ABSTRACT
The gastropod mollusc gastropod Strombus luhuanus, prey to some Conus snails,
exhibits a morphologically unique extendable foot utilized for fast escape response. The
pedal ganglion of specimens was identified using in situ stimulation of radiating axon
bundles and observing pedal response. Once the two lobes were removed, neurons were
dissociated using glass teasing needles and studied under whole-cell patch clamp.
Outward potassium currents were observed to have complex activation kinetics and
biphasic inactivation. These kinetics were characterized and used to develop a pre-pulse
protocol for current separation. Two distinct voltage-gated potassium currents were
identified and isolated using this pre-pulse procedure. The fast activating and
inactivating current resembled a classic A-current and could reach peak current within 2
milliseconds after pulse initiation for large depolarizations, and inactivated completely in
about 30 ms. The second component of potassium current resembled a delayed rectifier
and exhibited slow and incomplete inactivation, with peak current occurring within 5 or 6
milliseconds for large depolarizations and partial inactivation over the much longer
period of about 150 milliseconds. The kinetic properties of each individual current were
analyzed and described and a model based on Hodgkin-Huxley was used to compute
conductance time course as a function of voltage.
INTRODUCTION
The development of the voltage-clamp technique (Cole, 1949; Hodgkin, Huxley
and Katz, 1949 and 1952) allowed measurement and description of the various currents
due to voltage-gated ion channels in a neuronal membrane. Studies of the properties of
excitable membranes have led to the identification of many ion channels controlled by
several mechanisms, but voltage-gated sodium and potassium channels form the
backbone of excitation and action-potential propagation (Hodgkin and Huxley, 1952)
Many different current types arise from these various channels within the
membranes of neurons, some sharing similar enough characteristics to be classified into
subgroups. "Transient inward" currents are those usually involved in the rising phase of
an action potential, and are carried predominantly by sodium ions. "Delayed rectifier
has been used to describe the repolarizing potassium currents involved in the falling
phase of the action potential. Another porassium current type, deemed "A-current" by its
original describers (Conner and Stevens, 1971a-c), plays a unique role that may not be
directly involved in the falling phase of the action potential. A-type currents have the
general form of an outward potassium current that activates at quite negative voltages and
inactivates rapidly and completely, also at fairly negative voltages.
The physiological significance of this category of current is not entirely agreed
upon within the literature-perhaps mostly due to the large number of transient outward
currents that have been given its title or the current lack of an identified molecular
subtype. However there is general consensus that A-currents allow stimulus-intensity
encoding through frequency modulation (Hille, 1992). Membranes lacking such currents
generally respond to a steady stimulus with high, constant frequency of firing or a single
spike followed by constant hyperpolarization. With A-current channels, membranes can
respond to stimuli of varying intensity and encode this information in a graded frequency
response.
More current types than those described here exist (Lancaster and Pennefather,
1986), and many studies have sought to describe the physiological purposes of each.
After Conner and Stevens work, a paper by Stephen Smith (1978) showed the role of A¬
current in the bursting nature of neurons in Tritonia diomedia.
The currents in neurons of the gastropod mollusc Strombus luhuanus have not
been previously described, and unique and rapid escape response displayed by this snail
formed the basis for the present work. Strombus uses a large muscular foot to jump away
from possible danger, a very unusual and fast behaviour, atypical of slow-moving
gastropods. Most organsisms, such as the squid, (a cephalopod mollusc), make use of
high conduction speed to initiate and coordinate fast escape responses, and the ion
channels underlying activity in the relevant neurons appear to have fast kinetics (Gilly et
al., 1997). The present description of the potassium currents within neurons from the
Strombus pedal ganglion leads to the identification of two current types. One is a delayed
rectifier with slow inactivation, the other an A-type current with fast and complete
inactivation qualities.
METHODS
Preparation
Strombus snails were obtained from American Samoa and maintained in
oxygenated tanks at room temperature (about 24 °C). Dissection was carried out under
light microscope using magnifications from 6x to 50x. The ganglia of the Strombus
encircle the esophagus and were located with incisions near the base of the eye stalks.
The twisted nature of the snail makes direct identification of the pedal ganglion difficult,
however it is distinguishable by having only two fused lobes and a large number of
nerves radiating into the foot musculature. The other ganglion complex has two primary
lobes, each with a smaller auxiliary lobe attached. Functional identification of the pedal
ganglion was accomplished during each dissection using direct stimulus of the radiating
motor nerves and observation of subsequent contractions of the foot.
Once removed, the pedal ganglion from each organism was placed in LIS-based
medium that had been osmotically balanced to seawater and mixed with antibiotics,
(Gilly et al., 1990)
Dissociation
Dissected ganglia were treated for 45 minutes in filtered seawater containing 7 mg
of bacterial protease type XIV per mL, and desheathed using sharp forceps and a razor-
blade knife. Under 50x magnification round neurons were distinguishable in desheathed
areas, and were subsequently teased onto glass cover slips coated with Con A, following
procedures previously described (Gilly et al. 1990). The teasing procedure used glass
micro-pipettes made from type 7052 glass. After dissociation, the cover slips with cells
were left undisturbed for 45 minutes or longer without motion to allow the neurons to
adhere. Cells were then incubated overnight at 12 °C to allow recovery, (most neurons
appear swollen immediately after dissociation.) The bathing medium was replaced every
other day as the cell stock was used, and most cells would not produce reliable seals after
one week post-dissection.
Patch-Clamp
Whole-cell, voltage clamp recordings were carried out at 20 °C as described in
detail elsewhere (Gilly and Brismar, 1989). The largest cells were selected for recording.
as they often expressed more sodium current and were consequently the putative motor
neurons. The internal solution (electrode) contained 20 KCl, 305 K-glutamate, 50 KF,
180 glycine, 115 sucrose, 1 EFTA, I EDTA, 10 lysine, 10 Hepes, with a pH of 7.8. The
external (bathing) solution contained 470 tetra-methyl ammonium (TMA), 10 KCl, 10
Cachz, 20 MgCl, 20 MgSO4, 10 Hepes, also with a pH of 7.8.
RESULTS
General observations
Preliminary experiments were carried out to examine the potassium currents in
the isolated neurons of the Strombus pedal ganglion. A series of voltage steps from the
holding potential of-80 mV (Fig. 1.) showed currents with little or no inactivation at
small depolarizations, complicated activation kinetics at intermediate depolarizations
(e.g. late peaks, arrows in Fig. 1), and fast inactivation at large depolarizations. These
current characteristics were found in a sample of three cells, and suggest the presence of
multiple current types.
A set of long pulses revealed biphasic inactivation kinetics (Fig. 2), further
suggesting the possibility of two or more current types. The inactivating currents were
plotted on a semi-logarithmic scale to better highlight the slow and fast exponential
decays. Fig. 3 depicts such a plot for a step from the holding potential of-80 mV to +20
mV. The main plot shows the two components and a fit to the slow component of
inactivation; the inset outlines the residual fast component.
Current separation
The relative time scales of the fast and slow inactivating components (henceforth
referred to as Igand Iks) allowed the possibility that a pre-pulse protocol might serve two
separate the two current types by selectively inactivating Ig without affecting Ig, to an
appreciable extent. A series of twin pulses were run with different recovery intervals
anat several voltages to test this possibility, and to describe recovery from inactivation for
Ifast.
Fig. 4A through C depict the current measurements for a series of twin-pulse
experiments in which all interval durations were varied identically at each of three
recovery voltages (see pulse pattern in Fig 4D). These data describe the time course of
recovery from inactivation and its voltage dependence, showing total inactivation in some
of the traces. Examination of the dependence of total inactivation revealed that pulses to
-25 mV were sufficient to totally inactivate Igg (data not shown).
The information outlined above was used to construct a pre-pulse procedure that
would selectively remove the fast inactivating current before test pulses. This technique
yielded current traces like those shown in Fig. 5, which depicts the currents from two
stimulation regimes, one with a pre pulse to-25 mV and one without. Test pulses with a
pre pulse contain only Igs, allowing Igrto be isolated by subtracting these traces t from
their respective non-pre-pulse counterparts (which contain both currents). Igris thus pre-
pulse sensitive and Ig, is pre-pulse resistant. The technique was applied to a series of
such traces at varying stimulus amplitudes to yield the individual currents plotted in Fig.
6. Fig. 7 shows current-voltage plots for these currents.
Conversion to conductance and correction for series resistance
To complete Hodgkin-Huxley-like characterization of the two currents displayed
in Fig. 6 these traces must be converted into units of conductance (siemens) and
normalized by the size of the cell. Furthermore, the sensitivity of the fitting procedure
necessitates compensation any significant residual series resistance of the electrode tip.
Series resistance was calculated from the capacitance transients of a-10 mV step
made with fast (electrode) capacitance balanced, slow-capacitance compensation turned
off, and series resistance compensation set to the same level used to record currents. A
sample pulse is shown in Fig. 8. The exponential decay is fit, giving a time constant
equal to Rsenes times the total membrane capacitance of the cell. Cell capacitance is
calculated from the time-integral of the transient current, and the time constant (tap) is
divided by this number to give the estimate of Rses. The membrane capacitance is also
used to approximate the surface area of the cell, under the assumption that the membrane
capacitance per area is near 1 uF per cm (Hille 1992). Values of these parameters for
each of the three cells studies are listed in Table 1
The combination of these parameters shown in Eq. 1 yields the conductance per
square centimeter of the cell, including compensation for series resistance:
8 1 Pns Rne
where A is the surface area of the cell. The Variing term in this equation refers to the
driving force, which is equal to the command voltage minus the reversal potential, which
was estimated using tail current readings (data not shown). Eq. 1 was applied to each of
the traces for lgand Iks. While this equation gives more accurate traces than
compensation accomplished through offsetting the membrane command voltage by Ipeak
Rseres for each step, the fraction within the denominator tends to amplify noise for small
currents and small driving voltages. Therefore the traces from stimuli that elicited no
discernable increases in conductance were removed from the each series. The
calculations were also made without series resistance compensation to assess its
significance. As shown in Fig. 9, for large depolarizations there is a significant offset due
to series resistance. Fig. 10 shows the final, compensated conductance traces as
calculated for both Igr and Iks.
Characterization of Ixt
The procedure used for estimating the various parameters utilizes two
simultaneous approaches to the same values. First, approximations of the values are
made by fitting single exponentials to specific regions of curves for large depolarizations,
(to be explained in more detail later). These values are then used as the initial guesses for
parameterized functions that are then fit iteratively using a computer program
(NEURON, developed by Michael Hines and John W. Moore at the Department of
Neurobiology, Duke University). Because the empirical approximations are only
reasonably valid for large depolarizations, they are only used as initial guesses to fit the
largest command step, after which the fit values for the previous step are used as guesses
for the next smaller step. The equation used for fitting the conductance traces is a
variation on the equations used in Hodgkin and Huxley's original 1952 paper, the
primary difference being that the potassium model has an inactivating particle similar to
sodium channels. The equations for the Igemodel are thus:
gy -nhg,
(2)
n-n.-(n.-n)exp(-1/.),
(3)
h-h.-(h.-ho)exp(-1/7,),
(4)
where
1o 9. 19.
ho
G,+B.
and
r. 9. 18.
(6)
8. 19.
The traces in Fig. 1OB show near complete inactivation for all pulse amplitudes, thus he
can be neglected. Furthermore, pulses from holding potentials more negative than -80
mV (data not shown) did not produce an appreciable decrease in peak current amplitude
for large depolarizations, indicating that ho is at a steady level, and can be assumed to
equal 1. The gxV curve for Ig(Fig. 11) shows no conductance at the holding potential,
so no equals 0. These simplifications lead the following relation when Eq.'s (3) and (4)
are substituted back into the equation for fast conductance (gr, Eq. (2):
8y - 8 y 1- exp(-1/1,) exp(1/1.)
(7)
where
(8)
8y -8n
This equation was used in the computational fitting of the conductance curves.
and the parameters g'kt tn, and ti were approximated and used for the initial guess; N
was determined to be 11, the lowest number for which the lag in the activation kinetics
was fit to a reasonable level (by eye only). The large value for N is necessitated by the
long lag after stimulus initiation before the beginning of the rising activation phase. As
all known voltage-gated potassium channels are probably tetramers, the Hodgkin-Huxley
model begins to show its weaknesses here. However, as it is applied in this paper, it
serves to dissect and characterize many parameters of a given current type, making it an
excellent tool for fingerprinting and comparing different currents, regardless of the
underlying structural accuracy of the model.
g'ky and t, were estimated by fitting the top third of the activation curve (to peak)
with a single exponential of the form:
KO +Klexp(-K2*1)
(9)
KO was used as the estimate for g'gyand 1/K2 was used to approximate ty. The same
exponential was used to fit the inactivation phase of the conductance curve, using 1/K2 to
estimate ti. Once initial guesses were made, each subsequent step used the previous
steps fit values for its guesses, and the final set of curves thus fit are depicted in Fig. 12.
The values for the parameters and the calculated rate constants are listed in Table 2.
Because the gkV curve (Fig. 11) indicates that the saturation point was never reached, an
arbitrary adjustment of 20% was added to the highest conductance to approximate gre,
(a conservative approximation that will have to stand until future experiments can assess
its validity). As would be expected by the complete lack of inactivation recovery in Fig.
4C, ap is 0 for all pulses analyzed.
Characterization of Iks
The model for Ig, currents is similar to Igg however it varies slightly in applicable
assumptions. The most important of these pertains to ha. For Ig, it was assumed that
inactivation was complete for all command voltages studied, yet this assumption is not
necessarily correct for Iks. The long pulses depicted in Fig. 2 show incomplete
inactivation for large depolarizations, a fact that not only invalidates the total inactivation
assumption, but creates other complications as well. It is possible that Ig, is comprised of
two currents, one that inactivates slowly and one that does not inactivate at all. Even
assuming that it is only one current type, the long pulses in Fig. 2 are taken from a
different cell than the properly isolated currents in Fig. 10, and it may be that incomplete
inactivation is not a constant characteristic in all the cells studied. While every cell
studied displayed the complicated activation and inactivation kinetics identifying two
current types, the specific questions raised here require further research to be
appropriately addressed.
In light of these confounding factors, a study and analysis of the inactivation
characteristics of Ig, will be reserved until such a time that proper experiments have been
completed. However, the activation parameters did not show a high degree of sensitivity
to the assumptions necessitated by insufficient inactivation data. Fig. 13 shows curves
for three large depolarizations, fit by the following equation:
(10)
8k - 8'k 1-exp(-1/1.)I.-(h. -D)exp(1/1,)
where
(11)
8'k.- 8.7
The curves calculated assuming total inactivation (ha equals 0), and those
calculated assuming approximately two-thirds inactivation (an approximation obtained
from KO/(KO +Kl) of an exponential fit of the inactivating current, Eq. (9)), are
superimposed over the original traces. The fit (in terms of mean-squared-error) is slightly
better for the total-inactivation assumption than for partial, but this difference is minimal
and barely discernable by eye. The difference between these curves is outlined in Table
3, in which the values for t, are shown to vary significantly between the two assumptions.
This sensitivity increases with smaller pulses to the point that a variation of twenty
percent in estimates of ha can cause an order of magnitude difference in ty. In contrast,
the variation of the activation parameters (g'k and t,) is minimal. This insensitivity
allowed analysis of the activation kinetics of Ik, for comparison with those of Igr The
difficulty in approximating a changing ho necessitated the use the full-inactivation
assumption (ha equals 0).
The same procedure described for Igrwas used to fit and calculate the parameters
for Ix, the one difference being the use of Eq.'s (10) and (11) in place of (7) and (8). The
results of these calculations are summarized in Table 4. (For completeness, the table
includes values for the inactivation kinetics as calculated under the assumption of full-
inactivation.)
DISCUSSION
The grV curves (Fig. 11) for the two currents characterized in this study are
consistent with two distinct potassium channel types; they display different steepness as
depolarization levels increase. This voltage-dependence provides a means for
information integration, one of many that these two currents provide. Any relative
variation in a parameter between Igrand Igs, with respect to voltage or time, is a possible
mechanism for information integration.
The relation between the t,'s shown in Fig. 14B outlines the possible mechanism
by which the A-type Igcurrent can modulate frequency response for graded stimuli. The
time constant of activation for Igris much faster than that for Ig, at negative voltages, and
recovery from inactivation is also dependent on negative voltages (Fig. 15). It is likely
that the level of Iginactivation plays a major role in establishing the threshold stimulus
required to create an action potential. Activation of Igrduring an action potential would
lead to rapid and probably incomplete inactivation, and a string of rapidly occurring
action potentials would thus produce a progressive increase in excitability as larger
portions of A-current were inactivated.
This mechanism is just one example of the sort of information processing
available to a neuron that possesses multiple current types, and it is the generally
accepted means by which A-current modulates frequency output to graded stimuli
intensity. Useful speculation towards the physiological purposes of the many other
variations is premature for a paper of this scope and the current level of research.
The rate constants for the two currents are plotted in Fig. 16. Both currents show
little rise in ß at the most negative voltages studied, which in the case of the Igg is result
of the 11" order activating term required in fitting its conductance curves. Whether this
is artifact or truth will require further study (similarly for the relatively constant value of
no).
Future studies will include complete characterization of the steady-state
inactivation kinetics for Igs, as well more description of the other parameters for relevant
voltage ranges outside those studied thus far. With sufficient data, it should be possible
to fit continuous functions the graphs of the rate constants, which can then be used to
calculate and predict action potentials across the membrane. These topics all serve as
avenues for further study in the description of the Strombus pedal-ganglion currents.
ACKNOWLEDGEMENTS
Matt Brock, for his technical and academic advice and endless patience for inexperienced
inquiry.
Joseph Schultz for his constant suggestions—often solving problems before they occur
and answering questions before they are asked.
Professor Stuart H. Thompson for his many insights and conversations on all subjects of
neurobiology.
And a special thanks to Professor William F. Gilly, for all of his support and late hours of
help and encouragement. His high standards are often a cloaked blessing, but a
blessing nonetheless.
References
Cole, K. S. (1949). Dynamic electrical characteristics of the squid axon membrane.
Arch. Sci. Physiol. 3, 253-258.
Connor, J. A. and C. F. Stevens (1971a). Inward and delayed outward membrane
currents in isolated neural somata under voltage clamp. J. Physiol. 213, 1-19.
Connor, J. A. and C. F. Stevens (1971b). Voltage clamp studies of a transient outward
current in gastropod neural somata. J. Physiol. 213, 21-30.
Connor, J. A. and C. F. Stevens (1971c). Prediction of repetitive firing behaviour from
voltage clamp data on an isolated neurone soma.. J. Physiol. 213, 31-53.
Gilly, W. F. and T. Brismar (1989). Properties of appropriately and inappropriately
expressed sodium channels in squid giant axon and its somata. J. Neurosci. 4.
1362-74.
Gilly, W. F., M. T. Lucero, and F. T. Horrigan (1990). Control of the spatial distribution
of sodium channels in giant fiber lobe neurons of the squid. Neuron. 5, 663-674.
Gilly, W. F., R. Gillette, and M. McFarlane (1997). Fast and slow activation kinetics of
voltage-gated sodium channels in molluscan neurons. J. Neurophysiol. 77(5).
2373-84.
Hille, B. (1992). Ionic Channels of Excitable Membranes, 2"“ Edition. Sinauer
Associates, Inc.. Sunderland, Mass.
Hodgkin, A. L. and A. F. Huxley (1952). A quantitative description of membrane
current and its application to conduction and excitation in nerve. J. Physiol. 117
500-544.
Hodgkin, A. L., A. F. Huxley and B. Katz (1949). lonic currents underlying activity in
the giant axon of the squid. Arch. Sci. Physiol. 3, 129-150.
Hodgkin, A. L., A. F. Huxley and B. Katz (1952). Measurements of current-voltage
relations in the membrane of the giant axon of Loligo. J. Physiol. (Lond.). 116,
424-448
Lancaster, B. and P. Pennefather (1986). Potassium current evoked by brief
depolarizations in bull-frog sympathetic ganglion cells. J. Physiol. 387, 519-548.
Smith, S. J. (1978). The mechanism of bursting pacemaker activity in neurons of the
mollusk Tritonia diomedia. Ph.D. Thesis, University of Washington.
Table 1: Values calculated using the technique outlined in the text and shown in Fig. 8.
These values were used in conversion from current to conductance per area.
Cmenbrane (pE)
Reris (M9.
Cell Teg
Cell surface area (emt
48.176
1.307705
4.8179E-5
49.55
0.585267
4.955 E-5
23
25.189
0.913097
2.5189 E-5
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Table 3: Values comparing the sensitivity of various parameters to the full- and
partial-inactivation assumptions explored in analysis of Ilow.
VCommand
gk. (mSem)
In (msec)
1h (msec)
(mV)
Full
Partia
Full
Partial Full Partial
60
1.8582 1.9327
1.2852 1.3214 0
0.3
1.8167 1.9058
1.5323 1.5796
0.3
40
1.7133 1,8081 1,8212 1.8779 0 0.3
800
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Figure Legends
Fig. 1: Current traces showing the complicated activation and inactivation kinetics
described within the text. Notice the delayed peaks at intermediate voltages.
Fig. 2: 250 ms pulses from the holding potential of-80 mV to +20 mV in 10 mV
increments. These traces show biphasic inactivation.
Fig. 3:
Semi-logarithmic plot of the biphasic inactivating current from a 250 ms pulse
from-80 mV to +20 mV. The smooth line is a fit for the slow-phase
exponential, and the inset depicts the residual fast-inactivating current.
Fig. 4:
Twin-pulse traces displaying the voltage and temporal dependencies of recovery
from inactivation.
Fig. 5: Example current separation using trace-subtraction. The top trace is the current
measured from a step from the holding potential of-80 mV to +60 mV. The
middle trace is the same test pulse with a pre pulse of 55 mV.
Traces showing the currents measured from a sequence of pulses with no pre
Fig. 6:
pulse (A); with a 55 mV pre pulse (to-25 mV command voltage)(B); and the
isolated fast-inactivating current (C), calculated using trace subtraction.
Fig. 7: IV curves for the currents shown in Fig. 6.
Fig. 8: This figure depicts the initial capacitance transient measured for a-10 mV step.
Fig. 9: Two sets of conductance-per-area curves, calculated from the same current
measurements of Ik, using Eq. (1), the solid line included the Rseries term, the
dotted line did not. This shows the significance of the series resistance.
Fig. 10: Calculated conductance curves for Ik. (A) and IkT(B).
Fig. 11: Relative grV curves for Iks and Igg each scaled independently.
Fig. 12: Changes in conductance for Igrin response to various depolarizations (command
voltages are listed by each trace). The smooth curves were calculated from fits
using Eq. (7), with the resulting parameters described in Table 2.
Fig. 13: Traces showing an enlarged fitting of the conductance changes of Ik, in
response to three different depolarizations. The smooth curves represent the fits
calculated using the assumption of total and partial inactivation, and show the
accuracy with which the fit is achieved regardless of the assumption used, as
well as the insensitivity of the activation phase to the assumption choice.
Fig. 14: Graphs displaying the voltage dependence of na (A) and z, (B).
Fig. 15: Semi-logarithmic plot of relative recovery from inactivation. See Fig. 4D for
the stimulus pattern.
Fig. 16: Plots of the various rate constants for Ik, and Iyg taken from Tables 2 and 4.
(inactivation parameters for Ig, are omitted for reasons outlined in the text.)
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