92
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[4]
both single-channel and whole-cell recordings. They are good initial choices but, of course, must be checked for each cell type for problems associated with leaching of blockers, etc., from the glass. Coming 8161 is the best glass studied to date with respect to electrical and thermal properties but must be checked carefully for leachable components. If perforatedpatch whole-cell recordings are to be used, 8161, KG-12, or some other high lead, low melting point glass are probably the best choices.
[4] I o n C h a n n e l S e l e c t i v i t y , P e r m e a t i o n ,
and Block
By TED BEGENISICH Introduction One of the first steps in an effort to understand how cells perform their observed function is to determine what ion channels are in the membrane of the cell of interest and the properties of those channels. The channels can be classified by the ion that is most permeant and by what other ions can also permeate the channel. Further information can be obtained from a proper analysis of blockage of the channel by impermeant ions. The procedures described here assume the ion permeation pathway is a waterfilled pore and that ions diffuse through the pore without associated large movements of the protein channel as might occur in "carrier"-mediated transport. As we have learned more of the details of these two general types of mechanisms, the distinction between them has diminished. However, single-channel currents that represent more that l0 s ions/see (0.02 pA) clearly fall into the pore category.~,2 Most of the permeation properties of pores can be determined through the use of macroscopic currents obtained with the whole-cell variant of the patch clamp technique. In most cases, use of these macroscopic currents is preferred but there are situations where single-channel currents more easily reveal specific permeation properties) Unless specifically stated, the pro-
B. Hille, "Ionic Channels of Excitable Membranes." Sinauer Associates, Sunderland, Massachusetts, 1984. 2 B. P. Bean, this volume [11]. 3 E. Moezydlowski, this volume [54].
METHODS IN ENZYMOLOGY, VOL. 207
Copyright © 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.
[4]
ION CHANNEL SELECTIVITY AND BLOCK
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cedures to follow apply to either macroscopic or single-channel currents. The references in this chapter were chosen to provide specific examples and not to critically review the field.
Experimental Procedures General Considerations
The theoretical background for studies of ion channel permeation has followed two general courses. One of these uses the electrodiffusion approach developed by Nernst 4,5 and Planck, 6,7 and the other employs absolute reaction-rate theory, s Much of the characterization of ion channel permeation can be done independently of the particular theoretical formalism, especially if many of the terms are considered empirical values. Ion Channel Selectivity
One of the first properties to determine for a channel is its selectivity: which ions are permeant. If a pore is permeable to a single ion (X) of valence z, the net current through the pore is zero at a potential (Vx) given by the Nernst (or equilibrium) potential for that ion [Eq. (1)]: Vx -- (R T / z F ) ln(a o/ai)
(1)
where R, T, and F have their usual thermodynamic meanings; R T / F at 20 ° is approximately 25 inV. This voltage is an equilibrium property and does not depend on the theoretical framework from which it is derived. It is a function only of the ion concentrations and is independent of any impermeant ions and independent of the presence of any fixed charges on the membrane. The terms ao and al represent the external and internal activities of ion X related to the concentration by activity coefficients, ?o and ~,i: Vx = ( R T / F ) ln(?o[X]o/Yi[X]t )
4 W. Nernst, Z. Phys. Chem. 2, 614 (1888). 5 W. Nemst, Z. Phys. Chem. 4, 129 (1889). 6 M. Planck, Ann. Phys. Chem. Neue Folge 49, 161 (1890). 7 M. Planck, Ann. Phys. Chem. Neue Folge 411, 561 (1890). 8 H. Eyring, R. Lumry, andJ. W. Woodbury, Rec. Chem. Prog. 1 ~ , 100 (1949).
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ELECTROPHYSIOLOGICAL TECHNIQUES
[4]
These activity coefficients depend on the ionic strength of the solution. In a dilute salt solution, a monovalent ion has an activity coefficient of approximately 0.85, and so the ion activity is not much different from the ion concentration. At higher salt concentrations, the coefficients become rather small and very small for divalent ions. 9 However, if the internal and external solutions are similar, the activity coefficients are often ignored: Vx = (RT/F)
ln([X]o/[X]i )
(3)
not because they are near unity but rather because they are approximately equal. If the solutions are not of similar concentration or if only one contains a moderate concentration of divalent ions, then these coefficients should not be ignored. With this caution, the remaining discussion will use concentrations rather than activities. Equation (3) suggests a test that a pore is permeable to a specific ion, say K+: measure the channel zero-current potential (or reversal potential) with known internal and external concentrations of the test cation and see if this potential is equal to the Nernst potential for the ion. To allow a valid comparison, the measured potential must be corrected for the appropriate liquid junction potential) ° In addition, the solutions should not contain other ions that may be permeant. Candidates for possibly impermeant cations include Tris, tetramethylammonium, and N-methyl-D-glucamine; large anions may be impermeant to anion channels and include isethionate and glucuronate. It may be difficult to find impermeant ions for some very nonselective channels (e.g., see Adams et al. ~). The use of Eq. (3) requires knowing the intracellular concentration of the ion of interest. Unfortunately, in many experimental situations, this concentration is not accurately known. This is sometimes true even for the usual whole-cell variant of the patch clamp technique since it relies on diffusion of the pipette contents into the cell interior) 2 So, rather than compare the computed Nernst potential to a single measurement, the reversal potential is measured at several external concentrations of the test ion and (often) plotted as a function of the logarithm of the external ion concentration. Equation (3) predicts a linear relationship in such a plot with a 58/z mV/decade slope (at 20°), and such a finding demonstrates
9 R. A. Robinson and R. H. Stokes, "Electrolyte Solutions." Butterworth, London, 1965. io E. Neher, this volume [6]. i1 D. J. Adams, T. M. Dwyer, and B. Hille, J. Gen. Physiol. 75, 494 (1980). 12R. S. Eisenberg, this volume [10].
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that the pore is permeant to the tested ion. Furthermore, with such data the internal concentration of the ion can be computed. Seldom is a perfectly linear relationship found when using physiological solutions (but see Lucero and Pappone 13for a recent example). Rather, the results of many such experiments are in agreement with Eq. (3) only at high concentrations of the test ion. At low concentrations the slope is often much less than predicted (see Sah et al.~4 for a recent example). Such a result suggests that the pore may not be perfectly selective for the tested ion. Indeed, few channels are permeant to only a single type of ion, and the expected dependency of pore zero-current potential (V~,) on ion concentration is, in general, both model dependent and more complicated. However, if two ions (X and Y) of the same valence (z) are considered, a relatively simple equation can be derived (see Hille ~for some of the details of these computations) from either of the two limiting theoretical formalisms: • Px[X]o + Pv[Y]o
V,~, = (RT/zF) m ~
+ PvIY]i
(4)
where Px and Pv are the permeabilities of ions X and Y. The reversal potential of Eq. (4) actually depends only on the relative permeabilities: [X]o + (Py/Px)[Y]o V,~, = (RT/zF) m ~ i + (PY/Px)[Yli •
(5)
At high external concentrations of ion X, Eq. (5) predicts a linear relationship between the measured reversal potential and the logarithm of [X]o. Deviations from linearity are expected at lower concentrations owing to the second term in the numerator of Eq. (5). The relative X to Y permeability can be obtained by fitting Eq. (5) to the data. Biionic Conditions. While Eq. (5) suggests experiments that can determine the relative ion permeability of a pore, a simpler method can be used if the solution on the cytoplasmic face of the membrane can be accurately controlled (e.g., perfused giant axons, excised patches, whole cell measurements with perfused pipettest2). This experimental control allows the use of a simplified form of Eq. (4) if ions of type X are the only permeant ones
13 M. T. Lucero and P. A. Pappone, J. Gen. Physiol. 94, 451 (1989). 14 p. Sah, A. J. Gibb, and P. W. Gage, J. Gen. Physiol. 92, 264 (1988).
96
ELECTROPHYSIOLOGICAL TECHNIQUES
[4]
in the external solution and Y ions are the only permeant species in the solution on the cytoplasmic side of the membrane: V~, = (RT]zF) In (Px [X]o/Pv [Y]i)
(6)
P x / P v ----([Y]i/[X]o) e x p [ ( z V ~ F ) / R T ]
(7)
or
When experimental conditions allow such a situation, the relative permeabilities are easily computed from the measured reversal potential and the known ion concentrations. Chandler and Meves ~5 used this technique to show that the squid axon Na + channel is permeable to several other cations including Li+, K +, Rb +, and Cs +. Internal Ions Not Known but Constant. Hille ~6 showed how relative permeability can be determined even if the internal medium cannot be controlled but is constant. In this technique, the channel reversal potential is measured twice: once with only ion X in the external solution (V~,x) and again with only ion Y in the external solution (V,~,,,v). Under these conditions, the relative permeability can be computed [using a form of Eq. (4)] from the difference between these two measurements: P x / P y = ([X]o/[Y]o) exp[zF(V,~,,~x -- V~,v )/RT]
(8)
Using this technique, Hille 1~showed that the selectivity of the Na + channel in myelinated nerve is similar to that of the squid axon Na + channel and extended the list of permeant ions to include several organic cations) 6 It is important to note that the Eqs. (4)-(8) are valid only for ions of the same valence and for a pore that obeys independence. ~s Independence means that the movement of each type of ion is independent of the presence of the other. Very few ion channel pores allow independent ion movement. Rather, ions transiently bind during passage to sites within the pore. Ions compete for these sites, and so the ion movements do not obey independence. Consequently, these equations are not, in general, expected to be valid but still have considerable utility. 15W. K. Chandler and H. Meves,J. Physiol. (London) 180, 788 (1965). ~6B. Hille,J. Gen. Physiol. 58, 599 (1971). ~7B. Hille, J. Gen. Physiol. 59, 647 (1972). is B. HiUe,in "Membranes--A Seriesof Advances, Volume 4: Lipid Bilayersand Biological Membranes: Dynamic Properties" (G. Eisenman, ed.), p. 255. Dekker, New York, 1975.
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Classification of Ion Pores Pores that do not allow independent ion flow can be classified by the maximum number of ions that can simultaneously occupy the pore. In one-ion pores, the presence of a single ion prevents entry (perhaps through electrostatic repulsion) of any other ion. Multiion pores allow simultaneous occupancy by more than one ion. One-Ion Pores. Hille is has shown that Eq. (7) applies to one-ion pores even if independence is not obeyed. The permeabilities in Eq. (7) may not be constant for such a pore but, rather, may be functions of membrane potential but not functions of ion concentration. However, in many situations the voltage dependence may be small or nonexistent. Consequently, Eq. (7) is very useful for determining relative selectivities even for one-ion pores. The nonindependent nature of such pores makes the current through such pores very sensitive functions of the concentrations of the ions. Consequently, ion selectivity cannot be judged by the relative current carried by different types of ions but can be determined from measurements of the V~. Ion currents are also affected by many pore-blocking ions (see below). If these ions are impermeant, however, they will not contribute to the measured reversal potential, and Eq. (7) may still be used. Multi-ion Pores. Not surprisingly, the permeation properties of multiion pores are more complex than those of one-ion pores. Nevertheless, Hille and Schwarz 19have shown that Eq. (7) may apply even to these more complicated situations but that the permeability ratio may be a function ion concentration. Consequently, a finding of concentration-dependent permeabilities in Eq. (7) indicates that the pore under study has multi-ion characteristics. It may be difficult to separate the effects of voltage and concentration since changing ion concentrations will necessarily shift the reversal potential to a new value. However, it is sometimes possible to separate these two effects: squid axon Na + channel selectivities are concentration but not (significantly) voltage dependent. 2°
Pore-Blocking Studies Valuable information on ion channels can be obtained from studies of current inhibition by impermeant ions (see Moczydlowski3). For example, Armstrong 21 used tetraethylammonium (TEA) ions and similar analogs to ~9 B. Hille and W. Schwartz, J. Gen. Physiol. 72, 409 (1978). 20 T. Begenisich and M. Cahalan, J. Physiol. (London) 407, 217 (1980). 2~ C. M. Armstrong, J. Gen. Physiol. 58, 414 (1971).
98
ELECTROPHYSIOLOGICAL TECHNIQUES
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probe the structure of the cytoplasmic portion of the squid axon, delayed rectifier K + channel. In one of the best studies of this type, Miller 22 used monovalent and bis-quaternary ammonium compounds to determine the spatial dependence of the electric potential in part of the pore of a K + channel from sarcoplasmic reticulum. One experiment in these types of studies is to determine the voltage dependence of current inhibition produced by a charged ion. As described by Woodhul123 (and see Moczydlowski3 for more details) the dissociation constant for the blocking ion, of valence z, binding to a site within the membrane electric field is given as Kd(Vm) -- Kd(0 ) exp(--tSzFV,./RT)
(9)
where Ka(O) is the zero-voltage dissociation constant and ~ is the location of the binding site as a fraction (measured from the inside) of the membrane voltage. Then, the fraction of current (channels) blocked, f ( Vm), will not only be a function of the concentration of blocking ions, [B], but also a function of voltage: f(V=) =
[B] [B] + Kd(V=)
(10)
A determination of the fraction of current blocked as a function of membrane potential will, through the application of Eqs. (9) and (10), yield a value for the electrical distance to the blocking site. There are, however, two potential problems with such an analysis: (1) a voltage dependence of block is neither a necessary nor sufficient condition to identify the block as within the pore; and (2) multiple ion occupancy of the pore makes it impossible to determine the fraction of the electric potential present at the blocking site. 19 A better test of the presence of the blocking site within the pore is to demonstrate that increases in permeant ion concentration on the side opposite to that with the blocking ion interacts with the blocking ion. Armstrong 2~ showed that increased external K + increased the rate of recovery from block of squid axon K + channels by internal TEA analogs. Similar results have been obtained for relief of internal Cs + block of squid axon K + channels by external K +24 and Begenisich and Danko 2s showed that increased intracellular Na + reduces block of squid axon Na + channels by external H +. In perhaps the most elegant study of this type, MacKinnon 22 C Miller, J. Gen. PhysioL 79, 869 (1982). 23 A. Woodhull, J. Gen. Physiol. 61,687 (1974). 24 W. J. Adelman, Jr., and R. J. French, J. Physiol. (London) 276, 13 (1978). 25 T. Begenisieh and M. Danko, J. Gen. Physiol. 82, 599 (1984).
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and Miller 26 studied block of single high-conductance, Ca2+-activated K + channels by the scorpion toxin charybdotoxin. External application of this toxin inhibits current through these channels. McKinnon and Miller found that internal application of the permeant ions Rb + and K + increased the toxin dissociation rate but that impermeant ions like Cs +, Na +, and Li+ were without effect. These authors have termed this phenomenon "transenhanced dissociation" and, rightly, argue that, while not "air-tight proof," such findings are simply and naturally explained by physical occlusion of the pore by the blocking ion. A good example of the difficulty of obtaining the fractional field location of a blocking site can be found in the work of Adelman and French. 24 A literal application of the Woodhull-type analysis reveals that the blocking site reached by an external Cs + is more than 100% across the membrane voltage drop. This apparently nonsensical result can be a consequence of a multi-ion pore, 27 and, indeed, the data of Adelman and French can be reproduced by a specific multi-ion pore model. 2s In such a pore, any permeant ions must vacate the blocking ion binding site before block can occur. Consequently, the voltage dependence of block will reflect not only the voltage-dependent binding of the blocking ion with this site but also the voltage-dependent evacuation of the pore by permeant ions.~9 In these modeling exercises, specific locations for permeant and blocking ion binding sites are specified, but, because of the large number of adjustable, offsetting parameters, these locations cannot be unambiguously determined. Consequently, any effort to determine the position of a blocking ion binding site must be preceded by experiments demonstrating the lack of multi-ion effects in the pore under investigation. A description of these types of experiments is beyond the scope of this chapter but can be found in Hille and Schwartz ~9,27and Begenisich)9,3° Conclusion As described here, ion channel pore permeation can be a complicated process, and a detailed analysis may be model dependent. However, a determination of pore selectivity is relatively straightforward, and suitable 26R. MacKinnonand C. Miller,J. Gen. PhysioL91,445 (1988). 27B. Hilleand W. Schwartz,Brain Res. Bull. 4, 159 (1979). 2sT. Begenisichand C. Smith, in "Current Topics in Membranesand Transport," Vol. 22. AcademicPress,New York, 1984. 29T. Begenisich in "Membranesand Transport" (A. N. Martonosi, ed.'), Vol. 2, p. 274. Plenum, New York, 1982. 3oT. Begenisich,Annu. Rev. Biophys. Chem. 16, 247 (1987).
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experimental techniques are readily available. Information on pore structure can be obtained from an analysis of block produced by ions, but such an analysis is complicated and model dependent unless it can be shown that the pore does not exhibit multi-ion properties. Acknowledgments This work was supported by a grant (NS 14138) from the U.S. Public Health Service.
[5] A c c e s s R e s i s t a n c e a n d S p a c e C l a m p P r o b l e m s Associated with Whole-Cell Patch Clamping
By CLAY M. ARMSTRONGand WILLIAMF. GILLY Introduction The exhilaration of forming a seal and recording from a living cell with the whole-cell patch clamp technique often makes one forget two important sources of error. Series resistance and space clamp artifacts can render worthless the handsomest results once they are subjected to critical review. Stated briefly, without proper compensation for series resistance and demonstration of a good space clamp, all measurements of membrane current are qualitative. In many cases, difficulties associated with these two problems cannot be completely eliminated, and separating justified from unjustified conclusions necessarily becomes a matter of judgment, experience, and cautiously working through every possibility for artifactual explanations of the phenomenon in question. This chapter discusses these impediments that have harried investigators since the first development of the voltage clamp. A careful analysis of series resistance errors was performed by Cole and Moore ~over thirty years ago, and series resistance and space clamp problems have been clearly recognized since that time. Examples exist, however, that clearly show the dangers of ignoring these problems and forging ahead. Investigations of ionic currents in cardiac muscle, for example, were handicapped for many years by lack of an adequate space clamp. 2 Consequently, the fundamental principles outlined here are not original, but we hope to present them in a new way. We write this chapter to prov.~de a helpful guide for separating fact from fiction in evaluating voltage-clamp data, and as a reminder not to K. S. Cole and J. W. Moore, J. Gen. Physiol. 44, 123 (1960). 2 E. A. Johnson and M. Lieberman, Ann. Rev. Physiol. 33, 479 (1971).
METHODS IN ENZYMOLOGY,VOL. 207
Copyright© 1992by AcademicPress,Inc. Allflightsofreproductionin any form reserved.
ELECTROPHYSIOLOGICAL TECHNIQUES
[4]
both single-channel and whole-cell recordings. They are good initial choices but, of course, must be checked for each cell type for problems associated with leaching of blockers, etc., from the glass. Coming 8161 is the best glass studied to date with respect to electrical and thermal properties but must be checked carefully for leachable components. If perforatedpatch whole-cell recordings are to be used, 8161, KG-12, or some other high lead, low melting point glass are probably the best choices.
[4] I o n C h a n n e l S e l e c t i v i t y , P e r m e a t i o n ,
and Block
By TED BEGENISICH Introduction One of the first steps in an effort to understand how cells perform their observed function is to determine what ion channels are in the membrane of the cell of interest and the properties of those channels. The channels can be classified by the ion that is most permeant and by what other ions can also permeate the channel. Further information can be obtained from a proper analysis of blockage of the channel by impermeant ions. The procedures described here assume the ion permeation pathway is a waterfilled pore and that ions diffuse through the pore without associated large movements of the protein channel as might occur in "carrier"-mediated transport. As we have learned more of the details of these two general types of mechanisms, the distinction between them has diminished. However, single-channel currents that represent more that l0 s ions/see (0.02 pA) clearly fall into the pore category.~,2 Most of the permeation properties of pores can be determined through the use of macroscopic currents obtained with the whole-cell variant of the patch clamp technique. In most cases, use of these macroscopic currents is preferred but there are situations where single-channel currents more easily reveal specific permeation properties) Unless specifically stated, the pro-
B. Hille, "Ionic Channels of Excitable Membranes." Sinauer Associates, Sunderland, Massachusetts, 1984. 2 B. P. Bean, this volume [11]. 3 E. Moezydlowski, this volume [54].
METHODS IN ENZYMOLOGY, VOL. 207
Copyright © 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.
[4]
ION CHANNEL SELECTIVITY AND BLOCK
93
cedures to follow apply to either macroscopic or single-channel currents. The references in this chapter were chosen to provide specific examples and not to critically review the field.
Experimental Procedures General Considerations
The theoretical background for studies of ion channel permeation has followed two general courses. One of these uses the electrodiffusion approach developed by Nernst 4,5 and Planck, 6,7 and the other employs absolute reaction-rate theory, s Much of the characterization of ion channel permeation can be done independently of the particular theoretical formalism, especially if many of the terms are considered empirical values. Ion Channel Selectivity
One of the first properties to determine for a channel is its selectivity: which ions are permeant. If a pore is permeable to a single ion (X) of valence z, the net current through the pore is zero at a potential (Vx) given by the Nernst (or equilibrium) potential for that ion [Eq. (1)]: Vx -- (R T / z F ) ln(a o/ai)
(1)
where R, T, and F have their usual thermodynamic meanings; R T / F at 20 ° is approximately 25 inV. This voltage is an equilibrium property and does not depend on the theoretical framework from which it is derived. It is a function only of the ion concentrations and is independent of any impermeant ions and independent of the presence of any fixed charges on the membrane. The terms ao and al represent the external and internal activities of ion X related to the concentration by activity coefficients, ?o and ~,i: Vx = ( R T / F ) ln(?o[X]o/Yi[X]t )
4 W. Nernst, Z. Phys. Chem. 2, 614 (1888). 5 W. Nemst, Z. Phys. Chem. 4, 129 (1889). 6 M. Planck, Ann. Phys. Chem. Neue Folge 49, 161 (1890). 7 M. Planck, Ann. Phys. Chem. Neue Folge 411, 561 (1890). 8 H. Eyring, R. Lumry, andJ. W. Woodbury, Rec. Chem. Prog. 1 ~ , 100 (1949).
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ELECTROPHYSIOLOGICAL TECHNIQUES
[4]
These activity coefficients depend on the ionic strength of the solution. In a dilute salt solution, a monovalent ion has an activity coefficient of approximately 0.85, and so the ion activity is not much different from the ion concentration. At higher salt concentrations, the coefficients become rather small and very small for divalent ions. 9 However, if the internal and external solutions are similar, the activity coefficients are often ignored: Vx = (RT/F)
ln([X]o/[X]i )
(3)
not because they are near unity but rather because they are approximately equal. If the solutions are not of similar concentration or if only one contains a moderate concentration of divalent ions, then these coefficients should not be ignored. With this caution, the remaining discussion will use concentrations rather than activities. Equation (3) suggests a test that a pore is permeable to a specific ion, say K+: measure the channel zero-current potential (or reversal potential) with known internal and external concentrations of the test cation and see if this potential is equal to the Nernst potential for the ion. To allow a valid comparison, the measured potential must be corrected for the appropriate liquid junction potential) ° In addition, the solutions should not contain other ions that may be permeant. Candidates for possibly impermeant cations include Tris, tetramethylammonium, and N-methyl-D-glucamine; large anions may be impermeant to anion channels and include isethionate and glucuronate. It may be difficult to find impermeant ions for some very nonselective channels (e.g., see Adams et al. ~). The use of Eq. (3) requires knowing the intracellular concentration of the ion of interest. Unfortunately, in many experimental situations, this concentration is not accurately known. This is sometimes true even for the usual whole-cell variant of the patch clamp technique since it relies on diffusion of the pipette contents into the cell interior) 2 So, rather than compare the computed Nernst potential to a single measurement, the reversal potential is measured at several external concentrations of the test ion and (often) plotted as a function of the logarithm of the external ion concentration. Equation (3) predicts a linear relationship in such a plot with a 58/z mV/decade slope (at 20°), and such a finding demonstrates
9 R. A. Robinson and R. H. Stokes, "Electrolyte Solutions." Butterworth, London, 1965. io E. Neher, this volume [6]. i1 D. J. Adams, T. M. Dwyer, and B. Hille, J. Gen. Physiol. 75, 494 (1980). 12R. S. Eisenberg, this volume [10].
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ION CHANNEL SELECTIVITY AND BLOCK
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that the pore is permeant to the tested ion. Furthermore, with such data the internal concentration of the ion can be computed. Seldom is a perfectly linear relationship found when using physiological solutions (but see Lucero and Pappone 13for a recent example). Rather, the results of many such experiments are in agreement with Eq. (3) only at high concentrations of the test ion. At low concentrations the slope is often much less than predicted (see Sah et al.~4 for a recent example). Such a result suggests that the pore may not be perfectly selective for the tested ion. Indeed, few channels are permeant to only a single type of ion, and the expected dependency of pore zero-current potential (V~,) on ion concentration is, in general, both model dependent and more complicated. However, if two ions (X and Y) of the same valence (z) are considered, a relatively simple equation can be derived (see Hille ~for some of the details of these computations) from either of the two limiting theoretical formalisms: • Px[X]o + Pv[Y]o
V,~, = (RT/zF) m ~
+ PvIY]i
(4)
where Px and Pv are the permeabilities of ions X and Y. The reversal potential of Eq. (4) actually depends only on the relative permeabilities: [X]o + (Py/Px)[Y]o V,~, = (RT/zF) m ~ i + (PY/Px)[Yli •
(5)
At high external concentrations of ion X, Eq. (5) predicts a linear relationship between the measured reversal potential and the logarithm of [X]o. Deviations from linearity are expected at lower concentrations owing to the second term in the numerator of Eq. (5). The relative X to Y permeability can be obtained by fitting Eq. (5) to the data. Biionic Conditions. While Eq. (5) suggests experiments that can determine the relative ion permeability of a pore, a simpler method can be used if the solution on the cytoplasmic face of the membrane can be accurately controlled (e.g., perfused giant axons, excised patches, whole cell measurements with perfused pipettest2). This experimental control allows the use of a simplified form of Eq. (4) if ions of type X are the only permeant ones
13 M. T. Lucero and P. A. Pappone, J. Gen. Physiol. 94, 451 (1989). 14 p. Sah, A. J. Gibb, and P. W. Gage, J. Gen. Physiol. 92, 264 (1988).
96
ELECTROPHYSIOLOGICAL TECHNIQUES
[4]
in the external solution and Y ions are the only permeant species in the solution on the cytoplasmic side of the membrane: V~, = (RT]zF) In (Px [X]o/Pv [Y]i)
(6)
P x / P v ----([Y]i/[X]o) e x p [ ( z V ~ F ) / R T ]
(7)
or
When experimental conditions allow such a situation, the relative permeabilities are easily computed from the measured reversal potential and the known ion concentrations. Chandler and Meves ~5 used this technique to show that the squid axon Na + channel is permeable to several other cations including Li+, K +, Rb +, and Cs +. Internal Ions Not Known but Constant. Hille ~6 showed how relative permeability can be determined even if the internal medium cannot be controlled but is constant. In this technique, the channel reversal potential is measured twice: once with only ion X in the external solution (V~,x) and again with only ion Y in the external solution (V,~,,,v). Under these conditions, the relative permeability can be computed [using a form of Eq. (4)] from the difference between these two measurements: P x / P y = ([X]o/[Y]o) exp[zF(V,~,,~x -- V~,v )/RT]
(8)
Using this technique, Hille 1~showed that the selectivity of the Na + channel in myelinated nerve is similar to that of the squid axon Na + channel and extended the list of permeant ions to include several organic cations) 6 It is important to note that the Eqs. (4)-(8) are valid only for ions of the same valence and for a pore that obeys independence. ~s Independence means that the movement of each type of ion is independent of the presence of the other. Very few ion channel pores allow independent ion movement. Rather, ions transiently bind during passage to sites within the pore. Ions compete for these sites, and so the ion movements do not obey independence. Consequently, these equations are not, in general, expected to be valid but still have considerable utility. 15W. K. Chandler and H. Meves,J. Physiol. (London) 180, 788 (1965). ~6B. Hille,J. Gen. Physiol. 58, 599 (1971). ~7B. Hille, J. Gen. Physiol. 59, 647 (1972). is B. HiUe,in "Membranes--A Seriesof Advances, Volume 4: Lipid Bilayersand Biological Membranes: Dynamic Properties" (G. Eisenman, ed.), p. 255. Dekker, New York, 1975.
[4]
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Classification of Ion Pores Pores that do not allow independent ion flow can be classified by the maximum number of ions that can simultaneously occupy the pore. In one-ion pores, the presence of a single ion prevents entry (perhaps through electrostatic repulsion) of any other ion. Multiion pores allow simultaneous occupancy by more than one ion. One-Ion Pores. Hille is has shown that Eq. (7) applies to one-ion pores even if independence is not obeyed. The permeabilities in Eq. (7) may not be constant for such a pore but, rather, may be functions of membrane potential but not functions of ion concentration. However, in many situations the voltage dependence may be small or nonexistent. Consequently, Eq. (7) is very useful for determining relative selectivities even for one-ion pores. The nonindependent nature of such pores makes the current through such pores very sensitive functions of the concentrations of the ions. Consequently, ion selectivity cannot be judged by the relative current carried by different types of ions but can be determined from measurements of the V~. Ion currents are also affected by many pore-blocking ions (see below). If these ions are impermeant, however, they will not contribute to the measured reversal potential, and Eq. (7) may still be used. Multi-ion Pores. Not surprisingly, the permeation properties of multiion pores are more complex than those of one-ion pores. Nevertheless, Hille and Schwarz 19have shown that Eq. (7) may apply even to these more complicated situations but that the permeability ratio may be a function ion concentration. Consequently, a finding of concentration-dependent permeabilities in Eq. (7) indicates that the pore under study has multi-ion characteristics. It may be difficult to separate the effects of voltage and concentration since changing ion concentrations will necessarily shift the reversal potential to a new value. However, it is sometimes possible to separate these two effects: squid axon Na + channel selectivities are concentration but not (significantly) voltage dependent. 2°
Pore-Blocking Studies Valuable information on ion channels can be obtained from studies of current inhibition by impermeant ions (see Moczydlowski3). For example, Armstrong 21 used tetraethylammonium (TEA) ions and similar analogs to ~9 B. Hille and W. Schwartz, J. Gen. Physiol. 72, 409 (1978). 20 T. Begenisich and M. Cahalan, J. Physiol. (London) 407, 217 (1980). 2~ C. M. Armstrong, J. Gen. Physiol. 58, 414 (1971).
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probe the structure of the cytoplasmic portion of the squid axon, delayed rectifier K + channel. In one of the best studies of this type, Miller 22 used monovalent and bis-quaternary ammonium compounds to determine the spatial dependence of the electric potential in part of the pore of a K + channel from sarcoplasmic reticulum. One experiment in these types of studies is to determine the voltage dependence of current inhibition produced by a charged ion. As described by Woodhul123 (and see Moczydlowski3 for more details) the dissociation constant for the blocking ion, of valence z, binding to a site within the membrane electric field is given as Kd(Vm) -- Kd(0 ) exp(--tSzFV,./RT)
(9)
where Ka(O) is the zero-voltage dissociation constant and ~ is the location of the binding site as a fraction (measured from the inside) of the membrane voltage. Then, the fraction of current (channels) blocked, f ( Vm), will not only be a function of the concentration of blocking ions, [B], but also a function of voltage: f(V=) =
[B] [B] + Kd(V=)
(10)
A determination of the fraction of current blocked as a function of membrane potential will, through the application of Eqs. (9) and (10), yield a value for the electrical distance to the blocking site. There are, however, two potential problems with such an analysis: (1) a voltage dependence of block is neither a necessary nor sufficient condition to identify the block as within the pore; and (2) multiple ion occupancy of the pore makes it impossible to determine the fraction of the electric potential present at the blocking site. 19 A better test of the presence of the blocking site within the pore is to demonstrate that increases in permeant ion concentration on the side opposite to that with the blocking ion interacts with the blocking ion. Armstrong 2~ showed that increased external K + increased the rate of recovery from block of squid axon K + channels by internal TEA analogs. Similar results have been obtained for relief of internal Cs + block of squid axon K + channels by external K +24 and Begenisich and Danko 2s showed that increased intracellular Na + reduces block of squid axon Na + channels by external H +. In perhaps the most elegant study of this type, MacKinnon 22 C Miller, J. Gen. PhysioL 79, 869 (1982). 23 A. Woodhull, J. Gen. Physiol. 61,687 (1974). 24 W. J. Adelman, Jr., and R. J. French, J. Physiol. (London) 276, 13 (1978). 25 T. Begenisieh and M. Danko, J. Gen. Physiol. 82, 599 (1984).
[4]
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and Miller 26 studied block of single high-conductance, Ca2+-activated K + channels by the scorpion toxin charybdotoxin. External application of this toxin inhibits current through these channels. McKinnon and Miller found that internal application of the permeant ions Rb + and K + increased the toxin dissociation rate but that impermeant ions like Cs +, Na +, and Li+ were without effect. These authors have termed this phenomenon "transenhanced dissociation" and, rightly, argue that, while not "air-tight proof," such findings are simply and naturally explained by physical occlusion of the pore by the blocking ion. A good example of the difficulty of obtaining the fractional field location of a blocking site can be found in the work of Adelman and French. 24 A literal application of the Woodhull-type analysis reveals that the blocking site reached by an external Cs + is more than 100% across the membrane voltage drop. This apparently nonsensical result can be a consequence of a multi-ion pore, 27 and, indeed, the data of Adelman and French can be reproduced by a specific multi-ion pore model. 2s In such a pore, any permeant ions must vacate the blocking ion binding site before block can occur. Consequently, the voltage dependence of block will reflect not only the voltage-dependent binding of the blocking ion with this site but also the voltage-dependent evacuation of the pore by permeant ions.~9 In these modeling exercises, specific locations for permeant and blocking ion binding sites are specified, but, because of the large number of adjustable, offsetting parameters, these locations cannot be unambiguously determined. Consequently, any effort to determine the position of a blocking ion binding site must be preceded by experiments demonstrating the lack of multi-ion effects in the pore under investigation. A description of these types of experiments is beyond the scope of this chapter but can be found in Hille and Schwartz ~9,27and Begenisich)9,3° Conclusion As described here, ion channel pore permeation can be a complicated process, and a detailed analysis may be model dependent. However, a determination of pore selectivity is relatively straightforward, and suitable 26R. MacKinnonand C. Miller,J. Gen. PhysioL91,445 (1988). 27B. Hilleand W. Schwartz,Brain Res. Bull. 4, 159 (1979). 2sT. Begenisichand C. Smith, in "Current Topics in Membranesand Transport," Vol. 22. AcademicPress,New York, 1984. 29T. Begenisich in "Membranesand Transport" (A. N. Martonosi, ed.'), Vol. 2, p. 274. Plenum, New York, 1982. 3oT. Begenisich,Annu. Rev. Biophys. Chem. 16, 247 (1987).
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experimental techniques are readily available. Information on pore structure can be obtained from an analysis of block produced by ions, but such an analysis is complicated and model dependent unless it can be shown that the pore does not exhibit multi-ion properties. Acknowledgments This work was supported by a grant (NS 14138) from the U.S. Public Health Service.
[5] A c c e s s R e s i s t a n c e a n d S p a c e C l a m p P r o b l e m s Associated with Whole-Cell Patch Clamping
By CLAY M. ARMSTRONGand WILLIAMF. GILLY Introduction The exhilaration of forming a seal and recording from a living cell with the whole-cell patch clamp technique often makes one forget two important sources of error. Series resistance and space clamp artifacts can render worthless the handsomest results once they are subjected to critical review. Stated briefly, without proper compensation for series resistance and demonstration of a good space clamp, all measurements of membrane current are qualitative. In many cases, difficulties associated with these two problems cannot be completely eliminated, and separating justified from unjustified conclusions necessarily becomes a matter of judgment, experience, and cautiously working through every possibility for artifactual explanations of the phenomenon in question. This chapter discusses these impediments that have harried investigators since the first development of the voltage clamp. A careful analysis of series resistance errors was performed by Cole and Moore ~over thirty years ago, and series resistance and space clamp problems have been clearly recognized since that time. Examples exist, however, that clearly show the dangers of ignoring these problems and forging ahead. Investigations of ionic currents in cardiac muscle, for example, were handicapped for many years by lack of an adequate space clamp. 2 Consequently, the fundamental principles outlined here are not original, but we hope to present them in a new way. We write this chapter to prov.~de a helpful guide for separating fact from fiction in evaluating voltage-clamp data, and as a reminder not to K. S. Cole and J. W. Moore, J. Gen. Physiol. 44, 123 (1960). 2 E. A. Johnson and M. Lieberman, Ann. Rev. Physiol. 33, 479 (1971).
METHODS IN ENZYMOLOGY,VOL. 207
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