Correspondence to: Richard W. Aldrich, Department of Molecular and Cellular Physiology, Howard Hughes Medical Institute, Stanford University, Stanford, CA 94305. Fax:650-725-4463 E-mail:raldrich{at}leland.stanford.edu.
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Abstract |
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Middendorf et al. (Middendorf, T.R., R.W. Aldrich, and D.A. Baylor. 2000. J. Gen. Physiol. 116:227252) showed that ultraviolet light decreases the current through cloned cyclic nucleotidegated 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.
Key Words: cyclic guanine monophosphate, electrophysiology, ligand-gated channel, ion channel gating, ultraviolet light
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INTRODUCTION |
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Cyclic nucleotide-gated (CNG)1 ion channels are activated cooperatively by the binding of multiple cyclic nucleotide ligands to a cytoplasmic COOH-terminal domain of the protein (
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 doseresponse 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 (
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 (
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 (
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MATERIALS AND METHODS |
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Channel expression, electrical recordings, solutions, and UV irradiation apparatus were described in the preceding paper (
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RESULTS |
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Effect of UV on Ligand DoseResponse Relation
As shown previously (
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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 (
Fig 1 C displays the combined results for the patch in A and B as a series of pre- and post-UV ligand doseresponse 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 4.7x 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:
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(1) |
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 (
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We also investigated the effect of UV on currents through a second type of CNG channel from rat olfactory epithelium (denoted OLF) (
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 doseresponse 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 (5.6x 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 x 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 (
What parameters of channel activation are changed by UV? The current through a membrane patch containing N channels is given by Equation 2:
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(2) |
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 (
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 doseresponse 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 continuous curves in Fig 3 A are fits to the UV doseresponse relations using the all-or-none model of the preceding paper (
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(3) |
The parameter in Equation 3 is the absorption cross section of a UV target, and
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 doseresponse 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 1.
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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 (
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 (
Energy Additive Model
Of the various physical models considered in the preceding paper (
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:
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(4) |
Here, G 0(0) is the standard free energy difference between channel states before irradiation, and
G 0(1) is the free energy "cost" of modifying a single target residue. Equation 4 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
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(5) |
Since irradiation decreases Po, modification of the UV targets favors channel closing (i.e., G 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 2). 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.
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The current varies with dose according to Eq. 40 of
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(6) |
where f(k, D) denotes the fraction of channels containing k modified target residues after a UV dose D:
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(7) |
The first term in brackets in Equation 7 is the appropriate binomial coefficient, is the absorption cross section of a target residue, and
is its photochemical quantum yield.
The UV doseresponse relation (Equation 6) depends on five parameters: (a) the absorption cross-section of the target residues, ; (b) the photochemical quantum yield of the targets,
; (c) the number of target residues per channel subunit, n; (d) the free energy difference between the channels' open and closed states before irradiation,
G 0(0); and (e) the free energy cost of modifying a single target residue,
G 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 (
= 2.17 x 10-17 cm2 (
0.2 (
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 (
n
10. (d) The open probability of RET channels in saturating cGMP is ~0.95 (see Table 2), corresponding to
G 0(0) = -3.0 RT (see Equation 4 and Equation 5). For OLF channels,
G 0(0) = -9.9 RT. (e) As noted above, the observed decrease in Po after irradiation implies that
G 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 Equation 6:
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(8) |
Solving Equation 8 for G 0(1) yields:
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(9) |
Using the estimate M 0.05 (
G 0(0) (
G 0(1)
+0.15 RT for RET channels and
G 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; G 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 doseresponse relations calculated using the energy additive model. The curves predict how the UV doseresponse relation should vary for channels with different values of G 0(0). The theory is then compared with the observed UV doseresponse relations for CNG channels.
Effects of Varying G 0(0) on the UV DoseResponse Relation in Saturating Ligand: Simulations
UV doseresponse relations were calculated using Equation 6, G 0(0) values from Table 2 and values of n and
G 0(1), consistent with the constraints discussed in the previous section. When the simulated UV doseresponse 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
and
by transforming the abscissa to the dimensionless coordinate
·
·D and comparing only the relative positions of the simulated curves on the dose axis.
The effect on the theoretical relations of varying G 0(0) depended on the relative magnitudes of the free energy parameters
G 0(1) and
G 0(0), and on the number of target residues per subunit, n. Three limiting cases were examined.
Case I.
If G 0(1) is much larger than |
G 0(0)| (Fig 4 B), then Equation 6 reduces to Equation 10:
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(10) |
In this limit, the simulated UV doseresponse relations were independent of G 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.
Case II.
When G 0(1) and |
G 0(0)| were comparable in magnitude (Fig 4 C), decreasing
G 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.
Case III.
If G 0(1) was much smaller than |
G 0(0)| (Fig 4 D), then increasing -
G 0(0) relative to
G 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·
G 0(1), is not much larger than |
G 0(0)|. In the limit that 4n·
G 0(1) << |
G 0(0)|, Equation 6 reduces to Equation 11:
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(11) |
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 G 0(0) on the UV DoseResponse Relation in Saturating Ligand: Experimental Results
This section compares the simulated curves of Fig 4BD, to the observed UV doseresponse 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 G 0(0). In saturating cGMP, channel opening is much less favorable for RET than for OLF channels [
G 0(0) = -3.0 vs. -9.9 RT]. Results from several laboratories (
The UV doseresponse 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 Equation 3. 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 doseresponse relations for each channel type (Fig 5 B). OLF channels were roughly four times less sensitive to UV than RET channels, and their UV doseresponse relations were two and a half times steeper (Table 1). 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 (
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 doseresponse 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 (
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 (
Fig 7 shows UV doseresponse 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 doseresponse 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 doseresponse 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 1. Varying G 0(0) by the three types of energetic perturbations had similar effects on the channels' UV doseresponse relations. Making
G 0(0) more negative shifted the UV doseresponse 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
G 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 doseresponse 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 G 0(0) on the UV doseresponse 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)
G 0(1) is comparable in magnitude to |
G 0(0)| for RET and OLF channels.
Fig 5 Fig 6 Fig 7 show only 4 of 10 possible pairwise comparisons between the UV doseresponse 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 -G 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 -
G 0(0) is only about half as large (Fig 8 A and Table 2). A more significant deviation from the expected trend is shown in Fig 8 B. The fit to the UV doseresponse 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 -
G 0(0) is much larger (Table 2).
The energy additive model also predicts a positive correlation between -G 0(0) and the slope factor for a channel's UV doseresponse 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 -G 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 -
G 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 -
G 0(0). The slope factors of the UV doseresponse relations for OLF channels were also larger than those for RET channels after correcting for differences in
G 0(0) (Fig 8 D).
What factors are responsible for the differences between the UV doseresponse relations of RET and OLF channels with the same value of G 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 doseresponse 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 (Equation 6). As predicted, the
G 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
G 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 G 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
G 0(1) values would almost certainly differ if any of these tryptophans were UV targets. Furthermore, the
G 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 (
The differences in G 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 is expected due to their appearance as a product in the exponent in Equation 7.
UV Sensitivity of Pore Tryptophan Mutants
In the preceding paper (
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 (
Due to the difficulty in obtaining cyclic nucleotidedependent 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 (
Since UV light may modify tyrosine residues in proteins (
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 doseresponse 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 (
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, G 0(1+), has the effect of decreasing Po (Fig 4 A). The quantity
G 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 doseresponse relations were calculated for channels with different G 0(0) values using Equation 6 with
G 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 G 0(0) on the Current Increase by UV: Simulations
The calculated UV doseresponse relations were characterized by fitting with a modified version of the all-or-none model (
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(12) |
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). Equation 12 ignores the effect of modifying the (+) targets, which will be incorporated at a later stage.
The UV doseresponse relation for the modified all-or-none model is obtained by combining Equation 12 of this paper with Eq. 25 of the preceding paper (
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(13) |
In Equation 13, and
are the absorption cross section and quantum yield of a (-) target, respectively, and D is the photon dose. The slope factor n* provides a measure of the steepness of the relation.
As before (Fig 4, BD), the effect of varying G 0(0) on the simulated UV doseresponse relations depended on the relative magnitudes of the free energy parameters
G 0(1-) and
G 0(0). Three limiting cases were considered.
Case IV: in the limit that -G 0(1-) is much larger than |
G 0(0)| (Fig 13 B), Equation 6 reduces to:
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(14) |
Using Equation 4 and Equation 5, Equation 14 simplifies further to Equation 15:
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(15) |
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 G 0(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
G 0(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 -G 0(1-) was comparable to |
G 0(0)| (Fig 13 C), the fractional current increase after UV again depended on
G 0(0). For n = 1, the magnitude of the current enhancement by UV increased as
G 0(0) was made more positive, but did not reach the maximum possible value of 1/Po(0). For
G 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
G 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
G 0(0) was made more positive], but these effects were modest compared with those on the current amplitude.
Case VI: in the limit that -G 0(1) was much smaller than |
G 0(0)| (Fig 13 D), the simulated curves again shifted to the right along the abscissa and became steeper as
G 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 ·
G 0(1), was insufficient to offset a large, positive value of
G 0(0). In the limit that -4n ·
G 0(1) << |
G 0(0)|, Equation 6 reduces to Equation 16:
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(16) |
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 doseresponse 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 G 0(0) on the Current Increase by UV: Experimental Results
The open probability of RET channels activated by saturating cAMP is only ~1.5% (
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 (
Exposure to 9.49 x 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 doseresponse 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 x 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 1). Fitting the combined results in Fig 15 C with Equation 13 yielded estimates of 2.4 x 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.
Fits of the results with a Langmuir single binding isotherm (Equation 17):
![]() |
(17) |
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 2), 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 doseresponse 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 G 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 |
G 0(0)| if the channels contain only a few (-) targets, but
G 0(1-) may be significantly smaller than |
G 0(0)| if the number of (-) targets is closer to 10 per subunit. The results are clearly inconsistent with -
G 0(1) being much larger than |
G 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, 57, 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 (Equation 6) 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 doseresponse relation for the expanded energy additive model is given by:
![]() |
(18) |
The symbols in Equation 18 are analogous to those in Equation 6 and Equation 7, except for the inclusion of subscripts specific to the (+) and (-) targets.
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 doseresponse 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 doseresponse relation of RET channels in saturating cAMP is actually biphasic. The current was predicted to reach a maximum after exposure to ~8 x 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 G 0 for the (+) targets followed the same trends as those obtained from the fits using Equation 6 (Fig 9):
G 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
G 0(1+) for each channel/ligand combination was somewhat larger than that estimated using the simpler version of the model (Equation 6), presumably because modification of the (-) targets partially offsets the free energy deficit caused by modification of the (+) targets. The estimated values of
G 0(1-) were similar for all channel/ligand combinations studied.
The estimates for G 0 and
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 1001,000-fold enhancement for some of the experimental conditions employed (Table 2). 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 x 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 DoseResponse 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 (Equation 18).
We only considered activation models that include unliganded openings, a well-documented phenomenon (
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 (
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The Appendix 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 (Equation 18). 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. A3A5).
Since UV increased the current through unliganded OLF channels (Fig 15), the free energy cost for modifying an L target must be negative (see Equation A8). 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 Equation A9). 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 doseresponse relations of RET channels before and after UV were fit using each of the three hybrid UV-cyclic allosteric models (Fig 17, DF). The initial value of L for each cyclic allosteric model was estimated from the channels' spontaneous open probability, Psp, using the relation:
![]() |
(19) |
In Equation 19, 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 2), using the relation:
![]() |
(20) |
Equation 19 and Equation 20 were obtained by considering the limiting behavior of Equation A1 and Equation A2 (see Appendix), 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 doseresponse relation before UV, using Equation A1 and Equation A2 and the initial values of c and L determined from Equation 19 and Equation 20.
The post-UV ligand doseresponse relations were fit simultaneously using Equation A1 and Equation A7, with the quantum yields and free energy costs of the L and c targets as the only adjustable parameters. The results of
Fig 17DI, shows the fits of the hybrid UV-cyclic allosteric models to the ligand doseresponse 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.
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DISCUSSION |
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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, 57, 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 (Equation 18) 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 (
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 (
Identification and Characterization of Target Residues
As described in the preceding paper (
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 (
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 (G 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 2), and to the energetic effect of cytoplasmic Ni2+ ions on the gating of RET channels in saturating ligand (approximately -5 RT;
The pore tryptophan residue is conserved in all known CNG channels, as well as the related voltage-gated potassium 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 doseresponse 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 G 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 (
We estimated the maximum possible contribution of channel destruction to the UV effect on CNG channels by comparing the UV doseresponse 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 G 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 x 109 photons · µm-2 reduced the current through OLF channels by only ~10%, but reduced the current through the pore mutant channels by 8590% (Fig 10A and Fig B). This comparison suggests that channel destruction accounts for no more than ~1020% 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 (Equation 18) 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 (
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:
![]() |
(21) |
where G 0(0) is expressed in RT units. Equation 21 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
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Fig 18 B shows the UV doseresponse 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, G 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 2]. Fig 18 B, 24, are calculated for hypothetical channels with even larger
G 0(0) values, but the same UV parameters as used for 1. For example, 24 might correspond to UV doseresponse 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
G 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 (
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 (
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 (
The relatively high photobleaching quantum yields of protein tryptophans (
10-110-3) compared with fluorescent dyes (
10-410-6) 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 doseresponse relations and may provide additional constraints for testing and refining channel activation models (Fig 17).
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Footnotes |
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1 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.
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Acknowledgements |
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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.
Submitted: 27 March 2000
Revised: 1 June 2000
Accepted: 5 June 2000
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Appendix |
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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 doseresponse relations of RET and OLF channels (Fig 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:
![]() |
(A1) |
In Equation A1, 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:
![]() |
(A2) |
where is equal to [A]/KR.
We combined the expanded energy additive model (Equation 18) and the cyclic allosteric models by replacing the phenomenological (+) and (-) targets in Equation 18 with KR, c, and L targets. By analogy with Equation 4, UV modification of these targets alters the gating parameters KR, c, and L according to the relations:
![]() |
(A3) |
![]() |
(A4) |
and
![]() |
(A5) |
where kK, kc, and kL refer to the number of modified targets of each type, and G 0(1K),
G 0(1c), and
G 0(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 Equation 4 is missing in Eqs. A3A5 because the convention used in defining KR, c, and L is opposite that used in Equation 4.)
Equation A2 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 Equation A2 that accounts for the symmetry breaking induced by UV is:
![]() |
(A6) |
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, Equation A6 may be combined with Eqs. A3A5 to yield the following expression for PR as a function of ligand concentration and UV dose:
![]() |
(A7) |
In Equation A7, kKij, kcij, and kLi refer to the number of modified KR, c, and L targets in the subunit identified by the indices i and j, nc and 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 Equation 7. Equation A7 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, G 0(1K) =
G 0(1c).
What is the correspondence between the molecular free energy parameters G 0(1c) and
G 0(1L) in the cyclic allosteric models and the phenomenological free energy parameters
G 0(1+) and
G 0(1-) in the expanded energy additive model (Equation 18)? It is useful to consider the channels' gating behavior in two limits. In the absence of ligand, Equation A7 simplifies to:
![]() |
(A8) |
Factors related to KR and c do not appear in Equation A8 because the spontaneous open probability depends only on L for the cyclic allosteric models. Since UV increased the spontaneous currents through OLF channels (Fig 15), G 0(1L) is negative. For a saturating concentration of ligand, Equation A7 reduces to:
![]() |
(A9) |
indicating that the current after irradiation depends on both c and L. Since G 0(1L) is negative and UV decreased the current through OLF channels activated by 1 mM cGMP,
G 0(1c) must be positive.
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