From the Department of Physiology and Biophysics, University of Colorado School of Medicine, Denver, Colorado 80262
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ABSTRACT |
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Cyclic nucleotide-gated channels contain four subunits, each with a binding site for cGMP or cAMP in the cytoplasmic COOH-terminal domain. Previous studies of the kinetic mechanism of activation have been hampered by the complication that ligands are continuously binding and unbinding at each of these sites. Thus, even at the single channel level, it has been difficult to distinguish changes in behavior that arise from a channel with a fixed number of ligands bound from those that occur upon the binding and unbinding of ligands. For example, it is often assumed that complex behaviors like multiple conductance levels and bursting occur only as a consequence of changes in the number of bound ligands. We have overcome these ambiguities by covalently tethering one ligand at a time to single rod cyclic nucleotide-gated channels (Ruiz, ML., and J.W. Karpen. 1997. Nature. 389:389-392). We find that with a fixed number of ligands locked in place the channel freely moves between three conductance states and undergoes bursting behavior. Furthermore, a thorough kinetic analysis of channels locked in doubly, triply, and fully liganded states reveals more than one kinetically distinguishable state at each conductance level. Thus, even when the channel contains a fixed number of bound ligands, it can assume at least nine distinct states. Such complex behavior is inconsistent with simple concerted or sequential allosteric models. The data at each level of liganding can be successfully described by the same connected state model (with different rate constants), suggesting that the channel undergoes the same set of conformational changes regardless of the number of bound ligands. A general allosteric model, which postulates one conformational change per subunit in both the absence and presence of ligand, comes close to providing enough kinetically distinct states. We propose an extension of this model, in which more than one conformational change per subunit can occur during the process of channel activation.
Key words: allosteric proteins; ligand-gated ion channels; photoaffinity labeling; patch clamp; retinal rod photoreceptors ![]() |
INTRODUCTION |
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Cyclic nucleotide-gated (CNG)1 channels form a
unique family of ion channels that are activated by the
binding of cGMP or cAMP (reviewed in Finn et al.,
1996). These channels are thought to be formed by the
association of four subunits (Liu et al., 1996
; Varnum
and Zagotta, 1996
), each containing a COOH-terminal
binding site for ligand (Kaupp et al., 1989
; Brown et al.,
1995
). In retinal photoreceptors and olfactory receptor
neurons, two types of subunits (
and
) coassemble to
form heteromultimeric channels (Kaupp et al., 1989
;
Dhallan et al., 1990
; Chen et al., 1993
; Bradley et al.,
1994
; Liman and Buck, 1994
; Körschen et al., 1995
;
Biel et al., 1996
). Activation of these channels is allosteric in nature, thus the binding of several cyclic nucleotide molecules to the cytoplasmic binding domains induces conformational changes that cause the channel
pore to open (Fesenko et al., 1985
; Haynes et al., 1986
;
Zimmerman and Baylor, 1986
; Nakamura and Gold,
1987
; Karpen et al., 1988
; reviewed in Zimmerman,
1995
). CNG ion channels are excellent proteins in
which to study allosteric activation because the binding
sites for cGMP are readily accessible in excised inside-out patches, conformational changes induced by ligand
binding can be observed in a single protein molecule
in real time, and there is no detectable desensitization
in the continued presence of ligand.
Although structure-function studies are beginning
to shed light on which parts of the protein are involved
in activation (e.g., Goulding et al., 1994; Liu et al.,
1994
; Gordon and Zagotta, 1995a
; Varnum et al., 1995
;
Bucossi et al., 1997
; Gordon et al., 1997
; Tibbs et al.,
1997
; Varnum and Zagotta, 1997
; Brown et al., 1998
; Zong et al., 1998
), the sequence of events leading to
channel opening remains largely unclear. A complete
kinetic model is required to piece together the structural changes that occur. Various allosteric models have
been proposed that can fit dose-response data. However, as demonstrated for other allosteric proteins,
equilibrium or steady state data are not sufficient to
support one model to the exclusion of others. Even
when kinetic transitions are studied at the single channel level, the constant binding and unbinding of cyclic
nucleotides makes it difficult to correlate any particular event to a specific number of ligands bound. As a result, the intermediate states of activation, in particular,
are poorly understood. Hence, previously proposed
mechanisms tend to be oversimplified due to the limitations of the assays.
We have shown previously that these problems can be
circumvented by locking single channels into each possible liganded state (Ruiz and Karpen, 1997) with the
use of a photoaffinity analogue of cGMP, 8-p-azidophenacylthio-cGMP (APT-cGMP; Brown et al., 1993
; Karpen and Brown, 1996
). Two criteria were used to establish the number of ligands covalently attached to
each channel. First, dose-response relations for free
cGMP were measured before and after covalent attachment of ligand. Four discrete shifts from the control relation were observed corresponding to the attachment of one to four ligands. These shifted relations reflected
graded changes in both the Hill coefficient and the effective concentration of cGMP (K1/2). Second, the
liganding assignments were supported by the obvious
changes in opening behavior. It was then possible to accumulate minutes of data at each level of liganding, resulting in sufficient representation of all conformational
states. We found that the channel locked in a certain
liganded state could assume multiple conductance states.
In other words, although ligands were fixed in their
binding sites, the channel was not frozen into a single
conformation, or conducting state. This was the key observation that allowed us to rule out the simple concerted allosteric model Monod-Wyman-Changeux (MWC;
Monod et al., 1965
) and the sequential model Koshland-Nemethy-Filmer (KNF; Koshland et al., 1966
).
Recently, a complementary approach for determining the contribution of individual binding events to activation of CNG channels was described by Liu et al.
(1998). Multiple binding site mutations were made that
apparently destroy binding to the retinal channel subunit. Heteromeric channels were expressed in Xenopus
oocytes by coinjecting RNA for this binding site-deficient subunit with RNA coding for an "intact" retinal
subunit, in which the pore sequence was replaced by
that from the higher conducting catfish olfactory channel. Single channel patches were then isolated and the
unaltered binding sites in each channel were saturated
with cGMP. Since the higher conducting pore region
accompanied each unmutated binding site, different
levels of conductance reported different numbers of
active binding sites present in each channel. The findings in this study agree with our previous results that there is significant opening in partially liganded channels. However, there are discrepancies in the degree of
opening for some of the liganded states. These differences are discussed below.
The major purpose of this paper is to present the first kinetic analysis of a CNG channel in every liganded state. Surprisingly, at each level of liganding, as many as five closed states were revealed, and each conducting state exhibited transient and sustained conformations. This information provides further evidence against the simple, limiting mechanisms mentioned above, and allows us to propose a more complete model that describes the opening process of the retinal rod cGMP-gated channel.
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MATERIALS AND METHODS |
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Electrophysiology
Xenopus laevis oocytes were injected with cRNA encoding the subunit of the bovine retinal rod cGMP-gated channel. After 3-5 d
of incubation at 15°C, single channels were isolated in excised
inside-out membrane patches. Electrodes were coated with Sylgard and resistances varied from 15 to 20 M
. All patches were studied in symmetrical control solution containing (mM): 130 NaCl, 2 HEPES, 0.02 EDTA, 1 EGTA, pH 7.6 with NaOH. For recording, channels were held at ±50 mV for at least 10 s, and
switched to 0 mV for at least 15 s in between. Multiple segments
at +50 mV were recorded under each condition so that at least
30 s of channel activity was used for all analyses. For dose-
response assays, cGMP was added to the control solution. Patches
that contained single channels were identified by the lack of multiple openings stacked on top of each other at high concentrations of cGMP. Although at low concentrations step-wise openings between subconducting levels were observed, single transitions from closed to fully open and vice versa occurred much
more frequently than would be expected if the larger openings
arose from multiple low conductance channels. The procedure
at saturating cGMP normally took about 5 min, which has been
shown to be a sufficient period of time to avoid spontaneous shifts in K1/2 (Molokanova et al., 1997
). Furthermore, during dose-response assays, most concentrations were checked at least twice. After each channel was subjected to a dose-response assay, a nearly saturating concentration (20 µM) of APT-cGMP (see
Scheme I; Brown et al., 1993
; Karpen and Brown, 1996
; Ruiz
and Karpen, 1997
) was perfused onto the patch, and UV light
(360 nm) was shone for timed periods (10-180 s) (Scheme I).
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APT-cGMP binds to the channel's binding pockets and, upon
UV photolysis, covalently attaches to the channel. In this way, cGMP becomes "locked" into the binding sites (Brown et al.,
1993, 1995
; Karpen and Brown, 1996
; Ruiz and Karpen, 1997
).
After UV exposure, patches were washed with control solution
for at least 20 min to remove completely all unattached nucleotides from the patch (Karpen and Brown, 1996
). After this treatment, behavior of partially liganded channels was recorded in
control solution in the absence of free cGMP. Finally, a second
dose-response assay was performed that proved to be shifted
from the first if covalent attachment of ligand had occurred. It
should be noted that UV exposure alone did not produce any
shifts in the dose-response relation: in three patches, the relations were identical before and after typical exposure times. The
number of ligands attached to individual channels was determined by the change in the slope of the dose-response relation
(Hill coefficient) and by the change in behavior of the partially
liganded channel in the absence of free ligand (see Ruiz and
Karpen, 1997
). Sometimes the channel entered into long closed
states on the order of several hundreds of milliseconds, some as
long as tens of seconds (Matthews and Watanabe, 1988
; Nizzari et
al., 1993
; Taylor and Baylor, 1995
). Since these sojourns were infrequent, we did not acquire enough events to analyze them adequately. However, they could be easily distinguished from "normal" channel activity with the use of stability plots (Colquhoun
and Sigworth, 1995
), and were excluded from the analyses. Single
channel data were filtered at 50 kHz with a four-pole Bessel filter
in the patch-clamp amplifier (Axopatch 200A; Axon Instruments),
subsequently filtered at 5 kHz with an eight-pole Bessel filter, digitized at 88 kHz (Neuro-corder DR-484 PCM unit; Neuro Data Instruments), and stored on VHS tape. For most analyses, data were
played back, filtered at 1 kHz (eight-pole Bessel filter), and sampled at 5 kHz. In some cases, the data were filtered at 5 kHz and
sampled at 25 kHz. One record (from a triply liganded channel)
was later digitally filtered at 500 Hz for compiling events.
Data Analysis
Each opening or closing event was idealized by simultaneously measuring the amplitude and dwell time (Pclamp6; Axon Instruments). Events were comprised of consecutive sample points that occurred within a single conductance class. The amplitudes of the sample points were averaged and the durations were summed to give the mean amplitude and dwell time of an idealized event. When a sample point fell into a different conductance class, a new event began. For identifying the conductance class of each event, three mean current amplitudes were typically set with horizontal lines at 0 (baseline), 0.3-0.4 (O1), 0.7-0.9 (O2), and 1.2-1.4 (O3) pA. These ranges reflect patch-to-patch variations; there were no systematic differences in current amplitudes between locked channels and channels activated by free ligand. Thresholds fell half way between the horizontal lines that defined the conductance classes. At a bandwidth of 1 kHz, events <0.6 ms were marked as "short" events with uncertain amplitudes (Pclamp6). The baseline was adjusted when it varied by more than ±0.015 pA for more than a few milliseconds. Once the event was accepted, its average amplitude and dwell time were added to the events list, and the conductance class was recorded. Noise and artifacts were excluded by eye during this process. After compiling the events list, dwell times were converted into probabilities (event time/total record time) for plotting against amplitudes in the amplitude histograms. The entire events list was binned for the amplitude histogram, including the short events. I/Imax was calculated as the mean current divided by the maximum current measured at saturating cGMP, on the same patch.
Conductance states were plotted separately for dwell-time fitting. Distributions were plotted as the square root of the normalized observations against the log10 of the dwell times (Sigworth
and Sine, 1987). All distributions were fit with the maximum likelihood method. The "goodness of fit" for multiple components
was determined by fitting a distribution with different numbers
of components. The extent to which the addition of a component improved the fit was evaluated by the log-likelihood ratio
test (Pclamp6). The rise-time of the filter (Tr) was 0.34 ms at 1 kHz,
calculated as described (Howe et al., 1991
; Colquhoun and Sigworth, 1995
). Dwell times <2 Tr (0.6 ms) were not included in
the exponential fits. The amplitude of the baseline noise at 1 kHz
was typically ±0.1-0.15 pA about the mean, with a standard deviation (root mean square) of 0.02-0.03 pA (the false event detection rate was 1.6 × 10
19 s
1). No corrections were made for
missed events. However, the number of components in a fit are
usually not affected by missed event errors, although the time
constants may be somewhat overestimated (Colquhoun and Sigworth, 1995
). The distributions provide only a lower bound for
the number of states. In addition, errors arising from missed
events are not nearly as severe when multiple thresholds are employed (Colquhoun and Hawkes, 1995
).
Adjacent events were analyzed to determine the connections
between states. The resolution of fast events was limited by the cutoff frequency of the filter. Thus, fast events classified as O1 or
O2 might actually be O3 or closed events that were cut off during
the rise time of the filter. This was handled at several different
steps in the analysis. For adjacent state analysis, transitional
events (on a rising or falling phase) less than Tr were combined
with the following event. Peaks that were too brief to ascertain an
amplitude were not removed initially, because they marked an interruption in an opening or closing event. Next, adjacent events
were grouped by current amplitude (e.g., closed-O1 pairs would
comprise one group). The first events in the pair were then
sorted into kinetic classes based on the time constants and areas
of the exponential fits. Subsequently, the second events were
sorted into kinetic classes; again, the approximate number of
events was dictated by the areas of the exponential fits. To rule
out uncertain openings or closings, all open events shorter than
2 Tr were thrown out. The resolution of closings could be more
precise (>Tr) because any event with an amplitude lower than 2 SD
below the O1 state must be a closed event (Howe et al., 1991). Thus, only reliable events were used to determine the number of observed adjacent events for each kinetic class. When one connection occurred more often than any other, it was taken as a direct connection (see Appendix ). These results were supported by
component dependency calculations (Magleby and Song, 1992
).
In brief, component dependency is the percentage of observations that one state, i (which for simplicity is defined as one exponential component), was followed by another state, j, compared
with the independent probability that those two states would occur adjacent to each other. This is calculated as follows: for any
two states, i and j,
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where Obs(ij) is the observed number of adjacent events for states i and j, and Ex(ij) is the expected number of adjacent events that would be observed if the two events occurred independently of one another. Ex(ij) is the product of the probabilities that the two events could occur individually:
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where Pi and Pj are the individual probabilities:
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Simulations
For simulations of the connected state models, the rate constants
between each pair of connected states were put into a matrix format. As an initial screen for candidate models, steady state occupancies and mean currents were computed as described (Colquhoun and Hawkes, 1995) in order to predict the I/Imax value
(mean current/maximum current). For further testing, current
traces were simulated by starting at the longest closed state. The
dwell time of each event was a randomly generated number
within the exponential distribution for that kinetic state. The following event was chosen based on the probability of going to
each connected state. The amplitude of an open event was randomly chosen from a Gaussian distribution with a mean and standard deviation based on experimental amplitude histograms
(constructed from idealized events). This accounted for an observed variation in mean amplitudes (±10%) that was not included in the model. The amplitude of each event was stored along with the dwell time. The list of events stopped when the sum of the dwell times reached the maximum time of the record designated by the operator. Next, the simulated data were sampled with the same protocol employed for the experimental data.
Events were sampled at 25 kHz, and random Gaussian noise was
added to the sampled data (±0.25 pA, about the mean amplitude of the baseline, the noise typically observed at 5 kHz).
These data were put through a Gaussian filter program (Colquhoun and Sigworth, 1995
) with a 5-kHz cutoff frequency. To simulate the playback step, data were resampled at 5 kHz and filtered at 1 kHz. The resulting simulated data could be plotted as
single channel traces (amplitude versus time). Events lists were
compiled as described above, and subsequently analyzed just as
those obtained from experimental data. Once the simulation of a
connected state model produced parameters that came close to
the experimental parameters, the rate constants in the connected state diagram were adjusted by small degrees, where necessary, to reproduce the parameters more closely. In all cases, the
rates between states were adjusted to comply with the principle
of microscopic reversibility. For this, the lifetimes of individual
states were constrained, but the proportions of events that went
to adjacent states were adjusted. It should be noted that a single
exponential component may harbor several hidden states, so
what we have called a single state could be a group of states with
an average lifetime represented by a single time constant.
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RESULTS |
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Behavior of Locked Channels and Comparison to Channels Activated by Free cGMP
Fig. 1 shows the opening behavior of single CNG channels locked in each liganded state. When one ligand was bound, the channel opened with very low probability and mostly to a low conducting level. With two ligands, the channel opened to multiple conducting levels, and entered into a bursting behavior characterized by frequent openings separated by brief closures. Three ligands caused significant opening, and each conducting level exhibited transient and sustained life times (see also below). In the fully liganded channel, the probability of opening approached unity. Moreover, the most prominent opening was to the highest conducting level. Overall, the behavior of the channel locked into any particular liganded state was intricate, indicating an intrinsic flexibility of the protein.
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The flexible nature of the protein was particularly
clear in triply liganded channels, where the probability
of opening was large enough to allow examination of
the myriad states and behaviors. Fig. 2 A shows a longer
record (~5 s out of 100 s total) of a triply liganded
channel on an expanded time scale. The small horizontal lines at the right of each trace indicate the mean
current levels for the closed state (C), two subconducting states (O1 and O2), and fully open state (O3). A
fascinating and prominent feature was the tendency
to open to subconducting states. In fact, the triply
liganded channel preferred opening to these states
over the fully open state. Many of the openings to subconducting states were quite stable, as shown in the
stretch between the two asterisks. These states did not
arise from overfiltering of fast events as shown in the
same stretch filtered at 5 kHz (Fig. 2 B) instead of 1 kHz
(Fig. 2 A). Note in particular the long sojourns into the
O2 state. In the catfish olfactory CNG channel, rapid
subconductance states have been shown to arise from
protons binding in the pore (Root and MacKinnon,
1994). However, the entire record in Fig. 2 argues
against subconductance states being the result of proton block in the rod channel. For example, if proton
block were responsible for some of the briefer openings to subconductance states as in row 2 of Fig. 2 A,
then it would be difficult to explain the absence of proton block in row 8 and elsewhere during long openings. We cannot completely rule out the possibility that
different conformational states could have different
susceptibilities to proton block; however, this scenario
would simply support our contention that locked channels are flexible and can assume a variety of conformational states. It should be recognized, however, that
proton block of this channel has never been demonstrated at this pH (7.6) and membrane potential (+50
mV) (e.g., Tanaka, 1993
; Picco et al., 1996
), and that
subconducting behavior was indistinguishable at pH
8.6 and +50 mV (Ruiz and Karpen, 1997
). These latter
conditions have been shown to eliminate proton block
in the catfish olfactory CNG channel (Goulding et al.,
1992
).
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There are several features apparent in locked channels that are usually assumed to arise from the binding
and unbinding of free ligands. For comparison, the
properties of single channels activated by free cGMP
are illustrated in Fig. 3. At low ligand concentrations,
the channel exhibited bursting behavior, openings to
the same three current levels (Fig. 3, inset, and see Fig. 4 D), and both transient and long-lived openings; at saturating ligand concentrations (200 µM cGMP, Fig. 3),
long, stable openings (*) occurred. Bursts are normally
thought of as periods of repeated openings arising
from highly liganded states, while the intervals between
bursts are attributed to latency of binding. However, Figs. 1 and 2 illustrate that bursting also occurred in
locked channels, in the absence of binding and unbinding of free ligands. Subconductance states are
thought on occasion to be an obligatory consequence
of a multiply liganded channel losing one or more ligands (e.g., Ildefonse and Bennett, 1991; Rosenmund
et al., 1998
). However, in each liganded state, the
locked channel freely moved between three conductance states without the loss or gain of ligands. Finally,
both transient and sustained events were observed in
locked channels. With three ligands attached (Fig. 1), the
appearance of stable openings in the middle of a burst of
rapid transitions is striking. Such different lifetimes are usually thought to reflect transient and stable binding
events. However, the channel can exhibit these behaviors
independent of ligand binding and unbinding.
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There are two reasons to believe that these locked channel behaviors do not arise from tethered cGMP moieties momentarily "falling out" of the binding site. First, the length of the linker chain in APT-cGMP is very short (<10 Å) so that if the cGMP moiety unbinds, its effective concentration is expected to be on the order of hundreds of millimolar at that single cGMP binding site. Thus, unbinding events would be undetectable (<0.1 µs) within our time resolution. Second, if the effective concentration (which would dictate the tendency to rebind after unbinding) were much less than expected, we should be able to measure an increase in opening probability when free ligand is added to locked channels that are fully liganded. However, addition of 2-1,000 µM cGMP never increased the open probability of fully liganded channels. It is clear that locked channels exhibit many of the same properties as channels activated by free ligand. This indicates that intricate behaviors are intrinsic to the channel protein.
We now consider subconductance states in more
quantitative detail. All partially liganded channels
showed a preference for opening to subconductance
states over the fully open state. This is demonstrated in
the amplitude histograms in Fig. 4 A, which represent
extended periods of channel behavior at each level of liganding. Channel opening with one ligand attached
was similar to spontaneous channel opening, even
though singly liganded channels required fewer ligands
to activate fully (data not shown; see Ruiz and Karpen,
1997). These openings, however, were very infrequent and did not allow for a detailed analysis. In doubly, triply, and even fully liganded channels, it is clear that the
channel opened to multiple conductance states. A sum
of four Gaussian functions, including one for the
closed state, was required to fit the histograms with two,
three, and four ligands attached (Fig. 4 A). All-points
amplitude histograms, although naturally broader than
histograms of idealized events (see MATERIALS AND METHODS), fully support the existence and prominence
of subconductance states. Fig. 4 C shows a comparison
of these two types of histograms for the same triply
liganded channel record. Interestingly, different channels that had equal numbers of ligands attached (not
shown) sometimes showed a preference for one subconductance state over the other (O1 or O2). However,
partially liganded channels always had a higher probability of opening to subconductance states than opening to the fully conducting state. The overall degree of
opening (I/Imax) in partially liganded channels also varied (see Fig. 4, legend). When four ligands were attached (Fig. 4 A), the channel favored opening to the
fully conducting state (O3) at the expense of the subconducting states. Thus, opening to any given conducting state is dependent on how many ligands are bound.
This is summarized in Fig. 5 A. In locked channels,
both subconductance states peaked with three ligands
attached. An important control for these experiments is the response of untethered channels to free ligand
(Fig. 5 B). The individual dose-response relations revealed that the probabilities of observing both subconducting states peaked at the same concentration of
cGMP. This is predicted from the results in Fig. 5 A. It
should be noted that the probability of observing a subconductance state of the native rod channel also peaks
at a subsaturating concentration of cGMP (Ildefonse
and Bennett, 1991
; Taylor and Baylor, 1995
). Overall,
the findings in Figs. 1-5 strongly support the notion
that subconducting states are fundamental intermediate steps in the process of gating.
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Probability of Opening of Locked Channels Explains the cGMP Dose-Response Relation
As a further test of whether data acquired from locked
channels reflect the channel's natural response to
cGMP, we determined whether the open probabilities
predict the single channel dose-response relation. It is
important to use a single channel dose-response relation for this analysis because the typically low Hill coefficient (~2.0) observed in macropatches does not reflect the consistently higher Hill coefficient (~3.0) observed in single channel patches (Ruiz and Karpen,
1997; Ruiz et al., 1999
). A dose-response relation can
be generated from locked channel data with the use
of a minimum model (Fig. 6 A) that simulates the
opening of locked channels as well as the binding of
cGMP. We assumed initially that cGMP binds independently to the four identical subunits when the channel is
in the closed state, and each liganded closed state
opens to the degree predicted from the locked channel
data. To simplify this analysis, the multiple open states
we observed were contracted into a single open conformation. This is reasonable, because for a dose-
response relation it is only necessary to know the overall equilibrium between open and closed states. The degree of opening in locked channels can be expressed as
the ratio of the mean current to the maximal current at
saturation (I/Imax). These values were as follows: singly
liganded, 9.6 × 10
6; doubly liganded, 0.0097; triply
liganded, 0.33; and fully liganded, 1.00. For this application, these values were converted to open probabilities and equilibrium constants as described in Fig. 6 A,
legend.
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Fig. 6 B shows dose-response relations from 16 single channel patches. I/Imax is the fractional current activated by cGMP. Because K1/2 varied significantly between individual single channel patches, the cGMP concentrations were expressed relative to each channel's K1/2. This simply aligned the dose-response relations along the x axis. The overall dose-response relation was fit with a Hill coefficient of 2.9, and the Hill coefficients for each single channel were also very high, ranging from 2.5 to 3.9. The solid curve shows a simulation from the model, which could be described by a Hill coefficient of ~2.8. As mentioned above, the opening of partially liganded channels exhibited some variability from patch to patch. For this simulation, the highest values were used because we felt these were the most reliable (see Fig. 4, legend). However, the lowest values (given in the legend) produced simulations that could be described by a Hill coefficient of ~3.1, which falls within the observed range of single channel Hill coefficients. The only free parameter in the model is the ligand dissociation constant, and the value of the Hill coefficient was virtually insensitive to changes in Kd. The reproduction of the dose-response curve is consistent with the idea that locked channels open normally, and is further evidence that the assignment of the numbers of tethered ligands in those channels is correct.
Liu et al. (1998) reported the following open probabilities for the different liganded states of mutated
channels (see INTRODUCTION), which they regard as
behaving like wild-type channels: singly liganded,
0.017; doubly liganded, 0.16; triply liganded, 0.32; and
fully liganded, 0.95. Before this, the same group (Tibbs
et al., 1997
) reported spontaneous open probabilities
in unliganded channels of 1.25 × 10
4, which contrasts
with an I/Imax value of 6.8 × 10
6 in our experiments
(Ruiz and Karpen, 1997
). The numbers from the
former group suggest more opening of unliganded,
singly, and doubly liganded channels. When we applied
the same minimum model to test their open probabilities, the dashed curve in Fig. 6 B was obtained, which
exhibits pronounced curvature and clearly cannot explain the wild-type single channel dose-response relations. Again, the simulation was insensitive to the value
assumed for Kd. We also tested the effects of adding different degrees of binding cooperativity to closed states
in the mechanism in Fig. 6 A, using Kd values that
decreased progressively with each bound ligand. (It
should be noted that favorable opening already confers a significant degree of binding cooperativity to the
open states.) Using the opening numbers of Liu et al.
(1998)
, the upper portions of the experimental relation (which are most sensitive to binding cooperativity)
could be fit, but these simulations still deviated markedly from the foot of the relation (low I/Imax values). In contrast, adding an equivalent amount of binding cooperativity using our open probabilities yielded a good
fit to the upper part of the curve and a slightly steeper
fit to the foot of the relation that was still well within
the spread of the data. The foot of the relation primarily reflects the number of ligands that have to bind for
substantial activation, and significant deviations indicate discrepancies in the opening of lower liganded
states. Finally, we tested whether a coupled dimer
model proposed by Liu et al. (1998)
could fit the single
channel relations. In this model, four subunits associate as two functional dimers. Each dimer undergoes a
concerted transition, and the channel opens when
both dimers are activated in this way. Simulated data
from this model (using the parameters of Liu et al.,
1998
) produced the dotted curve shown in Fig. 6 B. Although this is slightly closer to the wild-type dose-
response behavior, it is still too shallow, and also exhibits pronounced curvature at low values of I/Imax. This
model incorporates a significant degree of closed-state binding cooperativity like that described above. It comes
closer to the foot of the experimental dose-response
relations in Fig. 6 B largely because it predicts lower
open probabilities in unliganded and singly liganded
channels than those observed in the experiments of
Liu et al. (1998)
. Later, we discuss possible reasons why
their approach may have yielded somewhat distorted
numbers for channel opening at different levels of
liganding. In summary, locked channels appear to reflect accurately the activity of normally liganded channels; thus, we are confident in the reliability of this approach for dissecting the allosteric mechanism of channel opening.
Evaluation of Simple Allosteric Models
Eigen (1968) pointed out that the KNF sequential
model (diagonal box) and the MWC concerted model
(two vertical boxes) are both limiting cases of a more
general allosteric model shown in Fig. 7. In this model,
there are four subunits in a protein, each capable of
undergoing a single conformational change (from
to
). The bound ligand is represented by G. In the
KNF sequential model, ligand binding is required for
conformational changes to occur; thus, for a tetrameric
channel, different open states would arise with different numbers of ligands bound. Early studies of single
retinal CNG channels seemed to support the sequential
model, because subconducting states were observed at
low cGMP concentrations and exhibited a dose dependence that suggested that they reflect intermediate
steps in activation (Haynes et al., 1986
; Zimmerman and Baylor, 1986
; Hanke et al., 1988
; Ildefonse and
Bennett, 1991
; Taylor and Baylor, 1995
; see also Fig. 5
B). However, the sequential model is inadequate to describe the multiple open states observed at every level
of liganding in locked channels (Ruiz and Karpen, 1997
; and Fig. 4).
|
The MWC concerted model is a simple and appealing scheme that has been used to describe steady state,
macroscopic current data for CNG channels. In this
model, a channel protein assumes only two conformations, closed and open. The interconversion involves a
synchronous change in all four subunits. Ligand binding increases the open probability by stabilizing the
open conformation. Spontaneous channel openings in
the absence of ligand have been reported for CNG
channels (Picones and Korenbrot, 1995; Ruiz and
Karpen, 1997
; Tibbs et al., 1997
). This finding is consistent with a concerted mechanism of opening; however,
spontaneous openings are also predicted by the general allosteric model (see below). The very existence of
subconductance states described above indicates that a
two-state model is insufficient. Furthermore, at the
level of resolution afforded by locked channels, it is
clear that subconductance states were the most prominent open states in four of the five liganded conditions
(zero to three ligands attached; Fig. 4). On occasion, the simple concerted model has been expanded to include two or three conformational transitions. An important prediction of any strictly concerted mechanism
is that the channel opening equilibrium constant
should increase by a constant factor with each ligand that binds. However, such models cannot describe our
data because the overall equilibrium constants for each
open (conductance) state did not change by a constant
factor for each ligand that bound (Table I). The equilibrium constants (Ko) were calculated as the ratio Po/Pc,
where Po is the probability of observing a particular
open state, and Pc is the probability of observing the
closed state. It is striking that for the two subconductance states the equilibrium constants not only did not
change by a constant factor with each ligand (shown by
the ratios of Ko between liganded states), but these factors actually varied by more than two orders of magnitude. The data for the fully conducting state are less
complete since we rarely observed (and in some
patches did not observe) this state with zero ligands or
one ligand attached. However, kinetic data presented
below argue strongly against concerted models even
when the channel's opening behavior is simplified to
consider only the fully conducting state.
|
In contrast, the general allosteric model in Fig. 7 captures some of the complex behavior that we have observed in single channels. For example, multiple channel conformations are allowed with a fixed number of
ligands bound. In each row, the channel undergoes the
same conformational changes regardless of the number of ligands bound. Thus, spontaneous opening of
the unliganded channel is easily accommodated. The
effect of ligand binding is to enhance the probability
that those conformational changes occur. The actual
scheme is more complex than the diagram shown, because a channel with a ligand bound to a subunit in a
square conformation is different than a channel with a
ligand bound to a subunit in a circle conformation.
The total number of distinct states depends on assumptions about symmetry (recently reviewed in Cox et al., 1997). For the assumption of fourfold rotational symmetry, 55 distinct channel states are expected. This is a
reasonable assumption for a channel with a single pore
comprised of four identical subunits. With this assumption, adjacent subunits perform differently than diagonally opposed subunits. That is, if conformational
changes occur in adjacent subunits, the channel behaves differently than if they occur in opposing subunits. Similar considerations apply to ligand binding to
adjacent or opposed subunits. However, when ligands
are locked into binding sites, only one binding configuration can be considered. This affects only the doubly
liganded states (here, adjacent binding is assumed)
and reduces the original 55 states to 46 total states (or
45 total states if two ligands bind to diagonally opposed
subunits). Each state shown in the diagram represents
the number of subunits that have undergone a conformational change (
to
) and the number of ligands
bound (G). The number of distinct states is indicated
in parentheses above each representative state. For example, consider the case with three ligands bound, and
three of the subunits have undergone conformational
changes to a circle (row 4, column 4). There are three
nonequivalent configurations possible. First, all three
subunits with ligand bound could be in the circle conformation, as shown. Alternatively, the unoccupied subunit could be a circle, and one of the three bound subunits a square. For the latter case, there are two possibilities. One is when the two bound circles are adjacent
to each other, and the other is when the two bound circles are opposed to each other.
At each step of liganding, conformational changes
that occur in one, two, three, or all four subunits are
predicted to give rise to identifiable closed and open
states. In evaluating the general allosteric model,
locked channels allow us to examine channel opening
behavior in each row, because the number of ligands attached is constant. We begin by examining channel behavior in the absence of ligand. The closed times for
unliganded channels were fit with only one time constant (c ~ 15 s, not shown). Interestingly, spontaneous
openings exhibited multiple conductance states. Although the most favorable was the lowest conductance
state, the other two open states were occasionally observed, indicating that all three conductance states are
an intrinsic property of the protein. The observation of
multiple states is consistent with the general allosteric
model; in fact, the model predicts more conformational states (6) than we observed (4). This may be due
to the low probability of opening (Po ~ 10
5). Channel
behavior with one ligand bound (Fig. 1) was not significantly different than the behavior observed in unliganded channels. Again, the low number of events may
not allow for a meaningful test of the model.
For doubly, triply, and fully liganded channels, all
states were sufficiently populated. Dwell-time histograms for closed states and each conductance state
(O1, O2, O3) were constructed and plotted in Fig. 8 as
the square root of the number of observations versus
the log10 of the dwell intervals (Sigworth and Sine,
1987). This method allows a wide range of dwell times
to be displayed. An additional advantage is that each
exponential peaks at the value of its time constant. Interestingly, in the doubly liganded channel, the closed
time distribution was fit with five exponentials. This indicates that the channel can assume at least five distinct closed state conformations. Triply and fully liganded
channel closed time distributions required only three
exponentials for a reasonable fit. Although we have already identified three open states based on different
conductances, fits to individual open dwell-time distributions revealed multiple kinetic states. In some panels
in Fig. 8 (e.g., C, F, and G), the need for two exponentials is not readily apparent. However, a single exponential would not accommodate all the long and short
events; thus, some excess events would have to be omitted. First, we cannot justify omitting excess long-lived
events because they contribute significantly to the overall open probability. Second, when a single exponential
is constrained to accommodate the longest dwell times,
excess brief events must be omitted. This results in simulated data with markedly fewer fast transitions, a
prominent feature of single channel behavior (see Fig.
1). For the fully liganded channel, a third long-lived
open state was observed that was not apparent in partially liganded channels (Fig. 8 L). As an important
control, the dwell times for O3 were fit with the same
three exponentials in channels activated by saturating
free cGMP, though the proportion of the longest-lived
state (O3LL) was slightly lower than that observed in
locked channels (data not shown; see also Nizzari et al.,
1993
). Table II lists the time constants and their fractional contributions for all liganded states that were
fully analyzed.
|
|
Since the fully liganded channel record was filtered
at 1 kHz, we were concerned that very short events in
between O3 open times could have been missed, thus
giving rise to artifactually long open events. To check
whether the longest component was real, the same
record filtered at 5 kHz was analyzed. The open channel noise was high (root mean square = 0.28 pA), and
it was difficult to distinguish noise spikes from rapid
events (false event detection rate ~450 s1). Thus,
we chose to compile indiscriminately all events that crossed a threshold set midway between the bottom of
the open channel noise and the O2 level. Afterwards, a
resolution of 80 µs was imposed (Colquhoun and Sigworth, 1995
) (the filter rise time is 70 µs at 5 kHz, as
opposed to 340 µs at 1 kHz). The maximum likelihood
fits (not shown) to all O3 events detected in this analysis still required three exponentials with the following time constants and proportions: 1.6 ms and 0.113; 7.8 ms and 0.867; and 23 ms and 0.02 (7,128 total events).
The proportion of the longest component was lower;
however, this was expected with such a high false detection rate and a threshold set very close to the noise
level. The important result was that three components were still measured. Thus, the filtering at 1 kHz did not
produce a third component that was not real. It should
be noted that when records like this are corrected for
missed events, the number of components usually does
not change, although the time constants and proportions may be altered (Colquhoun and Sigworth, 1995
).
Overall, the kinetic analysis indicates that there were 11 distinguishable states in doubly liganded channels, 9 in triply liganded channels, and 10 in fully liganded channels. The general allosteric model described above predicts 10 states in doubly liganded channels, 12 in triply liganded channels, but only 6 in fully liganded channels. (It should be noted that an alternative assumption of twofold symmetry still predicts only seven states in the fully liganded channel.) This model comes close to accounting for the number of states observed in our single channel data. However, the large number of states in the fully liganded channel points out that we need to expand on the general allosteric model by allowing for more than one conformational change per subunit. To evaluate fully the general allosteric model or any expanded version, it is necessary to determine how the various channel states are connected to each other and what the transition rates are.
Development of a Connected State Diagram
The first question is whether each conducting level can
arise directly from a closed state, or whether closed
states always open to a particular conducting level. A
simple inspection of the raw records from doubly, triply, and fully liganded channels indicates that all conducting states can directly follow a closed state. The second question is whether the different conducting states
are connected to each other. Again, simple inspection
indicates that the conductance states are connected to
each other. Finally, given that there are multiple closed
states and open states, we would like to know which individual states are directly connected to each other. We
considered using maximum likelihood methods, but
the large number of states and the presence of stable
subconductance states made these methods impractical. Thus, we examined the connections between individual closed and open states by means of an adjacent state analysis (Magleby and Song, 1992; Colquhoun and
Hawkes, 1995
; Rothberg et al., 1997
). An assessment of
bursting behavior was used to corroborate the adjacent
state analysis. We then used simulations to test the models, which also provide a realistic correction for missed
events. The Appendix describes how the adjacent state
analysis, burst analysis, and model simulations led to the development of a connected state model.
We found that the single connected state model shown in Fig. 9 A, with rate constants given in Table III, could explain the kinetic data for doubly, triply, and fully liganded channels. The solid lines indicate connections that were used in all three liganded conditions, while the dashed lines indicate connections that were necessary to simulate data in only one or two of the liganded conditions. An additional closed state was observed in doubly liganded channels (CLL) and an additional open state was observed in fully liganded channels (O3LL). Furthermore, different connections between long-lived open states were used to simulate the behavior in doubly liganded versus triply and fully liganded channels. In triply and fully liganded channels, long-lived openings to the O3 states were interrupted by rapid transitions to and from the subconductance and closed states (see Fig. 1). This pattern was simulated most easily by connecting state O3L and the two short-lived conductance states (O2S and O1S), instead of connecting the long-lived open states.
|
|
|
Comparisons between real and simulated single channel traces for the three liganded conditions are shown in Fig. 10. Amplitude histograms are compared in Fig. 4, A and B, dwell-time constants are compared in Table II, and the adjacent state analyses (see Appendix ) are compared below in Fig. 11 and Table IV. Clearly, the connected state diagram in Fig. 9 A reproduces most of the single channel characteristics. We do not propose that this connected state diagram is unique. For instance, equivalent states could have been missed by equating the number of exponentials with the number of distinct states. However, adding more states does not change the main conclusion that locked channels can assume a large number of stable kinetic states. Including a larger number of states would probably obviate the need for diagonal connections in Fig. 9 A. Also, it may have allowed us to capture some of the more complex single channel behavior. For example, the tendency for short- and long-lived events to occur in clusters is not fully reproduced. Also, the bursting properties were similar, but not as robust as observed in the data (see Table V). At this resolution, however, there is not enough information to include more states. The fact that the data at each liganded level is reproduced by similar diagrams lends credence to the notion that the channel assumes a similar set of conformational states. Thus, this feature of the general allosteric model shown in Fig. 7 is supported by the data, where each row could be represented with the connected state diagram. However, a single conformational change as depicted in the general allosteric model is insufficient to account for all the states observed in the connected state model. A plausible extension of the general allosteric model is discussed below.
|
|
|
Although there are details of our model that remain uncertain, there are several salient features that
emerge from this analysis. First, subconductance states
are ligand dependent and are particularly prominent
in triply liganded channels. Thus, any successful model will have to include subconductance states as critical intermediate steps in gating. Furthermore, models will
have to include multiple kinetic states at all conducting
levels. Another noteworthy feature is the tendency for
bursting behavior to transpire without binding and unbinding of ligand. This bursting occurs at intermediate levels of liganding, when the channel is observed to
leave absorbing closed states, and then shuttle between
activated closed and open states. This suggests that in
locked channels two or more ligands give rise to bursts
by overcoming an energy barrier between the absorbing closed states and the activated states. Conversely, in
fully liganded channels, open states are so favorable
that returning to absorbing closed states is rarely observed. This behavior is described by the connected
state model and a mechanism for bursting very much
like this will have to be incorporated into any successful
model. Another feature that is essential to any model is
that in the fully liganded channel there is a direct, favorable path from an activated closed state to a stable,
long-lived fully open state. That is, opening to the O3
state rarely occurs in a staircase fashion (through subconductance openings). Such a sequential mechanism
appears to be operating in glutamate receptors (Rosenmund et al., 1998). However, in those channels, even
when one conductance state predominates (proposed
to arise from a particular liganded state), there are
brief transitions to other states. These transitions might
reflect a flexibility in those channels similar to that observed in the rod CNG channel.
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DISCUSSION |
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Mechanistic Implications of Locked Channel Data
To determine the effects of ligand binding on conformational changes in allosteric proteins, investigators
have generally been limited to adding different concentrations of free ligand. Even in single channel recording, in which there is an unprecedented resolution
of conformational states, it is difficult with this limitation to assign any observed behavior to a particular
liganded state. At any instant, it is virtually impossible
to know how many ligands are bound. Taking advantage of a method we developed for covalently tethering
ligands to single CNG channels (Ruiz and Karpen,
1997; Brown et al., 1993
), we have presented here a
complete kinetic analysis of single rod CNG channels
locked in each liganded state.
Remarkably, we have found that channels with a
fixed number of ligands in place exhibit interconversions among 9 or 10 different states: 4 different conductance levels (including closed) and more than 1 kinetically distinguishable state at each of those conductance levels. Many of these states were stable on the
millisecond time scale. The large number and complex
behavior of states (Fig. 2) cannot be explained by simple phenomena such as proton block, which has been
shown to cause two rapid subconductance states in catfish olfactory CNG channels (Goulding et al., 1992;
Root and MacKinnon, 1994
). The number of conducting states we observed at each liganded level is clearly
inconsistent with either simple concerted (MWC) or sequential (KNF) allosteric models. An attempt to explain the behavior with a somewhat more complicated
concerted model in which each conducting state arises
from a separate concerted transition from the closed
state also fails: when each conducting level is treated as
a single state, the apparent channel opening equilibrium constant does not change by a constant factor
with each ligand that binds (Table I). Most importantly,
the observation of two to five kinetically distinguishable
states at each conducting level violates both the letter
and intent of strictly concerted models, which were
proposed for their simplicity. However, with some limitations to our resolution of the precise rate constants for the different kinetic states, and lacking detailed
structural information, we cannot rule out that there
are some concerted transitions in the channel's activation pathway (see Varnum and Zagotta, 1996
).
The fact that approximately the same number of states
were observed in doubly, triply, and fully liganded channels suggests that the channel undergoes the same series
of conformational changes. On this idea, different numbers of bound ligands would favor certain states over
others. The success of the connected state model (Fig. 9) in simulating the intricate behavior in each liganded
state lends strong support to this overall hypothesis. The
number of distinct states that were observed at each
level of liganding is most easily explained by assuming
that there are activating conformational changes in
each individual subunit. The general allosteric model
(Eigen, 1968) shown in Fig. 7 postulates only a single
conformational change per subunit, and yet it comes
close to providing enough states. The only condition in
which it obviously falls short is the fully liganded channel. The model postulates 6 states with an assumption
of fourfold and 7 states for twofold rotational symmetry,
while 10 states were observed. If this model is part of activation, the fact that it provides enough states at lower
levels of liganding could indicate either that there are
additional conformations in fully liganded channels, or
that these additional states exist in lower liganded channels but were not resolved. The latter could be due to
limited kinetic resolution, to functionally equivalent
states, or to some states not being sufficiently populated.
In comparing the general allosteric model with the
connected state model (or, for that matter, with the behavior of any channel), it is not clear which states
would be closed and which would be open. Given that
there are four observed conductance states and five
stages of activation in the model, the following assumptions seemed quite reasonable (Fig. 9 B): channels with
zero and one activated subunits are closed; channels
with two adjacent subunits activated give rise to an
open state (O1), and channels with diagonally opposed
subunits activated are still closed; channels with three and four activated subunits give rise to different open
states (O2 and O3, respectively). This can account for
all of the closed states and is enough (or more than
enough) to account for the short-lived open states.
However, multiple O3 states, which probably require all
four subunits to be activated, are not easily explained. Furthermore, in the fully liganded channel, there are
four states missing. We assume therefore that the four
long-lived open states require additional conformational changes. The simplest way to expand the general
allosteric model is by introducing a second conformational change per subunit. Such a scheme has been
proposed for the activation of Shaker K+ channels (Zagotta et al., 1994). In this scenario, the fully liganded
state would be permitted 21 distinct conformations.
While possible, this seems a bit of an overcompensation
since the fully liganded state lacks only four open
states. An alternative way to expand the model is by
introducing a conformational change that requires a
change in the association of two adjacent subunits that have undergone a square-to-circle conformational
change (Fig. 9 B, crossed lines). In this speculative
model, we can limit the number of total states by requiring that this association occurs only on adjacent
subunits that have ligands bound. This predicts long-lived open states will occur only after at least two ligands are bound to the channel, in accordance with
our observations. The longest-lived open state (O3LL)
would arise from the association of two pairs of subunits in unison, which is possible only in the fully
liganded channel. Thus, the size of the conductance state (O1, O2, O3) could be determined by the number of subunits in the active conformation (circle conformations), and the lifetime (OS, OL, or OLL) could be
determined by whether or not adjacent subunits were
interacting. Altogether, this adds three conformations each to the doubly and triply liganded states and four
conformations to the fully liganded state.
Disparate regions of the channel protein have been reported to move during gating (see INTRODUCTION for references). This is not surprising given that binding of ligand in the COOH-terminal tail induces opening of the pore some distance away. These findings suggest that there is an intrinsic flexibility in each subunit, and lend support to our proposal that subunits undergo conformational changes in the absence or presence of ligand.
The connected state model allows us to examine
whether these apparent subunit-based changes occur
independently of each other or cooperatively. As closed
states proceed from inactive to activated states (that
lead to open states), it is clear that there is a progressive
increase in rates, apparent in all liganded states (Table
III). This contrasts with the expected decrease in rates (4, 3
, 2
,
) that would be predicted by subunits behaving independently. This suggests that as each subunit undergoes a conformational change, it increases
the probability that another subunit will do the same.
Thus, these subunit-based conformational changes appear to be occurring cooperatively. Similarly, the rates
from closed to open states do not appear to follow the
pattern for independence. This makes it more difficult
to predict the underlying structures for each state.
The speculative structural scheme in Fig. 9 B implies
that some of the conformational changes can occur in
more than one subunit simultaneously. These can be
thought of as concerted transitions that occur alongside single subunit-based changes. Two types of concerted transitions are depicted in Fig. 9 B: diagonal
lines indicating square-to-circle changes that occur simultaneously, and crossed lines indicating associations
between adjacent subunits. Sometimes the concerted
transitions would dominate (e.g., the transition between CS and O3S in the fully liganded channel), and
other times they would be relatively minor (e.g., the
transition between CS and O1S in the fully liganded
channel). Regarding the proposed changes in association between pairs of subunits, there is evidence that interactions between adjacent subunits can stabilize the
open state (Gordon and Zagotta, 1995b). These authors
showed that Ni2+ potentiation, which stabilizes the
open state, requires two histidine residues in adjacent
subunits. In another study (Varnum and Zagotta, 1996
), activation properties were different between homotetrameric channels that had two mutated subunits
adjacent to each other compared with channels with
the same two mutated subunits diagonally opposed to
each other. Recently, Liu et al. (1998)
proposed a mechanism that employs adjacent subunit interactions
(coupled dimer model) as the only means of opening
the channel. This model, however, was not based on
any kinetic analysis. Here, we have shown that there are
many more kinetic states than can be explained by
their two-step mechanism; however, we incorporate adjacent subunit interactions as a plausible means to extend the total number of conformational states of the
general allosteric model. It is important to realize that,
although the structural scheme depicted in Fig. 9 B can
explain the number of observed states with only two
types of conformational changes, there is no direct evidence for these particular structures.
Two Approaches for Studying the Contribution of Ligand Binding to Channel Gating
Liu et al. (1998) have recently taken issue with our assignment of the number of ligands attached to channel
binding sites, based on discrete shifts (in K1/2) in the
cGMP dose-response relations (Ruiz and Karpen,
1997
). They have suggested that spontaneous shifts in
our dose-response relations led to mistaken liganding assignments; however, such spontaneous shifts have
been ruled out in our experiments (see MATERIALS AND
METHODS). An advantage of our method is that we are
able to assess behavior in the same channel before and
after tethering ligands. A large number of dose-
response relations for single channels superimposed in
the control condition (Fig. 6 B), making the subsequent shift caused by the attachment of one ligand unmistakable (Ruiz and Karpen, 1997
). Most importantly,
the Po values obtained from locked channel data can
reconstruct the dose-response relation obtained from unmodified single channels (Fig. 6). In contrast, Fig. 6
also demonstrates that it is difficult to reconstruct the
single channel dose-response relation from wild-type
channels using the data of Liu et al. (1998)
. This fit to
unmutated, unmodified single channel data is crucial
since both approaches introduce modifications to the
normal ligand-bound channel.
We suggest that the data of Liu et al. (1998) are not
consistent with the opening of wild-type channels either because extensive mutagenesis has altered channel gating or because their assignment of the number
of active binding sites is incorrect. It remains a possibility that slightly different experimental conditions (e.g.,
high KCl on both sides of the membrane in their experiments) could have contributed to the observed differences. Nonetheless, the effect on gating that might
be caused by substituting a foreign pore region into retinal channels (RO133 subunits containing a catfish olfactory CNG channel pore) has been studied only in
homomultimeric channels and only at the macroscopic
current level (Goulding et al., 1993
). This is insufficient to determine whether single channel behaviors
change. In this vein, subtle single amino acid mutations in the pore have been shown to alter gating (e.g., Bucossi et al., 1997
). In addition, the mixing of replaced
pore regions and multiple binding site mutations may
have unforeseen effects on gating. For example, in the
study by Liu et al. (1998)
, a subunit with a double binding site mutation and a retinal pore expressed, while a
subunit with the same double binding site mutation
and an olfactory pore did not express.
Regarding the assignment of the number of active
binding sites, Liu et al. (1998) may have missed singly
liganded channels because they were limited to searching for robust channel activity with a well-defined conductance level. We have found that a singly liganded
channel rarely opens, and when it did open it was usually to brief subconducting levels. Thus, discrimination
between channels with a single active binding site and
those with no active binding sites would be challenging.
Their use of Ni2+ to improve the resolution of channel
conductance may not be reliable because some channel constructs could not be potentiated, and it has not
been shown which open states Ni2+ will stabilize. The
variability of Ni2+ potentiation among channel constructs further suggests that the extensive mutagenesis
affects gating.
The Potential Physiological Importance of Subconductance States
The low levels of channel activity (1-5%) that comprise
the dark current of rod outer segments (Nakatani and
Yau, 1988) suggest that under physiological conditions
subconductance states are likely to play a role in phototransduction. Fig. 4 D shows an amplitude histogram
averaged over five different channels in which free
cGMP produced activation between 1 and 5% (3% average). Subconductance states were occupied roughly
half the time [Po(O1 + O2) = 0.014 and Po(O3) = 0.013], and contributed about one third of the total current. Recently, Hackos and Korenbrot (1998)
reported the intriguing result that the Ca2+/Na+ permeability ratio changes as a function of cGMP concentration in retinal rod outer segments, suggesting that subconductance states may play an important role in
regulating internal Ca2+ concentrations.
Conclusions
Using a powerful approach that allows us to tether one ligand at a time to single CNG channels, we have presented a thorough kinetic analysis of channel gating at every level of liganding. The richness of channel behavior we observed indicates a complex mechanism of gating that has not been recognized before. Simple concerted and sequential mechanisms, as well as the simple coupled dimer model proposed recently, are easily ruled out. Instead, we propose that the same 10-state mechanism, including two subconducting levels and a fully conducting level, can explain gating in each liganded state. In structural terms, such a model can be accounted for by invoking more than one conformational change in each subunit.
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FOOTNOTES |
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Original version received 13 October 1998 and accepted version received 29 March 1999.
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APPENDIX |
---|
We present here adjacent state analysis, burst analysis,
and model simulation procedures that led to a preliminary connected state model. The adjacent state analysis
was simplified by grouping events into conductance
states and then by studying connections between defined kinetic states. When this procedure (see MATERIALS AND METHODS) was applied to doubly liganded
channels, strong evidence for two particular connections between open and closed states emerged. In Fig.
11 A (), the fraction of observations of the short-lived
O2 state (i.e., number of O2S events followed by CS/total number of O2S events that went to all closed states)
is plotted as a function of the closed times that immediately followed (grouped by ranges centered at the values of the different closed time constants). It is clear
that the highest proportion of O2S openings decayed to
the shortest closed state (CS), suggesting that there is a
direct transition from O2S to CS. The reverse transition (all closed states to O2S, Fig. 11 A,
) showed the same
trend, indicating that opening to the O2S state occurred from the CS state more often than from the
other closed states. The second clear connection was
between the short-lived O1 state (O1S) and an intermediate-length closed state (CM). The adjacent state analysis (Fig. 11 B) showed that the highest proportion of
O1S openings decayed to CM (
). The reverse transition from the CM state to O1S (
) was also more probable than opening to O1S from other closed states. However, there was also a significant fraction of transitions
between O1S and CS (~30%, compared with 42% between O1S and CM). When the percentages are this
close, it is possible that both connections are direct. Alternatively, it could happen that all O1S events are directly connected to CS, and go to CM only through a
connection between CS and CM. Since both CS and CM
are closed states, the only way a CS event can be observed is when the channel immediately reopens. Otherwise, a closed time that falls into the exponential distribution of the CM state (e.g., 11.5 ms) cannot be distinguished from a closed time made up of combined CS
and CM events [e.g., 1.5 ms (CS) + 11.5 ms (CM) + 2.0 ms
(CS), total closed time = 15 ms]. However, to observe
more O1S events go to CM than to CS, the rate between
CS and CM must favor the CM transition over any reopening transition. If this were the case, we would expect to observe more O2S events decay to CM. However,
the graph in Fig. 11 A clearly shows that ~90% of the
O2S events were adjacent to CS events, meaning the
rates for reopening must be higher than the rate to CM.
Therefore, we propose that both closed states (CS and
CM) can directly open to a single open state (O1S). The
O3 state was less prominent; however, the data also suggested a connection between the O3S state and short
closed states (not shown). For this analysis, we focused
on connections between short-lived states. Connections between long-lived states are generally more difficult to
determine since several short-lived states could occur in between.
To verify the simplified analysis described above, we
then calculated two-dimensional component dependencies that compare the number of observed adjacent
events to the number of expected adjacent events if the
events occurred independently of each other (Magleby
and Song, 1992; see MATERIALS AND METHODS). Table
IV shows that the component dependencies support
the connections deduced above. Independent pairing
of states results in a component dependency = 0; positive numbers reflect the percentage of observations that were in excess of the expected number (i.e., 0.08 means 8% more adjacent events were observed than expected), and negative numbers are the percentage below the expected number of observations. Thus, positive numbers suggest a direct connection is likely between two states, and a negative number suggests a
direct connection is unlikely. The numbers in the
"data" columns suggest that there are direct connections between O1S and CM, and between O2S and CS.
The value of 0.08 for O1S to CS suggests a possible direct connection, but does not provide strong support.
Conversely, direct connections from O2S to either CM
or CL are not indicated. The apparent connection from
O1S to CL may arise from an indirect O1S-CM-CL pathway, although we cannot rule out a direct connection.
A preliminary diagram that takes into account the number of observed states (see Table II) as well as the connections suggested by adjacent state analysis is shown in Scheme II (connections between the bracketed states are not yet determined).
|
As a first estimation, these connections appear to be consistent with the behavior observed in Fig. 1 for the doubly liganded channel. The most notable feature of the doubly liganded channel was that, although the overall open probability was very low, most openings occurred in bursts with short closings. This suggests that openings arise from short closed states or, put another way, that long closed states (CL, CLL, and CLLL) do not directly give rise to open states. Furthermore, it implies that short closed states represent more highly activated conformations than long closed states. Thus, close examination of bursting behavior seemed a good way to check our preliminary connections. First, we defined a burst as a group of consecutive events that contained at least 10 open events, and the only closed states within the burst could be classified as either CM or CS (the burst delimiter is the longest closed time allowed within the burst). This number of events was chosen to define a burst because there were three open and two closed states that we wanted to examine; 10 events seemed reasonable for all states to be represented. Results of the burst analysis are given in Table V. Interestingly, the mean number of openings per burst shows that all three open states (O1, O2, and O3) were accessible in the bursting state, as expected, but the O1 state was the predominant open state outside of bursts. This supports the notion that there might be two ways to open to O1: one in between bursts through CM, and another during bursting through CS. To test this idea further, the bursts were restricted to include mostly the shortest closed state (CS), and open states were reexamined. Since the exponentials we have attributed to the shorter closed states (CM and CS) were somewhat overlapping (see Fig. 8), it was not possible to obtain a complete separation of CM and CS events. However, the average closed time within the burst (Table V) shows that the CS state was in the majority. Upon inspection, all three open states occurred both before and after closing events within the burst, supporting the direct connections between CS and all three open states. Moreover, O1 events also occurred outside the bursts. This suggests that opening in between bursts probably occurs most often from the CM to the O1S state. Thus, the long interburst intervals appear to be transitions between long closed times that must pass through the CM state before opening.
Similar connected-state and burst analyses were applied to data from triply liganded channels, and the same direct connections from the shortest closed state (CS) to all three open states were observed. It is possible that what we are treating here as a single short closed state (CS) is really several states with similar time constants, but a single CS state is the most economical assumption.
Connections to long-lived openings are a bit more speculative. Long-lived openings were placed next to short openings of the same conductance, because transitions between short-lived openings of one conductance state and long-lived openings of another were sometimes observed without a closing between them. However, as discussed above, it is difficult to distinguish between transitions that enter long-lived states directly and transitions that enter a long-lived state by first passing through a short-lived state of the same conductance (e.g., O1S-O2S-O2L). Nonetheless, the data suggest there might be direct, diagonal connections between the long-lived O2L and both the short-lived O1S and O3S states in doubly liganded channels. These connections appeared to change with liganding so that more ligands caused direct diagonal connections between O1S (and possibly O2S) and O3L.
Further refinements to the preliminary model were made from simulating a variety of different configurations. For these simulations, the rate constants were first put into a matrix format. The rate constants for each transition were calculated by using the relationship:
![]() |
where ksi is the rate constant from state s to adjacent
state i, psi is the percent of total observed events from
state s that go to a given adjacent state i, and is the
lifetime of state s. Although there were five closed states
measured in doubly liganded channels, only four
closed states were used for simulations. This was reasonable, because the longest time constant was on the
order of seconds, similar to the long closed times that
were removed from the analysis by means of stability
plots (see MATERIALS AND METHODS). The omission of
this long-lived state did not significantly affect the
opening behavior that was simulated in the doubly
liganded model, although I/Imax was slightly higher
than that measured from real data. To compare the
properties of each configuration tested, the simulated
data were analyzed in exactly the same way as the original data: single channel traces were inspected for their
qualitative features, and amplitude and dwell-time histograms were constructed and fit. The overall configuration that best described all these aspects of the data at
different levels of liganding is the connected state
model shown in Fig. 9 A.
We thank R.W. Aldrich, R.L. Brown, Y. He, A.R. Martin, and T.C. Rich for comments on the manuscript.
This work was supported by a grant from the National Eye Institute (EY-09275 to J.W. Karpen). ML. Ruiz was the recipient of a National Research Service Award (EY-06713).
![]() |
Abbreviations used in this paper |
---|
APT, 8-p-azidophenacylthio; CNG channel, cyclic nucleotide-gated channel; KNF, Koshland-Nemethy-Filmer; MWC, Monod-Wyman-Changeux.
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