From the * Departments of Physiology and Anesthesiology, University of California at Los Angeles, Los Angeles, California 90095; and Instituto Venezolano de Investigaciones Científicas, Centro de Biofísica y Bioquímica, Laboratorio de Fisiología Renal, Caracas 1020A,
Venezuela
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ABSTRACT |
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Ionic (Ii) and gating currents (Ig) from noninactivating Shaker H4 K+ channels were recorded with
the cut-open oocyte voltage clamp and macropatch techniques. Steady state and kinetic properties were studied in
the temperature range 2-22°C. The time course of Ii elicited by large depolarizations consists of an initial delay
followed by an exponential rise with two kinetic components. The main Ii component is highly temperature dependent (Q10 > 4) and mildly voltage dependent, having a valence times the fraction of electric field (z) of 0.2-0.3
eo. The Ig On response obtained between 60 and 20 mV consists of a rising phase followed by a decay with fast
and slow kinetic components. The main Ig component of decay is highly temperature dependent (Q10 > 4) and
has a z between 1.6 and 2.8 eo in the voltage range from
60 to
10 mV, and ~0.45 eo at more depolarized potentials. After a pulse to 0 mV, a variable recovery period at
50 mV reactivates the gating charge with a high temperature dependence (Q10 > 4). In contrast, the reactivation occurring between
90 and
50 mV has a Q10 = 1.2. Fluctuation analysis of ionic currents reveals that the open probability decreases 20% between 18 and 8°C and the
unitary conductance has a low temperature dependence with a Q10 of 1.44. Plots of conductance and gating
charge displacement are displaced to the left along the voltage axis when the temperature is decreased. The temperature data suggests that activation consists of a series of early steps with low enthalpic and negative entropic
changes, followed by at least one step with high enthalpic and positive entropic changes, leading to final transition
to the open state, which has a negative entropic change.
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INTRODUCTION |
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Voltage-dependent ionic channels play a crucial role in
the generation and propagation of the action potential
(Hodgkin and Huxley, 1952). Significant progress in
our understanding of the operation of these channels
has been made possible by the manipulation of the
gene encoding the channel and its subsequent study in
an expression system. One classical example of a voltage-gated channel is the Shaker K+ channel, which has
been studied in extensive detail, and for which a number of kinetic models have been proposed to explain its
voltage sensing properties (Perozo et al., 1992
; Bezanilla et al., 1994
; Zagotta et al., 1994
), though none
have been successful in determining its temperature
dependence.
Temperature is known to have important effects on
the kinetics of activation of the channels (Hodgkin and
Huxley, 1952; Keynes and Rojas, 1974
; Kimura and
Meves, 1977
, 1979
; Meves and Vogel, 1977
; Bezanilla
and Taylor, 1978a
, 1978b
; Jonas, 1989
; Correa et al.,
1992
; Bendorf and Koopmann, 1993
; Rodríguez and
Bezanilla, 1996
). Temperature affects reaction rates depending on the activation energy involved in a particular reaction that contains an energetic component, or
more precisely the enthalpic component, and an order-disorder or entropic component. As their name implies, these two components have very different interpretations with regard to the operation of the protein
as it progresses through the activation steps that finally
gate the channel open. By just measuring the rates in the activation, one gets the total free energy involved
and it is not possible to separate the two components,
while by using different temperatures, the order/disorder component can be dissociated from the energetic
component. The aim of this work was to characterize the effects of temperature on activation kinetics, in an
attempt to resolve the enthalpic and entropic contributions of the more readily visible components of the gating and ionic currents, and thus obtain more insight on
the type of conformational changes the channel undergoes during activation. To gain further insight on the
details of the process, we then fit a kinetic model of Shaker activation to the temperature data set in the temperature range 10-20°C.
The main conclusion of this study is: steps far from
the open state have low temperature dependence while
steps near the transition to the open state have higher
temperature dependence, not including the last closed
to open step, which has a low temperature dependence (Rodríguez and Bezanilla, 1996).
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MATERIALS AND METHODS |
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RNA Synthesis and Oocyte Injection
cDNA encoding Shaker H4 K+ channel and Shaker H4 K+ channel
with the W434F mutation, which have just a few silent amino acid differences with the ShakerB clone (Hoshi et al., 1990; Murrel- Lagnado and Aldrich, 1993) in an optimized vector (Starace et al.,
1997
) were used. All the experiments shown here were done in
clones with the fast inactivation removed, shH4ir (Hoshi et al., 1990
;
Stefani et al., 1994
). cRNA was injected and expressed in Xenopus
laevis oocytes and tested for expression with the cut-open oocyte voltage clamp technique (Stefani et al., 1994
), 2-4 d after injection.
cRNA was prepared using the same procedure described in
Rodríguez and Bezanilla (1996). 50 nl cRNA solution (~2-3 µg/
µl) was microinjected per oocyte. Xenopus laevis oocytes (stage
V-VI) collagenase defolliculated were used.
To perform cell-attached macropatches, the vitelline membrane of the oocyte was removed using forceps after incubation in a hyper-osmotic solution (200 mM NaCl, 2 mM KCl, 1 mM MgCl2, 5 mM HEPES, pH 7.5 with 1 M NaOH).
Solutions
Solutions were made by mixing stock isotonic solutions (245 mOsm) of the principal cation containing 10 mM HEPES at pH 7.2.
In most of the experiments, gating currents were obtained with the external solution (0 K+) containing: 120 mM Na-methanosulphonate (MES),1 1.8 mM CaCl2. The internal solution contained: 120 mM K-MES, 1 mM EGTA-N-methyl-glucamine (NMG). Some of the experiments were done in 0 K+/0 Na+ solutions, using stock isotonic solutions (235 mOsm) of NMG as the main cation. In these cases, the external solution contained: 110 mM NMG-MES, 1.8 mM CaCl2. The internal solution contained: 110 mM NMG-MES, 2 mM NMG-EGTA.
Ionic current was obtained mostly with the external solution (60 K+), containing (mM): 60 Na-methanosulphonate, 60 K-methanosulphonate, 1.8 CaCl2. In some cases, external solutions were used with 0, 10, or 120 mM K+ as required. The internal solution contained 120 mM K-methanosulphonate, 1 mM EGTA-N-methyl glutamine.
Cut-Open Oocyte Voltage Clamp Technique
Before recording, the oocyte was permeabilized with 0.3% saponine in 0 K+ external solution. For details of the cut-open oocyte
voltage clamp technique (COVC), see Stefani et al. (1994). The
intracellular microelectrode was filled with 3 M KCl. Capacitive
cancellation and series resistance compensation (Rs) were used.
Series resistance compensation was important for the low temperature experiments because we found that between 22 and 4°C
the Rs can increase 1.7×. In the experiments shown here, typical
values for Rs were <0.4 k
. The capacitive transient was measured to check the voltage clamp speed. Typically, the capacitive
transient decayed in <50 µs (between 17 and 22°C) and <80 µs
at low temperatures. In some cases, linear leak and capacitive
currents were subtracted using the P/
4 or P/4 subtraction protocols (Armstrong and Bezanilla, 1977
) with a subtracting holding potential of
100 mV for ionic currents or
120 mV for gating currents. Unsubtracted gating currents records were obtained also in some experiments, by adjusting the capacity
cancellation with a holding potential of 0 mV, and returning to
the usual holding potential of
90 mV during the recording. Linear leak compensation was used also, as required.
Macropatch Technique
Cell-attached patch configuration with pipettes with external diameters of 5 µm (tip resistance <1.6 M) and Sylgard coated were used. Typical seal resistances were 1-20 G
. Experiments with stretch channel contamination were discarded.
Ionic current fluctuations are mostly due to the opening and
closing of ion channels (Silberberg and Magleby, 1993). The
principal assumption in noise analysis experiments of a particular channel is that the fluctuations in membrane current are recorded from a homogeneous population of channels (in this
case, the ShH4ir) under conditions where the background noise
due to intrinsic currents is minimal and there is a single conduction state. Ionic current noise of ShH4ir was analyzed with the
mean and variance of the currents from >100 traces per voltage,
obtained at different voltages (between
50 and 80 mV) to estimate the number of channels, unitary conductance, and open
probability. At each temperature tested (usually 18, 7-8, and
4°C) at least two different voltages were analyzed. Error due to
long-term drift was minimized by performing pairwise analysis in
calculating the variance.
Assuming n independent channels with a single conducting
level, values of the total number of channels (n), the open probability (Po) and the single-channel current (i) can be estimated by
fitting the variance (2(t), current fluctuation) vs. the mean current (I(t)) curve (Sigworth, 1980
; Silberberg and Magleby, 1993
;
and one example is shown in the inset of Fig. 6) with:
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and the Po was calculated from the value of the mean current at steady state (Iss):
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The unitary conductance () was calculated from:
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where VK is the reversal potential and V is the test pulse.
To estimate the elementary gating charge q, fluctuation analysis was performed on gating current ensembles using >100 traces per experiment. This was repeated for several voltages in the saturated portion of the charge versus voltage curve (Q-V curve). We used the same procedure reported by Sigg et al. (1994).
Mean-variance plots of the decay of On and Off responses were
fitted to:
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where B is the effective bandwidth (equal to 1.064 fc, where fc is the corner frequency of a gaussian filter), Ig is the mean gating current, q is the elementary gating charge movement, and c is a constant.
Even as it is known that this simple experiment does not reflect
the nuances of the entire activation process, it is a useful tool in
estimating the largest carrying charge transition. The value of the
elementary charge movement is consistent with the value obtained
from simulated data from a multistate model (Sigg et al., 1994).
Data Acquisition
IBM-clone personal computers with hardware and software previously described (Stimers et al., 1985) were used for data acquisition. Analogue signals were filtered at 1/4 or 1/5 of sampling frequency using an eight-pole Bessel filter. The temperature was
controlled by a peltier device with negative feedback using a thermistor as a temperature sensor.
Fitting and Simulation
The gating current traces were fit with a sum of three exponential functions. Q-V curves were fit using a two-step sequential Boltzmann equation (see Eq. 6). Fits were done with the NFIT (The University of Texas Medical Branch at Galveston, Texas) program using the chi-squared criterion for the goodness of fit.
A multistate sequential kinetic model (see Fig. 16 and Table
III) describing the activation pathway was evaluated using ScoP (Simulation Resources, Barrien Springs, MI) and the fit of the parameters was done directly with the experimental records using ScoPfit. To apply enough constraints to the model, a set of 10 unsubtracted gating current traces elicited as a response of a variable test pulse between 120 and 0 mV from the holding potential (at
90 mV) obtained at two different temperatures (21 and
11°C), were used to fit the parameters of the kinetic model.
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RESULTS |
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Effects of Temperature on Ionic Currents
Raising the temperature speeds the kinetics of ionic currents dramatically, as shown in Fig. 1. It is not possible to account for all the changes by assuming a common temperature coefficient for all the exponential components of the current, and it was found that the temperature dependence of a single component could change with voltage. This is not surprising, as the individual transitions are expected to have different entropic and enthalpic components, the eigenvalues of the system will vary their temperature sensitivity according to the predominance of the rate constants that make them up. This poses a challenge to the study of how temperature is really affecting the elementary rate constants that compose the operation of the channel. The approach we have followed is to extract the most obvious eigenvalues from the ionic currents under different initial conditions or pulse protocols and describe their temperature dependence. By performing these experiments at limiting values of voltage, we tried to infer the behavior of some of the more important elementary transitions of the multistep process. Notice that by using this procedure we may not get the real eigenvalues of the system because frequently there are a multitude of eigenvalues of similar values that are not experimentally separable and for this reason we will refer to them as observed eigenvalues.
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The Kinetic Components at Depolarized Potentials
In a previous study (Rodríguez and Bezanilla, 1996), a
double pulse protocol was used in an attempt at extracting the temperature dependence of the transition
leading to the open state. An extension of this study is
the description of the temperature dependence of the
main observed eigenvalues of the On ionic currents.
Fig. 2 displays the extracted rate constants from such
an experiment. Ionic currents exhibit a lag before they
rise in a quasi-exponential time course to their final
value. By fitting a sum of two exponential functions to
the late part of the current trace, after the initial lag, we
obtain an empirical description of two main observed
eigenvalues in the process: one fast component with a
time constant between 1.31 and 0.68 ms, and a slow
component, with a time constant between 6.43 and
3.12 ms, at 17-22°C, 20 and 80 mV, respectively. This fitting process is especially successful at large depolarization when the approach to the steady state current
may be very well described with only two exponential
functions, and for this reason we restricted our analysis
to depolarizations to ~+50 mV. Fig. 2 A shows that the
proportion of the two exponential components definitely favors a predominant fast component for both 19 and 5°C and both components are affected by temperature as shown in Fig. 2 C. We studied the fast component in more detail because, as it is larger (~70-80% of
all kinetic components), it can be characterized more
accurately. The second component corresponds to
<30% of all kinetic components and may reflect some
of the transitions near the open state (Bezanilla et al.,
1994; Rodríguez and Bezanilla, 1996
). The voltage dependence of the fast component at different temperatures is shown in the range of 20-80 mV. It demonstrates a mild voltage dependence that can be described by a valence times the fraction of the field (z) of
0.25 ± 0.02 eo (n = 4, mean ± SEM, between 19.2 and
5.1°C). At temperatures below 2°C, the slope of the plot
is not statistically different from zero (z = 0 eo). Rodríguez and Bezanilla (1996)
demonstrated with the
double pulse protocol that the forward rate of the last transition close to open step is voltage independent
(no charge movement is involved during the last step
of the activation process). Neither is it temperature dependent. With test pulses >20 mV and at very low temperatures, we were able to isolate this transition from
the other transitions near the open state.
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The fast component has a strong temperature dependence, and an Arrhenius plot using the time constant obtained at 50 mV gives a straight line with a Q10 of ~4 (Fig. 2 D), corresponding to an Ea of 23-25 kcal/mol. This main observed eigenvalue is clearly different from the observed eigenvalue obtained with the double pulse experiment, which is much larger and independent of voltage and temperature. This indicates that the time course of the ionic current is rate limited by one or several steps that precede the opening transition.
The Temperature Dependence of Early Transitions
The initial lag of the ionic current reflects the early
transitions of the activation pathway, which can be studied with the Cole-Moore pulse protocol (Cole and
Moore, 1960). A large negative conditioning pulse will
populate most of the channels in closed states further
removed from the open state, which is reflected in a
longer lag in the activation of the ionic current.
Fig. 3 A shows superimposed ionic currents for a
pulse to 40 mV for different conditioning pre-pulses
ranging from 150 to
50 mV with the longest lag observed for the
150 mV conditioning pulse. The current lag was measured by shifting one trace with respect
to the other until their time courses coincide. This procedure is shown in Fig. 3 B for two sets of conditioning
pulses. If the prepulse is varied between
150 and
90
mV (Fig. 3 B, top left), the superposition is very good after a shift of 0.2 ms (Fig. 3 B, bottom left). However, a
shift of 0.47 ms for currents obtained for prepulses of
150 and
50 mV failed to superimpose the traces at
long times. A different amount of shift can superimpose the traces at long times but not at short times,
showing that the time courses of the current traces differ. This result is expected if the conditioning pulse approaches a voltage in which the probability of reaching
the open state is relatively high, which is the case for
the
50 mV prepulse.
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The plot of the shift as a function of the conditioning pulse is shown Fig. 4 A for three different temperatures. Notice that the shift increases significantly as the prepulse is made more positive and that the temperature has little effect for very negative conditioning pulses. This indicates that the rate constants of transitions far removed from the open state have a smaller temperature coefficient than the rate constants that are closer to the open state. An Arrhenius plot of the reciprocal value of the shift for five different conditioning voltages is shown in Fig. 4 B and the inset shows that the Q10 values obtained become larger as the conditioning pulse is made more positive. When the Q10 was computed for conditioning pulses in which the time course of the currents coincided after shifting, the value was 1.69 ± 0.09 (n = 11) between 8 and 19°C. In contrast, from 13 experiments, the Cole-Moore shift obtained from current traces that did not superimpose completely gave a Q10 that varied from 2 to 5. These results are consistent with the idea that the energy barriers of the transitions between closed states that are far removed from the open state have small enthalpic changes, and that when the Q10 of the shift increases, it is because temperature-dependent transitions closer to the open state are being sampled.
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Temperature Effects on the Steady State Properties of the Open Probability
The effects of temperature on the functional relationship between the relative open probability and voltage (Por-V) in the steady state gives information about the thermodynamics of channel activation. In the simple case of a two- state channel, the assignment of the equilibrium constant is unique when either the Q-V or Por-V is measured. This is not the case for the activation of the Shaker K+ channel because there are multiple transitions and the Por-V curve will contain a combination of equilibrium constants. For such channels, modeling is required to assign the thermodynamic parameters to each of the equilibrium constants. A further complication is that, due to fast blocking of the channel in the open state, the experimentally derived Por-V curve is dependent on the method used to compute it. Although we tried several procedures to estimate Por-V, we will only present one here (called Delta-V protocol) that was found to maintain the shape of the G-V curve at different temperatures.
The method estimates the voltage dependence of the
conductance as shown in Fig. 5. After the pulse to the
potential V, the membrane is only partially repolarized
to a new potential V1 that differs from V by a magnitude V. The difference of the current at the end of
the pulse and the beginning of the V1 pulse is used to
compute the conductance for the
V as a function of
voltage (see Fig. 5). The conductance thus calculated
includes the open probability, the number of channels,
and the single channel conductance. The low temperature G-V distribution shows a shift to the left in the voltage axis with respect to the G-V curve at high temperature, which is consistent with the result obtained with
the double pulse that revealed temperature dependence only in the backward rate of the transition to the
open state (Rodríguez and Bezanilla, 1996
).
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Temperature Dependence of Channel Number, Open Probability, and Unitary Conductance
The conductance measurements just presented cannot
determine whether temperature is changing the open
probability, the number of active channels, or the unitary conductance. We approached this question using
nonstationary noise analysis to estimate the number of
channels and the open probability (Sigworth, 1980). The results are presented in Fig. 6. The inset shows a
typical plot of mean and variance that was used to estimate the single channel current, the number of channels, and the open probability. Experiments were done
with macropatches in the range of 18-4°C and, although the plot shows considerable scatter, grouping
the measurements at all positive potentials shows a significant difference in the open probability with temperature. The Po decreases by 20% between 18 and 4°C (P = 0.0008, t test). At temperatures below 8°C, there is no
detectable further decrease in the open probability.
A valid question is whether the number of active channels n remain constant when lowering the temperature. To improve the accuracy of the estimation of n, measurements were done at several voltages at the same temperature and the mean number of channels estimated from these was compared with the equivalent estimate at another temperature. In four reversible experiments (i.e., the ionic current was unchanged before and after experimental runs at different temperatures), the differences in the mean values of n among the different temperature groups were not statistically significant (P = 0.48, Kruskal-Wallis one way analysis of variance on ranks test). This result, however, should be taken with caution due to the variability of the measurements.
The noise analysis experiments also allowed the estimation of the single channel conductance, at different temperatures. The estimation was done for potentials ranging from 0 to 80 mV, voltage range where the
unitary conductance seems to be voltage independent.
From several macropatches at 17-18°C, the mean value of
was 10 pS, at 8°C the mean value was 7.4 pS, and at
4°C the mean value decreased to 5.6. The results are
summarized in Table I and the calculated Q10 for conduction is 1.44, as expected from a process with a low
energy barrier and in agreement with previous estimates of the conductance in other channels using single channel measurements (i.e., Correa et al., 1992
).
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Effect of Temperature on Gating Currents
Gating currents show the movement of charge between states; therefore, it gives kinetic information about transitions that may be far removed from the open state, which may be difficult to identify by measuring ionic currents. We have performed a systematic study of the effects of temperature on the kinetics of gating currents and steady state properties of the charge movement.
Temperature Effects on the Time Course of Charge Movement
Fig. 7 shows a family of gating currents recorded at 21 and 5°C. At low temperatures, the overall kinetics slow down. It is noticeable that the largest effect is on the Off response, particularly at high depolarizations, indicating that transitions near the open state are more temperature dependent than earlier transitions of the activation pathway, in agreement with the analysis of temperature effects on ionic currents.
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A simple way to measure the effects of temperature
on the time course of the gating currents is to use expansion and superposition between two records at two
different temperatures. For example, we selected the
On response recorded at 50 mV obtained at two different temperatures (21.1 and 11°C, see Fig. 8). The
currents were first vertically scaled to match the peak
amplitudes (Fig. 8 A), and then the high temperature
record time course was scaled until the two traces could
be superimposed (Fig. 8, B and C). The On responses
could not be completely superimposed, indicating the
presence of more than one component with different
temperature coefficients. Using two different expansion factors, it was possible to superimpose the early
part of the records with a factor 1.98 and the late part
with a factor of 2.8. Thus, at
50 mV, there is a fast
component with a Q10 of ~2 and a slower component
with a larger Q10 of ~2.8.
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The Off response exhibits more complex behavior.
Fig. 9 shows the Off response of the gating currents obtained at 20.9 and 10.7°C upon return to 90 mV from
a pulse of 20 mV. The prominent rising phase observed
at high temperatures is replaced by a faster component
preceding the very slow decay of the current to baseline. It is quite clear that these traces are so different
that time expansion of the low temperature record will
not superimpose onto the high temperature record.
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Temperature Dependence of the Kinetic Components of Gating Currents
The time course of the On and Off responses of the
gating current may be described by a sum of three exponentials: a rising phase followed by a fast and a slow
decaying component. A simple interpretation of this kinetics is that the rising phase and the first decaying
component of the On response represent transitions distant from the open state, while the slow component
corresponds to transitions near to the open state. We
deduce this from the fact that the fast component is
predominant at small depolarizations that favor closed
states, and the slow component becomes more prominent at higher depolarizations that favor the open state. Guided by this simple interpretation, we selected two
potentials to analyze the effect of temperature on the
kinetic components of the charge movement: 60 mV
where the open probability of the channel is quite low
(backward rates are predominant) and
10 mV where
the channel is open or near to the open state (forward rates are predominant).
At negative potentials (60 mV, Fig. 10), a linear Arrhenius plot can describe the temperature dependence
of the fast component and the rising phase in On and
Off responses. The Q10 for the activation and deactivation process at this voltage is between 2.5 and 3.2. For
the slow component, two lines were required to fit the
Arrhenius plot.
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At potentials when the channel is open or near to the
open state (10 mV, Fig. 11), the temperature dependence becomes more complex. The Arrhenius plot for
the fast decaying component of the On response is
linear with a Q10 = 2.6, similar to the one obtained at
60 mV, but for the rising phase and slow component two lines were required to fit the Arrhenius plot. This
result is consistent with the idea that transitions near
the open state involve high energy barriers with large
enthalpic changes. For the Off response (Fig. 11 B),
the Arrhenius plot of the rising phase and decay is linear with a Q10 > 3.5.
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Voltage Dependence of the Kinetic Components of Gating Currents
The plots of time constants measured from the two decaying components of the On response as a function of
voltage are shown in Fig. 12. It is apparent that the fast
decay (1, closed symbols) is less voltage dependent than
the slow decay (
2, open symbols), in agreement with the
idea that the first closed transitions carry less charge
than the transitions near the open state (Sigg et al.,
1994
). At potentials more positive than 20 mV, a single
exponential decay fit provides an adequate fit of the
current, making it difficult to determine whether the
remaining kinetic component belongs to the functional relation of the fast or slow component as a function of voltage. For these potentials, the symbols (Fig.
12) have been filled gray.
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To characterize the slow component of the gating
current in more detail, the reciprocal value of the
larger time constant was plotted as a function of voltage
for three temperatures, as shown in Fig. 12 B. This plot
allows the estimation of the voltage dependence of the
slower observed eigenvalue by computing the slope of
ln(1/2) versus voltage for all temperatures. The estimated lines are reasonably similar to each other for the
three temperatures tested. It is possible to distinguish
three regions in this plot. For potentials more negative
than
50 mV, the observed eigenvalue increases with
hyperpolarization with an apparent valence times fraction of the field z
= 2.7 eo. At potentials in the range of
50 and
10 mV, the apparent valence is z
= 1.6 eo
and, at potentials more positive than
10 mV, the apparent valence is 0.45 eo. From four different experiments (8-10 plots at each voltage range), z
of the
backward rate was
2.6 ± 0.2 eo (n = 8), and z
of the
forward rate was 1.9 ± 0.2 eo (n = 10). These values are
similar to the value of the elementary charge movement measured by gating fluctuation analysis (~2.4 eo,
see below and Sigg et al., 1994
), suggesting that the
slow decaying component could be dominated by a single transition whose backward and forward rates are
measurable with the method just described.
Reactivation Experiments: The Rates of the Early and Late Transitions
A three-exponential function fit of the gating current is
unlikely to isolate the kinetic components contributed
by early transitions of the activation pathway. This is because these transitions carry a small charge, and it is expected that the rising phase and first decaying components are contaminated by charge movement from late
transitions. In fact, the temperature coefficients (Q10) of the fast component measured at small depolarizations
is much larger than the Q10 estimated from the Cole-Moore shift experiments (see Figs. 3 and 4). In an attempt
to isolate these early transitions, we measured the reactivation of the charge movement after a variable recovery
period between 50 and
90 mV, a voltage range that
detects mainly the early charge movement, or Q1. Fig.
13 shows the plot of the charge movement (Q) as a
function of time (t) between
50 and
90 mV and between
50 and 0 mV. Data were fitted to a single exponential of the form Qon(t) = Qmax (1
aexp
t/
),
where Qon(t) is the area under the On response of the
gating current, Qmax is the total charge movement, a is
the exponential coefficient, t is time, and
is the time
constant. The fitted function is the continuous line in
Fig. 13. In this experiment, the temperature coefficient
(Q10) of the charge movement as a function of time was
1.03 for a pulse to
50 mV, and 3.3 for a pulse to 0 mV.
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In four different experiments, the energy of activation (Ea) for charge moving between 90 and
50 mV
was 2.6 ± 1.3 kcal/mol, corresponding to a Q10 = 1.2 ± 0.09, suggesting that this part of the process can be described using multiple steps with low energy barriers, in
agreement with the results obtained from Cole-Moore protocol experiments. On the other hand, data from
eight different experiments using a pulse to 0 mV, which
should activate also the late gating charge-laden transitions that carry more charge, the Q10 was >4 (Q10 = 4.5 ± 0.3, n = 8, Ea = 24.5 ± 1.2 kcal/mol). To study
the late charge (Q2) in isolation, we studied the charge movement between
50 and 0 mV, which gave an Ea = 20.5 ± 3.3 kcal/mol (n = 3) corresponding to a Q10 = 3.6 ± 0.7 (n = 3). This is in agreement with the idea
that transitions that make up the second part of the total activation charge dominate the gating current record
and contain high energy barriers.
The Effects of Temperature on the Steady State Charge Distribution
The mean charge movement from one membrane potential to another may be obtained from the time integral of gating currents. The results from a typical experiment that covered the 5-22°C temperature range
is shown in Fig. 14 A. In experiments that showed reversibility in the total charge after changing temperature, such as the one shown in Fig. 14, the maximum
charge did not change significantly by lowering the
temperature from 20 to 10°C. However, in all reversible experiments, the total charge displacement invariably showed a tendency to decrease at lower temperatures, as illustrated in Fig. 14 A. In this experiment, the
possible error produced by incomplete integration
due to very slow kinetics was minimized by speeding
the currents up with a pulse to 130 mV. Thus, the decrease at very low temperatures appears real but, as it is
small and variable, it is difficult to describe or quantify
accurately.
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The voltage dependence of the Q-V curve did not change much with temperature. The Q-V curves were fitted to a two-step sequential model of the form:
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(6) |
where n is the total number of channels and z1 and z2 are the valence times fraction of the field of steps 1 and 2, respectively. By calling nz1 = Q1 and nz2 = Q2, we define the total charge moving in each transition and we found that the ratio of Q1/(Q1 + Q2) remained practically constant in the range of 3-22°C. This result indicates that a change in temperature leaves the two charge components intact. V1 and V2 are the potentials at which the forward and backward rates are equal in steps 1 and 2, respectively. The midpoint of the Q-V is shifted to more negative potentials when the temperature was lowered, as is shown in the normalized plots of Fig. 14 B. The effect is small, but it is found consistently that at low temperatures the charge is larger than at high temperatures at hyperpolarized potentials. This is reflected in the fit to Eq. 6 in four experiments (see Table II) that showed a shift in the V1 and essentially no shift in V2.
As each exponential term in Eq. 6 represents the ratio of the backward to the forward transition, the preexponential factors of the rates cancel and do not appear
in the equation. The argument of the exponentials are
the total free energy difference G according to
![]() |
(7) |
where Hi and
Si are the enthalpic and entropic
changes on transition i, where i is 1 or 2. Then Vi in Eq. 6 is given by
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(8) |
By measuring Vi at temperatures T1 and T2, it is possible
to compute the entropic change as (Correa et al.,
1992)
![]() |
(9) |
The last column of Table II shows the entropic
change computed from the observed shifts of V1 expressed as TS in kilocalories per mole at 20°C. In all
cases, the entropic change is negative. As the Q1 comprises the most negative region of the Q-V curve, this
result indicates that, during activation, initial transitions reduce the number of degrees of freedom of the
voltage sensor. There is no evidence of an entropic
change for the Q2 component, but the results obtained
with ionic current measurements using the double
pulse procedure (Rodríguez and Bezanilla, 1996
) indicate that the opening step also has a negative entropic
change.
Effect of Temperature on the Elementary Charge Movement
The analysis of fluctuations of Shaker K+ channel gating
currents reveals an elementary charge shot event of
~2.4 eo (Sigg et al., 1994). Temperature may alter the
energy landscape of the charge movement, which could
have an effect on the size of the elementary event. To
investigate this possibility, the measurement of gating
current fluctuations were carried out in a range of voltages and temperatures and the results are shown in Fig.
15. The elementary event has a minimum value in the
range of 0-30 mV. As the method to estimate the elementary charge requires the measurement of fluctuations produced exclusively by unidirectional transitions
(Conti and Stühmer, 1989
; Crouzy and Sigworth, 1993
), the values at potentials more negative than 0 mV overestimate the elementary charge due to contamination
by backward transitions. At potentials more positive
than 40 mV, time resolution suffers due to merging of
transitions brought about by increased rates, which
leads to an overestimation of the elementary shot event. We thus confined our comparison to the 0-30 mV range
and found that there is no significant difference in the
size of the elementary event in the 7-18°C temperature
range. Although the gross simplicity of the estimate of q
with this technique does not allow us to distinguish small
differences, it is noteworthy that in this large temperature range there is not a drastic change in the elementary charge. This indicates that the basic sequence
of activation steps is not altered by temperature, at least
in the region where the large charge transition occurs.
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DISCUSSION |
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Total Charge and Ion Conduction
The total amount of charge moved in the range of
120 to 30 mV remains constant between 20 and 10°C,
but it tends to decrease at lower temperatures (Fig. 14).
Excluding the possibility of incomplete integration,
which was minimized by repolarizing to extreme negative potentials, this could be the result of a decrease of
the total charge per channel or a reduction in the number of active channels. The noise analysis of ionic currents indicated that the number of channels remains
constant, suggesting that there is a decrease of the activation charge when lowering the temperature. This
point could be tested by measuring the charge per
channel as a function of temperature using limiting
slope (Sigg and Bezanilla, 1997
) or by counting channels and measuring total charge (Schoppa et al., 1992
;
Aggarwal and MacKinnon, 1996
; Seoh et al., 1996
),
but, as the reduction in total macroscopic charge is
small, it may prove difficult to detect. Noise analysis experiments also provided information on the effects of
temperature on the single channel conductance and
the results are consistent with previous findings of a Q10
of the order of 1.5, as expected from a process encountering low energy barriers.
Temperature and the Transitions in the Activation Pathway
In principle, the power of studying kinetics and steady state properties in a voltage-dependent channel as a function of temperature is that it makes it possible to dissect the free energy changes into its enthalpic and entropic components. In practice, however, the interpretation of the results is hampered by the complexity of a multistate process and the difficulty of isolating the elementary rate constants. Thus, the observed changes of kinetics are in fact changes in the observed eigenvalues of the system and not in the elementary rate constants and only by the use of special pulse protocols that enhance one component in favor of the others can one attempt the assignment of the changes to individual transitions.
In the present study, we have studied the effects of temperature on both ionic and gating currents because, as the information obtained with each type of experiment has a different bias, they complement each other. There is enough variability from oocyte to oocyte to make quantitative consistent measurements of ionic and gating currents difficult. In addition, there may be differences between the conducting and nonconducting clones in some of the transitions, and for this reason we have not attempted a global description.
Despite all these caveats, the effects of temperature
produce differential effects on the currents that make
it possible to draw a few general conclusions. The main
finding is that components of the gating current have
different temperature dependencies. If the observed
charge movement were a simple process or at least a
rate-limited process, the entire time course of the gating current would be equally affected by temperature
changes and the traces would be superimposable. The
results indicate that this is not the case because to superimpose the traces at early times gives a Q10 < 2, and
at long times the Q10 is ~3. Thus, we can conclude that
the recorded gating currents show the contribution of
charge movements from several transitions that differ
in their temperature dependence. The indication from
these experiments is that early transitions are less affected by temperature than late transitions and this was
verified by two different types of experiments. The analysis of the Cole-Moore shift on the ionic currents
confirmed that the temperature coefficient is quite
small when the voltage range is restricted to extreme
negative potentials. At these potentials, the channel
dwells in a set of closed states that are kinetically far
from the open state, and by modifying the prepulse potential, the initial distribution is changed among those
states. The conclusion is that those transitions are not
very temperature dependent. In contrast, the main observed eigenvalue of the ionic currents, which reflect
transitions closer to the open state, has a very large temperature dependence (Fig. 2). The other evidence
comes from gating current reactivation experiments
whereby the recovery at 90 mV of the charge moved
after a pulse to
50 mV has almost no temperature dependence (Fig. 13, left). This is in contrast to the temperature dependence at
50 mV for a pulse to 0 mV,
which has an important temperature dependence (Fig.
13, right). These results are in agreement with the notion that transitions between closed states, populated at
very negative potentials, are less affected by temperature than transitions that occur closer to the open state
of the channel.
The charge that moves at negative potentials (Q1)
has been previously distinguished from the subsequent
charge movement (Q2) on the basis of the steady state
Q-V curve and kinetics of the gating currents (Bezanilla
et al., 1994). Experimental confirmation that these two
types of charge are different has come from fluorescence experiments that show that Q1 correlates better
with conformational rearrangements near the S2 segment, while the Q2 correlates with changes near the S4
segment of the Shaker channel molecule (Cha and Bezanilla, 1997
). It is thus tempting to speculate that the low temperature coefficient of the early transitions corresponding to Q1 originate from a different region of
the channel molecule. The temperature dependence of
the steady state properties of Q1 further indicates that
those conformations experience a decrease in entropy
(Fig. 14 and Table II). A possible interpretation of these results is that the initial steps in channel activation require an ordering of the channel molecule that
may be required for the occurrence of the following
transitions that carry most of the charge that leads to
channel opening.
The separation of the exponential components of
the gating current transient show that at 60 mV the
fast and slow components have a smaller Q10 than the
corresponding components recorded from a pulse at
10 mV (Figs. 10 and 11). The difference is not as
large as one would expect when compared with the
measurements done with Cole-Moore and channel
opening. This may be the consequence of measuring
observed eigenvalues that are a composite of different rates with low and high temperature coefficient. In this
regard, it seems more appropriate to separate the components with the recovery experiments, as described
above, because the weight of the exponential components is changed by the initial conditions.
The results of the double pulse experiments reported before (Rodríguez and Bezanilla, 1996) indicate that the opening step is not rate limiting and that
it only has temperature dependence in the return from
the open to the first closed state. The prediction from
those results was that the steady state Por-V curve should be displaced to the left when the temperature is lowered and the G-V curve computed as indicated in Fig. 5,
indeed shows this shift consistent with the double pulse
experiment.
Kinetic Model
A kinetic model that is able to reproduce the features of the currents at all voltages and temperatures would allow the description of the enthalpic and entropic components of each of the elementary rate constants. Such models should be based on the results of ionic and gating currents recorded in a large range of potentials and covering a large range of temperatures. The recording of ionic and gating currents is normally done in different oocytes and, as there is a large variability in the kinetics of the Off currents among oocytes, a global fitting becomes difficult. The problem gets compounded by the fact that gating currents are best recorded in the W434F mutant, which may have subtle differences with the clone that has the intact pore region. For these reasons, we have settled for a fit of the gating currents traces only, while drawing information from ionic current data to constrain a few of the parameters of the fit.
We have tested two types of models. The first type
consists of four subunits, each having three states (Zagotta et al., 1994). In this model, when all four subunits
are in the last state the channel can progress to the
open state through one more transition. The second
type is a sequential model that has multiple transitions in a linear sequence (similar to the previously proposed model by Bezanilla et al., 1994
). We have not
seen a good fit to the data with the first type of model
because they do not reproduce well the drastic change
in kinetics observed in the Off gating currents when
the temperature is lowered. As the sequential model does seem to fit the data better than the three-state-four-subunit model, we are presenting here the fit obtained with a data set of five different membrane potentials done at two temperatures.
The model is presented in Table III along with the
rate equations and the fitted parameters. Fitted values
for the enthalpic barriers for the forward Hf and backward rate
Hb constants are presented for each one of
the transitions, as well as the net enthalpic change
Hss.
The fitted values of
i0 and
i0 in Table III include the
product of the preexponential factor times exp (
S/R)
and we have not attempted to compute the entropic
terms from these values because we do not have a value
for the preexponential factor. However, by assuming
the same preexponential factor for the forward and
backward rate constants, we could compute the entropic change for each transition (
Sss) that is indicated in the last column of Table III as T
Sss at 20°C.
The values of the valence times fraction of the field are
presented for the forward and backward rates in the
third and fourth columns of Table III.
The gating current traces and the fitted traces are
presented in Fig. 16. The rate constants and valence for
the transition from the open to the blocked state were
assumed to be independent of temperature and their
values were extracted from Zagotta el al. (1994). The
valence of the transition between the last closed state
and the open state was obtained from Rodríguez and
Bezanilla (1996), but the rate constants were obtained
through fitting of the gating current data. The general
features of the model roughly agree with the experimentally observed eigenvalues obtained from ionic and
gating currents. The model consists of a long series of
transitions (subindex 0) with low valence and low enthalpic changes, followed by two transitions with higher
enthalpic changes in which the first one (subindex 1)
has a very large valence and the second one (subindex
2) has a lower valence. These two transitions are followed by the last transition (subindex 3) that leads to the open state. In several attempts to reproduce the
marked changes in kinetics of the gating current tail
when lowering the temperature, it was found that one
of the backward rates near the transition carrying most
of the charge had a reverse temperature dependence. In the set of fitted parameters shown in Table III, that
occurs in
Hb2.
While the model seems to fit the gating current
traces fairly well, there are a few results from the model
that do not agree as well with the expectations based on
the analysis of the gating currents. One of them is that
the Q10 of the initial transitions seems higher than the
low Q10 measured from the Cole-Moore shift and charge
movement recovery. Also, the fitted parameters predict a total amount of charge per channel about half what
has been measured experimentally (Schoppa et al.,
1992; Aggarwal and MacKinnon, 1996
; Seoh et al.,
1996
), suggesting perhaps that the measured gating
current is the result of the concerted operation of two of the four subunits. Although the results of modeling
should then be viewed with caution, the discrepancies
of the models with this richer data set that includes
temperature dependence may be considered an indicator that none of the proposed models are good representations of the Shaker channel operation.
Conclusion
The differential effects of temperature on the ionic and gating currents suggest that, during activation, the Shaker K+ channel first evolves through a series of closed state transitions with relatively low enthalpic barriers that decrease the degrees of freedom of the channel structure. It then undergoes large enthalpic and positive entropy changes during at least one transition that moves most of the charge, ultimately finishing with an opening transition that requires an ordering of the molecule.
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FOOTNOTES |
---|
Address correspondence to Dr. F. Bezanilla, Dept. of Physiology, UCLA School of Medicine, Los Angeles, CA 90095. Fax: 310-794-9612; E-mail: fbezanil{at}ucla.edu
Original version received 30 March 1998 and accepted version received 3 June 1998.
Portions of this work were previously published in abstract form (Rodríguez, B.M., D. Sigg, and F. Bezanilla. 1995. Biophys. J. 68:A137. Rodríguez, B.M., D. Sigg, and F. Bezanilla. 1996. Biophys. J. 70:A143. Rodríguez, B.M., and F. Bezanilla. 1998. Biophys J. 74:A215).We thank Dagoberto Grenet for oocyte preparation and Jin Yuguang for oocyte injections.
This work was supported by Public Health Service grant GM30376 and CONICIT S1-95000502 (Venezuela).
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Abbreviations used in this paper |
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G-V curve, conductance versus voltage curve; MES, methanosulphonate; NMG, N-methyl-glucamine; Por-V curve, relative open probability versus voltage curve; Q-V curve, charge versus voltage curve.
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