Sampling membrane potential, membrane resistance and electrode resistance with a glass electrode impaled into a single cell

Journal of Neuroscience Methods, 2 (1980) 191--202 © Elsevier/North-Holland Biomedical Press

191

SAMPLING MEMBRANE POTENTIAL, MEMBRANE RESISTANCE AND ELECTRODE RESISTANCE WITH A GLASS ELECTRODE IMPALED INTO A SINGLE CELL

MICHAEL SCHIEBE and ULRICH JAEGER Department of Physiologie, Universitaet Ulm, D 7900 Ulm/Donau (G.F.R.) (Received May 18th, 1979) (First revised version received October 25th, 1979) (Second revised version received December 7th, 1979) (Accepted December 9th, 1979)

A method is demonstrated to measure membrane resistances and membrane potentials of single cells during impalement by a single glass microelectrode. The intention was to develop a procedure which would provide data almost continuously. Therefore, a frequency-dependent voltage divider network has been chosen to represent the basic electrical properties of the electrode and cell membrane, and used to explore its voltage response to a current stimulus, consisting of two rectangular pulses of different widths. It can be shown that the resolution of the method can be improved by inverting this stimulus so that each polarization becomes a relaxation and vice versa. In order to generate, analyze and display this signal continuously, a device has been designed which has been called 'Electrophysiological Monitor, (ELM2)'. ElM2 provides a current stimulus as input into a standard bridge network and can analyze the summed response of the electrode and cell by a set of sample-hold amplifiers. It then decodes and displays the data continuously, as membrane potential (Em), input resistance of the cell (Rinp) and the electrode resistance (Re) respectively. From Rinp the membrane resistance (Rm) can be deduced. The validity of the method has been examined by measuring these parameters in frog muscle cells. Technical design considerations, the accuracy and possible pitfalls with the suggested procedure are discussed.

DEVELOPMENT OF THE METHOD It is very o f t e n difficult t o m e a s u r e even t h e passive electrical p r o p e r t i e s o f several t y p e s o f cells (e.g. r e c e p t o r cells, s m o o t h muscle cells or o t h e r small o r highly t u r g e s c e n t cells) b y i m p a l e m e n t w i t h several individual glass m i c r o e l e c t r o d e s . Single e l e c t r o d e t e c h n i q u e s , h o w e v e r , have o f t e n been f o u n d to be unreliable ( S c h a n n e et al., 1 9 6 6 ) in t h a t t h e p a r a m e t e r u n d e r investigation ( m e m b r a n e p o t e n t i a l a n d / o r resistance) is easily m a s k e d b y u n p r e d i c t a b l e instabilities o f t h e e l e c t r o d e . Similar a r g u m e n t s h o l d f o r d o u b l e barreled electrodes, d u e t o the c o u p l i n g resistance a n d c a p a c i t a n c e b e t w e e n t h e respective barrels (for review see S c h a n n e a n d Ruiz P.-Ceretti, 1 9 7 8 ) w h i c h are rarely negligible. T h e m e m b r a n e resistance R m , t h e analysis o f

192

which shall be emphasized here, is certainly an interesting electrical cell constant by itself. But it is also useful in a more general sense, in accounting for the intactness of the membrane upon impalement, which otherwise is a source of major errors. Also, control over the electrode during the experiment would be useful and could be achieved by recording the electrode resistance (Re) before and during the impalement. In order to attack this and related problems a number of very useful suggestions have already been made by Brennecke and Lindemann (1971), Schanne and de Ceretti (1971), Cheval (1973) and Stanton (1973). The c o m m o n idea in these papers is, that upon impalement of a cell by an electrode, a frequency 50, which yields sufficiently different amplitude/frequency characteristics to allow a reasonable separation of each impedance in the network. This can normally be achieved by capacitative compensation through the feedback loop of the preamplifier, which is assumed to be part of a standard bridge amplifier. The choice of a suitable test signal as current stimulus requires some consideration and depends on whether the passive electrical properties of a membrane or of the cell as a whole are to be explored. In the latter case, a

I- M?Cell Fig. I. Equivalent network, consisting of the m i n i m u m n u m b e r of elements to describe an isodiametric cell, impaled by a glass microelectrode. S, an ideal current source; a, an ideal amplifier. M E , the microelectrode, has a resistance (Re) and capacitance Ce. R m is the m e m b r a n e resistance and C m the m e m b r a n e capacitance of the cell.

193 signal with a broad and fiat spectrum (e.g. a Dirac-pulse, or random noise) can be applied. A detailed analysis of the response could be used to draw a best-fit model to the recorded data. A transfer function would then be the mathematical equivalent to the wall and other electrically relevant constructs of a cell. Alternatively, a set of sinusoidal signals could be applied (Valdiosera et al., 1974). On the other hand, Rinp and Re of the cell model in Fig. 1 can be explored more conveniently b y rectangular current stimuli. For reasons which will emerge below, we have used an arrangement of t w o different rectangular pulses of different widths, the narrower of which should be just long enough to cause a voltage drop over the electrode impedance, but still t o o short to be short-circuited by the membrane reactance. In contrast, the only requirement for the wider pulse is to be long enough to cause a voltage drop over both impedances. It should be mentioned in passing that the respective capacitances can then be obtained analytically by the usual procedures. Two such combinations of pulses have already been suggested: (1) a train of narrow pulses, the envelope of which is the wide pulse (Brennecke and Lindemann, 1971); and (2) a combination of t w o consecutive rectangular pulses of different widths (Schiebe and Pauschinger, 1975). Explanatory examples of both procedures are considered below and are shown in Fig. 2D--F and A--C respectively. The input currents to the network in Fig. 1 are shown in Fig. 2A,D and the voltage drops are shown in B and E. The narrow pulse is repeated at a higher resolution as lower trace in Fig. 2A--F. It is used to balance the bridge, for visual inspection of the remaining Rinp at a higher amplification (cf. Fig. 2C and F). The advantage of a pulse-train is that it yields visible and continuous information of the performance of the electrode and shows the membrane response to the average current stimulus during the period of the pulse envelope. An assessment of the possible resolution of this method has to take into account that the magnitude of the voltage drop over the membrane depends on the pulse/period relationship of the elements of this train. In the example this relationship is 1 : 2 and therefore the voltage drop over Rinp can only be 1/2 in amplitude of the voltage drop produced by an equivalent single pulse. Furthermore, Eisenberg and Johnson (1970) have analyzed the dispersion of electric fields in 3 dimensions to a current step near a point source, like the tip of a glass microelectrode. He found that close to the tip, a transient convergence of current may cause a steep gradient in potential, which could drive the membrane near the electrode into the non-linear region o f the current/voltage relationship. Subthreshold action potentials could then be triggered or even local breakdown of the membrane dielectric might occur. Therefore, it m a y be desirable to reduce the number of surges of current and the current amplitude to one that would just allow a tolerable resolution for the assessment of Rinp. For this reason we favor the double pulse method, shown in Fig. 2A--C. Since it was our goal to record Rinp and Re b y sampling the appropriate

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parts of the respective voltage displacements directly, no averaging procedure could be applied and the suppression of hum, from which the preparation cannot normally be shielded by most Faraday cages {except where mumetal has been used), was very important. Due to the frequency content of the wider pulse, analog filtering could n o t be used. The analytical solution to this problem will be discussed separately. Another problem arose from the rectifying properties of high-impedance glass microelectrodes which have been explored b y Rubio and Zubieta (1961), who suggested that this effect is due to hydrostatic pressure differences and transient dilution of the solution within the tip of the electrode is produced when the direction of current is positive. When the direction of current is reversed, the response is largely independent of the outside solution since no dilution can occur.

195

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198 Fig. 3 illustrates these findings, where A shows the voltage response to a depolarizing current step, and B, the same pulse shifted by addition of a hyperpolarizing constant current. The depolarization in A is then turned into a relaxation from a hyperpolarization in B. Note, that if the sampling instant would be close to the leading surge (equivalent to SH1 in Fig. 4A), the transient overshoot in A would cause a considerable overestimation of the amplitude, hence an overestimation of Re, which would reduce the rather minor Rinp by the same amount. Using this procedure, the resolution of this method can be improved drastically thus eliminating the rectifying properties of the electrode. Although the addition of a constant current is not necessary for current flow from the solution (or cell-plasma) into the electrode (cf. b o t t o m line (h) of Fig. 4A), where similar transient overshoots do not occur, we still have used the same procedure in order that both pulses can be combined when studying the rectifying properties of a membrane. In this context it should be mentioned that the direction of current flow for the membrane during the relaxation period is n o t reversed because the current over Rinp originates mainly from the membrane capacitance. Therefore, the notation 'h' for hyperpolarization, as shown in Fig. 4A still applies, if it is used for the cell membrane. APPLICABILITY OF THE METHOD AND RESULTS The application of subthreshold stimuli to small single cells and the analysis and recording of the cell-response with the Electrophysiological Monitor can be applied as follows. (1) To trace the membrane resistance and membrane potential of single cells in response to a changing environment, at a sampling rate of 5/sec. (2) To monitor electrode characteristics before, during and after the impalement, by recording Re and by observation of its voltage response to the 'short' pulse, which can be viewed separately. (3) To trace the rectifier properties of membranes, by application of a bipolar pulse, at a (reduced) sampling rate of 3/sec. (4) To establish current/voltage characteristics of membranes by feeding the respective o u t p u t signals of ElM2 into the X- and Y-amplifier of an oscilloscope (not shown). (5) To study the dynamical behavior of membranes by recording changes of Rinp as a function of time and/or by comparison to Em. For example, in Fig. 5 the simultaneous response of the membrane potential and the input resistance of the membrane of the frog sartorius muscle is evoked by an increase in the external potassium concentration in the bathing solution. This example shows the conventional recording made with a multipen recorder, as well as the print-out of the absolute data in alphanumeric form. The drop in Rinp leads the drop in Em, although part of the phase-lag of the membrane potential must be attributed to the mechanical arrange-

199

m e n t of the recorder-pens (visible at 7,8 in Fig. 5). Re remains constant after impalement. Rm for a cylindrical cell with a known cytoplasmatic resistivity Ri, can be computed for a given input resistance following the formula given by Jenerick (1953): R m - Rinp27r2d [~'~ c m 2]

(1)

(Rinp [~'~], Ri [~-~ c m ] , d [ c m ] diameter of the fiber).

The term 'Re', however, should be interpreted further in the light of the findings of Engels et al. (1972). If the electrode is outside the cell, then Re refers to the electrode alone and may be called 'electrode resistance'. But after impalement the voltage drop over Re does not only change due to a different resistivity of the cytoplasm, but also in response to a spatial variation of potential near the electrode tip. This interpretatory problem must be kept in mind although it does not affect the measurement of the membrane resistance as it is suggested here. DESIGN CONSIDERATIONS, ACCURACY, SHORTCOMINGS

The design of ElM2 relies on the existence of the network shown in Fig. 1. This has been shown to be a legitimate simplification, at least for the purpose intended (Peskoff and Eisenberg, 1973). Certain practical restrictions must however be observed: the m a x i m u m current density applicable to the tip of a glass microelectrode that does not drive it outside the linear part of its current/voltage relationship, must be found empirically. The same applies to the preparation, i.e. the cell, itself. It seems in our own experiments that the magnitude of the current stimulus must not exceed 10 nA (Re < 20 M~2 in Ringer solution), which has therefore been chosen as the upper limit for ELM2. In order to control the capacitance compensation of the bridge amplifier, an oscilloscope with dual time-base is necessary (e.g. Tektronix 5100, with 5B20N) by displaying both parts of the double pulse separately (cf. Fig. 2A--C). After impalement of the cell, it is important to achieve a proper neutralization of stray capacitances, which can be accomplished by a suitable compensatory circuit in the feedback loop of the preamplifier stage of a bridge. In order to minimize stray capacitances, a preamplifier should directly be connected to the recording electrode. The resolution of the m e t h o d can be degraded by 3 major sources of error: (1) noise, introduced from outside t h e p r e p a r a t i o n , the preparation itself and from the circuitry; (2) operational errors (insufficient neutralization of stray capacitance, inappropriate choice of the sampling constants); and (3) errors, introduced by experimentally-provoked changes in Rinp as in Fig. 5 or, more generally, of Tm/re.

200

The major remaining source of noise in our system is produced by a chopper amplifier, which is used for the computation of URinp. This can be seen in Fig. 5 and amounts to about 5% of the signal, before an external filter has been switched on. But if it is switched on, the speed of the response is reduced. The filter has therefore been used only after a successful impalement. The system design has been chosen to help minimize operational errors by displaying all important data digitally and by including a voltage-controlled oscillator, which can be linked to each of the observable parameters to provide the appropriate audible signals. An inherent error, however, caused by changing values of K (e.g. when Rinp behaves as in Fig. 5) cannot be avoided and hence will be examined below in some detail. Fig. 6 has been drawn to illuminate the situation with a practical example. In order to compute the relative error for changes in Rinp as a function of time, the voltage response of the circuit in Fig. 1 to a step input current of magnitude 1 is given as: u(t) = I[Re(1 - - e -t/re)

+ Pt, i n p ( 1

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(2)

From eqn. 2 the error at a deliberately chosen sampling instant (ti) during the measurement of the voltage drop over Re (at SH1), and Rinp (at SH2) shall be called eUl(ti) and eU2(ti). Throughout the experiment in Fig. 5, Cm/Ce, the respective capacitances of the electrode and cell, shall be assumed to be constant. An error as a fraction of Rinp can be computed, depending on b = Re/Rinp a n d K = r m / r e (whereby in Table 1 K = 1/b(Cm/ Ce): eUl(ti) = ~1 I1 - - (be -ti + e _ t i / k )]

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eU:(ti) = b(e -ti + e - t i / K )

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and for the worst case in the assessment of URinp, when t l at SH1 and t2 at TABLE 1 ASSESSMENT OF ACCURACY OF SUGGESTED PROCEDURE F r o m the data of the e x p e r i m e n t in Fig. 5 s o m e typical values have been chosen for the assessment of the accuracy of the suggested procedure, as it is shown in Fig. 6. Rinpj [ k ~ ] sample drawn f r o m Fig. 5; Rej [ M ~ ] same, but of Re; bj [ -- ] c o m p u t e d value, R e / R i n p ; Kj [ - - ] Tm/Te for a c o n s t a n t C m / C e = 5000. j

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If in Fig. 6 Re is sampled at t l , close to 5.3 re, which can be achieved quite conveniently by adjusting SH1 under inspection of the narrow pulse, then the error in the evaluation of Re during changes in Rinp is small. But for decreasing K this becomes more difficult and SH1 becomes increasingly sensitive to maladjustments of the parameters. The choice of SH2 is less critical, since the error diminishes with increasing ti. It must therefore be said that the proper choice of sampling constants can only be achieved for large values of K = rm/re. ACKNOWLEDGEMENTS

We are indebted to Profs. P. Pauschinger and G. Gebert for their continuous practical help and advice, to K. Schefczik for many valuable hints, and particularly to G.W. Klose and E. Zwerger for their persevering technical assistance.

202 The financial help provided by the Forschungsfoerderungskommission der U n i v e r s i t a e t U l m is g r e a t l y a p p r e c i a t e d . REFERENCES Brennecke, R. and Lindemann, B., (1971) A chopped-current clamp for current injection and recording of membrane polarization with single electrodes of changing resistance, T.I.T., Life Sci., 1: 53--58. Cheval, J. (1973) Enregistrements simultan~s du potentiel et du courant transmembranaires a l'aide d'une seule microelectrode intracellulaire, C.R. Acad. Sci. (Paris), (Serie D) 277: 2521--2524. Eisenberg, R.S. and Johnson, E.A. (1970) Three-dimensional electrical field problems in physiology, Prog. Biophys. mol. Biol., 20: 1--65. Engel, E., Barcilon, V. and Eisenberg, R.S. (1972) Interpretation of current--voltage relations recorded in a spherical cell with a single microelectrode, Biophys. J., 12: 384-403. Jenerick, H.P. (1953) Muscle membrane potential, resistance, and external potassium chloride, J. cell and comp. Physiol., 42: 427--448. Peskoff, A. and Eisenberg, R.8. (1973) Interpretation of some microelectrode measurements of electrical properties of cells, Ann. Rev. Biophys. Bioengng, 2: 65--79. Rubio, R. and Zubieta, G. (1961) The variation of the electric resistance of microelectrodes during the flow of current, Acta physiol, lat. amer., 11: 91--94. Schanne, O.F. and de Ceretti, E. (1971) Measurement of input impedance and cytoplasmic resistivity with a single microelectrode, Canad. J. physiol. Pharmacol., 49: 713-716. Schanne, O., Kawata, H., Schaefer, B. and Lavall6e, M. (1966) A study on the electrical resistance of the frog sartorius muscle, J. gen. Physiol., 49: 897--912. Schanne, O.F. and Ruiz P.-Ceretti, E. (1978) Impedance measurements in biological cells, Wiley, New York. Schiebe, M. and Pauschinger, P. (1975) Continuous measurement of cell-membrane conductivity with single glass-microelectrodes, Pfliigers Arch. ges. Physiol., 359: R149. Stanton, M.G. (1973) Cell membrane resistance and capacity measured using lone singleban'elled micro-electrodes, J. Physiol. (Lond.), 234: 86--87P. Valdiosera, R., Clausen, C. and Eisenberg, R.S. (1974) Measurement of the impedance of frog skeletal muscle fibers, Biophys. J., 14: 295--315.