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Dependence of Cellular Potential on Ionic Concentrations. Data Supporting a Modification of the Constant Field Equation

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Dependence of Cellular Potential on Ionic Concentrations. Data Supporting a Modification of the Constant Field Equation DEPENDENCE OF CELLULAR POTENTIAL ON IONIC CONCENTRATIONS Data Supporting a Modification of the Constant Field Equation DONALD C. CHANG Department ofPhysiology, Baylor College ofMedicine, Houston, Texas 77030, and Department of Physics, Rice University, Houston, Texas 77001 ABSTRACT The resting potential in the squid axon has been measured at various concentrations of Cl, K, Na, and Ca ions. The results of these measurements are compared with the Goldman-Hodgkin-Katz (GHK) equation and a modified constant field equation. This modified equation was derived by including currents carried by divalent ions and the effects of the unstirred layer and the periaxonal space. It is shown that, although the GHK equation can fit the Vvs. [KJO data well, it has difficulty explaining the observed dependence of Von [Na]0 when the axon is bathed in K-free artificial sea water. The use of the modified constant field equation removes this difficulty. INTRODUCTION include the effects of currents carried by divalent ions and The Goldman-Hodgkin-Katz (GHK) equation is one of the effects of the unstirred layer and the periaxonal space. the most widely used equations in electrobiology. This This modified constant field equation seems to fit the equation not only provides a theoretical basis to explain the experimental data satisfactorily. relationship between the membrane potential and the ionic concentration gradients, but it also allows one to calculate METHODS AND MATERIALS the permeability ratios of the ions, using measurements of The biological sample used in this study is the giant axon of the squid potential. It has long been recognized, however, that the loligopealei, supplied by the Marine Biological Laboratory, Woods Hole, GHK equation is an approximation that involves many MA, where the experiments were conducted. Use of the squid axon to study the resting potential provides several advantages: (a) the structure idealized assumptions (Hodgkin and Katz, 1949; Tasaki, of the giant axon is simple, so that complications due to transport among 1968; Schwartz, 1971). Some ofthese assumptions, such as multiple compartments are eliminated; (b) the giant axon is large, so that constant field and ion independence, may be hard tojustify an axial electrode can be inserted and damage to the membrane can be in a biological system. Furthermore, the derivation of the avoided; (c) the giant axon can be perfused internally, so that both the GHK equation does not consider currents carried by internal and external ionic concentrations can be changed; and (d) because of the large cell size and the low impedance of the axial electrode, divalent ions, and the effect ofthe "unstirred layer" outside the resting potential of the squid axon usually is very stable and varies the membrane has been ignored. Thus, it is important to little (at most a few millivolts) from axon to axon. see how well the GHK equation can be applied to different The design of the experimental apparatus was similar to those used in biological systems. the laboratories of Narahashi (Wu and Narahashi, 1973) and Tasaki In this paper, I report results of measurements of the (Tasaki et al., 1965). The axon was perfused through a single glass cannula; the technique is a modification of that of Tasaki (Tasaki et al., resting potential in squid axons as a function of the 1965). The resting potential was measured by using an axial internal external concentrations of Cl, Na, K, and Ca ions, and of electrode and an external reference electrode. These electrodes are glass the internal concentration of Cl ions. I show that the GHK capillaries filled with 3 M KCI solution that was in contact with an equation can fit the observed data only partially. Some of Ag-AgCI electrode. Each of these electrodes was connected to a high the ionic dependence of the resting potential is difficult to input impedance operational amplifier (Analog Devices, Inc., Norwood, MA, model AD506), the differential output of which was recorded by explain. digital electronics. One wonders whether this observed difficulty of the The junction potentials of the electrode system are corrected by using GHK equation is due mainly to the deficiency of the an experimental arrangement similar to those used by Baker et al. (1964). constant field approach, or to the failure of other simplify- That is, before it was inserted into an axon, the internal electrode was first ing assumptions involved in the derivation of the GHK placed into a reservoir of 0.6 M KCI solution that was connected to a pool of artificial sea water by a salt bridge (made with artificial sea water equation. In this study, the latter case has been investi- [ASW] in 3% agarose). The reference electrode was in contact with the gated. Without abandoning the constant field assumption, pool of ASW through another salt bridge. The differential output of the I have suggested a modification of the GHK equation to two electrodes is defined as Vff,, which supposedly contains all junctional BIOPHYS. J. e Biophysical Society * 0008-3495/83/08/149/08 $1.00 149 Volume 43 August 1983 149-156 TABLE I COMPOSITION OF ARTIFICIAL SEA WATER (ASW) ASW KCI NaCl CaC12 MgC12 HEPESbuffer NaOH chlorideCholine CsOH mM mM mM mM mM mM mM mM Normal 10 420 20 50 5 5 0 0 K-free 0 420 20 50 5 5 0 0 K and Na-free 0 0 20 50 5 0 430 3 Kand Mg-free 0 470 50 0 5 4 0 0 High Ca 0 50 250 0 5 5 20 0 Variable same as normal except part of NaCl is replaced by KCI Variable same as K-free except part of NaCl is replaced by choline chloride [Cl]a same as K and Mg-free except part of NaCl is replaced by Na propionate Variable same as high Ca except part of CaC12 is replaced by choline chloride potentials. When the internal electrode was inserted into the axon, the where R, T, and F are the universal gas constant, tempera- newly recorded differential potential was denoted V. The experimental ture (in Kelvin), and Faraday's constant, respectively; PK, value of the resting potential was taken as the difference between V and PNa, and are the relative membrane permeabilities of K, V,ff*. As a standard procedure, V0ff,, was determined again at the end of Pcl each experiment. It usually stayed within 2 mV of the initial value. Na, and Cl; (K), (Na), and (Cl) are the activities of K, Na, Because one ofthe most important factors that affect the measurement and Cl; subscript o denotes the outside of the cell, and ofa resting potential is leakage, all axons used in this study were dissected subscript i denotes the inside of the cell. In this paper, (S) carefully so that leakage was at a minimum. At the beginning of each means activity of ion S, while [SI means concentration of experiment, the resting potential had to be at least -60 mV and the = In most a magnitude of the action potential not less than 100 mV. Otherwise, the ion S. (S) ys[S]. biological studies, however, axon would be rejected. simplified form of the GHK equation often is used, i.e., The composition of the ASW is given in Table I. The control internal perfusion solution (IPS) was composed of 360 mM KF, 40 mM K- V= RT/Fln [(K), + b(Na)ol (2) phosphate, 50 mM NaF, and 200 mM sucrose. This solution is similar to (Ki+ b(Na)iJ' that used by Tasaki et al. (1965). The ASW and IPS were buffered and the pH adjusted to 7.9 and 7.3, respectively. The activity coefficients of K where b = PNa/PK. This "simplified GHK equation," and Na in the various solutions were estimated from data compiled by proposed by Hodgkin (1958), has the advantage of con- Robinson and Stokes (1959). 7K and YN. in ASW were taken as the taining only one unknown parameter, b. If the ionic average activity coefficients (-y) of KCI and NaCl, respectively, in are the ratio can be deter- solutions of the same ionic strength as the ASW, while 7K and 7N. in IPS activities known, permeability were taken as the 'y, of KF and NaF, respectively. The values I used for mined simply by measuring V. the activity coefficients were YK = 0.632 and yN. = 0.670 for the ASW; 7K - 0.676 and yN. = 0.641 for the internal solution. For the purpose of Dependence of the Cellular Potential on calculation, the activities ofNa and K inside an intact axon were assumed Concentrations of Cl to be the same as in the normal IPS. Except for those specified, the experiments were done at a temperature of 50C. To determine whether the simplified form of the GHK When the axon was'perfused with a solution that contained a different equation (Eq. 2) can be used safely, I have examined the concentration of electrolyte, the resting potential of the axon changed quickly and often reached a new, stable value within minutes. The time effects of [Cl]0 and [Cl]o on the cellular potential. It is course of the change of potential usually simulated an exponential curve. stated often in the literature that the Cl terms in Eq. 1 can The asymptote of the potential curve was chosen to be the final value of be dropped, because Cl ion distributes passively across the the resting potential. I often recorded two asymptotes in each measure- cell membrane, and hence the net Cl current is zero. This ment, one determined by a change from a high concentration to a low argument cannot be applied to the experiments with squid concentration, and another by a change from a low concentration to a high concentration.
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