) conformation, and is given by:
where α is equal to [A]/KR.
We combined the expanded energy additive model () and the cyclic allosteric models by replacing the phenomenological (+) and (−) targets in with KR, c, and L targets. By analogy with , UV modification of these targets alters the gating parameters KR, c, and L according to the relations:
where kK, kc, and kL refer to the number of modified targets of each type, and ΔΔG0(1K), ΔΔG0(1c), and ΔΔG0(1L) denote the corresponding free energy costs (in RT units) of modifying one target of that type. (Note: the minus sign in the argument of the exponential term in is missing in Eqs. A3–A5 because the convention used in defining KR, c, and L is opposite that used in .)
assumes that all of a channels' gating units are identical before irradiation. UV modification of the L, c, and KR targets in different subunits breaks this functional symmetry. A more general form of that accounts for the symmetry breaking induced by UV is:
where the index i counts over the gating units of the channel and j counts over the subunit components of the gating units. For example, i = 1 and 1 ≤ j ≤ 4 for the MWC model, while 1 ≤ i ≤ 2 and 1 ≤ j ≤ 2 for the CD model. Assuming that the UV targets are modified independently, may be combined with Eqs. A3–A5 to yield the following expression for PR as a function of ligand concentration and UV dose:
In , kKij, kcij, and kLirefer to the number of modified KR, c, and L targets in the subunit identified by the indices i and j, ncand nL are the number of c and L targets per subunit, respectively, and the f (kcij, D), and f(kLi, D) factors are analogous to f(k, D) in . was simplified by assuming that the entire effect of UV on the activation parameter c (= KR/KT) is due to an effect on KR; thus, ΔΔG0(1K) = ΔΔG0(1c).
What is the correspondence between the molecular free energy parameters ΔΔG0(1c) and ΔΔG0(1L) in the cyclic allosteric models and the phenomenological free energy parameters ΔΔG0(1+) and ΔΔG0(1−) in the expanded energy additive model ()? It is useful to consider the channels' gating behavior in two limits. In the absence of ligand, simplifies to:
Factors related to KR and c do not appear in because the spontaneous open probability depends only on L for the cyclic allosteric models. Since UV increased the spontaneous currents through OLF channels (15), ΔΔG0(1L) is negative. For a saturating concentration of ligand, reduces to:
indicating that the current after irradiation depends on both c and L. Since ΔΔG0(1L) is negative and UV decreased the current through OLF channels activated by 1 mM cGMP, ΔΔG0(1c) must be positive.
Abbreviations used in this paper: CD model, coupled dimer model; CNG, cyclic nucleotide-gated; HH model, Hodgkin-Huxley model; MWC model, Monod-Wyman-Changeux model; OLF channel, rat olfactory CNG channel; RET channel, bovine retinal CNG channel.