Device to Measure the VoltageCurrent Relations in Biological MembranesRichard Conley La Force Citation: Review of Scientific Instruments 38, 1225 (1967); doi: 10.1063/1.1721070 View online: http://dx.doi.org/10.1063/1.1721070 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/38/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Voltage–current characteristics of high-current glow discharges Appl. Phys. Lett. 78, 2646 (2001); 10.1063/1.1369612 AC loss analysis on high-temperature superconductors with finite thickness and arbitrary magnetic fielddependent voltage–current relation J. Appl. Phys. 84, 5652 (1998); 10.1063/1.368825 Voltagecurrent characteristics of a high Tc superconducting field effect device Appl. Phys. Lett. 61, 2353 (1992); 10.1063/1.108241 Voltagecurrent relationship for pulsed arc discharges J. Appl. Phys. 52, 5476 (1981); 10.1063/1.329528 Versatile Power Supply for Low Level VoltageCurrent Characteristic Measurements Rev. Sci. Instrum. 34, 1265 (1963); 10.1063/1.1718203

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THE REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 38, NUMBER 9 SEPTEMBER 1967

Device to Measure the Voltage-Current Relations in Biological Membranes

RICHARD CONLEY LA FORCE

Department of Biophysics, Michigan Cancer Foundation, Detroit, Michigan 48201

(Received 30 March 1967; and in final form, 8 May 1967)

A device has been designed and constructed, largely of commercially available oj'lerational amplifiers to measure the voltage-current relations in biological membranes due to the ion flux through them. The devic: operates in three modes: to clamp the voltage across the membrane to some predetermined value and record the current to cla~p the current through the membrane and record the trans-membrane voltage, and to record dV jdI, 'the resistance of the membrane measured in a time short compared to the ion redistribution time.

INTRODUCTION

THE transport of ions is found to occur through a large number of biological membranes even in the

absence of an externally applied electrochemical gradient,l This kind of transport is called active because it relies upon some mechanism coupled to a metabolic energy source for its existence. Some membranes, notably the squid giant axon, are excitable. This means that a sudden , externally produced change in the voltage drop normally developed by the resting membrane will cause a pulse of current through the membrane. This pulse is of large peak amplitude and short duration (a few milliamperes in amplitude and milliseconds in length in the case of the squid axon), Other membranes, the frog skin for example, show no excitability, but do show an active transport of ions which is influenced by the external electrochemical gradient in which the skin finds itself.

In making experimental observations of active trans­port, it is necessary to control the external electrochemical gradient across the membrane. In particular, it is neces­sary to be able to clamp the voltage across the membrane and record the time evolution of the current, to clamp the current through the membrane and record the voltage drop, and to also measure the value of dV /dI for the membrane.

Herein is described a device designed, constructed, and used to make these measurements. The device employs commercially available, inexpensive, solid state opera­tional amplifiers and is, consequently, free from critical construction problems.

Although the apparatus was not designed for use with excitable membranes, but rather for the study of mem­branes like frog skin, toad bladder, cornea, etc., it should be applicable to excitable membranes by employing ampli­fiers of greater frequency response.2

DESIGN CONSIDERATIONS

Consider first the problem of clamping the voltage across the membrane and recording the current. A sche-

1 E. J. Harris, Transport and Accumulation in Biological Systems (B

2utterworths Scientific Publications Ltd., London, 1960). K. S. Cole and J. W. Moore, J. Gen. Physiol. 44, 123 (1960).

matic representation of a typical experimental arrange ment is shown in Fig. 1. The voltage across the membrane is measured with the pair of voltage electrodes and the current, supplied through the current electrodes, adjusted by means of the variable resistor R until the voltage drop becomes some predetermined value.3 The schematic of the same arrangement, incorporating a feedback ampli­fier, is shown in Fig. 2. In Fig. 2, the membrane has been replaced by an approximately equivalent circuit, a battery and series resistance, and the electrodes by resistances representing their internal impedances at de. The battery with potentiometer across it supplies the standard refer­ence to which the voltage drop across the membrane is clamped. The gain required of the feedback amplifier for a precise clamping of the membrane voltage to the refer­ence can be derived by the following considerations. The voltage appearing between the differential inputs of the amplifier is

1225

(1)

R

~IG. 1. This fi~re is a semischematic representation of the dif­fuslOn cell used III transport experiments. The two outer calomel el~trodes, connected to a battery through the microammeter and resistor R, supply current to the membrane. The two inner calomel electrodes momtor the voltage across the membrane.

3 H. H. Ussing and K. Zerahm, Acta Physiol. Scand. 23,110 (1951).

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1226 RICHARD CONLEY LA FORCE

-R.

r-- -, Circuit : Rm :

representing : v.:: membrane I m I

I _ I I-I I I

R.

L ___ J R.

R.

v,

FIG. 2. Here is shown the basic control circuit used to clamp the transmembrane voltage to some predetermined value, Ve. The cur­rent supplied to the membrane by the output of the amplifier is monitored as a voltage drop across Ro.

assuming no current drawn by the input circuit of the amplifier. The output voltage is just - A Yin where A is the open loop gain of the amplifier. The current i is then given by

i=(-AVin-Vm)/(2Re+Rm+Ro). (2)

Substituting Eq. (2) into (1) and rearranging,

(2Re+Ro)V m+ Ve ( 2Re+ R m+Ro) (3)

In order that the voltage across the membrane be pre­cisely clamped to Ve, it is necessary that Yin be small. Since V m is typically 50 to 100 m V, a value of V in of about 0.1 mV should be considered a reasonable criterion of good damping. The resistance of the current electrodes Re is found to be about 3 kn or less for calomel electrodes coupled to the diffusion cell through 10% KCl-agar salt bridges.

The effective resistance of the membrane itself, Rm, depends on the area of membrane used, but for frog skin ()f about 2.5 em in diameter, it is roughly 200 n. The re­sistance Ro is used to translate the current through the electrode membrane ensemble into a voltage suitable for recording. The value of Ro is typically 10 kn or less. If it is supposed for concreteness that Vo is zero and V m is 60 mV Eq. (3) becomes

6X 10-2 X 16X 103

16.2X 103+ 2X 102A (4)

If A = 5Xl0\ Vin= 1 X 10-4 V, and the criterion for good clamping is satisfied. There are many solid state non­chopper stabilized amplifiers available now which possess this open loop gain.

There remains the common mode problem to consider. A change b..i of i in Fig. 2 produces a change of b..iRm in the differential signal and change of b..i(Re+Ro) in the

Voltage Electrodes

Voltage Electrodes

To recorder

To recorder

FIG. 3. This figure shows the bare essentials of the actual circuit used to (a) clamp the voltage across the membrane to any desired value and record the current and, (b) measure the open circuit volt­age of the membrane. The circuit in (b) has the advantage of a very high differential input impedance. Both circuits exhibit excellent common mode rejection.

common mode signal. Since the common mode rejection of differential amplifiers is almost always beLter than 1000 to 1 and often as good as 20000 to 1, the common mode error in the differential signal, for the poorer amplifiers, will be about

(5)

or expressed as a fraction of the differential signal,

Re+Ro (6) %error ---X 100.

1000XRm

For Re+ Ro= 13 kn and Rm= 200 n, this error is about 6%. The actual circuit, in fact, has less common mode error than this.

A schematic of the actual circuit is shown in Figs. 3(a) and 3(b). In Fig. 3(a) the amplifiers are shown connected as a voltage clamping circuit. In Fig. 3(b) they are con­nected as a voltage measuring circuit. The use of three amplifiers, rather than one, increases the input impedance,

A

1M

Current Electrodes

FIG. 4. This figure is a schematic of the standard Howland configu­ration for clamping the current through an arbitrary impedance. See Ref. 4 for a detailed de­scription.

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VOLTAGE-CURRENT RELATIONS 1227

FIG. 5. A schematic diagram of the final circuit as it evolved after a year of use. . 2.2k

53

IOk.1 f ,t. LfJ

an important consideration in the voltage measuring cir­cuit, and reduces the common mode error.

The analysis of the circuit in Fig. 3(a) follows in the same manner as that for the circuit of Fig. 2, with the exception that in Fig. 3 (a) the two input amplifiers to­gether with their feedback and coupling resistors increase the open loop gain of the circuit by a factor of 5/3 over the open loop gain of the third amplifier alone. This means that A appearing in Eqs. (2) and (3) will be, typically, 50 000 X 5/3, rather than 50000.

In choosing operational amplifiers for this circuit, some consideration must be given to the leakage currents at the input. The size of the leakage current per se is not so important, because it can be balanced out, but the change in leakage current with temperature merits some concern. F or the amplifiers used in the final device, the leakage current is 200 nA and the temperature dependence of the leakage current is 2 nA/Co. Since the largest feedback re­sistor is 50 kG, a drift in leakage current of 2 nA corre­sponds to a drift in output voltage of 100 p.V, a value con­sidered tolerable for the present application.

The circuit for damping the current through the mem­brane is shown in Fig. 4. It is standard and is described in Ref. 4. It serves two purposes; to damp the direct current through the membrane at some desired value and, through a constant amplitude ac voltage applied at input A, to also clamp the alternating current through the membrane.

4 For an excellent compendium including this circuit and others useful in biological application, see: Application Manual for Com­puting Amplifiers (George A. Philbrick Researchers, Inc.), Nimrod Press Inc., Boston, Mass., 1966.

)

S"

To recorder

+15-fV R ~-15V • R,

25k o!""" 25k 1M'

R .. 1M" 10k

6k' 4.7k

6Bn

from a.c, Sine Wave generator

v

1.0

,-",IM;"""""--,f91 To recorder

o.IT

v

V

By damping the alternating current through the mem­brane and measuring the value of the ac component of the voltage drop across the membrane, a value can be ob­tained for the dynamic resistance dV /dI of the mem­brane. The dynamic resistance is the value of resistance obtained by varying the current and measuring the re­sulting voltage change in a time short compared to the time for ion redistribution.

The Final Circuit

A schematic diagram is shown in Fig. 5 of the final circuit arrived at after about a year of use. The operational amplifiers are all manufactured by the Zeltex Corporation and are either the model 115B, 116B, or 115M7. The 115B and 116B are essentially identical; only the physical packaging differs between them. The model 115M7 operates on a ±24 V power supply rather than ±15 V and, consequently, has a larger dynamic range. The switch Sl allows the device to be operated in three modes: to clamp the voltage and record the current; to record the open cir­cuit voltage developed by the membrane; and to clamp the current, either dc, ac, or both, and record the voltage drop. There is also provision to further amplify the ac component of the voltage, phase detect it, and display the resulting average amplitude on a strip chart recorder. The transistor 2N1309 is used as the phase detector.

The closed loop gain of the amplifier is ten in the voltmeter mode. When the voltage across the membrane is damped at some value, between ±200 mY, predeter-

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1228 RICHARD CONLEY LA FORCE

300

280 700

260

240 600

220

200 500

160 400

140

120 300

100

80 200

60

10 9 8

7

6

5

"

2

1 .9 .8

.7

.6

. 5

FIG. 6. A display of short circuited current, resistance, and devel­oped power for a bio­logical membrane (ab­dominal skin of frog, Rana pipiens). The bathing solution, sodium Ringer, was identical on each side of the skin. At 11 on the time axis, dinitrophenol, sufficient to make its concentra­tion 0.2mM, was added to each bathing solution and removed at 30.5 by flushing with fresh Ringer solution .

40 1'00 l---------__ ~ -----..--"-----~,...... ........ .4

20 I R

,3

P 0~--~--r_-r~--~~~~_r--r_,__.--.__,--r__r~~,_~--~_r_4

o 2 4 6 8 10 12 14 16 18 20 22 H 26 28 30 32 3 4 3 6 3 8 40

J k 400 sec.

mined by tbe Helipot R 1, the switch S3 allows a selection of three current ranges, Soo !LA, 200 !LA, or 100 !LA, if a one volt full scale recorder is used. Switch S2 selects be­tween the actual membrane and a calibration circuit. Resistors R6 and R7 provide means of calibrating the ten turn potentiometer R 4• This potentiometer selects the value at which the direct current through the membrane is to be clamped. The range provided is ±200 !LA. Potentiom­eter R. selects the value to which the alternating current through the membrane is to be clamped. The variable re­sistor R2 is used to zero the operational amplifiers.

To illustrate somewhat the capabilities of the instru­ment, Fig. 6 is a multiple plot showing short circuited current, dynamic resistance, and power developed by a frog skin over about a six-hour period during which an antimetabolite, dinitrophenol, was added to and later removed from the bathing solution.

Although the circuit was designed for the study of biological membranes showing active transport, it is evi­dent that it is applicable to the study of voltage-current relations in any membrane system in which there is ion transport.

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