Relaxation Spectra of Potassium Channel Noise from Squid Axon Membranes. (fluctuation phenomena/conductance models/membrane patch/ion permeation).
Proc. Nat. Acad. Sci. USA Vol. 70, No. 3, pp. 876-879, March 1973
Relaxation Spectra of Potassium Channel Noise from Squid Axon Membranes (fluctuation phenomena/conductance models/membrane patch/ion permeation)
HARVEY M. FISHMAN Neurobiology Research Center and Department of Biological Sciences, State University of New York at Albany, Albany, N.Y. 12222
Communicated by Kenneth S. Cole and Terrell L. Hill, January 11, 1973
Power density spectra of electrical fluctuaABSTRACT tions in potential and current (during voltage clamp) in the steady state, measured from electrically isolated patches of squid axon membrane, contain a noise component that is of the form [1 + (f/fc)21-1. For potential and temperature changesf, = (27rTr) -1, where Tn is the HodgkinHuxley relaxation time for the potassium channel. These and other data strongly suggest that this noise is due to the potassium ion passage process in the membrane. Furthermore, by comparison of the values of fc from relaxation spectra of membrane channel noise with those from calculated (Hodgkin-Huxley equations) power spectra, it is possible to relate and compare channel models that previously could only be applied to macroscopic potassium conductance data. An initial result of this comparison suggests that a two-state (open-closed) conductance model, which is based upon a literal interpretation of the Hodgkin-Huxley equations, is not likely to be correct.
paper reports measurements of fluctuations of this type that are associated with potassium channels in the squid axon and presents data suggesting that a two-state conductance model, which is based upon a literal interpretation of the HodgkinHuxley equations, is not likely to be correct. MATERIALS AND METHODS
Data were obtained from 138 giant axons of the squid Loligo pealei, that were received live at Woods Hole, Mass. Fluctuations of membrane potential (noise) were observed by electrically isolating a small patch (10-4 cm2) of the external axon surface with sucrose (4). The inner of a coaxial pair of drawn-glass pipettes (tip diameter, 40-75,um) was placed in contact with the axon and filled with sea water. An electrically floating platinized-platinum wire (25 Mm/diameter) within the length of the inner pipette acted as an ac shunt to the sea water and lowered the equivalent resistance of the pipette (i.e., access resistance to the patch) to less than 30 ko (5). This pipette was mounted in a plexiglass holder filled with sea water in which two electrodes were placed-one for applying current and the other for measuring potential. The outer pipette (tip diameter, 200-300 Mm) was shorter than the inner by 300-400 Mum, and directed the flow of isosmotic sucrose solution (0.8 M) over the ring of axon surrounding the membrane area within the aperture of the inner pipette. The sucrose flow was very slow (one drop every 30 sec) and was swept out of the chamber (6) by flowing sea water, which was directed normal to the long axis of the axon. The solution in the chamber was grounded through a platinized-silver electrode. Axons were internally perfused as described (6). The standard internal perfusate was 0.5 M KF, buffered with 5 mM Tris * HCl to pH 7.4 at 250. The same patch isolation procedure was used for both intact and internally perfused axons. Measurement of the isolation, by application of constantcurrent rectangular pulses to the axon patch through the inner pipette during sucrose flow, gave apparent patch impedances, Zap, (i.e., membrane patch impedance in parallel with the sucrose shunt-path impedance) of 1-6 MU. By raising the current-source level, patch action potentials of 50-80 mV amplitude were recorded between the inner pipette and the chamber ground while the axon was in the flowing sea water and without any electrodes in the axon. These and other tests indicated that the isolation was more than adequate for observing the patch noise without high-level background noise (e.g., thermal noise of access resistances to the patch surfaces). Additional tests showed that the fluctuation wave-
Two general classes of models for conducting channels in squid axon membrane follow from the Hodgkin-Huxley (1) description of the ion current flow. The first of these, the twostate channel conductance, was suggested by them as a possible interpretation of their data. In these models their parameters m, n, and h represent the probability that a channel gate, consisting of subunits, is either in a position that allows ion passage (open configuration) or in a position that completely prevents it (closed configuration). The exponents on each of the parameters are thought to reflect the number of subunits associated with each channel gate. A channel gate is open only if all of its subunits are in the same state. The channel conductance would, therefore, have only two discrete states, depending upon whether the channel were open or closed. An alternative class of models, the multistate channel conductance, results if channel conduction can occur even if the subunits of a gate are not in the same state. This condition allows the channel conductance to have more than two states or, perhaps, a sufficient number to approach a continuum of states. Recently, Hill and Chen (2) and Stevens (3) have independently calculated, from the HodgkinHuxley equations, power spectra for fluctuations in discretestate conductances of the potassium channel that are described by the equation: x
G(f) = Ad Ka[1 + (f/fa)2' and fa
=
[1]
a/2irr5, where the Ka consist of several terms that
are constant for a given a and voltage, Tfl is the
HodgkinHuxley relaxation time for the potassium channel and x is the exponent of the Hodgkin-Huxley n parameter. This 876
Proc. Nat. Acad. Sci. USA 70
(1973)
K+ Channel Noise from Axon Membrane
form was not an artifact of electrodes, isolation process, or instrumentation. These tests, together with the spectral analysis instrumentation, will be described elsewhere. Since membrane potential fluctuations are "filtered" by the membrane impedance, voltage spectra may not reflect the spectra of conductance fluctuations (3). In order to establish that the membrane impedance did not significantly alter the form of the voltage spectra, patches in 20 axons were voltage clamped (7), and power spectra of the current fluctuations were obtained. The voltage clamp system (6) used for these measurements was not optimized for low noise operation. However, the low-frequency power densities of the membrane current fluctuations were an order of magnitude or more greater than the noise-power level of the measurement system. In general, the current spectra appeared to be of the same form as voltage spectra from other axons. In a few axons, voltage and current spectra were obtained from
+
3OmV
1015M
%\
1
----
TWO-STATE MULTI-STATE
*.19.5°
° 12.50 . 4.20
fH
Hz
To
-40
-20
0 V, mV
20
40
60
1W0
10
20
30
T, 8C
(a)
(b)
FIG. 2. Noise-spectrum transition frequency of the potassium channel as a function of potential (a) and temperature (b) at the resting membrane potential. Dashed lines are computed from the Hodgkin-Huxley power spectrum for two-state models [Eq. 1] (2,3). Solid lines are computed from fc = (27T7n)-I by use of the Hodgkin-Huxley values for Trn and a Qjo of 3 (1). In (a), since the shape of the solid and dashed curves do not change with temperature (the fc values only change by a constant scale factor), the curves shown are for 12.5°. The data points at temperatures other than 12.50 have been scaled to this temperature. Data points in (a) are from the same axon, whereas in (b) they are for the same axon as (a) (solid squares) and another axon (open circles).
RESULTS AND DISCUSSION
+
2~~~~~~~~~~~~~~~~~~~~~~~
V/HHz
+W
+
\
10-12
CONTROL
Et4N'
I00
108
the same axon patch and compared. These spectra showed good agreement in the frequency range 1-500 Hz.
.0
3011
877
10210
I0~
f, Hz
FIG. 1. Power density spectra of steady-state membrane
potential fluctuations in an internally perfused squid axon for the indicated applied displacements from the resting membrane potential. Each spectrum is a smooth composite reproduction of four analysis bands (400 points per band). "Control" (solid lines) indicates perfusion with standard perfusate and "Et4N +" (interrupted solid lines) after perfusion with 50 mM Et4N+ added to the standard perfusate. The dashed curves are obtained by subtracting graphically the Et4N + from the control curves, and are of the form [1 + (f/f,)2I -It, where f, is the transition frequency indicated by arrows. The vertical scale for the lowest set of spectra also apply to each of the upper spectra for which the 101 V2/Hz level is indicated. Z.,a = 3.5 MD. T = 7.5°0.
Power density spectra, S(f)= AV2/Af versus f, for bandwidths, Af= 0.125-2.5 Hz, in the frequency range 1-1000 Hz, and patch membrane potential fluctuations, AV, in a squid axon are shown in Fig. 1. Since absolute transpatch potentials were not usually measured, the potentials indicated in both Figs. 1 and 2 represent displacements from the resting membrane potential. These data were obtained from an internally perfused axon, with "control" indicating perfusion with the standard perfusate (control spectra in axons not internally perfused were similar). The magnitude of the power density in each of the spectra are 2-3 orders of magnitude in excess of the thermal level expected from the measurement of Zap and computed from the Nyquist relation (8). A pronounced "hump" is noticeable in each control spectrum. Power spectra with a similar "hump" have been observed (9) at high temperature in nodes of single nerve fibers from frogs. The transition frequency*, fe, at which the extrapolated 1/f2 decline intersects the low frequency limit, clearly changes with potential. The additionof 50mM tetraethylammonium (Et4N+) ion, which blocks potassium channels (10, 11), to the standard perfusate in the same axon eliminated the humps at each potential. In addition, perfusion with low K+ (50 mM) perfusates or 100 mM CsF (12, 13) also removed this portion of the spectrum. The spectra then declined at approximately a 1/f slope, with a magnitude that was still in excess of the thermal level. Noise of the 1/f type has been reported in two axons (14, 15), as well as in the squid axon (4). Furthermore, if the residual 1/f spectrum (after addition of Et4N+) is graphically removed from the control spectra, each spectrum *
Note that in Eq. [11, f. F-' f,, except for x
=
1.
878
Physiology: Fishman
Proc. Nat. Acad. Sci. USA 70 (1973)
has the formt [1 + (f/f,)2] -, which was calculated for channel noise (2, 3). The absence of any effect when tetrodotoxin (1 MAM) (16) was applied externally eliminated the possibility that this noise might be associated with the sodium process. It is also unlikely that the noise is related to active transport, since internal perfusion with KF eliminates pump activity (17, 18). Therefore, I conclude that the observed noise is potassium channel noise. Consequently, the 1/f noise (14, 15, 4) is relegated to some phenomenon associated with potassium current flow, rather than to the potassium channels. With the measurement of potassium channel noise, it is possible to relate and compare channel models that previously could only be applied to macroscopic potassium conductance data. An immediate test of a two-state (Hodgkin-Huxley type) conductance model can be made by comparison of the transition frequencies from noise spectra with those computed from Hodgkin-Huxley power spectra [Eq. 1 ] (2, 3). Fig. 2 shows typical data of spectral transtion frequency as a function of applied potential at a fixed temperature (a) and transition frequency with temperature at the resting potential (b) for the same axon as in (a) and for another axon, in which data were obtained at eight temperatures spanning the range 5-30°. The dashed curves (Fig. 2) in each graph are the transition frequencies obtained from Hodgkin-Huxley power spectra for two-state models. Eventually, as the number of states increases, multi-state models become indistinguishable from continuous-state models. Stevens (3) explicitly considered this caset and calculated power spectra with fe = (2T'rj) -. The solid lines plotted in Fig. 2 correspond to fe for these "continuous" models, with the Hodgkin-Huxley values used forT,, (V) § and a Qjo of 3 assumed (1). Alternatively, there are two ways in which Eq. [1 ] can lead to the solid curves, which are labeled "multi-state," in Fig. 2a. (i) Assume only open or closed channel conductances and let x co . (ii) Keep x constant, but allow the channel conductance to be a linear combination of contributions from different substatesi, i.e., allow multi-state channel conduct In the limit
as
f
-
0
or
c,
G(f)
in
Eq. [1] is indistinguishable
from G'(f) = [1 + (f/f,)J] -. Thus, the only practical way of determining whether the measured power spectra are given by G(f) or G'(f) is to compare the spectral data with these functions at frequencies near fe, where the difference is greatest. It is not clear whether the present spectral data are of sufficient accuracy to allow such a comparison. $ Stevens states that the transition frequency for two-state models isfc = 2(WT-)-1, or four times the value for the continuous state model. However, since the n0,(V) terms in his Eq. 16 influence the shape of the spectrum, the discrete state f, must be evaluated by considering all terms in his Eq. 16. Thus, in general, the factor by which f, differs in the two models will vary with V. This can be seen in Fig. 2a, where the vertical displacement between the two-state (dashed lines) and multi-state (solid lines) model curves, at the same temperature, varies with V. § The values of -r(V) should come from fitting experimental IK (t) data with the same model as used for the noise data test. Since it was not possible to obtain IK (t) data together with noise data from the same axon, the generalized Hodgkin-Huxley values for n(V), for which x = 4, were used to determine T.(V). Nevertheless, changes in Tn(V) for higher or lower powers of n do not change the results significantly. This condition corresponds to the Hill and Chen (2) "conduction by closed channels," which is described in their Appendix III.
tances. From Eq. [1 ] and Fig. 2a, it is apparent that assumption (i) fits the data only for x= 1, and becomes progressively worse for x > 1. However, x = 1 is inconsistent with macroscopic kinetics from voltage clamp data, which require x > 4 in order to obtain sufficient delay in the potassium current (19). Thus, assumption (ii) appears to be the most likely possibility. Consequently, this initial test of a twostate potassium channel model in squid axon membrane suggests that this particular open-closed model (a literal interpretation of the Hodgkin-Huxley equations) is not likely to be correct. However, it is important to note that these results may not exclude some other possible two-state models within the Hodgkin-Huxley framework. Furthermore, spectra used in this paper have been interpreted based on the assumption of Hodgkin-Huxley channel kinetics. Although the Hodgkin-Huxley formulation is the most complete and thoroughly tested description of ion conduction in squid axons, there may be other models based upon alternative explanations of the kinetics that can fit the data presented. Frem an experimental point of view, refinements in the data§ and data analysist will be necessary in order to discriminate between various possible models. The primary significance of these measurements and results is that they establish a sensitive method for experimental tests of models of channel conductance in membranes. I thank Dr. Kenneth S. Cole for encouraging this work and the Marine Biological Laboratory, Woods Hole, Mass. for the use of facilities. This investigation was supported in part by the National Institutes of Health Grants NS09857 and RR07122 and SUNY Research Foundation Awards. 1. Hodgkin, A. L. & Huxley, A. F. (1952) "A quantitative description of membrane current and its application to conduction and excitation in nerve," J. Physwl. 117, 500-544. 2. Hill, T. L. & Chen, Y-D. (1972) "On the theory of ion transport across the nerve membrane. IV. Noise from the openclosed kinetics of K + channels," Biophys. J. 12, 948-959. 3. Stevens, C. F. (1972) "Inferences about membrane properties from electrical noise measurements," Biophys. J. 12, 1028-1047. 4. Fishman, H. M. (1972) "Excess noise from small patches of squid axon membrane," Biophys. Soc. 12, 119 abstr. 5. Fishman, H. M. (1973) "Low impedance capillary-electrode for wideband recording of membrane potential in large axons," IEEE BME, in press. 6. Fishman, H. M. (1970) "Direct and rapid description of the individual ionic currents of squid axon membrane by ramp potential control," Biophys. J. 10, 799-817. 7. Fishman, H. M. (1973) "Patch voltage clamp of excitable cell membranes without internal electrodes," J. Gen. Physiol. Abst. 61, in press. 8. Nyquist, H. (1928) "Thermal agitation of electric charge in conductors," Phys. Rev. 32, 110-113. 9. Siebenga, E. & Verveen, A. A. (1971) "The dependence of the 1/f noise intensity of the node of Ranvier on membrane potential," 1st Eurp. Biophys. Cong. 1st Absdr. 219-223. 10. Tasaki, I. & Hagiwara, S. (1957) "Demonstration of two stable potential states in the squid giant axon under tetraethylammonium chloride," J. Gen. Physiol. 40, 859-885. 11. Armstrong, C. M. & Binstock, L. (1965) "Anomalous rectification in the squid giant axon injected with tetraethylammonium chloride," J. Gen. Physiol. 48, 859-872. 12. Chandler, W. K. & Meves, H. (1965) "Voltage clamp experiments on internally perfused axons," J. Physiol. 180,
788-820.
13. Bezanilla, F. & Armstrong, C. M. (1972) "Negative conductance caused by entry of sodium and cesium ions into the potassium channels of squid axons," J. Gen. Physiol. 60,
.588-608.
Proc. Nat. Acad. Sci. USA 70 (1973) 14. Derksen, H. E. & Verveen, A. A. (1966) "Fluctuations of resting neural membrane potential," Science 151, 13881389. 15. Poussart, D. J-M. (1971) "Membrane current noise in lobster axon under voltage clamp," Biophys. J. 11, 211-234. 16. Moore, J. W. & Narahashi, T. (1967) "Tetrodotoxin's highly selective blockage of an ionic channel," Fed. Proc. 26, 16551663.
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17. Cannessa-Fischer, M., Zambrano, F. & Rojas, E. (1968) "The loss and recovery of the sodium pump in perfused giant axons," J. Gen. Physiol. 51, 162S-171S. 18. Brinley, F. J. & Mullins, L. J. (1967) "Sodium extrusion by internally dialyzed squid axons," J. Gen. Physiol. 50, 23032331. 19. Cole, K. S. & Moore, J. W. (1960) "Potassium ion current in the squid giant axon: dynamic characteristic," Biophys. J. 1, 1-14.
