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Biophysical Journal
Volume 109
October 2015
1312–1316
BJ Classics The Cole-Moore Effect: Still Unexplained? Toshinori Hoshi1,* and Clay M. Armstrong1,* 1
Department of Physiology, University of Pennsylvania, Philadelphia, Pennsylvania
ABSTRACT In the first issue, on the first page of the Biophysical Journal in 1960, Cole and Moore provided the first confirmation of the Hodgkin and Huxley formulation of the sodium and potassium conductances that underlie the action potential. In addition, working with the squid giant axon, Cole and Moore noted that strong hyperpolarization preceding a depolarizing voltageclamp pulse delayed the rise of the potassium conductance: once started, the time course of the rise was always the same but after significant hyperpolarization there was a long lag before the rise began. This phenomenon has come to be known as the Cole-Moore effect. Their article examines and disproves the hypothesis that the lag reflects the time required to refill the membrane with potassium ions after the ions are swept out of the membrane into the axoplasm by hyperpolarization. The work by Cole and Moore indirectly supports the idea of a membrane channel for potassium conductance. However, the mechanism of the Cole-Moore effect remains a mystery even now, buried in the structure of the potassium channel, which was completely unknown at the time.
The story of the Cole and Moore article published in 1960 (1) must begin eight years earlier with the publication of the Hodgkin and Huxley articles (2-6). These articles astounded the physiological world with their explanation of the nerve impulse, solving a mystery standing since the time of Galvani. The work of Hodgkin and Huxley followed much thought about the nerve impulse by, for example, Helmholtz (7) and Bernstein (8). The rediscovery of the squid giant axon by J. Z. Young (9) provided the experimental preparation necessary for elucidating its mechanism. The giant axon is big enough to insert electrodes inside, and was used by Curtis and Cole (10) to demonstrate an impedance change during the action potential, a great step forward. A further technical improvement was the space clamp (11). A wire was inserted into the axon to short out the longitudinal resistance and to functionally transform an axon segment into, electrically, a single manageable patch of membrane. Finally, the voltage clamp was developed by Marmont, using then recently elucidated feedback techniques to stably clamp membrane voltage (Vm) at a desired value. Hodgkin and Huxley used these techniques with an improved electronic circuitry and much insight and brilliance to solve the electrical and electrochemical basis of the action potential, and to show their model could simulate a propagated action potential (2). Retrospectively, Hodgkin and Huxley were very early pioneers of systems biology, and, importantly, the Biophysical Journal article by K. S. (Kacy) Cole and John Moore represented the first independent experimental confirmation of the HodgkinHuxley formulation.
Submitted June 9, 2015, and accepted for publication July 13, 2015. *Correspondence: [email protected] or [email protected]
The Hodgkin-Huxley formulation (2) invoked an increase in Naþ conductance of the axon membrane (GNa, roughly, Naþ permeability) to generate the upstroke of the action potential, and, the subject of this article, an increase of GK (Kþ permeability) to return Vm rapidly to the resting potential. (Note that in the Hodgkin-Huxley formulation, gNa and gK represent whole-axon Naþ and Kþ conductances; more recently, GNa and GK are used to signify macroscopic whole-cell/axon conductances and gNa and gK are used for single-channel conductances.) These ion conductances were detailed in a quantitative model that described their time course and magnitude after a change of Vm. The physical basis of GK was unknown at the time. Carrier molecules confined to the membrane seemed the most probable means for transporting Kþ ions across the membrane’s hydrophobic barrier. A carrier, rather than a pore, seemed best able to explain the selectivity for Kþ versus Naþ. Each of the many (hypothetical) Kþ carriers could be either resting or activated, as determined by the position of four identical, independent, and indistinguishable charged control particles, whose position in the membrane was determined by Vm. Because of the hydrophobic nature of the membrane, the charged control particles were always at the membrane edges except in brief instances of transmembrane transit. As an arbitrary choice, suppose that the particles are positive, attracted to the intracellular edge of the membrane at rest (~–60 mV) and driven progressively more strongly to the extracellular edge by a positive change of Vm (depolarization). This scheme was presented conveniently by FitzHugh (12) and later modified by Armstrong (13) as a five-state kinetic diagram: 4a
3a
2a
a
b
2b
3b
4b
N0 # N1 # N2 # N3 # N4 :
Editor: Brian Salzberg. Ó 2015 by the Biophysical Society 0006-3495/15/10/1312/5
http://dx.doi.org/10.1016/j.bpj.2015.07.052
The Cole-Moore Effect
Vm
where n represents the probability that any given control particle is at the extracellular edge. This kinetic behavior was incorporated into a comprehensive quantitative model of the action potential (2), of which the n4 model describing GK magnitude and kinetics as a function of Vm and time, was a critical component. In their quantitative article, Hodgkin and Huxley questioned the usefulness of empirical equations fitting an unknown physical problem. Clearly, however, the Hodgkin-Huxley model has stood the test of time very well, in part because it was not simply mathematical, but offered excellent mechanistic and electrical insights that have been improved but not overturned as a result of new information. The five-state n4 model of Hodgkin and Huxley seemed to presage the discovery made ~40 years later that Kþ channels are composed of four, often identical, subunits. However, Hodgkin and Huxley candidly noted that although an n6 formulation gave a better fit to the sigmoidal kinetics after a depolarization, it was not worth the trouble (on a handcranked calculator). After this 1952 revelation (2), many other groups investigated the kinetics of GNa and GK for a better understanding
of the physical mechanisms. Cole and Moore in this article (1) considered the idea that the rise and fall of potassium current (IK) was simply the result of electrodiffusion within the squid axon membrane and that no carrier or pore was involved in its generation. In the normal state for squid axons, extracellular Kþ concentration is 10 mM and intracellular Kþ concentration is ~550 mM. In the electrodiffusion model, the negative internal voltage at resting potential largely empties the membrane of Kþ, which is pulled out of the membrane into the axoplasm by the negative voltage. It is only partially replaced from the extracellular solution where the Kþ concentration is low. This provides, at most, a 1:55 conductance ratio for inward versus outward current (which is too low). When the membrane voltage is made less negative or even positive, Kþ enters the membrane from the axoplasm and electrodiffuses: it moves as dictated by the electric field and the concentration gradient at any point within the membrane. When the leading edge of the electrodiffusion wave reaches the outer surface after a distinct lag, IK is seen to rise, and increases until the Kþ concentration in the membrane reaches a steady state. Consistent with this general idea, the authors found that extreme hyperpolarization applied before a depolarizing pulse distinctly increases the lag in current development; i.e., in their theory, very negative voltage inside sweeps Kþ out of the membrane into the axoplasm. Hyperpolarization thus, in theory, increases the lag and enhances the sigmoidal characteristic of IK development on depolarization, because the Kþ-depleted membrane must be refilled as Kþ diffuses across. The experimentally observed increase in the lag as IK develops in a test pulse after strong hyperpolarization is called the Cole-Moore effect. The five-state n4 model of Hodgkin and Huxley provides an explanation of the lag in IK development that is quite different from the electrodiffusion hypothesis. A hyperpolarizing prepulse increases the lag predicted by the n4 model only when Vm before the test depolarization is not
–
Probability
In this diagram, N0, N1, N2, N3, and N4 represent those states with 0, 1, 2, 3, and 4 of the control particles of a given carrier at the membrane’s extracellular edge (activated position). The rate constant a is voltage-dependent and governs the movement of a control particle from inner to outer edge. The value b, also voltage-dependent, governs movement in the reverse direction. Because the control particles are identical and independent, the coefficients for a are 4, 3, 2, and 1, corresponding to the number of the control particles available to make the outward transition. The coefficients for b are the same, in reverse. A carrier is fully at rest in state N0 with no control particle at the extracellular edge. It is active only in state N4* (as indicated by the asterisk), with all four control particles at the extracellular edge. In normal behavior, most of the control particles are in state N0 at Vm ¼ –60 mV. After a depolarization, GK increases with a sigmoid time course after a distinct delay as the four control particles pertaining to a carrier, move, one by one, from the intracellular to the extracellular edge of the membrane. When Vm is returned to rest, only a single transition, from N4* to N3, is required to deactivate the carrier, and this occurs exponentially (no delay) with time constant ~1/4b. (In theory, the five-state diagram contains four exponential components, but at the voltages where b >> a, the dominant component has a time constant of 1/4b.) Turning on, it is sigmoidal; turning off, it is a simple exponential, as observed experimentally. Because the four control particles are identical and independent, the probability P that the carrier is in state N4* with all of its four control particles at the extracellular edge is P N4 ¼ n4 ;
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n n4 n6 n25
n4
n
25
n
FIGURE 1 Predictions of n, n4, n6, and n25 models. The probability of full activation is shown as a function of time. In each model, the carrier was assumed to be fully at rest before the depolarization onset. The near horizontal segments immediately after depolarization represent the lag, which is absent in the n model and longest in the n25 model. To see this figure in color, go online. Biophysical Journal 109(7) 1312–1316
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sufficiently negative to put essentially all of the control particles into state N0. Experimentally, however, Cole and Moore found that a good fit for IK after strong hyperpolarization required n25, not n4; that is, in Hodgkin and Huxley terms, there would have to be 25 particles controlling each Kþ-conducting unit. A modern day interpretation could be that the Kþ-conducting unit, whatever its nature, contains 25 identical and independent subunits. This is certainly less attractive than the four subunits implied by the Hodgkin-Huxley n4 model, perhaps enhancing the appeal of the electrodiffusion idea. The abstract of the article by Cole and Moore seems to suggest that electrodiffusion is operative, with mobility of Kþ in the membrane ~105 times lower than that in aqueous solution. The final two paragraphs of the text, however, point out that an electrodiffusion model cannot explain the negative resistance seen with isotonic Kþ on both sides of the membrane; i.e., experimentally, at negative Vm in the steady-state, IK is near zero even in the presence of high external Kþ, contrary to the predictions of electrodiffusion. It seems that the two authors of the article may have been of two minds on this question! Faced with this problem, the authors (one or both) then cite an idea of Mullins: a pore across the membrane that is deformed and conducts less well at negative voltage (14). The electrodiffusion model nonetheless died slowly, and was still invoked some years later in the 1960s (15). Then, if not electrodiffusion, what underlies GK? The idea of a pore seems very obvious now, but it was not favored initially because of then-perceived difficulties imagining ion selectivity. There was, however, early evidence for a pore—the ‘‘long pore effect’’ noted by Hodgkin and Keynes in 1955 (16). Mullins (14) in 1959 also wrote a stimulating article on the possibility of pores, and discussed, with great foresight, an idea to explain ion selectivity—that the pore must provide a close fit to the selected ion. Blockage of IK by intracellular TEAþ (tetraethylammonium) or derivatives reported in 1965 and 1971 strongly supported the idea of a Kþ pore (17,18). TEAþ, about the size of a Kþ ion with one hydration shell, enters a Kþ channel through an intracellular ion-conduction gate only when this gate is open. After entering, a TEAþ molecule is blocked about halfway through the membrane by a narrowing, i.e., the channel’s selectivity filter. A Kþ ion can pass through the selectivity filter by shedding its hydration shell, an impossibility for the covalently linked ethyl arms of TEAþ. Further confirmation of the pore hypothesis came in several ways. First, a calculation in 1969 (19) of the theoretical conductance of a pore (high conductance) versus a carrier (low conductance) was followed a few years later in the 1970s by single-molecule biophysics measurements of unitary current events, which were consistent with a pore but not a carrier (20,21). Then genes for voltage-gated Naþ and Kþ channels (22-24) were sequenced in the 1980s, and their pore regions were identified. Finally, the crystallographic atomic structures of Kþ channels starting at the end Biophysical Journal 109(7) 1312–1316
Hoshi and Armstrong
of the 20th century removed any possibility of doubt: Kþ ions move through a pore (25-27). Under space- and voltage-clamped conditions sufficient to ensure rapid changes in Vm, currents through most voltage-gated Kþ channels, including Drosophila Shaker and human KV1-type channels activate in a sigmoidal manner with some variable delay, typically a millisecond or less at room temperature (voltage-clamp conditions resulting in poor time resolution can significantly lengthen the apparent delay in current activation). The delay or lag is more noticeable when the currents are elicited by small depolarization from a very negative holding Vm. Experimentally, the sigmoidal characteristic can be quantified using the concept of sigmoidicity, which is the amount of delay relative to the overall activation kinetics such that the results obtained at different voltages and those from different channels are more readily compared (28). Conceptually, the sigmoidal activation characteristic is readily explained by the kinetic reasoning that channels traverse multiple closed states before reaching the (first) conducting state. When the holding Vm is very negative, the channels are pulled to the fully closed or most closed state (e.g., N0 in the earlier state diagram) and the channels must pass through additional closed states to open, thus creating a greater lag in activation. If hyperpolarization is strong enough, typically –90 to –100 mV, to force all channels into N0, greater hyperpolarization does not produce a greater lag (28). Once the initial lag is over, the IK kinetics are relatively similar such that the currents during test pulses after prepulses of different size can be easily superimposed by shifting the IK traces along the time axis (29,30) (see Fig. 1). A successful description of the activation delay in heterologously expressed voltage-gated Kþ channels was one of the important evaluation criteria in developing more recent models of Kþ channel gating, based on Drosophila Shaker Kþ channels, incorporating the knowledge that four identical subunits, each of which shows multiple conformational changes, can form a functional voltage-gated Kþ channel (29,30). As expected, the greater the number of closed states that channels must traverse, the greater the lag one observes. Additionally, the transition rate constants among the closed states contribute to the sigmoidicity of activation. The greatest degree of sigmoidicity is observed when the identical and independent assumption is relaxed and the opening rate constants are all made equal (compare to Fig. 1) (28). With the availability of crystallographic atomic structures of voltage-gated Kþ channels (27), structural connotations can be now assigned to various models of Kþ channel gating (29,30) including the original Hodgkin-Huxley model. For example, each Kþ channel subunit typically contains multiple voltage-sensing positively charged residues in the transmembrane S4 segments, which are referred to as R1 (arginine), R2, R3, R4, and K5 (lysine) starting numeration
The Cole-Moore Effect
from the extracellular side of the membrane (31,32). Details of S4 motion through the membrane on changes in Vm remain to be worked out because atomic structures of the closed states of voltage-gated Kþ channels have not been experimentally determined. However, based on the crystallographic open structure, Long et al. (27) present a plausible model of a closed state of the voltage-gated Kþ channel (KV1.2/2.1). In the proposed closed state, R1 occupies a site on the electrical interior of the membrane, electrostatically bound to E236, interior to F233 that defines the boundary between inside and out from the electrical point of view (Fig. 2). To open the channel, R1, R2, R3, and R4 move across the boundary to the (electrical) outside, leaving K5 bound to E236 (electrically inside) in the fully activated/open state. That is, for each of the four subunits, four positive charges move across the membrane field for a total movement of 16 e0, which agrees well with other estimates of the total charge movement required to open voltage-gated Kþ channels (29,30,35). Compared to the n4 Hodgkin-Huxley model, the movement of four voltagesensing charges in each of the four subunits obviously leads to many more states. The model of Kþ channel gating by Zagotta et al. (29) contains 16 kinetic states, but the structure of Long et al. (27), in which each of the four voltage sensors may assume five states (31), leads to at least 70 states in theory. Squid axon voltage-gated Kþ channels are likely to have just as many kinetics states because their amino-acid sequence (36) resembles that of KV1 and Drosophila Shaker channels. In the original Cole-Moore phenomenon, the activation kinetics after the initial lag were similar even with vastly different holding Vm (see Fig. 5 a in Cole and Moore (1)): if the currents obtained with different prepulses were shifted along the time axis, they nearly superimpose. More recently, the term ‘‘Cole-Moore effect/shift’’ has been expanded to describe general slowing of ionic current activation kinetics by hyperpolarizing prepulses, a related but distinct phenomenon. This type of slowing is observed particularly prominently in select voltage-gated Kþ channels such as Drosophila Ether-A`-Go-Go (EAG) channels and mamma-
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lian KV10 channels (coded by the gene KCNH1) expressed in many tumor cells (37). In EAG/KV10 channels, very negative holding Vm greatly slows the overall current activation time course by tens of milliseconds (38,39), a much larger effect than seen by Cole and Moore in squid axons and observed in Shaker-type Kþ channels (29,30). Furthermore, the slowing of activation in EAG channels is dependent on extracellular divalent cations, e.g., Mg2þ (38,40). These multivalent cations bind to certain negatively charged residues (Fig. 2, left) and impede the outward movement of the S4 voltage-sensing charges (40). In short, it seems inappropriate to apply the term Cole-Moore shift. So, what explains the original Cole-Moore effect seen in squid axonal Kþ channels? After many years, the answer is not clear, and we would echo the words of A. F. Huxley, ‘‘this effect has not yet been given a satisfactory explanation’’ (41). One relevant observation is that the original Cole-Moore effect shows no sign of saturation with very negative prepulses, even to –212 mV. In most other studies on Shaker and KV1 channels, however, no additional lag is observed with prepulses to Vm < –90 to –100 mV. We propose that very strong hyperpolarization (e.g., –212 mV or ˚ -thick membrane), never experi7 107 V/m across a 30 A enced in normal physiology, distorts the voltage-dependent gating apparatus of Kþ channels into conformations not seen at physiological voltages. Specifically, using KV1.2/ 2.1 (27,32) as an example, R1 and R2 in S4 may be pulled inward, away from E236 (Fig. 2), and replaced by a neutral amino acid, possibly alanine, which does not strongly bind to E236. Such a distortion may also cause the electrical leak that is evident in omega current (42). Omega current was not noted by Cole and Moore in the squid axon, possibly because of the high divalent cation concentration in sea water (10 mM Ca2þ, 50 mM Mg2þ). We postulate that recovery from this distorted state is relatively slow, and gives rise to the long lag in opening of Kþ channels seen by Cole and Moore (1). Whatever the underlying mechanism turns out to be, the article by Cole and Moore, the first confirmation of the Hodgkin-Huxley formulation
FIGURE 2 Plausible resting and activated conformations of the S4 voltage sensor domain. The relevant residues are labeled using the numbering of the KV1.2/2.1 chimeric channel (27) and of the Drosophila Shaker channel in parentheses. Adapted from Hoshi and Armstrong (33). Also see Jensen et al. (32) and Vargas et al. (34). To see this figure in color, go online.
Biophysical Journal 109(7) 1312–1316
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and the very first publication in the Biophysical Journal, has a secure place in the history of biophysics and physiology.
Hoshi and Armstrong 21. Neher, E., and B. Sakmann. 1976. Single-channel currents recorded from membrane of denervated frog muscle fibres. Nature. 260:799– 802.
ACKNOWLEDGMENTS
22. Noda, M., S. Shimizu, ., S. Numa. 1984. Primary structure of Electrophorus electricus sodium channel deduced from cDNA sequence. Nature. 312:121–127.
T.H. was supported in part through the National Institutes of Health (grant No. R01GM057654) and the German Research Foundation (grant No. DFG FOR 1738).
23. Papazian, D. M., T. L. Schwarz, ., L. Y. Jan. 1987. Cloning of genomic and complementary DNA from Shaker, a putative potassium channel gene from Drosophila. Science. 237:749–753.
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2. 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.
26. Long, S. B., E. B. Campbell, and R. MacKinnon. 2005. Crystal structure of a mammalian voltage-dependent Shaker family Kþ channel. Science. 309:897–903.
3. Hodgkin, A. L., and A. F. Huxley. 1952. Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. J. Physiol. 116:449–472.
27. Long, S. B., X. Tao, ., R. MacKinnon. 2007. Atomic structure of a voltage-dependent Kþ channel in a lipid membrane-like environment. Nature. 450:376–382.
4. Hodgkin, A. L., and A. F. Huxley. 1952. The components of membrane conductance in the giant axon of Loligo. J. Physiol. 116:473–496.
28. Zagotta, W. N., T. Hoshi, ., R. W. Aldrich. 1994. Shaker potassium channel gating. II: transitions in the activation pathway. J. Gen. Physiol. 103:279–319.
5. Hodgkin, A. L., and A. F. Huxley. 1952. The dual effect of membrane potential on sodium conductance in the giant axon of Loligo. J. Physiol. 116:497–506. 6. Hodgkin, A. L., A. F. Huxley, and B. Katz. 1952. Measurement of current-voltage relations in the membrane of the giant axon of Loligo. J. Physiol. 116:424–448. 7. Helmholtz, H. 1866. Handbuch der Physiologischen Optik. Verlag von Leopold Voss, Hamburg, Germany. 8. Bernstein, J. 1902. Untersuchungen zur thermodynamik der bioelektrischen stro¨me. Archiv f€ ur die gesamte Physiologie des Menschen und der Tiere. 92:521–562. 9. Young, J. Z. 1936. The giant nerve fibres and epistellar body of cephalopods. Quart. J. Microsc. Sci. 78:367–386. 10. Curtis, H. J., and K. S. Cole. 1938. Transverse electric impedance of the squid giant axon. J. Gen. Physiol. 21:757–765. 11. Marmont, G. 1949. Studies on the axon membrane; a new method. J. Cell. Physiol. 34:351–382. 12. FitzHugh, R. 1965. A kinetic model of the conductance changes in nerve membrane. J. Cell. Comp. Physiol. 66 (Suppl 2):111–117. 13. Armstrong, C. M. 1969. Inactivation of the potassium conductance and related phenomena caused by quaternary ammonium ion injection in squid axons. J. Gen. Physiol. 54:553–575. 14. Mullins, L. J. 1959. An analysis of conductance changes in squid axon. J. Gen. Physiol. 42:1013–1035. 15. Goldman, D. E. 1965. Gate control of ion flux in axons. J. Gen. Physiol. 48 (Suppl ):75–77. 16. Hodgkin, A. L., and R. D. Keynes. 1955. The potassium permeability of a giant nerve fibre. J. Physiol. 128:61–88. 17. Armstrong, C. M., and L. Binstock. 1965. Anomalous rectification in the squid giant axon injected with tetraethylammonium chloride. J. Gen. Physiol. 48:859–872. 18. Armstrong, C. M. 1971. Interaction of tetraethylammonium ion derivatives with the potassium channels of giant axons. J. Gen. Physiol. 58:413–437.
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Biophysical Journal 109(7) 1312–1316
Biophysical Journal
Volume 109
October 2015
1312–1316
BJ Classics The Cole-Moore Effect: Still Unexplained? Toshinori Hoshi1,* and Clay M. Armstrong1,* 1
Department of Physiology, University of Pennsylvania, Philadelphia, Pennsylvania
ABSTRACT In the first issue, on the first page of the Biophysical Journal in 1960, Cole and Moore provided the first confirmation of the Hodgkin and Huxley formulation of the sodium and potassium conductances that underlie the action potential. In addition, working with the squid giant axon, Cole and Moore noted that strong hyperpolarization preceding a depolarizing voltageclamp pulse delayed the rise of the potassium conductance: once started, the time course of the rise was always the same but after significant hyperpolarization there was a long lag before the rise began. This phenomenon has come to be known as the Cole-Moore effect. Their article examines and disproves the hypothesis that the lag reflects the time required to refill the membrane with potassium ions after the ions are swept out of the membrane into the axoplasm by hyperpolarization. The work by Cole and Moore indirectly supports the idea of a membrane channel for potassium conductance. However, the mechanism of the Cole-Moore effect remains a mystery even now, buried in the structure of the potassium channel, which was completely unknown at the time.
The story of the Cole and Moore article published in 1960 (1) must begin eight years earlier with the publication of the Hodgkin and Huxley articles (2-6). These articles astounded the physiological world with their explanation of the nerve impulse, solving a mystery standing since the time of Galvani. The work of Hodgkin and Huxley followed much thought about the nerve impulse by, for example, Helmholtz (7) and Bernstein (8). The rediscovery of the squid giant axon by J. Z. Young (9) provided the experimental preparation necessary for elucidating its mechanism. The giant axon is big enough to insert electrodes inside, and was used by Curtis and Cole (10) to demonstrate an impedance change during the action potential, a great step forward. A further technical improvement was the space clamp (11). A wire was inserted into the axon to short out the longitudinal resistance and to functionally transform an axon segment into, electrically, a single manageable patch of membrane. Finally, the voltage clamp was developed by Marmont, using then recently elucidated feedback techniques to stably clamp membrane voltage (Vm) at a desired value. Hodgkin and Huxley used these techniques with an improved electronic circuitry and much insight and brilliance to solve the electrical and electrochemical basis of the action potential, and to show their model could simulate a propagated action potential (2). Retrospectively, Hodgkin and Huxley were very early pioneers of systems biology, and, importantly, the Biophysical Journal article by K. S. (Kacy) Cole and John Moore represented the first independent experimental confirmation of the HodgkinHuxley formulation.
Submitted June 9, 2015, and accepted for publication July 13, 2015. *Correspondence: [email protected] or [email protected]
The Hodgkin-Huxley formulation (2) invoked an increase in Naþ conductance of the axon membrane (GNa, roughly, Naþ permeability) to generate the upstroke of the action potential, and, the subject of this article, an increase of GK (Kþ permeability) to return Vm rapidly to the resting potential. (Note that in the Hodgkin-Huxley formulation, gNa and gK represent whole-axon Naþ and Kþ conductances; more recently, GNa and GK are used to signify macroscopic whole-cell/axon conductances and gNa and gK are used for single-channel conductances.) These ion conductances were detailed in a quantitative model that described their time course and magnitude after a change of Vm. The physical basis of GK was unknown at the time. Carrier molecules confined to the membrane seemed the most probable means for transporting Kþ ions across the membrane’s hydrophobic barrier. A carrier, rather than a pore, seemed best able to explain the selectivity for Kþ versus Naþ. Each of the many (hypothetical) Kþ carriers could be either resting or activated, as determined by the position of four identical, independent, and indistinguishable charged control particles, whose position in the membrane was determined by Vm. Because of the hydrophobic nature of the membrane, the charged control particles were always at the membrane edges except in brief instances of transmembrane transit. As an arbitrary choice, suppose that the particles are positive, attracted to the intracellular edge of the membrane at rest (~–60 mV) and driven progressively more strongly to the extracellular edge by a positive change of Vm (depolarization). This scheme was presented conveniently by FitzHugh (12) and later modified by Armstrong (13) as a five-state kinetic diagram: 4a
3a
2a
a
b
2b
3b
4b
N0 # N1 # N2 # N3 # N4 :
Editor: Brian Salzberg. Ó 2015 by the Biophysical Society 0006-3495/15/10/1312/5
http://dx.doi.org/10.1016/j.bpj.2015.07.052
The Cole-Moore Effect
Vm
where n represents the probability that any given control particle is at the extracellular edge. This kinetic behavior was incorporated into a comprehensive quantitative model of the action potential (2), of which the n4 model describing GK magnitude and kinetics as a function of Vm and time, was a critical component. In their quantitative article, Hodgkin and Huxley questioned the usefulness of empirical equations fitting an unknown physical problem. Clearly, however, the Hodgkin-Huxley model has stood the test of time very well, in part because it was not simply mathematical, but offered excellent mechanistic and electrical insights that have been improved but not overturned as a result of new information. The five-state n4 model of Hodgkin and Huxley seemed to presage the discovery made ~40 years later that Kþ channels are composed of four, often identical, subunits. However, Hodgkin and Huxley candidly noted that although an n6 formulation gave a better fit to the sigmoidal kinetics after a depolarization, it was not worth the trouble (on a handcranked calculator). After this 1952 revelation (2), many other groups investigated the kinetics of GNa and GK for a better understanding
of the physical mechanisms. Cole and Moore in this article (1) considered the idea that the rise and fall of potassium current (IK) was simply the result of electrodiffusion within the squid axon membrane and that no carrier or pore was involved in its generation. In the normal state for squid axons, extracellular Kþ concentration is 10 mM and intracellular Kþ concentration is ~550 mM. In the electrodiffusion model, the negative internal voltage at resting potential largely empties the membrane of Kþ, which is pulled out of the membrane into the axoplasm by the negative voltage. It is only partially replaced from the extracellular solution where the Kþ concentration is low. This provides, at most, a 1:55 conductance ratio for inward versus outward current (which is too low). When the membrane voltage is made less negative or even positive, Kþ enters the membrane from the axoplasm and electrodiffuses: it moves as dictated by the electric field and the concentration gradient at any point within the membrane. When the leading edge of the electrodiffusion wave reaches the outer surface after a distinct lag, IK is seen to rise, and increases until the Kþ concentration in the membrane reaches a steady state. Consistent with this general idea, the authors found that extreme hyperpolarization applied before a depolarizing pulse distinctly increases the lag in current development; i.e., in their theory, very negative voltage inside sweeps Kþ out of the membrane into the axoplasm. Hyperpolarization thus, in theory, increases the lag and enhances the sigmoidal characteristic of IK development on depolarization, because the Kþ-depleted membrane must be refilled as Kþ diffuses across. The experimentally observed increase in the lag as IK develops in a test pulse after strong hyperpolarization is called the Cole-Moore effect. The five-state n4 model of Hodgkin and Huxley provides an explanation of the lag in IK development that is quite different from the electrodiffusion hypothesis. A hyperpolarizing prepulse increases the lag predicted by the n4 model only when Vm before the test depolarization is not
–
Probability
In this diagram, N0, N1, N2, N3, and N4 represent those states with 0, 1, 2, 3, and 4 of the control particles of a given carrier at the membrane’s extracellular edge (activated position). The rate constant a is voltage-dependent and governs the movement of a control particle from inner to outer edge. The value b, also voltage-dependent, governs movement in the reverse direction. Because the control particles are identical and independent, the coefficients for a are 4, 3, 2, and 1, corresponding to the number of the control particles available to make the outward transition. The coefficients for b are the same, in reverse. A carrier is fully at rest in state N0 with no control particle at the extracellular edge. It is active only in state N4* (as indicated by the asterisk), with all four control particles at the extracellular edge. In normal behavior, most of the control particles are in state N0 at Vm ¼ –60 mV. After a depolarization, GK increases with a sigmoid time course after a distinct delay as the four control particles pertaining to a carrier, move, one by one, from the intracellular to the extracellular edge of the membrane. When Vm is returned to rest, only a single transition, from N4* to N3, is required to deactivate the carrier, and this occurs exponentially (no delay) with time constant ~1/4b. (In theory, the five-state diagram contains four exponential components, but at the voltages where b >> a, the dominant component has a time constant of 1/4b.) Turning on, it is sigmoidal; turning off, it is a simple exponential, as observed experimentally. Because the four control particles are identical and independent, the probability P that the carrier is in state N4* with all of its four control particles at the extracellular edge is P N4 ¼ n4 ;
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n n4 n6 n25
n4
n
25
n
FIGURE 1 Predictions of n, n4, n6, and n25 models. The probability of full activation is shown as a function of time. In each model, the carrier was assumed to be fully at rest before the depolarization onset. The near horizontal segments immediately after depolarization represent the lag, which is absent in the n model and longest in the n25 model. To see this figure in color, go online. Biophysical Journal 109(7) 1312–1316
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sufficiently negative to put essentially all of the control particles into state N0. Experimentally, however, Cole and Moore found that a good fit for IK after strong hyperpolarization required n25, not n4; that is, in Hodgkin and Huxley terms, there would have to be 25 particles controlling each Kþ-conducting unit. A modern day interpretation could be that the Kþ-conducting unit, whatever its nature, contains 25 identical and independent subunits. This is certainly less attractive than the four subunits implied by the Hodgkin-Huxley n4 model, perhaps enhancing the appeal of the electrodiffusion idea. The abstract of the article by Cole and Moore seems to suggest that electrodiffusion is operative, with mobility of Kþ in the membrane ~105 times lower than that in aqueous solution. The final two paragraphs of the text, however, point out that an electrodiffusion model cannot explain the negative resistance seen with isotonic Kþ on both sides of the membrane; i.e., experimentally, at negative Vm in the steady-state, IK is near zero even in the presence of high external Kþ, contrary to the predictions of electrodiffusion. It seems that the two authors of the article may have been of two minds on this question! Faced with this problem, the authors (one or both) then cite an idea of Mullins: a pore across the membrane that is deformed and conducts less well at negative voltage (14). The electrodiffusion model nonetheless died slowly, and was still invoked some years later in the 1960s (15). Then, if not electrodiffusion, what underlies GK? The idea of a pore seems very obvious now, but it was not favored initially because of then-perceived difficulties imagining ion selectivity. There was, however, early evidence for a pore—the ‘‘long pore effect’’ noted by Hodgkin and Keynes in 1955 (16). Mullins (14) in 1959 also wrote a stimulating article on the possibility of pores, and discussed, with great foresight, an idea to explain ion selectivity—that the pore must provide a close fit to the selected ion. Blockage of IK by intracellular TEAþ (tetraethylammonium) or derivatives reported in 1965 and 1971 strongly supported the idea of a Kþ pore (17,18). TEAþ, about the size of a Kþ ion with one hydration shell, enters a Kþ channel through an intracellular ion-conduction gate only when this gate is open. After entering, a TEAþ molecule is blocked about halfway through the membrane by a narrowing, i.e., the channel’s selectivity filter. A Kþ ion can pass through the selectivity filter by shedding its hydration shell, an impossibility for the covalently linked ethyl arms of TEAþ. Further confirmation of the pore hypothesis came in several ways. First, a calculation in 1969 (19) of the theoretical conductance of a pore (high conductance) versus a carrier (low conductance) was followed a few years later in the 1970s by single-molecule biophysics measurements of unitary current events, which were consistent with a pore but not a carrier (20,21). Then genes for voltage-gated Naþ and Kþ channels (22-24) were sequenced in the 1980s, and their pore regions were identified. Finally, the crystallographic atomic structures of Kþ channels starting at the end Biophysical Journal 109(7) 1312–1316
Hoshi and Armstrong
of the 20th century removed any possibility of doubt: Kþ ions move through a pore (25-27). Under space- and voltage-clamped conditions sufficient to ensure rapid changes in Vm, currents through most voltage-gated Kþ channels, including Drosophila Shaker and human KV1-type channels activate in a sigmoidal manner with some variable delay, typically a millisecond or less at room temperature (voltage-clamp conditions resulting in poor time resolution can significantly lengthen the apparent delay in current activation). The delay or lag is more noticeable when the currents are elicited by small depolarization from a very negative holding Vm. Experimentally, the sigmoidal characteristic can be quantified using the concept of sigmoidicity, which is the amount of delay relative to the overall activation kinetics such that the results obtained at different voltages and those from different channels are more readily compared (28). Conceptually, the sigmoidal activation characteristic is readily explained by the kinetic reasoning that channels traverse multiple closed states before reaching the (first) conducting state. When the holding Vm is very negative, the channels are pulled to the fully closed or most closed state (e.g., N0 in the earlier state diagram) and the channels must pass through additional closed states to open, thus creating a greater lag in activation. If hyperpolarization is strong enough, typically –90 to –100 mV, to force all channels into N0, greater hyperpolarization does not produce a greater lag (28). Once the initial lag is over, the IK kinetics are relatively similar such that the currents during test pulses after prepulses of different size can be easily superimposed by shifting the IK traces along the time axis (29,30) (see Fig. 1). A successful description of the activation delay in heterologously expressed voltage-gated Kþ channels was one of the important evaluation criteria in developing more recent models of Kþ channel gating, based on Drosophila Shaker Kþ channels, incorporating the knowledge that four identical subunits, each of which shows multiple conformational changes, can form a functional voltage-gated Kþ channel (29,30). As expected, the greater the number of closed states that channels must traverse, the greater the lag one observes. Additionally, the transition rate constants among the closed states contribute to the sigmoidicity of activation. The greatest degree of sigmoidicity is observed when the identical and independent assumption is relaxed and the opening rate constants are all made equal (compare to Fig. 1) (28). With the availability of crystallographic atomic structures of voltage-gated Kþ channels (27), structural connotations can be now assigned to various models of Kþ channel gating (29,30) including the original Hodgkin-Huxley model. For example, each Kþ channel subunit typically contains multiple voltage-sensing positively charged residues in the transmembrane S4 segments, which are referred to as R1 (arginine), R2, R3, R4, and K5 (lysine) starting numeration
The Cole-Moore Effect
from the extracellular side of the membrane (31,32). Details of S4 motion through the membrane on changes in Vm remain to be worked out because atomic structures of the closed states of voltage-gated Kþ channels have not been experimentally determined. However, based on the crystallographic open structure, Long et al. (27) present a plausible model of a closed state of the voltage-gated Kþ channel (KV1.2/2.1). In the proposed closed state, R1 occupies a site on the electrical interior of the membrane, electrostatically bound to E236, interior to F233 that defines the boundary between inside and out from the electrical point of view (Fig. 2). To open the channel, R1, R2, R3, and R4 move across the boundary to the (electrical) outside, leaving K5 bound to E236 (electrically inside) in the fully activated/open state. That is, for each of the four subunits, four positive charges move across the membrane field for a total movement of 16 e0, which agrees well with other estimates of the total charge movement required to open voltage-gated Kþ channels (29,30,35). Compared to the n4 Hodgkin-Huxley model, the movement of four voltagesensing charges in each of the four subunits obviously leads to many more states. The model of Kþ channel gating by Zagotta et al. (29) contains 16 kinetic states, but the structure of Long et al. (27), in which each of the four voltage sensors may assume five states (31), leads to at least 70 states in theory. Squid axon voltage-gated Kþ channels are likely to have just as many kinetics states because their amino-acid sequence (36) resembles that of KV1 and Drosophila Shaker channels. In the original Cole-Moore phenomenon, the activation kinetics after the initial lag were similar even with vastly different holding Vm (see Fig. 5 a in Cole and Moore (1)): if the currents obtained with different prepulses were shifted along the time axis, they nearly superimpose. More recently, the term ‘‘Cole-Moore effect/shift’’ has been expanded to describe general slowing of ionic current activation kinetics by hyperpolarizing prepulses, a related but distinct phenomenon. This type of slowing is observed particularly prominently in select voltage-gated Kþ channels such as Drosophila Ether-A`-Go-Go (EAG) channels and mamma-
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lian KV10 channels (coded by the gene KCNH1) expressed in many tumor cells (37). In EAG/KV10 channels, very negative holding Vm greatly slows the overall current activation time course by tens of milliseconds (38,39), a much larger effect than seen by Cole and Moore in squid axons and observed in Shaker-type Kþ channels (29,30). Furthermore, the slowing of activation in EAG channels is dependent on extracellular divalent cations, e.g., Mg2þ (38,40). These multivalent cations bind to certain negatively charged residues (Fig. 2, left) and impede the outward movement of the S4 voltage-sensing charges (40). In short, it seems inappropriate to apply the term Cole-Moore shift. So, what explains the original Cole-Moore effect seen in squid axonal Kþ channels? After many years, the answer is not clear, and we would echo the words of A. F. Huxley, ‘‘this effect has not yet been given a satisfactory explanation’’ (41). One relevant observation is that the original Cole-Moore effect shows no sign of saturation with very negative prepulses, even to –212 mV. In most other studies on Shaker and KV1 channels, however, no additional lag is observed with prepulses to Vm < –90 to –100 mV. We propose that very strong hyperpolarization (e.g., –212 mV or ˚ -thick membrane), never experi7 107 V/m across a 30 A enced in normal physiology, distorts the voltage-dependent gating apparatus of Kþ channels into conformations not seen at physiological voltages. Specifically, using KV1.2/ 2.1 (27,32) as an example, R1 and R2 in S4 may be pulled inward, away from E236 (Fig. 2), and replaced by a neutral amino acid, possibly alanine, which does not strongly bind to E236. Such a distortion may also cause the electrical leak that is evident in omega current (42). Omega current was not noted by Cole and Moore in the squid axon, possibly because of the high divalent cation concentration in sea water (10 mM Ca2þ, 50 mM Mg2þ). We postulate that recovery from this distorted state is relatively slow, and gives rise to the long lag in opening of Kþ channels seen by Cole and Moore (1). Whatever the underlying mechanism turns out to be, the article by Cole and Moore, the first confirmation of the Hodgkin-Huxley formulation
FIGURE 2 Plausible resting and activated conformations of the S4 voltage sensor domain. The relevant residues are labeled using the numbering of the KV1.2/2.1 chimeric channel (27) and of the Drosophila Shaker channel in parentheses. Adapted from Hoshi and Armstrong (33). Also see Jensen et al. (32) and Vargas et al. (34). To see this figure in color, go online.
Biophysical Journal 109(7) 1312–1316
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and the very first publication in the Biophysical Journal, has a secure place in the history of biophysics and physiology.
Hoshi and Armstrong 21. Neher, E., and B. Sakmann. 1976. Single-channel currents recorded from membrane of denervated frog muscle fibres. Nature. 260:799– 802.
ACKNOWLEDGMENTS
22. Noda, M., S. Shimizu, ., S. Numa. 1984. Primary structure of Electrophorus electricus sodium channel deduced from cDNA sequence. Nature. 312:121–127.
T.H. was supported in part through the National Institutes of Health (grant No. R01GM057654) and the German Research Foundation (grant No. DFG FOR 1738).
23. Papazian, D. M., T. L. Schwarz, ., L. Y. Jan. 1987. Cloning of genomic and complementary DNA from Shaker, a putative potassium channel gene from Drosophila. Science. 237:749–753.
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Biophysical Journal 109(7) 1312–1316
