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Gating current associated with inactivated states
of the squid axon gating channel.
ARTICLE in PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES · DECEMBER 1990
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University of Zurich
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Nikolaus Greeff
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Available from: John M Bekkers
Retrieved on: 04 February 2016
Proc. Nati. Acad. Sci. USA
Vol. 87, pp. 8311-8315, November 1990
Biophysics
Gating current associated with inactivated states of the squid axon
sodium channel
(inactivation/voltage clamp/kinetic model)
J. M. BEKKERS*t*, 1. C. FORSTER*§,
AND
N. G. GREEFF*§
*Station Marine de Roscoff, 29211 Roscoff, France; tThe Salk Institute, Howard Hughes Medical Institute, 10010 North Torrey Pines Road, La Jolla, CA
92037; and §Physiologisches Institut, Universitat Zurich-Irchel, Winterthurerstrasse 190, 8057 Zurich, Switzerland
Communicated by Charles F. Stevens, August 2, 1990
Sodium (Na) channel gating currents were
ABSTRACT
measured in squid (Loligo forbesi) axons to study transitions
among states occupied by the Na channel when it is inactivated.
These measurements were made at high temporal resolution
with a low-noise voltage clamp. The inactivation-resistant
gating current, Ig,dCt, could be separated into a very fast (T =
5-25 jus) and a slower (T = 40-200 jps) component over a wide
range of test potentials (-140 mV to 80 mV) and for three
different starting potentials (-70 mV, 0 mV, and 50 mV). The
time constants for these components plotted against test potential lay on two bell-shaped curves; the time constants at any
particular test potential did not depend on the starting potential. Both components had charge-voltage curves that saturated between -150 mV and 50 mV. A fast spike, similar to the
fast component of Ig,hiact, was also apparent in recordings of the
fully recovered total "on" gating current. Iginct (fast) and
'ginact (slow) could not together be described by the simplest
possible model, a linear three-state scheme; however, Iginct
(fast) could be modeled by a two-state scheme operating in
parallel with other gating processes. Igfi.. (slow) and the
gating current due to recovery from inactivated states into
resting states could together be well described by a three-state
scheme. This lends support to models in which a pair of
inactivated states are connected by a single voltage-dependent
step to the resting states of the Na system.
The Na channel in the squid axon is known to have a complex
kinetic structure with perhaps several resting states (1), two
or three open states (2, 3), and two or more inactivated states
(4, 5). Many attempts have been made to devise models that
account for all possible states of the channel (e.g., refs. 3 and
6), but these often prove difficult to quantify because of the
many adjustable parameters. Our approach was to confine
the study to a manageable subset of the states that could be
studied in detail; the resultant model might then be fitted into
a larger scheme. The inactivated states of the Na channel
were chosen because (i) they are operationally well defined
(entered by applying an inactivating prepulse), (ii) they are
kinetically isolated because recovery from them into resting
states happens relatively slowly, and (iii) the form of the
gating current associated with them is known to be simple (1),
although the kinetics of this gating current has not been
analyzed in detail.
During our experiments we observed another, very fast
component in the gating current; this component could only
be observed in fresh axons, for which the membrane could be
rapidly voltage clamped. The very fast component appeared
independent of the inactivation state of the Na channel and
was adequately modeled as a two-state scheme functioning in
parallel with other gating processes. On the other hand, the
previously described slow component of the inactivationThe publication costs of this article were defrayed in part by page charge
resistant gating current (1) was well-modeled as a two-state
scheme connected via a single voltage-dependent step to the
resting states of the Na channel. This scheme can be regarded
under specific conditions as a subset of general schemes like
those of Armstrong and Bezanilla (3) and Armstrong and
Gilly (1).
These results were obtained by using a recently designed
low-noise voltage clamp system that assisted us in making
higher-resolution measurements than were hitherto possible.
MATERIALS AND METHODS
Axons from freshly killed squid (Loligo forbesi) were internally dialyzed as described (7) and voltage clamped at 5PC in
an air-gap chamber. Other details were as follows.
Data Acquisition. Membrane currents were filtered at 100
kHz (6-pole Bessel filter) and usually sampled at 3- or 5-,us
intervals. In a few experiments a transient recorder sampling
at 0.5-,u s intervals was used to confirm the fits found with the
slower sampling. The membrane holding potential was -70
mV. Linear currents were subtracted on-line by using a
scaled back-reference pulse (8) between -150 and -180 mV,
where no nonlinear charge transfer occurs. Membrane capacity transients were monitored throughout each experiment by using the transient recorder.
Solutions. The external solution was 11 mM CaC12/55 mM
MgCl2/524 mM Tris chloride/i ,AM tetrodotoxin (1155
mOsm). The internal solution was 350 mM tetramethylammonium fluoride/400 mM sucrose/10 mM Hepes (1350
mOsm). The pH of all solutions was adjusted to 7.2 at 5PC.
Voltage Clamp. Our ability to resolve a very rapid component of gating current was assisted by our use of a recently
designed fast low-noise voltage clamp (see ref. 9 for details).
This technique was important because experiments had to be
done quickly to avoid fatigue of the fiber and obliteration of
the rapid component (see Results); the low-noise clamp
reduced the need for time-consuming signal averaging.
Much effort was expended on tuning the clamp and associated electronics for optimum noise, speed, and linearity.
The total noise of the clamp plus signal conditioning hardware improved signal-to-noise ratio >10-fold compared to
previous clamp designs (e.g., ref. 7), with a corresponding
100-fold reduction in signal averaging. When series resistance
compensation was set for critical damping (7) and after
compromising with instrumentation asymmetry (see below),
the 10-90% settling time in the membrane for a command step
was 8 Azs. (Note that the capacity transient shown in Fig. LA
appears slower than this because it was filtered at 100 kHz.)
Abbreviations: Vp, voltage clamp test potential; r, time constant of
exponential decay; e, charge on electron; I inact, inactivationresistant gating current; IgON, fully recovered total "on" gating
current.
payment. This article must therefore be hereby marked "advertisement"
in accordance with 18 U.S.C. §1734 solely to indicate this fact.
tTo whom reprint requests should be addressed at: The Salk Institute, 10010 North Torrey Pines Road, La Jolla, CA 92037.
8311
Biophysics: Bekkers et al.
8312
The linearity and symmetry of all components between the
axon and the computer were studied by using a dummy
circuit, comprising passive elements, to model the membrane
and recording chamber. After optimization, there remained
only a small, brief asymmetry (e.g., Fig. 1B). Only for some
voltage protocols, when the gating current was very small,
was the accuracy of curve fits to the data affected (see
Results).
Curve Fitting. Gating currents were adjusted to the baseline at the end of the prepulse, and least-squares fits were
performed. Records were fitted to a sum oftwo or (at strongly
negative test potentials) three exponentials, plus a small
offset at negative potentials. Sometimes the time constant of
the slowest exponential was constrained (see below).
RESULTS
Clamp Speed as Determined from Capacity Transients.
Because an objective was to resolve very fast components of
gating current, it was important to know just how rapidly the
membrane could be stepped to the voltage clamp test potential (Vp). This was routinely determined for each fiber before
and after a gating current run by measuring the membrane
capacity transient (Ic), which gives the rate at which the
membrane is charged to Vp. Fig. 1 shows some typical results
for a voltage-clamped axon with series resistance (Rs) compensation critically adjusted (7). Fig. 1A shows the capacity
transient, measured a few minutes after mounting the fiber
(trace a) and its time integral (trace b), which traces the
approach of membrane potential to Vp. Fig. 1B shows a gating
current (Ig) measured shortly afterward in this fiber by using
the pulse protocol given in the Fig. 1 legend.
The capacity transient consists of a fast spike that is over
in -15 us, followed by a slow tail (x 30 us; arrow) that
becomes more prominent the longer the axon remains in the
chamber ("fatigue"; refs. 7 and 10). This tail cannot be
removed by Rs compensation: increasing the compensation
causes a damped oscillation about the tail, leading to an
Proc. Natl. Acad. Sci. USA 87 (1990)
oscillatory distortion in Ig (7, 11). The effect of the slow tail
is to decrease the speed of voltage clamp of the membrane
(trace b), leading to distortion of fast components of Ig (for
example, visible in Fig. 1B above the smooth curve, which is
a single exponential fitted to the slower phase of Ig; see
below).
An attempt was made to reduce the size of the slow
component of Ic by changing osmolarities of the solutions,
but this approach was unsuccessful (cf. ref. 12). Thus, our
strategy was to start with very fresh axons and complete all
critical measurements of Ig within 20-30 min.
Two or Three Components of Ig Can Be Distinguished When
the Na System Is Inactivated. Fig. 2 Insets show three
different ways of isolating the gating current that flows when
the Na channel undergoes transitions between its inactivated
states Ig.inact. In each case a long (20 ms) depolarizing
prepulse (either to 0 mV or 50 mV) is used to inactivate the
Na system. The membrane voltage is then either stepped
immediately to a range of test levels (only -100, -20, and 60
mV are illustrated) or else returned briefly (0.5 ms) to -70
mV before stepping to the test levels. A gap of 0.5 ms was
long enough for inactivated states to mostly attain the equilibrium distribution for the new potential but not so long that
significant recovery from inactivation could occur (13).
These protocols were chosen because they yield a gating
current that is predominantly Ig inact at a range of test potentials reached from three widely spaced starting potentials
(-70, 0, and 50 mV).
Two previously described components are apparent in the
gating current records in Fig. 2. (i) At the test potential of
-100 mV, Na channels recover rapidly enough from inactivation to give rise to a slow component in the gating current
(3), visible as an inward plateau on this expanded time scale.
(ii) The predominant faster component that is seen at each Vp
has been qualitatively described elsewhere and is thought to
arise from transitions among inactivated states of the Na
channel (3). We have now observed a third, very fast component of this gating current. The superimposed dotted lines
A
A
P-4i.....7m-~----1
-VI
0
:1 d
70
50 /s
0
70
B
_
(.
60
- 20
- 1 00
60
l
-20
I 00
+
0.5 ms
;;ii"
0.121
I
E
a>0.06
9
C
9{~i50
60
0
-
FIG. 1. The speed of voltage clamp at the membrane is limited,
as revealed by the capacity transient. (A) Typical membrane capacity
transient for a freshly mounted axon with critical series resistance
(Rs) compensation (trace a) and its time integral (trace b), both
normalized for clarity. Arrow, slow tail in the transient. (B) Gating
current recorded from the same axon for a command step from -100
mV to 40 mV preceded by a 20-ms prepulse to 0 mV and a 0.5-ms gap.
Smooth curve is a single exponential fit. Baseline trace is the system
asymmetry recorded for the same protocol by using a passive dummy
membrane. Vertical lines are 10-ps apart and indicate isochronicity.
All traces were filtered with a 6-pole Bessel filter at 100 kHz.
I
a.
70
. ,
5 D
- 1 00
PA/cm'-1
_AX
| 00 Ps
FIG. 2. (A-C) Inactivation-resistant gating currents, measured
using the three pulse paradigms (Insets), possess a very fast component. Dotted curves indicate single exponential fits, except for the
currents at Vp = -100 mV (largest negative-going current in each
panel), where the curves are double-exponential fits. Each trace is an
average of four sweeps.
Biophysics: Bekkers et al.
in Fig. 2 are single exponential fits, except at VP = -100 mV,
where a second exponential has been added to fit the slow,
recovery component. This third, very fast component is
especially obvious at Vp = -20 and 60 mV, less so at Vp =
-100 mV, but two exponentials (plus a third for recovery at
strongly hyperpolarized Vp values) were found necessaryand to provide an excellent fit-over the whole range of test
potentials used here (-140 mV to 80 mV). We do not think
that this very fast component (time constant 5-20 As) is an
artifact because it cannot be accounted for by instrument
asymmetry (Materials and Methods) or imperfect Rs compensation (14) and because the same component has been
seen by us with a different voltage-clamp system (7, 11).
Furthermore, a similar component is visible in the records of
Alicata et al. (15), obtained in crayfish axons. Note that the
fast component is quickly obliterated by slowing of the
capacity transient, which probably explains why this component has not yet, to our knowledge, been reported in squid
axon.
Time Constant Versus Voltage and Charge Versus Voltage
Data for the Components of Inactivated Gating Current.
Families of gating currents like those in Fig. 2 were fitted to
a sum of two or three exponentials. At Vp in the range of -100
mV to -60 mV the recovery time constant was constrained
to the value obtained from a separate run on the same fiber
using a long (20 ms) sampling window. The results of all fits
are summarized in Fig. 3: Fig. 3A shows (on a semilogarithmic plot) the behavior of the time constants; Fig. 3B gives the
charge-voltage (Q-V) relationships for the various compo-
B
nents for different pulse protocols. The superimposed
smooth curves were calculated from kinetic models presented in the Discussion. Note that most of the different fitted
time constants at each Vp differ from each other by about an
order of magnitude or greater; this emphasizes that the
multiexponential fit was robust, the components being wellseparated.
Each of the filled triangles at the top of Fig. 3A represents
the mean (n = 2-9) of time constants from single exponential
fits to the slowest ("recovery") component of each gating
current recorded at that potential. For comparison, the open
triangles plot the time constants for recovery of Na current
at each potential, as measured in one fiber with a doublepulse paradigm (13). The remaining symbols in Fig. 3 denote
individual double-exponential fits to Ig inact obtained using
the three different pulse protocols discussed above (see Fig.
3 legend). Note that the values of the time constants measured at a particular Vp are the same irrespective of the
starting voltage (-70 mV, 0 mV, or 50 mV), as expected for
a memoryless process. (The figure excludes fast time constants for the prepulse to 50 mV and Vp 2 -40 mV because
these gating currents were very small and sensitive to residual instrumentation asymmetries.) The fast time constants in
Fig. 3A may be distorted by the slow tail in the capacity
transient. On the other hand, the Q-V plot for the fast
component (Fig. 3Bd) is not affected by slowness of the
voltage clamp, provided that charge is integrated for long
enough that the membrane potential has, indeed, settled to
Vp. The fast Q-V curve is seen to saturate over a physiolog-
a
600-
CN
Ea
E
a
G/
0
0
L-
-C7
C.)
A
v
V'
5000-
I
I
a
Vp
0
500-
600 ,
0
50-
U
0
Qv
(N
E
. -'
4-i
E
10-
1
100
I
0
-150 -100 -50
(mV)
50
100
Vp (mV)
d
C
so
L3
00DI
(4
O-
E
a
17
IVbI...
a/
0-
-600 -
*I
a)
~~~~~0'1.
5-
50
40 -
4~~ ~ ~
100-
Cl)
0
-150 -100 -50
1000U)
8313
Proc. Natl. Acad. Sci. USA 87 (1990)
0
pI
p'tm
U7 -40 -
0
Im
1-1s50
-80-
-1800-100
-50
0
50
100
-150 -100
6
-50
5b
160
I
-150 -100 -50
Vp (mV)
Vp (mV)
Vp
0
I
l
50
100
(mV)
FIG. 3. Time constant versus voltage test membrane potential (Vp) and charge versus voltage data obtained from fits to gating currents like
those shown in Fig. 2. (A) Collected time constants, showing the three widely spaced components observed. *, Pulse paradigm of Fig. 2A; o,
paradigm of Fig. 2B; *, paradigm of Fig. 2C; v, mean of two to nine measurements of the slowest (recovery) component, error bars on first
three points being + SEM; v, time constants for recovery of Na current measured in a separate experiment. (B) Charge [in electrons- (e-) per
/Am2] carried by each component for the various pulse paradigms. (Ba-c) Q-V plots for the recovery component (E) and g inact (slow), for
paradigms A-C, respectively (same symbol convention as in A). (Bd) Q-V plots for gionact (fast) for paradigm A (-) and B (o). Broken curves
were calculated from a two-state scheme with a12
47 ms-1, a21 13 ms-1, q 0.75 e, n 0.5. Continuous curves were calculated from the
three-state scheme in the text with aR.11 = 0.2 ms-1, a1llR = 0.02 ms- qR.11 = 1 e, nR.I1 = 0.15, all.12 = 5.5 ms- aI2,11 = 1.5 msJ1,
q11.2 =
0.8 e, nl.12 = 0.33, where subscript I = inactivated and subscript R = resting.
=
=
=
=
,
8314
Biophysics: Bekkers et al.
Proc. Natl. Acad. Sci. USA 87 (1990)
ical range (around -100 mV to 50 mV). This, together with
the voltage-dependent time constant, suggests that the fast
component is truly an "asymmetry current" associated with
a membrane protein.
A Fast Component Is Also Observed in the "ON" Na Gating
Current. If the fast component is an asymmetry current, it
can arise either from transitions among inactivated states of
the Na channel (in which case it would be present only under
inactivated conditions) or else from gating transitions that
occur irrespective of the inactivation state of the channel (in
which case it could always be present, contained within the
total gating current). Fig. 4 provides evidence for the latter;
A and B show the gating current measured in the same fiber
at a constant test potential (20 mV) from a range of starting
potentials (-120 to -20 mV). However, in Fig. 4B an
inactivating prepulse is used, yielding Igsinact' whereas in Fig.
4A the prepulse is omitted, yielding the gating current arising
from transitions along the activation pathway and into the
inactivated state(s), IgON. A fast component, similar to Ig.jict
(fast), is apparent in '
I ON for all starting potentials. Such a
component was clearly seen in all fresh fibers and at all
positive test potentials and disappeared as the capacity
transient slowed, just as did the fast component of 'gwina~tAn attempt was made to fit exponentials to Ig,ON at test
potentials where its shape appears simple (Vp < -40 mV) to
look for a component with the same kinetic characteristics as
(fast). However, several time constants appeared
Igoinact
present, but these were not well separated as for Ig.inact,
rendering the fits inconclusive.
perhaps even a rising phase (after the initial spike) at some
starting potentials. On the other hand, Ig inact is a simple
biexponential process for all starting potentials and test
pulses. Moreover, the two time constants describing Iginact
appear to depend only on the test potential and not on the
initial conditions when these are varied from -70 mV to 50
mV (Fig. 3A).
It is important to note that, in general, the gating current
generated by a multistate Markov model depends upon the
rate constants and charge transfers between all the states
(e.g., ref. 16). However, under certain conditions one can
deal with a subset of the states in approximate isolation. If the
rate of recovery from inactivated into resting states is very
slow compared with the rates connecting the inactivated
states, one can show that the relaxation time constants for the
gating current originating in the inactivated states become
independent of the rates connecting the resting states (e.g.,
ref. 16). However, some recovery does occur, and transitions
among the resting states will give rise to gating current that
may also have fast components, although their amplitudes
may be small, depending on both the relative slowness of
recovery and the relative amount of charge transfer among
the resting and inactivated states. For present purposes it will
be assumed that the conditions are such that gating current
originating in the inactivated states predominates.
The problem is to find a simple kinetic model for the two
components of Igoinact because this might shed light on their
functional relationship. The following general scheme will be
used in the discussion:
k12
DISCUSSION
This work was motivated by the idea that Na channel gating
kinetics are more easily and rigorously studied by initially
focusing on small subsets of the channel's accessible states.
Here we have attempted to analyze only those states occupied by the channel when it is inactivated. The benefit of
doing this is immediately seen by comparing IgON and Ig inact
(Fig. 4). Ig&ON, which arises from all the activation steps plus
steps leading to inactivation, has a delayed decay, and
A
1
k23
S
k2l S2 132 3
Scheme I
with the indicated amount of charge flow q for each transition
(see also ref. 5). This is the simplest model that could account
for a biexponential process like Ig,inact* It is assumed that
Eyring-Boltzmann kinetics are applicable (17) and that the
transitions between the ith andjth states are governed by the
voltage-dependent, time-independent rate constants
kij= aijexp[nqV/kT],
[Il
kji= ajiexp[-(l - n)qV/kT].
[2]
and
20
B
........
,. . . . . . . . . . .
20
pA/cm2
100 Ps
FIG. 4. A fast component is present in both Ig,ON (A) and Ig.inut
(B). Note the spike that is always present at the beginning of Ig&ON and
which appears similar to that in 'gjinct. (Inset) Pulse paradigm: the
inactivating prepulse, shown as a broken line, was absent to record
Ig.ON and present to record Ig inact. Each trace is an average of four
sweeps.
Here the a values are the values of the rates when the
membrane voltage, V, is zero, q is the charge transfer when
going from state i toj, and n is a number between 0 and 1 that
gives the location of the peak of the energy barrier separating
i andj, expressed as a fraction of the distance between those
states. It can be shown that a plot of the logarithms of the
gating current time constants predicted by Scheme I yields
straight lines as V -+ ±00, with the slopes and intercepts of
these lines giving values for the parameters a, n, and q in Eqs.
1 and 2. This enables one to decide quickly whether the model
fits one's data.
The above approach was used to determine whether a
model like Scheme I could fit the two components of Ig.inact,
It was found that Scheme I could not fit Ig,inaict even allowing
for the possibility that the time constant of Ig,nact (fast) is
distorted by the slow tail in the capacity transient: discrepancies with the model were too striking (e.g., inward currents
measured where outward ones were predicted).
The next most complicated scheme is one with two independent two-step processes in parallel, which is equivalent to
a single four-state scheme with some restrictions on the
Biophysics: Bekkers et al.
interconnecting rates (4, 6). In this case, good fits to both
components of Igijnact were obtained. For the fast component,
the fitted parameters (see Fig. 3 legend) were used to calculate the broken lines in the T-V and Q-V plots in Fig. 3 A and
Bd. The agreement is satisfactory, except for the extremities
of the Q-V curves. However, owing to the above-mentioned
distortion of this component, this fit should be regarded with
caution. A good fit to Iginact (slow) could be obtained with q
and n similar to those for the fast component, but the a values
are an order of magnitude slower. The r-V curve for Ig inact
(slow) calculated from this model is very close to that shown
in Fig. 3A (lower continuous curve); however, this curve was
actually calculated from a slightly more general scheme for
Ig.inact (slow) that is discussed below.
The conclusion from the above is that the fast component
of Igoinact can be modeled most readily by assuming that it is
kinetically independent of Igoinact (slow). This assumption is
compatible with the result of Fig. 4 that a fast component of
gating current appears independent of the inactivation state
of the Na gating system; however, more complex models that
do couple the fast and slow components of Ig.inact can
certainly be conceived. An independent fast component
could originate in functionally uncoupled conformational
changes within the Na channel protein or in other membranespanning proteins, such as pumps (18), potassium channels
(19, 20), or a distinct class of modified Na channels (2, 21).
The above two-state scheme for Ig.inact (slow) might be
extended by incorporating a third state to account for the
recovery gating current (Ig.recov) that is seen at strongly
hyperpolarized potentials (Fig. 2). Thus, the following variant of Scheme I was tested: R ±5 Il ±5 12. Here I1 and I2
represent inactivated states, and all the resting states are
lumped under R, which is reasonable when transitions among
R states are fast compared with the recovery step (16). We
found that this did indeed provide a good fit to the r-V and
Q-V data for both Ig inact (slow) and Ig.Cov over a wide range
of voltages and without any arbitrary renormalization, even
in view of the fact that the data are pooled from different
axons (smooth lines in Fig. 3 A and Ba-c; see legend for
parameters). Thus, an inactivated squid Na channel seems
able to switch rapidly between just two nonconducting states
before eventually relaxing by means of a single step into other
states from which reactivation may occur.
How might the above scheme be reconciled with general
models of the squid Na channel, like those of Armstrong and
Bezanilla (3) or Armstrong and Gilly (1)? The latter have
inactivated states accessible both directly from the resting
states and via the open configuration. However, at hyperpolarized potentials these models reduce to a special case in
which recovery proceeds only by means of a single, voltagedependent step directly to the resting states, to account for
the observation that recovering channels do not conduct (22).
Thus, our three-state scheme can be equated with certain
parts of those more general schemes, at least under specific
conditions. According to the fit to our data, the charge
transfer in the recovery step is -1 e. This is the same as the
value cited by Armstrong (4) for the corresponding process in
his complete scheme. On the other hand, we find the charge
Proc. Natl. Acad. Sci. USA 87 (1990)
8315
flow between the two inactivated states to be 0.8 e, similar to
the value of Stimers et al. (5) (1 e), but somewhat less than
that given by Armstrong and Gilly (1) (2 e).
In summary, the experiments described here were designed to isolate and provide information about the inactivated states of the Na channel, as a prelude to integrating this
process into a more complete model of the channel. We have
also described a very fast component of gating current that is
revealed under optimized recording conditions. These findings may be important for future structure-function studies of
the Na channel.
We thank the Director and staff of the Station Marine, Roscoff, for
squid; Prof. R. D. Keynes for dissection and electrode construction;
and Prof. B. Neumcke and Dr. C. F. Stevens for helpful suggestions.
S. B. Cross provided technical assistance. This research was supported by the Swiss National Foundation, Grant 3.143-0.85, to
N.G.G.
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691-711.
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6. Keynes, R. D. (1990) Proc. R. Soc. London Ser. B. 240,
425-432.
7. Greeff, N. G., Keynes, R. D. & Van Helden, D. F. (1982)
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(1984) J. Physiol. (London) 352, 653-668.
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185-205.
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