Voltage-dependent potassium channels in the amphibian lens membranes: Evidence from radiotracer and electrical conductance measurements

Exp. Eye Res. (1980) 31,637-650 Voltage-Dependent Potassium Channels in the Amphibian Lens Membranes: Evidence from Radiotracer and Electrical Conductance Measurements L. PATMORE* AND G. DUNCAN

School of Biological Sciences, University of East Anglia, Norwich NR4 7TJ, England (Received 14 February 1980, London) The electrical potential and conductance of the perfused frog lens preparation was measured using a two internal mieroelectrode technique. When the lens potential was depolarized by perfusing with high potassium concentration ringer the increase in conductance could not be fitted by conductance equations where PK was assumed constant. It is suggested therefore that this increase is due to a voltage-dependent component of the conductance, namely voltage-dependent potassium channels. Direct evidence for the existence of a voltage-dependent conductance is presented in the form of conductance-voltage curves which show rectification similar to squid axon. Conductance-voltage curves mapped out in high potassium Ringe{show a blocking effect of potassium on the lens Conductance. The blocking effect was also observed in lenses where the membrane voltage Was clamped to a steady value during exposure to high potassium solutions. The increase in conductance at depolarized lens potentials is demonstrated by changes in potassium permeability as measured from the ettinx of 42K. Both the electrical conductance and 42K efttux are shown to be sensitive to potassium channel blocking agents, namely, tetraethylammoninm (TEA), caesium and rubidium ions. The 4~K efflux rate constant and lens potential were monitored simultaneously whilst depolarizing and hyperpolarizing currents were applied and the changes in 42K efflux dearly demonstrated the voltage-dependence of the potassium permeability. Key words: lens; conductance; potential; potassium; membrane.

1. Introduction

The lens is composed mainly of long, closely-packed fibre cells and Duncan (1969b) was the frrst to point out that the internal resistance was surprisingly low for such a dense tissue. Eisenberg and Rue (1976) confirmed these findings, but also maintained that the conductance associated with the lens membranes was strictly ohmic in behaviour. Recently, however, Patmore and Duncan (1979) have shown that the conductance changes produced i~ the lens by depolarizing with high external pot~ssiam concentrations were very much larger than could be explained in terms of linear electrical theory and they suggested that the lens membranes had n0n-ohmic, voltagesensitive channels. They also suggested, on the basis of preliminary tetraethylammonium (TEA) blocking experiments (Duncan and Patmore, 1979) that these channels had some properties in common with the voltage-sensitive potassium channels found ill excitable tissues (Hille, 1967, 1970). This study not only amplifies and confirms the earlier findings, but also examines the characteristics of the channels, firstly by determining the conductance-voltage characteristics of the lens directly and secondly by investigating the effects of a range of potassium channel blocking agents both in electrical and 42K flux measurements. * Presentaddress:SyntexResearchCentre,IIeriot-WattUniversity,l~iccarton,EdinburghEItI4 4AS. 0014-4835/80]120637+ 14 $01.00/0 O 1980AcademicPress Inc. (London)Limited 637

638

L. PATMO~E AND G. DUNCAN

2. Materials and Methods

Preparation Lenses from the Northern leopard frog Rana pipiens were used in these experiments. Healthy specimens 13-20 cm in length were pithed and the whole eye removed from the head. The lens was dissected free by a posterior approach. The globe was bisected revealing the posterior surface of the lens which was lifted free with a glass loop after cutting away the suspensory ligaments. Lenses that appeared cloudy or damaged in any way were discarded.

Solutions The lens was transferred to a 1 cm s perfusion chamber with a flow rate of 2 cm ~ rain -1. The composition of the perfusate was as follows: NaC1, 105 m~I; KC1, 2.5raM; CaC12, 2 raM; MgS04, 1.2 m~; NaHCOa, 6.5 m~; Hepes, 5 raM; D-glucose, 5 mM adjusted to pH 7.4 with NaOH or HC1 at 18~ In experiments where high potassium solutions were used potassium was substituted for an equivalent amount of sodium. The blocking agents TEA (BDH, Poole), caesium and rubidium were added in crystalline form to the solutions immediately prior to use. The pH of all solutions was adiusted as above.

Electrical recordings A two-internal microelectrode technique was used to measure lens conductance (Duncan, 1969b; Delamere and Duncan, 1977). Microelectrodes were pulled from thin-walled, filament glass tubing (Clarke Electromedical, Pangbourne, U.K.) and filled with 3 M-KC1. The tip-resistance was between 1-5 lvis The lens potential was measured between an internal microclectrode and a Ringer-agar reference electrode on which the lens was seated. The lens was positioned anterior surface down to allow easier microelectrode penetration through the thinner posterior capsule. The two electrodes were connected to a high impedance amplifier (W P Instruments, M750) and the output displayed on a dual channel storage oscilloscope (Tetronix, 5013). The oscilloscope output was connected to a four-channel F3I tape recorder (Tanberg Instrumentation, 100) and a chart recorder (Bryanns Southern, 18000). Lens conductance, expressed in Siemens (S), was measured by passing current from a second internal microelectrode to a virtual earth electrode in the bath and monitoring the voltage response of the previous electrode pair. The vixtual earth electrode consisted of a silver/silver chloride wire connected to earth via a current to voltage transducer. The output from this device, connected to the second oscilloscope channel gave an accurate measure of the current passed through the lens.

Isotope fluxes The potassium effiux was measured by preloading the lens for 4-6 hr in saline containing 1/~Ci/ml of radioactive potassium (a2K---code PES 1P, Radiochemicals, Amersham). The lenses were then transferred to the perfusion chamber and the overflow collected over 10 rain intervals. The activity in each sample was monitored by the Cerenkov method on an Intertechnique SL65A counter. At the end of the experiment the lens was removed from the chamber, homogenized in 10 ml of saline and counted as befc.:e. Rate constants (k) were calculated as described by Delamere and Duncan (19~'7).

Flux and conductance equations The Kimizuka-Koketsu (1964) flux equations have previously been successfully applied to the lens (Duncan, 1974) and will be used here. The relationship between potassium

LENS POTASSIUM CHANNELS

639

permeability (PK), membrane potential (E), rate constant (k) and surface to volume ratio of the lens (A/V) is given by kV P~: : ~ exp (--zFE/2RT)

(1)

The equation to describe the relationship between permeability, concentration (of potassium, sodium and chloride) and membrane potential can be derived either from Goldman (1943) or Kimizuka-Koketsu (1964) theory and has the form E = R T In Ko-k~Nao~-flCli Ki-]-o~Nai~-flClo

(2)

where a = P~a/PE and 19 = Pcl/P K. The Kimizuka-Koketsu equation to describe membrane conductance (Up) measured by passing a small pulse of current is: F2

ap = ~-~,/(AB) where

(3)

A = PKKo@PNaNao-t-PcICli and B = PKKi~-PsaNai~-PclClo

Although these equations take no account of the fact that part of the amphibian lens potential is electrogenic in nature (Duncan et al., 1980) recent work has demonstrated that this omission wii1 not affect the conclusions drawn in this presentation. Firstly, the electrogenic contribution to the normal resting potential is small (8 mV out of a total of 80 mV) and secondly, the changes in lens conductance-voltage relations and in aSK efflux observed in the presence of ouabain are precisely those expected from an 8 mV depolarization of the lens membranes alone (Patmore, 1979; Delamere et al., 1980). 3. Results

In common with other tissues that have a relatively high membrane permeability to potassium, the lens potential is sensitive to changes in the external potassium concentration [Fig. l(a)]. There is also a concomitant increase in the measured conductance [Fig. l(b)] on increasing potassium. The conductance changes involved are much greater than those predicted from the Kimizuka-Koketsu (1964) equation (3) where the potassium permeability is assumed constant throughout. The solid line in Fig. l(b) was generated from equation (3) by taking the internal ion concentrations and relative permeabilities defined by Patmore and Duncan (1979). PK was determined from a separate series of a2K efflux experiments and the mean value was 1.76 x 10-sin see 1 (see d~Kflux section). The same values for these parameters when substituted into the Goldman equation (2) in fact gave a close fit to the potential data shown in Fig. 1(@ but there were very large discrepancies indeed between the predicted and experimentally-determined conductance values [Fig. l(b)]. However, when 20 m~TEA was added to the bathing medium, the lens conductance was decreased throughout the potassium range tested and the experimentally determined values were very close to those predicted from equation (3), TEA is known to block voltage-sensitive potassium channels in nerve (Itille, 1967 ; Armstrong, 1975) and it was a preliminary series of blocking experiments of this type that led Patmore and Duncan (1979) to suggest that the lens also possessed voltage-sensitive channels. The contribution of a voltage-dependent potassium channel to the overall conductance can be obtained from the Hodgkin-Huxley model for nerve (Hodgkin and

L. P A T M O R E

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p.d. (mV) l [K+]o (m=l

:FIG. 1. (a) The effect of changing external potassium concentration on lens potential. The potentials ( 9 are the m e a n • s.~,.x, for at least three and in most cases more t h a n six lenses. At selected potassium concentrations T E A (20 m~1) was added to the test solutions. A mean depolarization of 3-4 mV was observed in each ease. The T E A data (open circles) are given as the me~n:]:s.~.M, for at least three lenses in each case. (b) The conductance was measured by applying a small test pulse of current (AI) and observing the resultant voltage change (4 V) at the same potassium concentrations. AI The values for the conductance (GT = ~ ) were corrected to specific conductance by dividing by the surface area of the lens (see Delamere and Duncan, 1977). The solid line shows the conductance predicted from equation (3) which assmnes P K remains constant. Kl, 5Tai and Cll were taken as 95, 8.1 and 6 mM respectively (Patmore and Duncan, 1979). The broken line is the s u m of the conductances predicted from equations (3) and (4) taking z and E~_ as 3.25 and --42.5 mV respectively. The solid line fits the T E A data (O) well while the broken line is a good fit to data obtained in high potassium solutions without T E A ( 9 The voltage scale was related to the potassium concentration by using the m e a n values from :Fig. l(a).

Huxley, 1952a,b,c). The conductances in the steady state would be given by an equation of the form (Patmore and Duncan, 1979) G ~ = 1 +exp(-zF(E~-E1/2)/RT ) (4) GE2 1 +exp( -zF(E 1 -Ei/2)/RT) where Gm is the voltage dependent component of the conductance at membrane potential E i and Gn2 the conductance at E2, z and E89 are parameters defining the shape of the conductance-voltage curve. If it is assumed that the voltage-dependent eharmel ties in parallel with other conductances in the lens membranes then the total measured conductance GT1 at any voltage E 1 is given by the sum G~i = Gri +Gin (5) where Gpi is defined by equation 3. The total measured conductance was fitted to the conductance ratios generated in this way for potassium clamped potentials between - 7 6 and - t 0 mV. The values for z and E~ were taken as 3.25 and -~2.5 mV respectively; these are in the middle Of a wide range of values found for excitable tissues (Jack et al., 1975). In contrast, the lens membrane potential is not very sensitive to TEA [Fig. l(a)] and this is in fact entirely to be expected as the potentials predicted from the Goldman

LENS POTASSIUM

CHANNELS

641

equation (2) are not very sensitive to changes in potassium permeability. For example, assumingPx remains constant at 1-76 • ]0-sin see-1, and using the data for concentrations and relative permeabilities given above, equation (2) predicts a value of -43 mV for the membrane potential in 25 mM external potassium. However, if it is assumed that P K increases threefold in 25 m~ K o [Fig. l(b)], then equation (2) predicts a value of --47 mV for E. Both of these values are well within the range found in the control solution and in the presence of TEA. The small changes in potential on application of TEA are in agreement with the results of experiments of a similar nature carried out on nervous tissue (Schmidt and Stampfli, 1966). -

(a)

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FIG. 2. (a) The relationship between a step pulse of current (I) and the resultant voltage deflection (V). The resting potential, in this case, --84 mV, was taken as the origin and depolarizing currents were positive. (b) The relationship between conductance and voltage measured directly from current-voltage curves [see (a) above]. In this case the conductance was measured from the slope (AI[AV) of the currentvoltage curve around a given voltage. The resting voltage Vn is marked and the slope conductance increases at depolarizing voltages. The solid line was generated from equation (6) taking the residual voltage-insensitive conductance (Go) as 1.7 x 10-4 S, z = 4.5 and E89 = --42.5 mV.

The dependence of the conductance on lens potential can be demonstrated directly by measuring the slope conductance from the current-voltage relation mapped out over a wide range of values [Fig. 2(a),(b)]. As the lens potential is depolarized by current injection, the conductance increases in a similar manner to that obtained when the potential was depolarised by increasing the external potassium concentration. At hyperpolarized potentials the conductance decreases and appears to approach a minimum conductance at a voltage where presumably the voltage-dependent potassium channels are completely closed. This relation is very similar to that obtained by Armstrong and Binstock (1965) for the squid giant axon. The contribution of the voltage-dependent conductance can also be modelled for the conductance-voltage relationship. The total measured conductance (GT) is assumed to comprise a voltage-dependent conductance (GE) defined by equation (4) and a voltage-independent conductance (Go) and thus Gz = Go +GH

(6)

L. PATi~IOEE A N D G. D U N C A N

642

where GO, the minimum conductance of the conductance voltage curve, is estimated by extrapolating the exponential relation to a value considerably negative from the resting potential. A fit of equation 6 to the data is shown in Fig. 2(b). The effect of TEA injected into squid axon is to block the potassium channels and remove the rectification. Under these circumstances depolarization of the neural membrane causes very little increase in conductance (Armstrong and Binstock, 1965). However, the injection of substances into the lens has proved to be a very difficult process (Rae and Blankenship, 1973; Rue, 1974) and so TEA has been applied to the outside of the lens membranes. The effect on the lens conductance-voltage relation (Fig. 3) is not as striking as that found in the squid axon although the range over which the conductance was measured is much smaller.

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Voltage(mV) Fro. 3. Lens conductance as a function of voltage. The data points were generated as described in the legend to Fig. 2(b). Control values ( 0 ) , control with 20 m ~ - T E A (O). Vn and Vn§ denote t h e resting voltages in control and T E A solutions.

It is now possible to compare directly these two techniques of estimating the voltage dependent component of the lens conductance. It has been shown that both the potassium clamped conductance data (Fig. 1) and the conductance-voltage relation [Fig. 2(b)] can be fitted by equations of the Hodgkin-Huxley type [equations (5) and (6)] and these equations can also be applied to slope conductance data determined in a series of external potassium concentrations. The conductance-voltage relations in potassium concentrations of 5, 10 and 15 m~ arc shown in Fig. 4(a), (b), (c). At potassium concentrations of 2.5, 5 and 10 mM [Fig. 4(a),(b)] the conductancevoltage relationships appear to be almost continuous and therefore the major change in conductance can be ascribed to an increase in the contribution of a voltagedependent component. However, at higher potassium concentrations (15 m• and upwards), although there is a considerable increase in the overall conductance, the data points are shifted well to the right of the predicted relationship [Fig. 4(c)]. This shift indicates that potassium also blocks the conductance and this effect may either be due to a blockade of the voltage-dependent potassium channels or the voltageindependent conductance (Go). In order to distinguish between these effects, the conductance was measured over a range of potassium concentrations under voltage-clamp conditions. The voltageclamp system used was of conventional design and high voltage-swing operational

LENS

POTASSIUM

CHANNELS

643

TABLE I

Effect of potassium on the voltage-clamped conductance Ko

GK/Gc

(Normal) 2.5 m a - K +

1.00

10 15 20 25

0.874-0.03 0.754-0.04 0.70:J:0.01 O-624-0.O2

The conductanees were measured at a clamp potential just above resting potential (--70 to --75 mV). Gc refers to the control conductance a n d GK to t h e conductance in the various test solutions. The d a t a represent the mean4-s.E, of at least three experiments in each case.

TABLE II

Sensitivity of the lens conductance to various blocking agents Conductance 2.5 mM-K + 25 m~I-K + Control + T E A (20 mM) Caesium (12.5 m~t) + R u b i d i u m (12.5 m~I) + 4-AP (10 ml~)

1.00 (4=[=0-85 S m -s) 0.924-0.09 0.90=[=0.07 0.95 1.40

1.00 (154-1.25 S m -2) 0.464-0-09 0.674-0-03 0.834-0.11 1.35•

The conductances have been normalized by taking the conductance in the control solutions as one unit. The actual values are given• in parentheses. The values for the blocking agents are t h e m e a n : L s . s . ~ , of three experiments in each case except for the effect of Rb + and 4-AP in 2.5 mM-K+ which were single experiments. W h e n l~b + and Cs + were added to 25 mM-K + Ringer the m e a n potential depolarized by 1.5 and 1.1 m V respectively. The effect of each of these agents on the lens potential when added to 2.5 m ~ - R i n g e r was negligible (less t h a n 1 mV). 4-AP in fact caused a m e a n hyperpolarization of approximately 1.5 mV in both solutions.

TABLE I I I

aSK e~ux measurements Perfusate 25 25 25 25

m~t-K + mM-K++TEA mM-K++Cs + m~I-K++Rb +

Control+TEA Control+Cs Control+Rb Control+4-AP

ld/b

F,.E' (my)

PK'/PK

2.3 I 0 . 1 2 1-124-0.06 1.154-0.08 1-4 4-0.04

--28.54-2-4 --29.94-1.2 --29.64-0.7 --30.04-0.4

1.3 0.62 0.64 0.77

0.86-4-0-02 0.554-0.01 0.724-0.02 2.224-0.28

--1.54-1.0 --0-75• --0.4 • + 1 . 5 4-0.5

0.83 0.54 0.74 2.29

k'/k is t h e ratio of rate constants observed in control (k) and test (k') solutions. Each value is t h e m e a n of at least two experiments in each case. PK'/PK is the ratio of potassium permeabilities in the control a n d test solutions calculated from equation (8). The change in potential (E-E') was determined in a separate series of experiments.

644

L. P A T ~ O R E

AND

G, D U N C A N

amplifiers were used so that relatively large clamping currents cmfld be passed through the intracellular microelectrodes (Patmore, 1979). The lens potential was clamped to a value slightly negative of the resting potential (--75 mV) and the conductance measured in a range of potassium concentrations by changing the command voltage by 1 mV and observing the resulting change in clamp current (Table I). The blocking effect of potassium, which was inferred from the data given in Fig. 4(a),(b), (c), can be more clearly seen on clamping the voltage and as expected the blocking 5

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Fro. 4. (a) Conductance v o l t a g e relations in t h e control solution ( a ) , 5 m_~-K+ ( l l ) ; 5 m ~ - K + w i t h 20 m51-TEA (2]). The solid line was g e n e r a t e d from e q u a t i o n (6) t a k i n g G o = 1.7 • 10 -4 S, z = 4.5 a n d E.~ = --42.5 inV. Vn, V5 a n d V~+T d e n o t e the r e s t i n g voltages in control, 5 zm~z-K+ a n d 5 mM-K + w i t h T E A . The s m a l l blocking effect in 5 mM-K + can be seen as a s h i f t in t h e c o n d u c t a n c e - v o l t a g e relation. The blocking effect of T E A is m u c h greater. (b) C o n d u c t a n c e v o l t a g e r e l a t i o n s in the control s o l u t i o n ( O ) 10 m ~ - K + ; ( l l ) a n d 10 m ~ - K + w i t h 20 m ~ - T E A ([3). The solid line in t h i s case was fitted b y t a k i n g G o = 1.1 • 10 4 S, z = 3.85 a n d E~ as above. (c) C o n d u c t a n c e - v o l t a g e r e l a t i o n s in control solution ( O ) , 15 m ~ - K + (11) a n d 15 m.~-K + w i t h 20 m ~ - T E A (f3). The solid line was fitted b y t a k i n g G o = 0.6 • 10 -4 S, z = 5.5 a n d E~. as before. The b r o k e n line was g e n e r a t e d b y t a k i n g G o as 0"5 X 10 -4 S w h i l e z a n d E~ were unchanged. The d a t a g i v e n in (a), (b) a n d (e) were o b t a i n e d from t h r e e s e p a r a t e lenses.

LENS POTASSIUM CHANNELS

645

,~ 2 O~

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FIG. 5. The effect of increasing external potassium and TEA on the rate constant (k) of potassium effiux. Note that the rapid and large increase in k produced by 25 m~-potassium is almost completely blockedby adding 20 m~-TEA.

effect increases with external potassium. Fig. 4(a),(b),(c) also show that 20 m~-TEA shifts the conductance voltage curves in a similar manner to high potassium solutions and hence the mechanisms of TEA and potassium blocking may be similar. The alkali earth metals rubidium and caesium have been shown to block the potassium channels in excitable tissues (Volle, Glisson and Henderson, 1972; Hille, 1973) and the effect of these blocking agents on lens conductance is shown in Table II. Since none of the blocking agents have a significant effect on the lens potential either at 2.5 or 25 mM external potassium their relative effects on the conductance are directly comparable. The ability of TEA to reduce the conductance in 25 raM-K+ Ringer to only 46% of the control value [see also Fig. l(b)] was not matched by

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FIG. 6. The effect of applying hyperpolarizing (--re) and depolarizing (-t-ve) currents on the efltux rate of 42K from the lens ( 9 me denotes the insertion of the current-passing and potential-measuring ruler9 and these did not cause a significant change in rate. The current pulses were applied for 30 see in each minute during the collection periods ( 9

646

L. P A T ~ 0 I ~ E

AND

G, D U N C A N

caesium or rubidium, although both reduce the conductance in high potassium by a significant amount. Caesium, rubidium and TEA have, however, little effect on the conductance in normal (2-5 m~-K§ solution. 4-Amino-pyridine (4-AP) also blocks voltage sensitive channels in a number of excitable tissues (Meres and Pichon, 1977) but when applied to the lens it actually increased the conductance both in 2.5 and 25 m~-K+ solutions (Table II).

ask e~ux measurements The et~lux of radioactive potassium from the lens is regarded as being passive in nature (Duncan, 1969) and essentially a one compartment phenomenon (Paterson, 1970; Duncan, 1970). For example, a graph of eltlux rate constant against time shows the presence of an initial fast component followed by a slower rate of etttux which is steady over the period of the experiment (Patmore, 1979). Duncan (1969), Delamere and Duncan (1977) and Delamere and Paterson (1979) have used the slow rate constant value as a measure of lens potassium permeability. The relationship between rate constant, potential and permeability is given by equation (1). In the present series of experiments a steady value of k was usually obtained within 120 rain (Fig. 5) and a mean value of 1.76• x 10-sin sec-1 was obtained for PK- This is close to that reported by Delamere and Duncan (1977). When the lens potential is depolarized to a new value E', the value of PK is increased to PK' and

PK' = k' V

exp

(-FE') 2RT

(la)

therefore, combining equations (1) and (la) P~c'

k'

Px-kexP~

,f(E- E' ),

~

~

(8)

The effect on the efltux rate constant of depolarizing the lens potential by perfusing with 25 m~-K + Ringer is shown in Fig. 5. In the experiment illustrated, the et~lux rate increased twofold and over a series of experiments the mean value for k'/k was 2.3. In a separate series of experiments [Fig. l(a)] the mean depolarization in 25 mMK+ was 28.5 mV and when these values were substituted into equation (8) a value of 1.3 was obtained for PK'/PK. This value indicates that the potassium permeability increases with depolarization of the lens potential and is further evidence for the existence of voltage dependent potassium channels. The blocking effect of adding TEA to the 25 m~-K + perfusate is very marked (Fig. 5). The rate constant is reduced to a level similar to that found in normal ringer and the ratio PK'/PK falls to 0.62 (Table III). This indicates that the increase in PE caused by depolarization is completely blocked and in fact TEA reduces the potassium permeability further by blocking the potassium channels which are presumably open at the resting potential. Complementary to the electrical conductance data, 42K efltux measurements were made on the blocking effects of caesium and rubidium in normal and high potassium ringer solutions. The data are summarized in Table II. It is interesting that caesium and rubidium exert a considerable blocking effect in 2.5 mM-K+ (control) whereas the TEA effect is less marked. In 25 m~-K + solutions, however, TEA is most effective.

LENS POTASSIUM CHANNELS

647

4-AP increases the potassium permeability both in the control and 25 m~-K + solutions which supports the unexpected increase in the electrical conductance obtained in high potassium solutions (Table II). In a further series of experiments the lens potential was perturbed by applying hyperpolarizing and depolarizing currents while simultaneously monitoring the rate of aSK efltux (Fig. 6). Current pulses were applied for 30 sec in each 60 sec and thus the mean change in potential was taken as half the maximum deflection voltage induced by the current pulse. From the mean change in potential the change in potassium permeability can be calculated from equation (8). The ratio FK'/Px when the lens potential is hyperpolarized by 9"7 mV is 0.9 indicating a decrease in potassium permeability and when the lens is depolarized by only 6 mV the ratio is 1-2 indicating a significant increase in the potassium permeability. These changes in permeability can be explained by the voltage-dependence of the lens membrane potassium channels.

4. Discussion

Although Duncan (1969) pointed out that the lens conductance should strictly be measured from the slope of the current-voltage curves at the resting potential most workers in the field (Eisenberg and Rue, 1976; Delamere and Duncan, 1977; Delamere and Paterson, 1978) have assumed the lens to behave entirely as an ohmia system similar to other epithelial tissues (Loewenstein and Kanno, 1964; Smith, 1975). In the face of this tradition it is necessary to justify in a rigorous fashion the assertion that the lens membranes have voltage-dependent characteristics. Our evidence is as follows: firstly the directly-measured conductance voltage curves are non-linear [Figs 2(b),3,1] with the conductance increasing as the membranes depolarise. Secondly, the conductance increases on depolarization with high external potassium solutions and the change in conductance can be blocked by known potassium channel blockers, namely TEA, caesium and rubidium [Figs l(b), l, Table II]. Thirdly, the changes in potassium permeability following changes in potential have been observed directly in perfused, current-clamped lenses using 42K. The potassium e/Itux decreased on h)Terpolarizing the lens and increased on de-polarisation and the change could not be explained entirely in terms of conventional flux equations where the permeability is assumed to be independent of voltage. The effect on the conductance of increasing the external potassium concentration is quite complex and appears to be determined by three separate actions. (1) Depolarization of the Iens potential causes the voltage-dependent potassium channels to open, thus increasing the conductance. (2) The conductance will also increase according to the Kimizuka-Koketsu model since there are more freely permeable current carrying ions (K +) available. (3) There is evidence from shifts in the conductance voltage curves (Fig. 4) that potassium ions block the conductance. Thus there are a number of considerations when fitting equation (6) to the conductance voltage relation in high potassium Ringer. The factors which determine conductance are summarized in equations (4) and (6). The voltage-sensitive component (Gu) is itself a function of z and E~ and either of these factors could be influenced in the blocking process. The voltage-insensitive component (Go) would be expected to increase in accordance with the Kimizuka-Koketsu theory but decrease due to blocking. Figure 4(c) illustrates a fit of equation (6) to the data at 2.5 and 15 m~-K+.

648

L. P A T M O R E AND G. D U N C A N

The fitted values at 2.5 m•-K+ were 0.6 x 10 48, 5.5 and -42.5 mVfor Oo, z and E89 respectively. We found that the 15 m•-K + data (broken line) could be fitted by taking Go as 0.5 x 10-4S whereas z and E89were unchanged. From the K - K theory, Go would be expected to increase from 0-6 • 10-4 to 0.9 x 10-4S simply due to the increase in external potassium ions. Therefore the total blocking effect is actually from a level of 0.9 to 0.5 x 10-4. Similarly, the blocking effect monitored by the voltage-clamp method (Table I) will also be underestimated. However, the relative amounts of blocking obtained from a direct estimate of the voltage clamped conductance ratio (G~-/G c = 0.75) and from the uncorrected ratio of fitted G0's (0.5/0.6 = 0.8) agree, indicating that the major blocking effect of potassium is probably on the voltage-insensitive component (Go). With the present technique it was unfortunately not possible to map out conductance voltage curves accurately in 25 raM-potassium because of the very great increase in conductance due to depolarization. However, the voltage clamp data (Table I) would predict that the conductance voltage curves should be shifted much further to the right of the control relationship and they would predict that the shift could be explained by a change in GOalone. As the result of this blocking effect it is likely that the contribution of the voltagedependent channels to the overall conductance is underestimated in the potassium clamp experiments [Fig. l(b)]. For example, a good fit of equation (5) to the potassium data was obtained using values of 3.25 and -42.5 mV for z and E~ respectively whereas in later experiments where conductance-voltage curves were measured directly in the control solution [Figs 2(b), l(a),(b),(c)] a range of values between 3.85 and 5.5 were fitted for z while E89 remained constant. The steepness (z) of the fitted curve in Fig. l(b) is underestimated because of the blocking effect of high potassium solutions. The general variability in the values of z determined in control solutions has also been reported in excitable tissues. Blocking by increased levels of external potassium has also been reported in squid axon (Armstrong and Binstock, 1965; Rojas, Taylor, Atwater and Bezaailla, 1969) and it was suggested that this may be due to the saturation of the non-voltage dependent conductance by potassium ions (Itodgkin and Keynes, 1955). The data given in Table II show that the conductance increases to almost fourfold when changing from 2.5 to 25 m~-K+ and this large increase in fact masks a significant blocking effect of 25 mM-K+ on the conductance (Table I). The addition of 12.5 mMCs+ or Rb + produces a much greater blocking effect which can also be seen in the potassium permeability estimates obtained from 42K efltux measurements (Table III). I n both conductance and flux measurements the blocking effects of TEA, Cs and Rb :are greater at the higher potassium levels. Caesium and rubidium have been shown :to block the potassium channel in excitable tissues directly by competing with :potassium for common membrane sites (Hille, 1973; Dubois and Bergman, 1977) and in these tissues caesium is the more effective blocking agent. Caesium is also a more effective blocker of lens conductance than rubidium (Tables II and III) and this can be explained by a blocking action which is proportional to atomic radius (Bezanilla and Armstrong, 1972). There do, however, appear to be significant differences between the potassium channel in nerve and that in the lens. For example, TEA makes the shape of conductance-voltage curves of excitable tissue much more linear (Armstrong and Binstock, 1965) whereas the principal effect on the lens seems to be a shift in baseline rather than in shape. Furthermore, 4-amino-pyridine is a very potent blocking agent

LENS POTASSIUM CHANNELS

649

in squid nerve (Meres and Pichon, 1977) and in invertebrate photoreceptors (Pepose and Lisman, 1978) while in the lens it actually increases lens conductance (Table II) and potassium permeability (Table III). The a2K eitlux data shown in Fig. 6 are i m p o r t a n t for two reasons. They represent the prime evidence t h a t potassium permeability is directly influenced b y changes in m e m b r a n e potential. However, the data also show t h a t injecting current into one point in the lens in fact influences the rate of exit of potassium from the whole lens and is further evidence for the view t h a t the lens fibre cells are closely coupled. I f this were not the case the change in potassium efftux rate would be extremely small. ACKNOWLEDGMENTS We wish to thank Dr Peter Croghan, Dr Paul Pynsent and Mr Tim Jacob for m a n y stimulating discussions. We also acknowledge receipt of equipment grants from the Royal Society and RNIB. L.P. acknowledges the receipt of an SRC studentship during the course of the work. REFERENCES

Armstrong, C. )/i. (1975). Potassium pores of nerve and muscle membranes. In Membranes: A Series of Advances. Vol. 3, (Ed. Eisenman, A.). Pp. 325-58. Dekker, New York. Armstrong, C. M. and Binstock, L. (1965). Anomalous rectification in the squid giant axon injected with tetraethylammonium chloride. J. Gen. Physiol. 489 859-72. Bezanilla, F. and Armstrong, C. M. (1972). Negative conductance caused by entry of sodium and caesium ions into the potassium channels of squid axons. J. Gen. Physiol. 60, 588-603. Delamere, N. A. and Duncan, G. (1977). A comparison of ion concentrations, potentials and conductances of amphibian, bovine and cephalopod lenses. J. Physiol. (London) 272, 167-86. Delamere, N. A., Duncan, G. and Paterson, C. A. (1980). Characteristics of voltage-dependent conductance in the membranes of a non-excitable tissue--the amphibian lens. J. Physiol. (London) (In press). Delamere, N. A. and Paterson, C. A. (1979). The influence of calcium-free solutions upon permeability characteristics of the rabbit lens. Exp. Eye Res. 289 45-53. Dubois, J. M. and :Bergman, C. (1977). The steady state potassium conductance of the Ranvier node at various external K-concentrations. Pflugers Arch. 3709 185-94. Duncan, G. (1969a). Relative permeability of the lens membranes to sodium and potassium. Exp. Eye Res. 89 315-25. Duncan, G. (1969b). The site of the ion restricting membranes in the toad lens. Exp. Eye Res. 8, 406-412. Duncan, G. (1969c). Kinetics of potassium movement, across amphibian lens membranes. Exp. Eye Res. 8, 413-20. Duncan, G. (1970). Permeability of the amphibian lens membranes to water. Exp. Eye Res. 99 188-97. Duncan, G. (1974). Comparative physiology of the lens membranes. In The Eye (Ed. Davson, It.) Vol. 5, Ch. 4, pp. 357-397. Academic Press, London. Duncan, G., Delamere, N. A., Paterson, C. A. and Neville, M. C. (1980). Contribution of an electrogenic pump to the electrical characteristics of frog lens membranes. Exp. Eye Res. 309 105-7. Duncan, G. and Patmore, L. (1979). The effects of tetraethylammonium on the impedance of the lens of the frog Rana pipiens. J. Physiol. (London) 2919 71-2p. Eisenberg, R. S. and Rae, J. L. (1976). Current-voltage relationships in the crystalline lens. J. Physiol. (London) 262, 285-300. Goldman, D. E. (1943). Potential, impedance and rectification in membranes. J. Gen. Physiol. 2, 37-49. Hille, B. (1967). The selective inhibition of delayed potassium currents in nerve by tetraethylammonium ion. J. Gen. Physiol. 50, 1287-302. ttille, B. (1970). Ionic channels in nerve membranes. Prog. Biophys. Mol. Biol. 219 1-32. ttille, B. (1973). Potassium channels in myelinated nerve. J. Gen. Physiol. 619 669-86.

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Hodgkin, A. L. and ]{uxley, A. iF. (1952a). Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo. J. Physiol. (London) 116, 449-72. Hodgkin, A. L. and Huxley, A. iF. (1952b). The components of membrane conductance in the giant axon of Loligo. J. Physiol. (London) 116, 473-96. Hodgkin, A. L. and Huxley, A. iF. (1952c). A quantitative description of membrane current and its application to conductance and excitation in nerve. J. Physiol. (London) I17, 500-544. Hodgkin, A. L. and Keynes, R. D. (1955). The potassium permeability of a giant nerve fibre. J. Physiol. (London) 128, 61-88. Jack, J. J. B., Noble, D. and Tsien, 1%.W. (1975). Electric Current Flow in Excitable Cells. Clarendon Press, Oxford. Kimuzuka, M. and Koketsu, K. (1964). Ion transport through cell membranes. J. Theor. Biol. 6, 290-305. Loewenstein, W. 1%. and Kanno, u (1964). Studies on an epithelial gland cell membrane. J. Cell. Biol. 22, 565-86. Meves, H. and Piehon, u (1977). The effect of internal and external 4-aminopyridine on the potassium currents in intraeellularly perfused squid giant axons. J. Physiol. (London) 268, 511-32. Paterson, C. A. (1970). Efflux of 22Na and S6Rb from the crystalline lens. Exp. Eye Res. 10, 331-9. Patmore, L. (1979). Eleetrophysiological studies on the lens. Ph.D. Thesis, University of East Anglia, Norwich. Patmore, L. and Duncan, G. (1979). A TEA-sensitive component in the conductance of a nonexcitable tissue (the amphibian lens). Exp. Eye Res. 28, 349-52. Pepose, J. S. and Lisman, J. E. (1978). Voltage sensitive potassium channels in Limulus ventral photoreceptors. J. Gen Physiol. 71, 101-20. Rae, J. L. (1974). The movement of procion dye in the crystalline lens. Invest. Ophthalmol. 13, 147. 1%ae, J. L. and Blankenship, J. E. (1973). Bioeleetric measurements in the frog lens. Exp. Eye Res. 15, 209-17. 1%ojas, E., Taylor, 1%.E., Atwater, I. and Bezanilla, iF. (1969). Analysis of the effects of calcium or magnesium on voltage-clamp currents in perfused squid axons bathed in solutions of high potassium. J. Gen. Physiol. 54, 532. Sehmidt, H. and Stampfli, 1%. (1966). Die wirkung yon tetraathylammoniumchlorid auf den einzelnen 1%anviersehenschnurring. Pflugers Arch. ges. Physiol. 287, 311-25. Smith, P. G. (1975). Frequency dependance of the frog skin impedance. Biochim. et Biophys. Acta 375, 124-9. Volle, 1%.L., Glisson, S. L. and Henderson, E. G. (1972). Blockade by tetraethylammonium (TEA) and rubidium of potassium fluxes in frog sartorius muscle fibres: distribution of 14C-TEA ill muscle. Arch. Eur. J. Physiol. (London) 333, 281.