From the Department of Molecular and Cellular Physiology and Howard Hughes Medical Institute, Stanford University, Stanford, California 94305
The kinetic and steady-state properties of macroscopic mslo Ca-activated K+ currents were studied in excised patches from Xenopus oocytes. In response to voltage steps, the timecourse of both activation and deactivation, but for a brief delay in activation, could be approximated by a single exponential function over a wide range of voltages and internal Ca2+ concentrations ([Ca]i). Activation rates increased with voltage and with [Ca]i, and approached saturation at high [Ca]i. Deactivation rates generally decreased with [Ca]i and voltage, and approached saturation at high [Ca]i. Plots of the macroscopic conductance as a function of voltage (G-V) and the time constant of activation and deactivation shifted leftward along the voltage axis with increasing [Ca]i. G-V relations could be approximated by a Boltzmann function with an equivalent gating charge which ranged between 1.1 and 1.8 e as [Ca]i varied between 0.84 and 1,000 µM. Hill analysis indicates that at least three Ca2+ binding sites can contribute to channel activation. Three lines of evidence indicate that there is at least one voltage-dependent unimolecular conformational change associated with mslo gating that is separate from Ca2+ binding. (a) The position of the mslo G-V relation does not vary logarithmically with [Ca]i. (b) The macroscopic rate constant of activation approaches saturation at high [Ca]i but remains voltage dependent. (c) With strong depolarizations mslo currents can be nearly maximally activated without binding Ca2+. These results can be understood in terms of a channel which must undergo a central voltage-dependent rate limiting conformational change in order to move from closed to open, with rapid Ca2+ binding to both open and closed states modulating this central step.
Key words: mslo; BK channel; voltage dependence; Ca2+ binding; gatingLarge conductance Ca-activated potassium channels
(BK channels)1 comprise a large group of membrane
proteins found in a wide variety of cells (Latorre et al.,
1989). These channels are identified by their potassium
selectivity and large single channel conductance, as
well as by their ability to sense changes in both membrane voltage and intracellular Ca2+ concentration (Lux
et al., 1981
; Marty, 1981
; Pallotta et al., 1981
; Barrett et
al., 1982
; Latorre et al., 1982
; Latorre et al., 1989
; Marty,
1989
; McManus, 1991
). When activated by an increase in intracellular Ca2+, BK channels respond with increased open probability and concomitantly increased
K+ flux. These channels therefore can serve as a link
between cellular processes which involve intracellular
Ca2+ elevation and those which involve membrane excitability.
The proper functioning of BK channels depends not
only on their ability to sense changes in membrane potential or intracellular Ca2+ concentration but also on
the time course of their response. This is perhaps best
exemplified in the inner hair cells of the turtle cochlea.
Here, it has been demonstrated that there is a correlation between the frequency to which a particular hair
cell is tuned and the kinetic properties of the BK channels native to that cell, suggesting that the kinetic behavior of these channels is critical for determining the
frequency of the electrical oscillations in the hair cell
during auditory stimulation (Hudspeth and Lewis, 1988a,
b
; Art et al., 1995
; Wu et al., 1995
).
Because the kinetic behavior of ion channels in general, and BK channels in particular, is critical for their
proper function, and this behavior necessarily reflects
the number and sequence of conformational states that
a channel assumes as it gates, researchers have been interested in relating channel kinetics to the protein's underlying conformations. For BK channels this effort
has been most successful at the single channel level
where BK currents can be unambiguously identified
and the internal Ca2+ concentration easily controlled.
Extensive single channel studies on native BK channels
have led to a kinetic picture in which there are at least
five closed states and three open states with many paths
between closed and open (McManus and Magleby,
1988; 1991
). Hill analysis indicates that from two to perhaps as many as six Ca2+ ions can bind to the channel
simultaneously, and it is likely that the different open
states differ in the number of Ca2+ molecules bound
(Barrett et al., 1982
; Methfessel and Boheim, 1982
; Moczydlowski and Latorre, 1983
; McManus et al., 1985
; Golowasch et al., 1986
; Oberhauser et al., 1988
; McManus,
1991
; McManus and Magleby, 1991
; Art et al., 1995
).
The voltage sensitivity of BK channel gating has been
less extensively studied than its Ca2+ sensitivity. Single
channel studies suggest, however, that the mechanism
by which BK channels sense the membrane voltage may not be the same as that used by purely voltage-gated K+
channels. In an extensive kinetic study, Moczydlowski
and Latorre (1983) suggested that the voltage dependence of the gating properties of single skeletal muscle
BK channels can be explained if it is supposed that the
binding of Ca2+ to the channel is influenced by the
transmembrane electric field, and it is this voltage sensitivity in Ca2+ binding that confers voltage-dependent
gating properties on the channel rather than the action
of voltage sensing elements intrinsic to the channel's
primary sequence (see also Salomao et al., 1992
). However, other studies have suggested, often on the basis of
less extensive data and analysis, separate voltage-dependent and Ca-dependent steps in activation (Methfessel
and Boheim, 1982
; Blair and Dionne, 1985
; Pallotta,
1985b; Cornejo et al., 1987
; Singer and Walsh, 1987
;
Wei et al., 1994
; DiChiara and Reinhart, 1995
; Meera et al., 1996
). Despite this previous work, the nature of the
voltage-sensitive gating remains an open question.
The cloning of the pore forming subunits of several
BK channels (Atkinson et al., 1991; Adelman et al.,
1992
; Butler et al., 1993
; Tseng-Crank et al., 1994
; McCobb et al., 1995
; Wallner et al., 1995
) has revealed some
structural similarity between slo channels and shaker -type, purely voltage-gated K+ channels. Although slo
channels contain approximately twice as many amino
acids as does a shaker channel, over the first ~330 amino acids of slo their predicted topologies are quite
similar. slo channels contain a sequence homologous to
the P region which forms a portion of the ion conducting pore and the selectivity filter of the shaker channel
(MacKinnon and Yellen, 1990
; Yellen et al., 1991
; Yool
and Schwarz, 1991
; Heginbotham et al., 1992
; 1994
), as
well as six (or seven, see Wallner et al., 1996
) putative membrane spanning regions. The fourth such region
(S4) contains several positively charged residues spaced
in a similar manner as those found in the corresponding S4 region of voltage-gated ion channels. The S4 regions form, at least in part, the voltage sensing elements of these channels (Liman et al., 1991
; Lopez et
al., 1991
; Papazian et al., 1991
; Logothetis et al., 1993
; Sigworth, 1994
; Yang and Horn, 1995
; Aggarwal and
MacKinnon, 1996
; Larsson et al., 1996
; Mannuzzu et
al., 1996
; Seoh et al., 1996
; Yang et al., 1996
). The sequence of the remaining ~840 amino acids of slo channels appear to be unique to this channel family and is
likely to contain Ca2+ binding domains (Lagrutta et al.,
1994
; Tseng-Crank et al., 1994
; Wei et al., 1994
).
The structural homology between cloned BK channels and voltage-gated K+ channels is perhaps surprising given the lack of intrinsic voltage sensitivity suggested by previous single channel experiments (Moczydlowski and Latorre, 1983). It again raises the question
as to whether the voltage-dependence of BK channel
gating may be due at least in part to an intrinsic voltage
sensing domain. Indeed the recent work of Wei et al.
(1994)
in which the COOH-terminal domain of dslo
was combined with the NH2-terminal domain of mslo
suggests that this may be the case. Reports of voltage-dependent activation of BK channel currents at very
low Ca2+ concentrations and after treatment to remove
Ca2+ sensitivity suggest the possibility of an intrinsic
voltage dependence as well (Barrett et al., 1982
; Methfessel and Boheim, 1982
; Wong et al., 1982
; Findlay et
al., 1985
; Pallotta, 1985b; Meera et al., 1996
).
To address this question, and to understand further the gating mechanisms of BK channels, we have taken advantage of the ability to express cloned channels at high density in Xenopus oocyte membranes to study the kinetic and steady-state properties of mslo macroscopic currents over a wide range of internal Ca2+ concentrations and membrane voltages. In this paper we present the basic steady-state and kinetic properties of these currents and discuss constraints these data place on any system designed to model the gating behavior of the mslo channel. A result of particular importance is that our data are not consistent with a model of mslo gating which ascribes the majority of the voltage dependence of activation to voltage-dependent Ca2+ binding; but rather, it is necessary to suppose that charges intrinsic to the channel protein are involved in voltage sensing. In fact, we find that with strong depolarizations it is possible to nearly maximally activate mslo channels at very low Ca2+ concentrations, so low as to not allow time for Ca2+ to bind to the channel before opening. Based on our analysis, a general scheme Is proposed to account for the relationship between Ca-dependent and voltage-dependent activation of the mslo channel.
Unless otherwise indicated, experiments were done using the
conditions defined in the preceding paper (Cox et al., 1997). These conditions together with the appropriate analysis techniques allow for the discrimination between current properties
arising from gating and those which are due to changes in channel permeation or block (Cox et al., 1997
).
Voltage-dependent Properties of mslo Gating
One of the goals of this study is an extensive characterization of the macroscopic gating kinetics of mslo channels. Shown in Fig. 1 A is an experiment designed to examine the voltage dependence of mslo activation at a
constant [Ca]i. [Ca]i was buffered to 10.2 µM, and at 2-s
intervals an excised membrane patch containing ~60
mslo channels was stepped from 100 mV to a series of
increasingly more positive potentials. Several features
of these currents are worth noting. First, at
100 mV
the mslo channels were very seldom open as is indicated
by the very low level of steady-state current. This was
the case despite the presence of 10.2 µM Ca2+ in the solution exposed to the intracellular face of the patch, and thus demonstrates that, at this concentration, a
negative membrane voltage can overcome any activating effects of Ca2+. Second, upon depolarization, outward currents were observed which relaxed to their new
steady-state level with a nearly single exponential time
course. This can be seen most clearly in the middle
panel in which a subset of traces have been expanded
and fitted with exponential functions. There is some evidence, however, for a brief delay in the activation process. That is, when exponential fits such as those in Fig.
1 A are extrapolated backward in time to the point of
zero current, they typically cross the time axis 75-175
µs after the beginning of the voltage step. After taking into account the appropriate filter delay (~33 µs, 4 pole bessel filter at 10 kHz), this result suggests an actual delay of 50-150 µs. Due to complications in directly observing the time course of ionic currents during the first ~100 µs after the voltage step, it is difficult
to assess whether this apparent delay is an inherent property of the gating of mslo channels, or rather, at
least in part an artifact produced by the subtraction of
capacity and leak currents from the raw data before
analysis. For this reason we have not emphasized this
delay in our analysis and, in order to avoid errors, have
fitted the time course of both activation and deactivation starting usually 200 µs after the beginning of the voltage step. Preliminary experiments specifically designed to examine very early times in the activation process, however, suggest that this brief delay may truly reflect an aspect of the mslo gating process (see also Ottalia et al., 1996
), and therefore further investigation is
certainly warranted. And third, over the voltage range
examined the time constant of mslo channel activation decreases with increasing voltage (Fig. 1 A, right).
The primarily exponential time course of activation suggests that, at 10.2 µM [Ca]i, a single conformational change limits the rate at which mslo channels move from closed to open. The increasing rate of activation with increasing voltage could be explained if this conformational change were voltage dependent. To estimate the charge associated with this forward rate limiting transition we fitted the relationship between the time constant of activation and membrane voltage (Tau-V) with an exponential function. We limited the fit to depolarized voltages where reverse rates are likely to contribute less to the time course of activation. The fit superimposed on the data in Fig. 1 A (right) yielded a gating charge of 0.71 e. We found this estimate to be sensitive to the exact voltage range used and to whether or not the minimum of the exponential was allowed to vary. This estimate therefore is likely to represent only a rough approximation of the charge associated with this transition. From patch to patch, allowing the minimum to vary, this method yielded charge estimates ranging from 0.55 to 0.76 e (for mean see Table II). To obtain a lower limit for this number we fit the Tau-V curve over a wider voltage range, and fixed the minimum of the exponential to 0. Considering a single voltage-dependent rate limiting step in activation, at intermediate voltages where forward and backward rates become comparable, the contribution of the backward rate constant will be to decrease the observed activation time constant. This method is therefore likely to lead to an under estimate of the true charge. For the data in Fig. 1 A, fitting in this way produced an estimate of 0.47 charges (for mean see Table II).
Table II. Rate Limiting Charge Estimates |
Standard tail current protocols were used to study the voltage dependence of mslo deactivation. At 10.2 µM [Ca]i (Fig. 1 B), depolarizing voltage steps were applied to near maximally activate the channels, followed by hyperpolarizing steps to various potentials. Upon hyperpolarization, the channels closed, and the extent of tail current decay was voltage dependent. The time course of deactivation could be well approximated by a single exponential function over the entire voltage range examined (Fig. 1 B, middle), again suggesting a rate limiting conformational change between open and closed. The deactivation time constant was appreciably voltage dependent, increasing with depolarization. In Fig. 1 B (right), the time constant of deactivation, determined from exponential fits, is plotted as a function of membrane voltage. The charge associated with the apparent rate limiting backward transition in deactivation was estimated in a similar manner to that of activation. Exponential fits to the most hyperpolarized region of the Tau-V data (Fig. 1 B, right) yielded charge estimates ranging from 0.54 to 0.80 e (for mean see Table II). Fitting these Tau-V curves over a wider voltage range provided lower limit estimates of between 0.42 and 0.57 e.
Shown in Fig. 1 C is the conductance vs. voltage (G -V)
relationship derived from the current traces in Fig. 1 A.
The maximum slope of this relation, which is an indication of the voltage sensitivity of the channel, is less
steep for mslo than for most purely voltage-gated K+
channels suggesting that there may be comparatively
less charge movement accompanying mslo gating. G-V
curves for mouse Kv1.1(Grissmer et al., 1994) and
Kv2.1(Pak et al., 1991
) channels have been placed on
Fig. 1 C for comparison. The mslo G-V curve has been
fitted (solid line) with a Boltzmann function with an associated equivalent gating charge of 1.54 e, and a half
activation voltage (V1/2) of +34.6 mV. Notice that the
equivalent gating charge associated with this fit (which
represents a lower limit for the true gating charge of
the channel) is approximately equal to the sum of the equivalent charges associated with forward and backward rate limiting kinetic transitions. Taking into account as well the monoexponential nature of current
relaxations, these data point to a channel which, at 10.2 µM [Ca]i, can be well approximated by a two-state system with similar voltage dependence in forward and
backward transition rates:
Scheme I.
Fits assuming such a model have been included in the Tau-V and G-V graphs of Fig. 1.
Ca2+-dependent Properties of mslo Gating
To examine the Ca2+ dependence of mslo gating, we recorded macroscopic currents with protocols similar to
that of Fig. 1 at a variety of [Ca]i, from 0.84 to 1,000 µM
(Figs. 2 and 3). In each experiment, as [Ca]i was increased it was necessary to hyperpolarize the holding
voltage to maintain a low level of basal activity, as well
as to adjust the range of the test voltages to accommodate the shifting activation range of the channels. What
is perhaps most interesting in these data is that the essential characteristics of the mslo current traces recorded with 10.2 µM [Ca]i (Fig. 1) were maintained
over the entire [Ca]i range tested. At each [Ca]i over
the voltage range in which the time course of current
relaxation could be accurately determined, the rate of
activation increased with depolarization, and the rate
of deactivation generally decreased. Also, the kinetics
of both activation and deactivation could be well fitted
with single exponential functions (Figs. 2 and 3, middle
panels), suggesting that the kinetics of activation and deactivation are dominated by a single conformational
change. As was the case at 10.2 µM [Ca]i, however, at
each [Ca]i when exponential fits to the time course of
activation were extrapolated to the point of zero current, they typically crossed the time axis between 50 and 150 µs after the onset of the voltage pulse, again
suggesting the presence of a brief delay in the activation process.
Shown in the right panels of Figs. 2 and 3 are plots of
the time constants of activation (Fig. 2) and deactivation (Fig. 3) as a function of voltage. The charges associated with the rate limiting transitions at each [Ca]i
were estimated in the same manner as was done for the
data in Fig. 1. As [Ca]i was varied the charge estimates
associated with both forward and backward rate limiting transitions remained similar to that observed at 10.2 µM [Ca]i. Although for activation there was a
trend toward somewhat smaller charge estimates as
[Ca]i was increased (see Table II), the predominant effect of raising [Ca]i was simply to translate the Tau-V
curves of both activation and deactivation leftward
along the voltage axis with little change in the voltage dependence of the kinetics (Fig. 4).
In addition to shifting the kinetics of mslo gating, raising [Ca]i caused a similar leftward shift in the G-V relationship. In Fig. 5 A is displayed a set of G-V curves recorded from a single membrane patch, and in Fig. 5 B
are shown average G-V relations from several experiments. Curves corresponding to 0.84, 1.7, 4.5, 10.2, 65, 124, 490, and 1,000 µM [Ca]i are displayed. With both Tau-V curves (Fig 4) and G-V curves, for a given fold increase in [Ca]i, we see a larger shift at low [Ca]i (e.g.,
between 0.84 and 10.2 µM) than at higher [Ca]i (e.g.,
between 124 and 1,000 µM). As will be discussed later,
this property with regard to the Ca2+ dependence of
the G-V relation is in agreement with previously published data (Wei et al., 1994) and has important implications for the physical relationship between Ca2+ binding
and voltage sensing. As [Ca]i was varied, the G-V relation maintained a shape which could be approximated by a
single Boltzmann function, and the slope of this relation was similar at each [Ca]i (Table I). That is, as with
the kinetics of activation and deactivation, the predominant effect of an increase in [Ca]i was to simply translate the G-V curve leftward along the voltage axis. Similar data have been published for both native (Barrett et
al., 1982
; Latorre et al., 1982
; Methfessel and Boheim,
1982
; Moczydlowski and Latorre, 1983
; Markwardt and
Isenberg, 1992
; Art et al., 1995
; Giangiacomo et al.,
1995
) and cloned (Butler et al., 1993
; Tseng-Crank et al., 1994
; Wei et al., 1994
; DiChiara and Reinhart, 1995
;
McCobb et al., 1995
; McManus et al., 1995
; Wallner et
al., 1995
; Meera et al., 1996
) BK channels.
Table I. Steady-state G-V Parameters |
We did, however, see some change in the slope factor
of fits to the mslo G-V relation as [Ca]i was varied. In
particular there was a trend toward shallower slopes as
[Ca]i was increased above 1.7 µM. In Fig. 5 A, for example, equivalent gating charge estimates as determined
from Boltzmann fits varied between extremes of 1.88, at 1.7 µM [Ca]i, to 1.18 at 1,000 µM [Ca]i. This is representative of the behavior observed in several experiments (see Table I and Fig. 5 B) and is therefore not
due to random variability in the data. As discussed in
the preceding paper (Cox et al., 1997), contaminant
Ba2+ block at high voltages might cause a small increase
in the steepness of the G-V curve measured at 0.84 µM
[Ca]i. At 1.7 µM [Ca]i and above, however, the G-V
curve spans less depolarized voltages, and Ba2+ block is
not likely to have a significant effect (Cox et al. 1997
).
Therefore, this trend may reflect a genuine change in
the voltage dependence of mslo gating as [Ca]i is increased.
The effects of varying [Ca]i are more easily seen
when a single voltage is considered (Fig. 6). In Fig. 6 A
are shown several traces recorded in response to voltage steps to +70 mV. Traces labeled a through f were
recorded at increasing [Ca]i (see legend). Several features of these currents are apparent. First, as expected for a Ca-activated channel, peak current amplitude increased with [Ca]i. This point is only strictly true for
the traces recorded in the [Ca]i range 0.84-124 µM. At
higher [Ca]i, peak current actually declined. This decline, however, became more pronounced as [Ca]i was
increased and was not associated with a decline in tail
current amplitude at 80 mV. It can therefore be attributed to voltage-dependent Ca2+ block (see preceding paper in this issue, Cox et al., 1997
) and as such is
not indicative of an actual reduction in channel activity. Second, as can be seen when the currents in A are
normalized to their maxima (Fig. 6 B), the rate of current activation increased with increasing [Ca]i, while
the rate of deactivation decreased (Fig. 6 C). And third,
as emphasized by the exponential fits superimposed on
the traces in B and C, the primarily monoexponential
nature of both activation and deactivation was maintained as [Ca]i was varied.
Plotted in Fig. 6 D is the relationship between relative
conductance and [Ca]i at +70 mV. This relation was
determined from the G-V curves of Fig. 5, amounting
essentially to a transformation of these data to [Ca]i
dose response form. As was the case for the G-V relations, G/Gmax plotted on the ordinate is proportional to open probability. The smooth curve through the
data represents a fit to the Hill equation below (Hill,
1910).
![]() |
(1) |
Here KD represents the apparent Ca2+ dissociation constant, n the Hill coefficient, and A the maximum value
of G/Gmax. The Hill coefficient (n = 3.08) from this fit
is within the range of values reported in studies of single BK channel gating (Barrett et al., 1982; Moczydlowski and Latorre, 1983
; Golowasch et al., 1986
; Oberhauser et al., 1988
; McManus and Magleby, 1991
). The
fact that this value is greater than 1 indicates that more
than one Ca2+ molecule binds to the mslo channel, and
that Ca2+ binds in a cooperative manner (Adair, 1925
).
The apparent KD determined from the fit is 1.44 µM.
Plotted in Fig. 6 E is the relationship between the macroscopic rate constant of mslo current activation (the reciprocal of the time constant) and [Ca]i also at +70 mV. There is not a linear relationship between these variables as would be expected from a system whose macroscopic rate constant was limited by a Ca2+ binding transition. The data are better described by a hyperbolic function which approaches a saturating value at high [Ca]i. This result indicates that changes in the rate constants of kinetic transitions which involve Ca2+ binding no longer affect the kinetic behavior of the system at high [Ca]i. This saturating behavior cannot be explained by kinetic schemes which involve only Ca2+ binding steps. Considering, for example, a scheme composed of a string of n Ca2+ binding steps:
[View Larger Version of this Image (36K GIF file)]Scheme II.
the activation time course for SCHEME II will contain
(n 1) exponential components. As [Ca]i is increased,
the forward rates become much larger than the backward rates, and each of the macroscopic rate constants
of the system approaches one of the first order forward
rate constants. Thus, at high [Ca]i, each of the macroscopic rate constants (ri) becomes a linear function of
[Ca]i.
![]() |
(2) |
To account for the saturating behavior in Fig. 6 E then, there must be at least one elementary step in the gating of the mslo channel which does not involve Ca2+ binding and serves to limit the rate of activation at high [Ca]i. The minimum scheme contains one Ca2+ binding step and one Ca-independent step (SCHEME III below).
[View Larger Version of this Image (22K GIF file)]Scheme III.
In general, a three-state kinetic scheme like SCHEME III will have a relaxation time course described by the sum of two exponential functions. This is contrary to the monoexponential nature of the mslo currents. The kinetic behavior of SCHEME III, however, will be dominated by a single exponential component if the rate constants for one step are fast relative to those for the other step. For mslo it would have to be the Ca2+ binding step which equilibrates most rapidly; otherwise, the activation rate could not become Ca-independent at high [Ca]i. Making this designation then, the dominant macroscopic rate constant r for SCHEME III becomes:
![]() |
(3) |
This function is the rectangular hyperbola used to fit the data in Fig. 6 E (solid line), thus demonstrating that by including a Ca-independent step a very simple system can account for the saturating behavior of the macroscopic rate constant of activation at high [Ca]i.
SCHEME III, however, is not sufficient to account simultaneously for the Ca2+ dependence of the macroscopic rate constant of activation at +70 mV and the
macroscopic rate constant of deactivation at 80 mV
(Fig. 6 F). As with activation, the kinetics of deactivation become much less Ca2+ sensitive at high [Ca]i. At
lower concentrations, however, deactivation kinetics
are slowed rather than accelerated as [Ca]i is increased. This behavior cannot be explained by SCHEME III because, according to Eq. 3, under no condition will the
relaxation rate of this system decrease as [Ca]i is increased. To account for the Ca2+ dependence of both
activation and deactivation kinetics it is necessary to
add another Ca-dependent step to SCHEME III.
Scheme IV.
If a Ca2+ binding step is added after opening (SCHEME IV), again assigning rapid Ca2+ binding on and off rates to maintain exponential kinetics, the macroscopic rate constant for SCHEME IV is approximated by:
![]() |
(4) |
This equation contains two terms, one containing weighted by the fraction of closed channels in C1 which
increases with increasing [Ca]i and the other containing
weighted by the fraction of open channels in O2
which decreases with increasing [Ca]i. Whether the
macroscopic rate constant of this system increases or
decreases as [Ca]i is increased will depend upon which
term is changing more rapidly. In general, depending
on the specific binding and unbinding rates, when
is
greater than
, the first term will increase more rapidly
than the second term decreases, and the macroscopic
relaxation rate constant of the system will increase with
increasing [Ca]i. Conversely, when
is greater than
,
the second term will change more rapidly than the first, and the macroscopic relaxation rate constant will decrease as [Ca]i is increased. In either case, at high [Ca]i,
saturation is expected with rsat equal to
. Therefore, if
the rate constants
and
were to change with voltage,
SCHEME IV could qualitatively explain both the increasing rate of mslo current activation as a function of [Ca]i
at +70 mV and the decreasing rate of deactivation as a
function of [Ca]i at
80 mV. The data in Fig. 6 E and F
have been fitted with Eq. 4 (dashed lines) simply by changing the values of
and
.
Another observation we might make with regard to the data in Fig. 6 is that at +70 mV it takes less Ca2+ to saturate the channel's steady-state conductance G/Gmax (which is proportional to open probability) than it does to saturate the macroscopic rate constant of activation. Can we understand this behavior in terms of SCHEME IV as well? To answer this question it is useful to write the open probability of SCHEME IV as:
![]() |
(5) |
and compare it to the expression for the relaxation rate
constant, Eq. 4. The differences between these expressions are that the terms involving and
in Eq. 4 are
now in the denominator of Eq. 5, and the term containing
is in the numerator. This term represents
weighted by the fraction of channels occupying state C1
at equilibrium. Supposing that
and
are voltage-
dependent and that
is several fold larger than
at
+70 mV, it will then not be necessary for the closed
state Ca2+ binding step to be saturated for the channel
to be very nearly maximally activated. It is necessary only
that
{1/(1 + k
1/k1[Ca])}, which increases with [Ca]i,
be much larger than
(1
{1/(1 + k
3/k3[Ca])}),
which decreases with [Ca]i. As is evident from Eq. 4,
however, in order for the kinetic behavior of the system
to be saturated, the closed state binding step must be fully saturated, and therefore [Ca]i must be severalfold
greater than KD1 (k
1/k1). Thus it is clear that, given a
wide rage of parameters, SCHEME IV predicts another
aspect of the data: the apparent KD estimated from
steady-state conductance measurements might be considerably smaller than that estimated from kinetic measurements.
mslo Gating Involves Voltage-dependent Steps which Are Distinct from Ca2+ Binding Steps
The preceding analysis illustrates that many aspects of
mslo gating can be understood, at least qualitatively, in
terms of a central closed to open, voltage-dependent,
conformational change flanked by rapid Ca2+ binding
steps. In fact, Methfessel and Boheim (1982) have proposed a model which takes the form of SCHEME IV to account for the Ca-dependent and voltage-dependent
gating properties of single skeletal muscle BK channels.
Moczydlowski and Latorre (1983)
, however, were able to account for many properties of those same channels
by considering a scheme Identical to SCHEME IV excepting that all of the voltage dependence of the system resided in the voltage dependence of Ca2+ binding. Models based on their idea can successfully predict several
features of our data: (1) approximately exponential kinetic behavior, (b) a G-V relation which can be approximated
by a Boltzmann function at any [Ca]i, (c) channels which
can be both maximally activated and deactivated at any
nonzero [Ca]i, and (d) a leftward shift in the G-V curve
when [Ca]i is increased. However, as also shown by Wei
et al. (1994)
such a gating mechanism can be tentatively excluded for mslo based on the observation that
for each 10-fold increase in [Ca]i the channel's G-V
curves are not evenly spaced (Fig. 5, see also DiChiara
and Reinhart, 1995
).
To see that this is the case, it is useful to first consider
the simplest form of a voltage-dependent binding mechanism in which there is a single Ca2+ binding site some
distance into the plasma membrane such that in binding, Ca2+ traverses a fraction of the membrane voltage
(the electrical distance). In this case the probability
of the binding site being occupied by Ca2+, and thus
the channel being open (Po), depends on [Ca]i as follows (Woodhull, 1973
).
![]() |
![]() |
(6) |
where F represents Faraday's constant, R the universal gas constant, T temperature, and KD(0) the Ca2+ dissociation constant at 0 mV. Analyzing Eq. 6 in terms of the voltage required to reach half maximal activation (V1/2), we see that for Po equal to 0.5, we must have
![]() |
(7) |
This equation can be rewritten as
![]() |
(8) |
(Wong et al., 1982) which predicts a logarithmic relationship between V1/2 and [Ca]i.
Plotted in Fig. 5 C is the relationship between V1/2
and [Ca]i for the data in Fig. 5 A (closed circles). Also
shown are the average V1/2 values from several experiments (open squares). The curvature in these plots is indicative of the closer spacing of the G-V curves at
higher [Ca]i. This behavior was seen in every experiment in which G-V curves where determined at 3 or
more [Ca]i (n = 13). In the experiment of Fig. 5 A
Ca2+ was presented to the patch in the following order:
1.7, 4.5, 65, 490, 124, 10.2, 0.84, and 1,000 µM, thus ruling out the possibility that the tendency toward closer
G-V spacing at high [Ca]i was due to a slow, time-dependent change in mslo current properties. From the curvature in the plot of Fig. 5 C then, we can rule out the single voltage-dependent Ca2+ binding site model. However, mslo is thought to be a tetramer (Shen et al.,
1994), and is likely to have more than one Ca2+ binding site (Fig. 6 D). Nevertheless, it turns out that for a
large class of models with multiple binding sites a logarithmic relationship between V1/2 and [Ca]i is predicted.
The following statement holds true: For models of
channel gating in which the voltage dependence of gating resides solely in the voltage dependence of Ca2+
binding, regardless of the number of Ca2+ binding sites
or their affinities for Ca2+, there will be a logarithmic
relationship between V1/2 and [Ca]i so long as the electrical distances of all the binding sites are equivalent. A
conclusion very similar to this was arrived at by Wei et
al. (1994)
through simulations of various possible gating schemes. Below we provide a mathematical argument which extends their analysis.
In a channel with multiple binding sites, whose occupancy somehow relates to channel opening, the probability of a given site being occupied by Ca2+ at any given time will depend on the Ca2+ concentration and the affinity of each site, such that the overall probability of the channel being open is a function of all of the dissociation constants:
![]() |
(9) |
where K1 through Kn represent the Ca2+ dissociation constants of binding sites 1 through n, and C represents the combined effects of all elementary steps not involving Ca2+ binding. If Ca2+ binding is voltage dependent, then each dissociation constant can be written as
![]() |
(10) |
where j ranges from 1 to n, Kj(0) represents the Ca2+
dissociation constant of the jth site at 0 mV, and j represents the electrical distance of the jth site. From Eq. 10 we may write for each binding site in Eq. 9:
![]() |
(11) |
![]() |
(12) |
![]() |
![]() |
(13) |
From Eqs. 11, 12, and 13, we see that Xj varies logarithmically with [Ca]i, and that in order to maintain (V Xj) constant in Eq. 11, and therefore [Ca]/Kj constant as
well, the necessary change in membrane voltage will be
equal to the change in Xj. That is,
![]() |
(14) |
If we suppose, as stipulated above, that all Ca2+ binding sites have the same voltage dependence,
![]() |
(15) |
then as [Ca] is varied the change in voltage necessary to maintain [Ca]/Kj constant is the same at each binding site and given as
![]() |
(16) |
Because we are considering cases in which all of the channel's voltage dependence resides in Ca2+ binding steps, the change in Po in response to a change in voltage is determined solely by the effects of voltage on the Ca2+ binding equilibria (i.e., C in Eq. 9 is independent of voltage), and therefore the change in voltage necessary to maintain Po constant as [Ca]i is varied is also given by Eq. 16. A logarithmic relationship is therefore expected between a change in [Ca]i and the change in voltage necessary to maintain any specific Po. Choosing Po equal to 0.5 as a convenient reference, the voltage necessary to maintain Po = 0.5 is explicitly given as the following function of [Ca]:
![]() |
(17) |
Here [Ca]1/2 is defined as the concentration of Ca2+ necessary to half maximally activate the channels at 0 mV.
Thus, we can say that the data in Fig. 5 are inconsistent with gating models in which the voltage dependence lies solely in Ca2+ binding to binding sites having
equivalent electrical distances. When the electrical distances are not the same, the effect of voltage is different at each site and the situation is more complex. Two
aspects of our data, however, suggest that if the voltage dependence of mslo gating were to arise solely from
voltage-dependent Ca2+ binding, then the electrical distances for the mslo Ca2+ binding sites would have to be
similar. The first is that computer simulations of models involving multiple voltage-dependent Ca2+ binding
sites indicate that as the values for the sites diverge, the predicted G-V relation deviates markedly from Boltzmann behavior at either low or high [Ca]i. No such effect is seen in the mslo data. The second aspect has to
do with the minimum slope of the V1/2 vs. log[Ca]i relation. From Eq. 17 we see that for the simple system discussed above in which all electrical distances are equal the minimum possible slope is reached when
is equal
to 1. In this situation voltage is exerting its maximum
possible effect on Ca2+ binding, and therefore, it takes
a minimum change in voltage to compensate for a
change in [Ca]i. Substituting
= 1 into Eq. 17 the minimum slope is found to be
29.4 mV per 10-fold
change in [Ca]i. If we assume that each Ca2+ binding
contributes positively towards channel activation, then this minimum slope applies to systems in which the
s
are not all identical as well. This is because if at some
binding sites
values were <1, these binding steps
would become less sensitive to voltage. It would take a
larger change in voltage to compensate for the effect of
changing [Ca]i at these sites, leading to a V1/2 vs.
log[Ca]i relation which could only be more steep. Between 124 and 1,000 µM the slope of the mean V1/2 vs.
log[Ca]i plot in Fig. 5 C is
28.9 mV per 10-fold change
in [Ca]i. This result indicates that if the channel's voltage dependence lies solely in Ca2+ binding, all sites
which contribute to channel activation must have a
value close to 1.2 If this is the case, however, a logarithmic relationship between V1/2 and [Ca]i is predicted
over the entire [Ca]i range, a prediction which is not
born out in the data. So, a wide variety of models of activation by voltage-dependent Ca2+ binding are incompatible with our data and that of Wei et al. (1994)
. We
can tentatively conclude, therefore, that there must be
an intrinsic voltage sensor in the mslo protein that is distinct from Ca2+ binding.
Kinetic observations strengthen this conclusion. As
was shown in Fig. 6 E, the macroscopic rate constant of
mslo activation at +70 mV increases with increasing
[Ca]i until a plateau is reached at high [Ca]i indicating
a Ca-independent step is rate limiting. Plotted in Fig. 7
A are similar data for a series of voltages. Clearly, the effect of an increase in membrane voltage is to increase the maximum rate of activation, while otherwise having
little effect on the shapes of these curves. This change
in the maximum macroscopic activation rate constant
(rmax) with voltage indicates that a Ca-independent step
(or steps), most likely that which is limiting the mslo kinetic behavior at high [Ca]i, is voltage dependent.
Considering SCHEME IV and Eq. 4 for example, if all
of the channel's voltage dependence resided in either
one or both Ca2+ binding steps, then at high [Ca]i, regardless of the membrane voltage, rsat would be simply
equal to . Depolarizing the membrane voltage would
have no effect on rsat but would reduce the amount of
[Ca]i necessary to reach saturation. Conversely, if the
channel's voltage dependence resided in the central
Ca-independent conformational change, then, rsat would
increase with depolarization as
(V) increased, while
less effect would be expected on the [Ca]i necessary to
achieve saturation. For mslo, the apparent affinity, as
defined by the [Ca]i necessary to half saturate the macroscopic activation rate constant, changes only to a small
degree with changing voltage (Fig. 7 C), whereas rmax is
voltage dependent (Fig. 7 B). These results are therefore most consistent with the voltage dependence of mslo
gating residing in large part in Ca-independent steps.
To estimate the charge associated with Ca-independent steps, we might examine the voltage dependence of the macroscopic activation rate constant at saturating [Ca]i (Fig. 7 B). This is essentially what was done when a charge estimate was made from the voltage dependence of the time constant of activation at 1,000 µM (Fig. 2, bottom). Fitting the most depolarized region of this curve yielded a charge estimate of 0.58 ± 0.03 (SEM) e with a lower limit 0.39 ± 0.03 (SEM) e (Table II). We can conclude therefore that in the gating of the mslo channel there is at least this much charge associated with Ca-independent steps. If the reverse rate constants associated with these steps are also voltage dependent, this number would be an underestimate.
Ca2+ Binding Is Not Required for mslo Activation
If there are both Ca2+ and voltage sensing elements in
the mslo protein, it is important to know whether the activation of either or both types of elements is necessary
for the channel to open. To address the question of
whether [Ca]i binding is necessary, we have looked for
mslo currents at very low [Ca]i. When Ca2+ is omitted
from our standard internal solution, and no Ca2+ chelator is added, we have measured the free Ca2+ concentration to be between 10 and 20 µM. Adding 5 mM
EGTA to this solution should then bring [Ca]i to ~0.5
nM (pH = 7.20, apparent Ca2+ KD 160 nM calculated
from the stability constants of Fabiato and Fabiato
[1979]). Fig. 8 A shows mslo currents recorded using such a low [Ca]i solution. The membrane voltage was
held at 50 mV and then stepped to increasingly more
positive voltages (+50 to +200 mV). Up until +90 mV,
no significant current was observed. At more positive
potentials, however, a large time-dependent outward current developed. The size of this current increased
with depolarization, and at +200 mV was typically equal
to 69 ± 7% (SEM) (n = 5) of the mslo current recorded
from the same patch with 124 µM [Ca]i (Fig. 8 B). Several lines of evidence indicate that this current is passing through mslo channels: It is not present in uninjected oocytes (Fig. 9 A). From patch to patch its size
correlates well with the amplitude of Ca-dependent
currents recorded with 124 µM [Ca]i (Fig. 9 B). It is almost completely and reversibly blocked by 3 mM external TEA as is expected for the mslo channel (Butler et
al., 1993
) (Fig. 9 C), and, its single channel conductance is large, and identical to that of mslo (Fig. 9 D). In addition to these observations Palotta (1985b) and Meera et
al. (1996)
have reported low probability BK channel
opening at very low [Ca].
It appears, then, that the mslo channel can open without binding Ca2+. However, it could be that there are voltage-dependent Ca2+ binding sites on the mslo channel, and at the extreme voltages necessary to activate the channel with ~0.5 nM [Ca]i, the affinity of these sites for Ca2+ increases to such an extent that a significant fraction of channels have Ca2+ bound. Considering for example a Ca2+ binding site with an electrical distance of 0.8, at +180 mV the dissociation constant for this site would decrease by a factor of 1.25 × 105 as compared to its value at 0 mV, moving perhaps from 10 µM to 0.125 nM. Such a site would be 80% occupied at 0.5 nM [Ca]i. The question then remains open as to whether Ca2+ must bind to the channel before it will open.
More can be learned about this question when the
rate of activation at very low [Ca]i is considered. Fig. 10
shows two current traces recorded from the same membrane patch, one at 10.2 µM [Ca]i after a voltage step
to +170 mV, and the other at ~0.5 nM [Ca]i (5 mM
EGTA) after a voltage step to +250 mV. At 10.2 µM
[Ca]i the voltage step to +170 mV fully activates the
channels as can be seen by examining the G-V relation
determined at 10.2 µM in Fig. 5. Judging by the similar
amplitudes of the traces recorded at 10.2 µM and ~0.5
nM [Ca]i in Fig. 10, the voltage step to +250 mV with
~0.5 nM [Ca]i must have brought the mslo channels
near to their maximum open probability as well (differences in driving force here are not an issue as the mslo
single channel current saturates at potentials above
~+120 mV, see Cox et al., 1997, in this issue). The
trace recorded with ~0.5 nM [Ca]i has been fitted with
an exponential function (dashed curve) whose time constant is 1.15 ms. In six similar experiments the mean
time constant of activation under these conditions was
1.4 ms ± 0.36 (SD). In these experiments the Ba2+ chelator (+)-18-crown-6-tetracarboxylic acid was added to
the internal solution to reduce the possibility of Ba2+
block altering current kinetics (Diaz et al., 1996
; Neyton, 1996
) (although such effects are likely to be small,
Cox et al., 1997
). At high open probability, such as is
the case here (see Figs. 5 and 8 in Cox et al., 1997
), the
above time constant (1.4 ms) represents the mean time
it takes for an mslo channel to move from closed to
open after the voltage step. This can be made more explicit by considering that at high open probability rates
entering open states are necessarily much larger than
rates leaving open states so that the rate of change of
the current (d[I/Imax]dt) becomes very close to the rate
of arrival of channels into open states. The mean transit time (mt) from closed to open is given by
![]() |
(18) |
In the present case, where the timecourse of current activation is described by an exponential function with
time constant , we have
![]() |
(19) |
![]() |
(20) |
![]() |
(21) |
demonstrating that the mean time for a channel to
move from closed to open after the voltage step under
these conditions will closely correspond to the time
constant of current activation. Inverting the mslo activation time constant at ~0.5 nM [Ca]i and +250 mV (1.4 ms) yields a first order rate constant of 714 s1. All the
elementary transitions that the channel undergoes on its way to opening, therefore, must have rate constants
at least this rapid, and if Ca2+ must bind to the channel
after the voltage step and before opening, then Ca2+
must bind at least this fast as well. The rate of Ca2+
binding, however, depends on its concentration. At 0.5 nM in order for Ca2+ to bind to the channel with a first
order rate constant of 714 s
1, the second order rate
constant for Ca2+ binding must be at least 1.4 × 1012
M
1s
1. Is this a reasonable on rate? We might use the
expression of Smoluchowski (1916)
below to calculate
the diffusion limited on rate constant for the Ca2+
binding reaction.
![]() |
(22) |
Here NA represents Avogadro's number, DCa the diffusion coefficient of Ca2+, and ro the reaction radius (the
distance between reacting particles at the point of collision). Considering that DCa equals 0.79 × 105 cm2s
1,
at 25°C (Hille, 1992
), and ro is on the order of a few
angstroms (Pauling radius of Ca2+ = 0.99 Å, Pauling radius of oxygen = 1.40 Å), the diffusion limited kon is on
the order of 109 M
1s
1. This value is three orders of
magnitude smaller than the value experimentally determined above to be necessary to allow time for Ca2+
to bind to its site after the voltage step and activate the
channel. This result therefore suggests that the mslo
channel can be activated by a change in membrane
voltage without binding Ca2+. This rate limiting value,
however, is calculated based on simple diffusion alone.
No electrical driving force is taken into the consideration. If the Ca2+ binding site is in the electric field, the
diffusion-limited rate at which Ca2+ approaches its
binding site may be increased due to the electrical driving force the field imparts on the ion with a factor of
about z F
/RT, where z = 2 is the valence of Ca2+,
is
the potential near the binding site, and F, R, and T
have their usual meanings (Getzoff et al., 1992
; Pilling
and Seakins, 1995
). The negative surface potential near
the Ca2+ binding site on the intracellular face of the
membrane (Frankenhaeuser and Hodgkin, 1957
; Chandler et al., 1965
) may contribute to this driving force.
The contribution of the surface potential should be
<
90 mV (Hille et al., 1975
). This would enhance the
Ca2+ binding rate to a value of 7 × 109 M
1s
1. This
limit is still ~200 times smaller than the value necessary to account for the rapid activation kinetics observed
(1.4 × 1012 M
1s
1).
Other evidence that indicates that at very low [Ca]i
the mslo channel can be activated by voltage without
first binding Ca2+ comes from experiments in which
[Ca]i was varied in the low nanomolar range. Several
internal solutions were prepared with the following calculated free [Ca]i: 0.5 nM (no added Ca2+, 5 mM
EGTA), 2 nM (no added Ca2+, 1 mM EGTA,), 10 nM
(0.28 mM added CaCl2, 5 mM EGTA), and 50 nM (1.18 mM added CaCl2, 5 mM EGTA). mslo currents were
then recorded from a single membrane patch using
each of these solutions. The rationale behind this experiment was that if at very low [Ca]i (~0.5 nM) and
high voltage, it is Ca2+ binding that is activating the
mslo channel, then we would expect to see changes in
the amplitude and time course of mslo currents as [Ca]i
is varied in the low nanomolar range. I-V curves from one such experiment are shown in Fig. 11 A. The clear
result is that there was no significant increase in the
amplitudes of currents recorded with internal solutions
containing 2 or 10 nM [Ca]i over those recorded with
~0.5 nM [Ca]i. Nor was there a clear increase in activation rate. (Fig. 11 B). The same result was obtained in five additional experiments, all supporting the conclusion that at very low [Ca]i the channel is opening without binding Ca2+. These results also indicate that if surface charges are concentrating Ca2+ near its binding
sites, then the channels are not sensitive to changes in
the surface charge enhanced Ca2+ concentration as
well. This is because the relationship between [Ca]bulk
and that which is concentrated by surface charge is expected to be linear. At 50 nM [Ca]i a small increase in
current amplitude relative to that at 0.5, 2, or 10 nM
was observed suggesting that at this [Ca]i the mslo channels may be just starting to bind Ca2+ appreciably.
To guard against errors in solution making, we measured the Ca2+ concentrations in the solutions employed in the experiment of Fig. 11 using the Ca2+ indicator fura II (100 µM) with the following results: calculated 0.5 nM, measured 0 nM; calculated 2 nM, measured 0 nM; calculated 10 nM, measured 1 nM; calculated 50 nM, measured 63 nM. The precision of these measurements, ± 20 nM, was limited by the sensitivity of the indicator. Nevertheless, they do confirm that the free Ca2+ concentrations in these solutions are in the high picomolar to low nanomolar range.
mslo Can Be Nearly Maximally Activated without Binding Ca2+
The experiments described above strongly support the
conclusion that the mslo channel has intrinsic voltage
sensing elements and that the action of these elements
is sufficient to activate the channel substantially. In fact
the similar amplitudes of the traces in Fig.10 argue that
with strong depolarizations the mslo channel can be
maximally activated without binding [Ca]i. More evidence to support this conclusion is shown in Fig. 12 B.
Here G-V relations determined from patches exposed
to both 10.2 µM (squares) and ~0.5 nM [Ca]i (circles)
are displayed. To maximally activate mslo channels at
~0.5 nM [Ca]i, it was necessary to depolarize to potentials greater than +200 mV. In 6 of 17 experiments,
voltages as high as +250 mV were attained (closed circles). In 3 experiments it was possible to depolarize to
+280 mV (open circles). At this potential the maximum
current observed with ~0.5 nM [Ca]i was on average
101 ± 6% (SD) of that measured with 10.2 µM [Ca]i at +150 mV (Fig. 12 A). Because the mslo channel's single
channel current saturates ~+120 mV (see Cox et al.,
1997, in this issue), current amplitude and open probability at these high voltages become directly comparable. These results therefore indicate that, in contrast to
the low probability openings reported previously in extremely low [Ca]i and lower voltages (Pallotta, 1985a
;
Meera et al., 1996
), by +280 mV the mslo channels were
very close to being fully activated.
The mslo G-V Relation Is Less Steep at Very Low [Ca]i than It Is at 10.2 µM [Ca]i
The data in Fig. 12 B also allow a comparison to be
made between the shape of the mslo G-V relation under
conditions in which the channel is activating without
binding Ca2+ (~0.5 nM [Ca]i) to that observed with
[Ca]i sufficient to regulate channel gating (10.2 µM
[Ca]i). In this experiment (+)-18-crown-6-tetracarboxylic acid was included in the internal solution to ensure
that the shape of the G-V relation was not distorted by
Ba2+ block. Also, to control for time-dependent changes
unrelated to changes in [Ca]i, in each experiment current families were recorded at 10.2 µM [Ca]i before
(filled squares) and after (open squares) families with ~0.5
nM [Ca]i (filled circles). Each set of data in Fig. 12 B is
fitted with a Boltzmann function of the form G/Gmax = 1/(1+e zF(V1/2 V)/RT). The equivalent gating charge estimates determined from these fits were 1.18 e (before)
and 1.19 e (after) for the G-V relations determined with
10.2 [Ca]i, and 0.87 e (voltages to +250 mV) and 0.83 e
(voltages to +280 mV) for those measured with ~0.5
nM [Ca]i. These numbers suggest that the mslo channel
is less sensitive to changes in membrane voltage when
gating without Ca2+ binding than it is in the presence
of 10.2 µM [Ca]i. There is an apparent 26 to 31% decrease in equivalent gating charge at low [Ca]i.
We have considered three possible explanations for
this observation. The first is that while most of the gating charge of the channel derives from intrinsic voltage
sensing elements, Ca2+, as it binds to the channel, may
bind a short distance into the electric field ( < 0.2)
and therefore contribute approximately a quarter to a
third of the total gating charge. Second, as pointed out
by Zagotta et al. (1994a)
, the steepness of a channel's
G-V relation depends not only on the amount of charge
moved through the membrane's electric field during
opening but also on the cooperativity of gating conformational changes. The decrease in maximum G-V slope
observed at low [Ca]i therefore might be attributed to
Ca-dependent changes in the cooperative interactions
between subunits, rather than to a change in gating
charge. And third, the more shallow maximum G-V slope
at ~0.5 nM [Ca]i as compared to 10.2 µM [Ca]i may be
not so much a consequence of the change in [Ca]i, as it is a consequence of the fact that when gating in a Ca-
independent way, the mslo G-V relation spans extreme
positive potentials. It may be that the equivalent gating
charge of the channel changes as a function of the voltage range examined. A physical interpretation of such
a phenomenon might be that there is a change in polarizability of the channel between open and closed
states such as might come about if dipoles can be induced by the electric field in one state and not the
other (Stevens, 1978
; Sigworth, 1994
). Such a change in polarizability would make the work done when the
channel moves from closed to open a nonlinear function of voltage (Stevens, 1978
) and could result in a
more shallow G-V relation at extreme potentials. Unfortunately, at present we are unable to distinguish between these possibilities. In the future, however, experiments involving gating current measurements and the
study of mutant channels whose G-V relations at low
[Ca]i are shifted to more hyperpolarized potentials
may help make such a distinction possible. At present,
however, the most we can say is that the mslo channel retains ~70% of its apparent voltage sensitivity at very
low [Ca]i as estimated by simple Boltzmann fitting.
Voltage Appears to Limit the Extent to which Ca2+ Can Activate the mslo Channel
The results of experiments with very low [Ca]i demonstrate that a lack of [Ca]i does not limit the extent to
which mslo channels can be activated by voltage provided sufficiently large depolarizations are used. It is
important to ask whether the converse is true. Can a
high enough [Ca]i maximally active mslo channels regardless of the membrane voltage? We can see from the
G-V curves of Fig. 5 that the answer to this question is
likely to be no. Even with 1,000 µM [Ca]i, applying a
membrane voltage of 180 mV essentially completely
prevented the mslo channels from opening.
The ability of membrane voltage to limit the extent
to which mslo channels can be activated by [Ca]i can be
better seen when steady-state open probability (Po) is
plotted as a series of Ca2+ dose response curves (Fig. 13
A). Here, the curves from top to bottom correspond to
data taken at successively more negative voltages in increments of 20 mV. Each curve has been fitted with the
Hill equation (Eq. 1). At +90 mV (top curve) the channels are essentially fully activated by 10.2 µM [Ca]i and
the fitted curve approaches 1 on the ordinate. Near full
activation is also reached at +50 mV (third from top), although here it takes more Ca2+ to bring the channels
to full open. By 10 mV (third from bottom), however,
the fitted curve reaches a maximum below 1 on the ordinate, and when the maximum of each fit is plotted as
a function of voltage (Fig. 13 B), the fraction of channels which can be activated decreases with decreasing
voltage. These data therefore suggest that negative potentials can limit the ability of [Ca]i to activate mslo.
Some studies, however, indicate that the BK channel G-V
relation moves further leftward along the voltage axis
with increases in [Ca]i above the maximum [Ca]i we
have used (1,000 µM) (Moczydlowski and Latorre, 1983
;
Meera et al., 1996
). That we have reached saturation of
the mslo channel's Ca2+ binding sites by 1,000 µM [Ca]i
is therefore not clear. Wei et al.(1994) have suggested
that leftward G-V curve shifts above ~100 µM [Ca]i are
due to a nonspecific divalent cation binding site rather
than the channel's primary Ca2+ sensors, and that saturation of the primary site is reached by ~100 µM [Ca]i.
Because of these complications, we can only tentatively conclude that membrane voltage limits the ability of
[Ca]i to activate the mslo channel at negative potentials.
How Many Ca2+ Molecules Bind to the Channel?
To gain further insight into the Ca2+-dependent activation of mslo it would be useful to know how many Ca2+
binding sites there are on the channel. We can determine a lower limit for this number by considering the
Hill coefficients determined from fitting the Ca2+ dose
response curves in Fig. 13 A. In general for a system
with N binding sites, this coefficient will be less than or
equal to N (Adair, 1925). In Fig. 13 C are plotted Hill
coefficients as a function of voltage for both the data in
Fig. 13 A (filled circles) and the mean of five similar experiments (open circles). The trend in these data is toward
larger Hill coefficients at more depolarized voltages.
Over the majority of the voltage range the Hill coefficient varied between 1 and 3 clearly indicating that at
least three Ca2+ binding sites are associated with channel activation.
In Fig. 13 D the apparent KD of the channel for Ca2+ as determined from fits to the Hill equation is plotted as a function of membrane voltage. As expected from the shifting behavior of the mslo G-V relation in response to changes in [Ca]i, the apparent KD declines sharply with increasing voltage. The mean data (open circles) have been fitted with an exponential function which changes e -fold per 21.6 mV.
Intrinsic Voltage Sensing
In this study we have examined macroscopic mslo currents over a wide range of membrane voltages and Ca2+
concentrations to address some fundamental questions
about the channel's gating mechanism. One important
question related to BK channel gating is whether the
channel's voltage dependence derives from intrinsic
gating charges which are part of the protein sequence
or instead from voltage-dependent Ca2+ binding? A
leading model from single channel studies of skeletal muscle BK channels has suggested that the channel's
voltage dependence resides in Ca2+ binding (Moczydlowski and Latorre, 1983). With the cloning of slo channels (Atkinson et al., 1991
; Adelman et al., 1992
; Butler et al., 1993
), however, it became apparent that BK
channels contain an S4 region which in purely voltage-gated channels is thought to span the membrane and
form at least a part of an intrinsic voltage sensor (Stuhmer et al., 1989
; Liman et al., 1991
; Papazian et al.,
1991
; Perozo et al., 1994
; Sigworth, 1994
; Smith-Maxwell et al., 1994
; Yang and Horn, 1995
; Aggarwal and
MacKinnon, 1996
; Larsson et al., 1996
; Mannuzzu et
al., 1996
; Seoh et al., 1996
; Yang et al., 1996
). These results suggested that slo channels may contain intrinsic
voltage-sensing elements like those of the shaker channel. The shaker channel, however, contains seven basic residues in this region, whereas slo channels have only
four. The reduced number of basic residues, therefore,
might reasonably have rendered the slo channels' S4 regions no longer able to sense changes in membrane potential. Furthermore, the presence of an S4 region
does not ensure that a channel will exhibit voltage- dependent gating. For example, the cyclic-nucleotide-
gated channel of rod outer segment also has structural
similarity to shaker channels including S4 and pore regions; this channel contains 5 positive charges in its S4
region (Kaupp et al., 1989
), yet shows very little voltage
dependence (Karpen et al., 1988
).
In this study we provide three lines of evidence which
indicate that the mslo channel does indeed have intrinsic voltage sensing elements which are distinct from
Ca2+ binding. The first is that the position of the mslo
G-V relation does not vary logarithmically with [Ca]i.
This observation is in support of the work of Wei et al.
(1994), who also observed smaller shifts in the position
of the mslo G-V relation per 10-fold change in [Ca]i at
high [Ca]i than at low [Ca]i. As they pointed out, it is
difficult to find markovian models whose V1/2 vs. log[Ca]i relation is not linear if voltage dependence is assigned
only to Ca2+ binding steps and these Ca2+ binding steps
have approximately equal voltage dependence. Extending their analysis, we have shown that for all systems
whose voltage dependence resides solely in Ca2+ binding, a logarithmic relationship between V1/2 and [Ca]i
is expected so long as the electrical distances of all
binding sites are the same (this was shown for a sequential binding model by Wong et al. [1982]). Given that
we and others have observed Hill coefficients as high as
3, and evidence suggests that slo
subunits expressed
alone form homotetrameric channels (Shen et al., 1994
), it is reasonable to suppose that slo channels contain
four identical Ca2+ binding sites, one per subunit. In
such systems all binding sites naturally have equivalent
electrical distances unless cooperative interactions between subunits serially alter the position of Ca2+ binding sites as each new Ca2+ molecule binds to the protein. Even without relying on simple symmetry, however,
between 124 and 1,000 µM [Ca]i the slope of the V1/2
vs. log[Ca]i relation is so shallow as to require that, if
the channel's voltage dependence were to reside solely
in Ca2+ binding steps, the electrical distance of each
binding site would have to be close to 1. If this were the
case, however, the V1/2 vs. log[Ca]i relation would necessarily be linear. This contradiction indicates that there
must be some gating charge associated with conformational changes which do not involve Ca2+ binding.
Further supporting this conclusion, we have found that the macroscopic rate constant of mslo activation approaches saturation at high [Ca]i. This saturating behavior indicates that gating transitions which do not involve Ca2+ binding are limiting the kinetic behavior of the mslo channel at high [Ca]i. The fact that the maximum value of this limiting rate is voltage dependent, as was shown in Fig. 7, indicates that transitions that are separate from Ca2+ binding are necessarily voltage dependent, and thus, there must be gating charges intrinsic to the channel.
The third line of evidence in support of intrinsic voltage sensing is the observation that mslo channels can be
substantially activated with [Ca]i as low as ~0.5 nM.
This observation agrees with several reports of low
probability BK channel activity at very low [Ca]i (Barrett et al., 1982; Methfessel and Boheim, 1982
; Wong et
al., 1982
; Findlay et al., 1985
; Pallotta, 1985b; Meera et
al., 1996
). In fact, we have found that with depolarizations to +280 mV the mslo channels can be nearly maximally activated at ~0.5 nM [Ca]i, indicating that a lack
of Ca2+ binding does not limit the ability of the channel to be activated by voltage. It is clear that this activation is truly Ca2+ independent, rather than due to very
high affinity Ca2+ binding, because the time constant
of current activation at ~0.5 nM [Ca]i is three orders of
magnitude faster than the mean diffusion-limited time
it would take Ca2+ to find its binding site after a depolarizing voltage step.
From the above analysis it is clear that, at very low
[Ca], Ca2+ is not binding to and activating the mslo
channels after the voltage step. We considered the possibility, however, that in the essential absence of Ca2+,
some other ion in our internal solution was binding to
Ca2+ binding sites and activating the channels. Oberhauser et al.(1988) have reported the following rank
order of activating ions for skeletal muscle BK channels: Ca2+ (KD = 8.98 × 104 mM) >> Cd2+(KD = 0.27 mM) > Sr2+(KD = 0.73 mM) > Mn2+(KD = 0.96 mM) > Fe2+(KD = 2.7 mM) > Co2+(KD = 3.81 mM). KD here indicates half-saturating ion concentration at +80 mV.
Excepting Ca2+, none of these ions were added to our
internal solutions. Some of them, however, may have
entered into these solutions as a contaminant. To
check this point the total concentrations of the most
potent of these ions were measured by atomic absorption spectroscopy (AA). Cd2+, Sr2+, and Mn2+ were not
detected indicating that if present their concentrations were lower than the resolution of the assay (~0.3 µM).
Iron was present at 4.56 µM. Given these results one
might still suppose that Cd2+, Sr2+, or Mn2+ present at
just below the AA detection limit, or perhaps Fe2+, is
able to rapidly activate mslo channels at high voltages. EGTA however has high affinity for all of these ions,
and calculations of the maximum possible free concentrations of these ions in our internal solution containing 5 mM EGTA indicates that only Sr2+ could be
present at a free concentration higher than Ca2+, and
then only at ~1.3 nM. This concentration is still too
small to account for the rapid activation of mslo currents in the presence of 5 mM internal EGTA. Based on
these results we do not believe that in our low [Ca]i experiments the mslo channels are being activated by a
contaminant ion.
Our conclusion that the mslo channel has intrinsic
voltage sensors differs from the mechanism proposed
by Moczydlowski and Latorre (1983) for the voltage-
dependent gating of a skeletal muscle BK channel.
They concluded that this channel's voltage dependence comes from the voltage dependence of Ca2+
binding. There are several differences between the two
studies including: native skeletal muscle channels vs.
cloned
subunits expressed alone in oocytes, and single channel vs. macroscopic currents. However, the
manner by which Moczydlowski and Latorre plotted
their data may have made the intrinsic voltage dependence of the channel they studied less apparent. Their
conclusion was based primarily on the observations
that the channel's mean open time (
open) and mean
closed time (
closed) were not clearly voltage dependent
when extrapolated to [Ca]i = 0 and 1/[Ca]i = 0, respectively. However, at these extremes the mean open
and closed times are at their minimum. Voltage-dependent changes in these values will appear small. Rather
than plotting the
closed vs. 1/[Ca]i as was done by Moczydlowski and Latorre (1983, Fig. 7), in Fig. 7 A we have
plotted the macroscopic activation rate constant, r (1/
activation) vs. [Ca]i. At high [Ca]i and moderate to high voltages this parameter approximates 1/
closed. Plotted
in this way voltage-dependent changes in the channel's
opening rate constant at saturating [Ca]i are more easily seen. Between +20 and +120 mV, rmax varied between 1,000 and 5,000 s
1. This corresponds to a variation in
closed of from 1 to 0.2 ms. In the plot of Moczydlowski and Latorre (1983, Fig. 7), this variation would
be very hard to discern from random variability in the
data, and the minimum
closed might easily be considered to be the same for each voltage. However, upon
closer inspection of this plot it appears that each curve
does not intersect the
closed axis at exactly the same
point. In fact, there is an increase in the
closed intercept
as the membrane voltage is made more negative. This is
expected for a kinetic system whose closed to open rate
constant increases with depolarization. It seems unlikely therefore that there is a fundamental difference
between the voltage-dependent gating mechanisms of
the channels in the two studies, and more likely that
methodological differences allowed for intrinsic voltage dependence to be more clearly seen in our study.
A Concerted Step between Closed and Open
A striking feature of macroscopic mslo currents is that
the time course of both activation and deactivation can
be well described by a single exponential function after
the first ~100 µs. This was found to be the case under
all conditions in which the relaxation time course was
accurately determined despite the fact that Ca2+ and
voltage had strong effects on the time course of mslo
current relaxation. These results are perhaps surprising
given that at least eight kinetic states are necessary to
describe the stationary gating behavior of single skeletal muscle BK channels (McManus and Magleby, 1988;
1991
), and they suggest that in the gating of the mslo
channel there is a single conformational change which is rate limiting over a wide range of stimuli. The observation that the time course of mslo current activation is
still voltage dependent at saturating [Ca]i argues that
the rate limiting conformational change is voltage dependent. Further supporting this idea the mslo G-V relation can be fairly well described by a Boltzmann function over a wide range of [Ca]i as is expected for a system which contains a single voltage dependent step between closed and open, and when estimates of the charge
associated with forward and backward rate limiting
steps at each [Ca]i are summed, they are similar to
equivalent gating charge estimates obtained by fitting
the G-V relation with a Boltzmann function (see Tables I and II). Taken together these results suggest that it
may be reasonable to model the gating of the mslo
channel as a single voltage-dependent conformational
change between closed and open states with Ca2+ binding shifting this equilibrium towards open.
Several observations, however, suggest that this view
may be too simple. Single channel records from both
native and cloned channels display complex kinetic behavior (Moczydlowski and Latorre, 1983; Pallotta, 1983
;
McManus and Magleby, 1988
; 1991
; DiChiara and Reinhart, 1995
; Giangiacomo et al., 1995
). Gating current studies indicate that there is a component of gating
charge which moves very rapidly before slo channels
open (Horrigan et al., 1996
; Ottalia et al., 1996
). Also,
we and others (Ottalia et al., 1996
) have observed a
brief delay before the exponentially rising phase of mslo
current activation. Although this delay lasted typically only ~100 µs and was not studied in depth, it did appear to persist over a wide range of [Ca]i and membrane potentials. The delay was evident even at ~0.5
nM [Ca]i where the channels were activating without
binding Ca2+. Ca2+ binding kinetics therefore cannot
explain the delay. To account for this delay we must
suppose that there are at least two kinetic steps between
closed and open. The presence of more than one step between closed and open is also suggested by the observation that while the mslo G-V relation appears fairly
well fitted by a simple Boltzmann function, it is often as
well or better fitted with a Boltzmann function raised to
a power between 1 and 3 (Fig. 14). A sequential scheme
with a single voltage-dependent transition along the
path from closed to open predicts a G-V relation which takes the form of a Boltzmann function. If there are
multiple voltage-dependent steps along this path, the
exact shape of the G-V relation will depend on the
equilibrium constants of all transitions and the magnitude of the associated gating charges. In general, multiple appreciably voltage-dependent elementary steps
lead to G-V relations that deviate from simple Boltzmann behavior, producing a curve whose maximum
slope is more shallow than would be observed if all of
the gating charge was associated with a single conformational change. For many schemes, the G-V relation
can be better approximated by a Boltzmann function
raised to a power greater than 1 (Zagotta et al., 1994b
).
That the mslo G-V relation can often be better fitted by
a Boltzmann function raised to a power greater than 1 suggests that more than one voltage-dependent step exists between closed and open states. Nevertheless, the
essentially exponential kinetic behavior of the mslo
channel coupled with fairly good single Boltzmann fits
to its G-V relation suggests that even if there are multiple conformational changes involved in activation, there must be a high degree of cooperativity between
them such that the probability of the channel existing
in an intermediate closed state at equilibrium is low.
Putting this discussion in more physical terms, if each
subunit of the tetramer has a voltage-sensing element,
then the observations discussed above suggest that these voltage-sensing elements are not acting independently,
but rather the movement of one voltage sensor facilitates the movements of others such that together these
elements move in a highly concerted manner. This
mechanism differs from that of the shaker K+ channel
whose voltage sensing elements appear to move independently (Zagotta et al., 1994a
). Based on our results
a high degree of cooperativity between subunits in mslo
channel opening seems inescapable.
It should be noted that while we have expressed a single species of mslo RNA, through some process, such as posttranslational modification, the mslo channel populations we have studied may not have been completely homogeneous. This could also give rise to deviation from exponential kinetic behavior, as well as simple Boltzmann steady-state behavior.
mslo Has Less Gating Charge than a Shaker Channel
Boltzmann fits to mslo G-V curves over a range of [Ca]i
yielded equivalent gating charge estimates of between
1.1 and 1.9 e. At very low [Ca]i, this estimate was somewhat reduced (~0.8 e). Other studies on both native
(Barrett et al., 1982; Latorre et al., 1982
; Methfessel
and Boheim, 1982
; Oberhauser et al., 1988
) and cloned
(Wei and Salkoff, 1986
; Butler et al., 1993
; Perez et al.,
1994
; Tseng-Crank et al., 1994
; DiChiara and Reinhart, 1995
; McCobb et al., 1995
; Wallner et al., 1995
) channels report values ranging between ~1 and 2 as well.
These values suggest that the equivalent gating charge
of BK channels may be as much as 12 e less than that of
the shaker channel (Schoppa et al., 1992
; Zagotta et al.,
1994b
; Aggarwal and MacKinnon, 1996
; Seoh et al.,
1996
) or DRK1(Kv2.1) (Islas and Sigworth, 1996
). However, the fact that the G-V relation for a sequential gating scheme comprised of multiple voltage-dependent
steps will be more shallow than it would be if all the gating charge moved in a single step means that fitting a
channel's G-V relation with a Boltzmann function will
often lead to an underestimate of the true gating charge of the channel. The severity of the underestimate will
depend on the number of voltage-dependent steps between closed and open, the extent to which the total
gating charge is spread throughout these steps, and the
degree of cooperativity of the system. As pointed out by
Zagotta et al. (1994b)
, as a gating scheme becomes more
concerted such that the equilibrium constant for the
last step before opening becomes large relative to early
steps, the deviation from simple Boltzmann behavior
decreases. In the limit that the relative magnitude of
the last step becomes very large, a Boltzmann function
which would describe the G-V relation for a two-state
system containing all of the gating charge is predicted. This suggests then that for a channel like mslo, which
appears to have a concerted conformational change between closed and open, Boltzmann fits to the G-V relation may not seriously underestimate the true gating
charge of the channel, at least not to the same extent as
is seen for the shaker channel whose G-V relation deviates more strongly from Boltzmann behavior and
whose activation kinetics are much more sigmoid (Zagotta et al., 1994b
). In the shaker channel Boltzmann fitting underestimates the gating charge by a factor of ~3
(Schoppa et al., 1992
; Zagotta et al., 1994b
). Equivalent gating charge estimates of between ~1 and 2 from Boltzmann fits to the mslo G-V relation are therefore likely to
be no less accurate. Even if these estimates are off by as
much as a factor of 3, however, they still indicate that
the total gating charge of the mslo channel is likely to
be no more than 6 e, at least ~2-fold less than the best
studied purely voltage-gated K+ channels. Whether the
smaller amount of gating charge in the mslo channel is
due to the fewer basic residues in its S4 region will be
important to determine.
A General Scheme for mslo Channel Gating
Despite the arguments above which suggest that it may be better to think of the mslo channel as having a highly concerted rather than a single step between closed and open, in considering SCHEME IV we have seen that several properties of mslo macroscopic currents can be understood in terms of a kinetic scheme In which there is a central voltage-dependent conformational change both preceded and proceeded by rapid Ca2+ binding steps. These properties include: exponential activation and deactivation kinetics, relaxation rates which increase with [Ca]i at depolarized voltages and decrease with [Ca]i at hyperpolarized voltages, saturating kinetic behavior at high [Ca]i, and an apparent affinity for Ca2+, as judged by half saturation of the macroscopic activation rate constant, which is much less sensitive to voltage than is the apparent affinity as judged by half saturation of the channels normalized conductance. SCHEME IV, however, cannot account for all aspects of our data as (a) it does not allow for channel opening with strong depolarizations in the absence of Ca2+ binding, (b) it does not predict that membrane voltage can limit the extent to which Ca2+ can activate mslo channels, and (c) it supposes that only two Ca2+ molecules bind to the channel. Still, its qualitative success with many aspects of mslo gating suggests that its general premise may be worth further consideration.
We can expand SCHEME IV to a form which can qualitatively account for all the properties listed above and yet maintain its essential nature by considering SCHEME V below (the portion of SCHEME V which corresponds to SCHEME IV has been boxed).
[View Larger Version of this Image (122K GIF file)]Scheme VI.
Like SCHEME IV, SCHEME V describes a channel which must undergo a central voltage-dependent conformational change in order to open. Here, however, the channel can open with 0 to n Ca2+ molecules bound. In order for this system to be activated by Ca2+, on average, Ca2+ must bind more tightly to the open conformation than to the closed. When this is the case the leftward shifting nature of the mslo G-V relation with increasing [Ca]i (Fig. 5) can be understood, because as more Ca2+ molecules bind to the channel, the central equilibrium will progressively shift toward opening. It therefore will take less voltage to bring the channel to its maximum open probability. The observation that the [Ca]i required to half maximally activate mslo currents decreases as the membrane voltage is depolarized (Fig. 13 D) can also be explained in terms of SCHEME V, as, according to this scheme, it would take fewer bound Ca2+ to maximally activate the channel as the membrane voltage is depolarized. In fact, at extremely positive voltages none are required, leading to Ca-independent opening as we have described.
As was the case for SCHEME IV, SCHEME V requires that Ca2+ binding is not rate limiting to reproduce the single exponential kinetics observed over a wide range of conditions, and the saturation of the macroscopic activation rate constant at high [Ca]i. It is interesting to consider the possibility more closely, however, that it is the Ca2+ binding steps which are rate limiting. If the horizontal rates in SCHEME V were very slow relative to the vertical rates, the channels would move predominately vertically before horizontally, and the activation time course of the population would have many exponential components, at least one for each vertical step in the scheme. If on the other hand the vertical rates were much slower than the horizontal rates, then the channels would redistribute laterally while moving to open, producing relaxation kinetics which would be much more simple. In fact, it can be shown that, in the limit that the Ca2+ binding and unbinding rates become very fast relative to the vertical rates such that each horizontal step can be considered to be in a steady state at all times, the kinetics of SCHEME V are described by a single exponential function. The time constant of this exponential will depend on [Ca]i, and on the values of all the vertical rates and horizontal equilibrium constants in the system. Due to the exponential nature of the mslo currents, therefore, we favor the idea that it is a Ca2+ independent conformational change which is limiting the kinetic behavior of the mslo channel over a wide range of conditions.
DiChiara et al. (1995) concluded that it was Ca2+ binding which was limiting the activation time course of dslo currents in part based on the observation that at high open probabilities the time course of dslo macroscopic current activation parallels the cumulative time to first opening of dslo single channels and that this time course changes as a function of [Ca]i. This observation, in fact, is not at odds with the above conclusion as, at high open probability and in the rapid Ca2+ binding limit, both the time to first opening and the macroscopic activation rate constant of SCHEME V will be determined by the same weighted average of all of the forward rate constants in the system, and the contribution of each rate constant to this average will change as a function of [Ca]i. Their observation that the time course of dslo and hslo activation is best described by two exponential components, however, may indicate that in these channels Ca2+ binding rates are contributing in a more direct way to the kinetics of relaxation than they do for mslo.
Wei et al.(1994) have studied the G-V relations of chimeric channels comprised of core (the NH2 terminus through S8) and tail (after S8 to the COOH terminus) regions from either mslo or dslo channels. mslo has a higher apparent affinity for Ca2+ than does dslo. Interestingly, they found that when a dslo tail was expressed together with a mslo core, the dslo tail had little effect on the chimeric channel's G-V relation at high [Ca]i (300 µM). That is, the chimeric channel's G-V relation was very similar to the parent mslo channel. At lower [Ca]i however, much stronger depolarizations were required to activate the chimeric channel as compared to mslo. They also found that the reverse chimera's (dslo- mslo) G-V relation at high [Ca]i was in a similar position on the voltage axis to that of the dslo channel but was shifted to more hyperpolarized voltages than that of dslo at lower [Ca]i. They interpreted these results to indicate that the slo channel's Ca2+ binding affinity is determined by its tail region, and that the dslo tail binds Ca2+ with lower affinity than does the mslo tail, whereas the channel's closed to open equilibrium at saturating [Ca]i is determined by its core region.
Some aspects of SCHEME V support this hypothesis. If the dslo tail region confers lower Ca2+ affinity on the channel than does the mslo tail, then, according to SCHEME V, at low [Ca] the chimeric channel's G-V relation would likely lie to the right of the mslo G-V relation due to the fact that fewer Ca2+ would be bound to the mslo-dslo channel. At saturating [Ca]i, however, the two G-V curves would not necessarily be expected to converge. This is because, according to SCHEME V, and indeed for any gating system activated by Ca2+, the position of the G-V relation on the voltage axis at saturating [Ca]i will not be determined solely by the intrinsic conformational free energy difference between closed and open (in SCHEME V this free energy difference determines the equilibrium constant between C0 and O0), but it will also depend on the difference in Ca2+ binding energy between closed and open. For SCHEME V the equilibrium constant between closed and open at saturating [Ca]i is given by
![]() |
(23) |
The term in square brackets represents the ratio of the product of the Ca2+ dissociation constants for Ca2+ binding to closed states, to the product of the Ca2+ dissociation constants for Ca2+ binding to open states. Therefore, changes in Ca2+ binding affinities can affect the closed to open equilibrium even at saturating [Ca]i, and changing from mslo tail to dslo tail might be expected to affect the position of the mslo-dslo G-V relation at saturating [Ca]i. Such an effect would not be observed, however, if in changing from mslo tail to dslo tail, the ratio of Ca2+ binding energies between closed and open states remained constant. The observations of Wei et al. therefore suggest that this may be the case. Our results, however, suggest that a more direct way to examine the effects of the core region on the intrinsic conformational energy of the channel would be to examine the G-V relations of the chimeric channels at very low [Ca]i where the channels are gating without bound Ca2+. If it is the core region that determines the intrinsic energy difference between closed and open, then one would predict that in the zero [Ca]i limit the mslo and mslo-dslo G-V relations would again converge. Whether this is actually the case will be interesting to determine.
McManus and Magleby (1991) have considered schemes
which take the form of SCHEME V to account for the Ca-dependent, stationary gating properties of skeletal muscle
BK channels at +30 mV and have proposed as the simplest model to account for their data a subset of this system shown below.
Scheme V.
One obvious difference between SCHEME VI and SCHEME
V is the absence of direct opening pathways from C0
and C1. However, we do not believe this to be an important discrepancy, because in SCHEME V these transitions
would not be favored with [Ca]i between 1 and 25 µM,
and at the moderately depolarized voltage they used. Although it was derived from data on different channels, the general form of their model is clearly quite
similar to, and a subset of, SCHEME V. McManus and
Magleby, however, did not study the voltage dependence of gating. As an exercise, we wondered whether if by supplying voltage dependence to the vertical transitions of SCHEME VI and using the kinetic parameters
defined for +30 mV by McManus and Magleby (cell
#1), we could account for the kinetics of macroscopic
mslo currents. We found that if we let the channels distribute among the closed states at negative potentials
and then jumped the voltage to +30 mV, the kinetics
of this system were similar to mslo at low (0.84 µM)
[Ca]i and high (124 µM) [Ca]i. At intermediate [Ca]i,
however, the model was either significantly slower (1.7, 4.5 µM [Ca]i) or faster (10.2 µM [Ca]i) than the mslo
currents, and more than one kinetic component was
usually evident. If we assigned to the McManus and Magleby model an amount of gating charge similar to that
estimated for mslo (qf = 0.7, qb = 0.7), over a range of
voltages, the modified McManus and Magleby model in
general showed much slower activation kinetics than
mslo at [Ca]i below 124 µM and much faster deactivation kinetics at negative potentials. This result is not
surprising as we have studied the
subunit of a cloned
channel in a heterologous expression system, while
their experiments were done with native skeletal muscle BK channels which may have been composed of
and
subunits. It does indicate, however, that we can
not co-opt this system as it stands to account quantitatively for the macroscopic kinetics of the mslo channel.
The type of detailed studies done by McManus and Magleby certainly must be applied to mslo channels. In the broader sense, however, that both detailed single channel analysis and macroscopic current measurements
are pointing to a channel with a concerted closed to
open conformational changed regulated by multiple
Ca2+ binding sites lends further credence to the idea
that this general view is correct.
Original version received 7 October 1996 and accepted version received 27 February 1997.
Address correspondence to Dr. Richard W. Aldrich, Department of Molecular and Cellular Physiology, Beckman Center B171, Stanford, CA 94305-5426. Fax: 415-725-4463; E-mail: raldrich{at}popserver.stanford.edu
2 Extreme cases can be found where this statement is not valid. In all such cases however it is necessary that the G-V relation be very strongly biphasic, drastically deviating from simple Boltzmann behavior. Since under no conditions does the mslo G-V relation show such biphasic character, such cases are not an issue here.We gratefully acknowledge Larry Salkoff for providing the mslo clone, Marcus Hoth and Richard Lewis for performing Ca2+ concentration measurements by fluorescence microscopy, Victor Corvalan for algorithms for Ca2+ concentration calculations, and Frank Horrigan for helpful comments on the manuscript.
This work was supported by a National Institute of Mental Health Silvio Conte Center for Neuroscience Research grant (MH 48108). J. Cui was supported by a postdoctoral fellowship from the Muscular Dystrophy Association. R.W. Aldrich is an investigator with the Howard Hughes Medical Institute.
BK channels, large conductance Ca-activated potassium channels.