Ion-selective microelectrodes suitable for recording rapid changes in extracellular ion concentration

Ion-selective microelectrodes suitable for recording rapid changes in extracellular ion concentration

Journal of Neuroscienee Methods, 31 (1990)207-213 207 Elsevier NSM 01050 Ion-selective microelectrodes suitable for recording rapid changes in ext...

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Journal of Neuroscienee Methods, 31 (1990)207-213

207

Elsevier

NSM 01050

Ion-selective microelectrodes suitable for recording rapid changes in extracellular ion concentration Rong Wen

i

and Burks O a k l e y II 1.2

1 Neuroscience Program, and 2 Department of Electrical and Computer Engineering and Department of Biophysics, Universi O' of Illinois at Urbana-Champai gn, Urbana, 1L (U.S.A.) (Received 12 July 1989) (Revised version received 6 November 1989) (Accepted 8 November 1989)

Key words': Extracellular potassium; K+-selective microelectrode; Vertebrate retina: Electroretinogram b-wave A method for fabricating double-barrel, ion-selective microelectrodes with fine tips (0,5-1.5 /.tm) and rapid response times is described. When made into K+-selective microelectrodes, the electrodes respond to changes in [K+]o with a time constant of 70-95 ms. The electrical response of these electrodes to c o m m o n - m o d e voltages can be made to have a time constant of < 2 ms, which minimizes electrical artifacts from field potentials. The application of these microelectrodes to the measurement of rapid, transient changes in retinal [K + ]o is presented.

Introduction

Ion-selective microelectrodes have been used to measure stimulus-evoked changes in extracellular ion concentration in a variety of tissues (although such electrodes actually sense ionic activity, the activity coefficient usually is considered to be constant in the extracellular microenvironment, and thus ionic activity and ionic concentration are directly proportional). Of particular interest are light-evoked changes in retinal extracellular potassium ion concentration, [K+]o, since the b-wave of the electroretinogram (ERG), a biopotential of clinical importance, is hypothesized to be generated by the glial cell response to a light-evoked increase in retinal [K+]o (Faber, 1969; Miller and

Correspondence: Dr. B. Oakley II, Dept. of Electrical and Computer Engineering, and Department of Biophysics, University of Illinois at Urbana-Champaign, 1406 West Green Street, Urbana, IL 61801-2991, U.S.A.

Dowling, 1970; Newman and Odette, 1984). Initial measurements of light-evoked increases in [K+]o were, in general, consistent with the K + / b - w a v e hypothesis (Dick and Miller, 1978: Kline et al., 1978; Karwoski et al., 1985). However, Odette and Newman (1988) recently performed a computer simulation of the K+/b-wave hypothesis and concluded that if the increase in [K +]o measured with K +-selective microelectrodes by Karwoski et al. (1985) was a valid measure of the actual increase in [K +]o, then this ionic change was too small and too slow to produce the b-wave. Although this simulation cast doubt upon the K + / b - w a v e hypothesis, it was possible that the K+-selective microelectrodes used for these measurements had tips that were too large to penetrate the retina without damaging the tissue, and consequently these electrodes would have been unable to sense the actual increase in [K+]o. We recently developed a technique of fabricating fine-tipped, K4-selective microelectrodes with rapid response times that allowed us to measure a

0165-0270/90/$03.50 ¢~ 1990 Elsevier Science Publishers B.V. (Biomedical Division)

208 light-evoked increase in retinal [K ~ ],, that was much larger and faster than observed previously, and these measurements provided strong support of the K + / b - w a v e hypothesis (Wen and Oakley, 1990). In this paper, we provide details of the procedures used to fabricate these ion-selective microelectrodes and to measure their response times, as well as an example of their use in measuring rapid, transient increases in retinal [K+]~,. This type of ion-selective microelectrode can easily be fabricated to sense various extracellular ions of electrophysiological importance (Ammann. 1986), and such electrodes should be useful in m a n y other preparations where rapid changes in extracellular ionic concentration occur.

/ K+-selective ~ . ~ barrel ] --

compression L ~ ~ fitting with teflon gasket

open to ~" silane vapor |

access to reference barrel

TMSDMA t (silane) vapor

Methods Ion-selective microetectrodes respond both to ion concentration and to field potentials. In order to obtain a voltage that is a measure of ion concentration only, it is necessary to use doublebarrel microelectrodes, in which one barrel is ion-selective and the other is a conventional microelectrode, and to record differentially between the two barrels. Potassium-selective microelectrodes were made from glass capillary tubing having a theta configuration with a thick septum (TST-150, World Precision Instruments, New Haven, CT, U.S.A.). Electrode tips could be made smaller with theta tubing than with double-barrel glass tubing having a side-by-side (figure 8) configuration (Oakley and Wen, 1989). A 100-mm length of theta tubing first was trimmed using a diamond cut-off tool (Brown and Flaming, 1977), so that - 5 m m of glass was removed from the back end of one barrel (which would become the K+-selective barrel). The back end of the other, longer barrel (which would become the reference barrel) was sealed by melting it in a flame. An access hole, 7-10 m m long, was cut into the side of the longer (reference) barrel, - 15 m m from the sealed end. Overall, this trimming left - 1 0 m m of theta tubing between the open access holes in each barrel. The shape of the trimmed glass is shown schematically in Fig. 1. The glass blanks were then vacuumed to remove

Fig. 1. Schematic diagram of the theta tubing and the silamzation set-up used to fabricate double-barrel. K*-selectivemicroelectrodes fnot to scaleL An electrode is shown here m crosssection. The electrode glass was clamped in a compression fitting that had a Teflon gasket, so that the back end of the electrode extended into a small chamber filled with TMSDMA (silane) vapor. The interior of the ion-selective barrel was exposed to the silane, whereas the interior of the reference barrel was not. The entire assembly was placed inside an oven during the silanization process. Additional details are given in the text.

any glass dust. A glass fiber ( - 80/~m diameter), which was pulled by hand from the same type of glass tubing, was placed into each barrel. This glass fiber was essential, since the ion-selective barrels of electrodes that did not contain fibers rarely would fill with ion-exchanger. The theta tubing then was pulled on a horizontal puller (P-77B, Sutter Instrument Co., San Rafael, CA, U.S.A.), which had a box-type filament (3 m m wide, 3 m m square). The resulting micropipette had an extremely rapid taper ( < 3 m m from the shoulder to the tip) and a small tip diameter (estimated to be < 0.2 /~m). The rapid taper was critical for lowering electrode resistance and chemical response time. To achieve this profile, the electrode puller was adjusted to use a very low heat setting (resulting in a long period of heating

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before the final pull) and a relatively strong final pull. The ion-selective barrel was silanized to render its interior hydrophobic, so that after filling, the ion-exchanger solution would not be displaced from the tip by an aqueous phase. The silanization set-up is shown schematically in Fig. 1. The back end of the double-barrel electrode was placed through a Teflon ferrule in a stainless-steel compression fitting ( 1 / 1 6 inch T × 1 / 8 inch P, Crawford Fitting Co., Solon, OH, U.S.A.); the back end of the ion-selective barrel and the sealed end of the reference barrel both extended through the ferrule into the body of the fitting, but the access hole in the side of the reference barrel did not. The Teflon ferrule was sealed around the theta tubing by tightening the compression fitting. Eight of these fittings were an integral part of the Teflon cover of a glass petri dish, and they were positioned to hold the electrodes tip-up. About 100 t~l of N-trimethylsilyldimethylamine ( T M S D M A , Fluka Chemical Corp., Ronkonkoma, NY, U.S.A.) were placed into the bottom of the dish, and the Teflon cover, containing 8 electrodes, was put in place. In this manner, the hole in the back end of the K~-selective barrel (and therefore the entire interior of this barrel) was exposed to the T M S D M A vapor, but the access hole in the side of the reference barrel, which was outside of the compression fitting, was not. The complete assembly was placed into a cool oven and was heated to 110-120°C. The chamber of the oven was connected to a vacuum line, so that there was a continuous exchange of air inside the chamber; this minimized the silane concentration surrounding the reference barrel. After 1 h of heating the electrodes were removed from the oven and placed in a box to cool. The silanized electrodes were beveled on a dry alumina plate (0.05 t~m, Sutter Instr.) for 30-60 s at a 30 ° angle to the beveling surface, using an axial illumination technique to visualize the electrode tip (Fox, 1985) while viewing through a stereo microscope under low-power magnification. The beveled tips were examined using phase-contrast optics (640 × ), and were estimated to range from 0.5 to 1.5 /~m in diameter (the tip size depended in large part on the time of beveling).

The microelectrodes were < 4 t~m in diameter 20 t~m back from the tip, and the overall profile of the final 50 # m was similar to electrodes that were pulled to have a much more gradual taper. After beveling, the tip of the ion-selective barrel was filled with K + ion-exchanger (~477317, Corning Medical Products, Medfield, MA, U.S.A.), and the rest of the barrel was backfilled by forceful injection with 150 mM KC1, so that the ion-exchanger column was < 2 m m long. The reference barrel was filled with a solution containing 110 mM NaCI and 2.4 m M KC1. Each microelectrode voltage was measured with respect to a grounded Ag/AgC1 electrode, which was connected to the bath solution by a 2.0 M K C l - a g a r bridge. The differential amplifier used for this purpose had an input resistance of 10 ~5 ~ (Axoprobe-1, Axon Instruments, Foster City, CA, U.S.A.). The differential voltage (V K) between the 2 barrels (K+-barrel positive) and the voltage of each barrel were monitored. The amplifier had self- and cross-capacitance compensation (Dick and Miller, 1985). The electrodes were calibrated as described previously (Oakley, 1983); they typically responded to changes in [K+]o with a logarithmic slope of 56-58 m V / d e c a d e and 70-80:1 selectivity for K ~ over Na +

Results

Electrode characterization The K+-selective microelectrodes were characterized by measuring their electrical and chemical response times. The electrical response time was measured as shown in Fig. 2A. With the electrode tip immersed in solution, a commonmode voltage step [10 mV amplitude, DC-160 Hz ( - 3 dB)] lasting 100 ms was applied using external circuitry. The capacitance compensation for the K+-selective barrel was adjusted to provide minimum rise time (without overshoot) to this step, and then the cross-capacitance compensation was adjusted to minimize the c o m m o n - m o d e signal in the differential voltage. Fig. 2A shows the voltage of the ion-selective barrel (V~on), the voltage of the reference barrel (Vref), and the differen-

210 A.

10 mV step

/

......

/

B.

1.0 mM to 3.0 mM K* step

Capacitancecompensation: o p t i m ~

Wiorl VK

Vref VK

II II position/

75ms IlO"m

Fig. 2. Electrical and chemical response times of a K *-selective microelectrode. A: the tip of a K+-selective microelectrode was submerged - 2 mm into solution. The voltage of the solution was displaced from ground by 10 mV for 100 ms, and the responses of the ion-selective barrel (Vion) and the reference barrel (Vref) , as well as the differential voltage between the two barrels (VK), were recorded. The self- and cross-capacitance neutralization were adjusted to produce a rapid rise time without overshoot for V~on, and to eliminate the voltage pulse from VK. All waveforms are averages of 22 similar responses. B: the tip of the electrode (same electrode as in part A) was moved rapidly between 2 flowing streams containing different [K+ ]o. This electrode movement took 25 ms, as indicated by the lower waveform labeled 'position', which was calculated from the output of the electrode advancement system. The changes in VK were recorded with optimal capacitance compensation (as in A), and with no capacitance compensation. With optimal capacitance compensation, the electrode voltage (VK) reached 50% of its final value 62 ms from the time the electrode movement began. For the electrode whose responses are illustrated in this figure, the tip diameter was - 0.5 #m, the ion-selective barrel had a resistance of 6.8 G~2, and the reference barrel had a resistance of 110 M~?.

tial voltage (VK), r e c o r d e d in r e s p o n s e to this c o m m o n - m o d e voltage step. W i t h o p t i m a l c a p a c i tance c o m p e n s a t i o n , each b a r r e l r e s p o n d e d with a n electrical time c o n s t a n t of < 2 ms, a n d it was p o s s i b l e to e l i m i n a t e c o m m o n - m o d e voltages f r o m V K. T h e r a p i d electrical r e s p o n s e to c o m m o n - m o d e voltages at the electrode tip m e a n s that a n y s t i m u l u s - e v o k e d changes in [ K + ] o will n o t b e cont a m i n a t e d b y electrical artifacts f r o m field p o t e n tials ( D i c k a n d Miller, 1978, 1985; Vogel, 1980). T h e chemical r e s p o n s e times of the K+-selec tive m i c r o e l e c t r o d e s were m e a s u r e d as shown in Fig. 2B. A steep g r a d i e n t of [K +] was m a d e outside the tip of a d o u b l e - b a r r e l m i c r o c a p i l l a r y , b y having solutions o f differing [K + ] flow o u t o f each barrel. This m i c r o c a p i l l a r y was p u l l e d b y h a n d f r o m thin-wall glass capillaries a n d its tip was b r o k e n until each c a p i l l a r y o p e n i n g h a d an inside

d i a m e t e r of - 3 0 /~m. The response to a step c h a n g e in [K + ]o was a p p r o x i m a t e d by moving the e l e c t r o d e tip r a p i d l y (16/~m in 25 ms) between the two streams; the e l e c t r o d e r e s p o n d e d to an increase in [K+]o f r o m 1.0 to 3.0 m M with a latency of - 12 ms f r o m the time the e l e c t r o d e m o v e m e n t b e g a n a n d 50% of the total response in 62 ms. F o r 8 electrodes, the 50% response time r a n g e d from 50 to 65 ms, a n d the form of the step response c o u l d b e fit a p p r o x i m a t e l y by an e x p o n e n t i a l with a time c o n s t a n t of 7 0 - 9 5 ms. F o r these electrodes, the resistance of the K + - b a r r e l was 4 - 8 G Q , while the resistance of the reference barrel was 100-120 M ~ . D u e to the fact that the step change in [K* ],, d i d n o t occur instantly, the time c o n s t a n t of 7 0 - 9 5 ms m e a s u r e d in these e x p e r i m e n t s p r o b a b l y und e r e s t i m a t e d slightly the actual time constant. W h e n the c a p a c i t a n c e c o m p e n s a t i o n was turned off, the chemical step r e s p o n s e was c o n s i d e r a b l y slower, as shown in Fig. 2B, since the changing e l e c t r o d e voltage was filtered by the low-pass characteristics o f the ion-selective barrel. It should be n o t e d that the c r o s s - c a p a c i t a n c e nentralization was not effective in d e c r e a s i n g the chemical response time of the electrode, since during a chemical response, only the voltage of the ion-selective barrel was changing.

Electrode use in the retina T h e v e r t e b r a t e r e t i n a is an e x a m p l e of a tissue in which ion-selective m i c r o e l e c t r o d e s with fine tips a n d r a p i d r e s p o n s e times must be used in o r d e r to sense a c c u r a t e l y s t i m u l u s - e v o k e d changes in ionic c o n c e n t r a t i o n ( N e w m a n a n d Odette, 1984; K a r w o s k i et at., 1985). W e recently have used such K~-selective m i c r o e l e c t r o d e s to m e a s u r e rapid, light-evoked changes in retinal [K+]o in the isolated retina p r e p a r a t i o n of the toad, Bufo marinus ( W e n a n d Oakley, 1990). In Fig. 3, l i g h t - e v o k e d changes in e l e c t r o d e voltage (V K) are shown f r o m different retinas that were r e c o r d e d with different electrodes; one elect r o d e was f a b r i c a t e d as d e s c r i b e d above, with a small tip d i a m e t e r ( < 1 ~m), a n d the o t h e r was f a b r i c a t e d b y the i d e n t i c a l m e t h o d , b u t beveled to a larger tip d i a m e t e r ( - 2 ~m). I n each case, the electrode tip was p o s i t i o n e d n e a r the o u t e r plexif o r m layer (OPL), at the d e p t h where the light-

211

A.

smaller V electrode tip

B.

larger electrode tip

~

105mY C.

superimposed

~

LM Fig. 3. Light-evoked change in retinal [K + ]o. These VK waveforms were recorded from different retinas using different K +-selective microelectrodes; each waveform is the average of 3 similar responses. In each experiment, the 100 ms flash of 500 nm light (indicated by the vertical deflection of the light monitor trace, labeled LM) led to the absorption of 60 quanta per rod. The microelectrode used to record the response shown in part A had a tip diameter that was <1 ~m, while the microelectrode used to record the response shown in part B had a tip diameter that was - 2 ~m. The responses from parts A and B are shown superimposed in part C. In each experiment, the electrode tip was positioned near the outer plexiform layer+ where the more distal of the two light-evoked increases in retinal [K + ]o was of maximum amplitude (Kline et al+, 1978: Dick and Miller, 1978, 1985; Karwoski et al., 1985; Wen and Oakley, 1990). The light-evoked increase in VK in part A corresponds to an increase in [K + ]o of 0.27 mM, while that in part B corresponds to an increase of 0.13 mM (based on a baseline level of 2.50 mM K + and 110 mM Na +, a 57 mV/decade electrode response to changes in [K ÷ ],,, and a 70:1 selectivity for K + over Na+; Oakley, 1983).

e v o k e d increase in [K+]o that generates the E R G b - w a v e was of m a x i m a l a m p l i t u d e ( W e n a n d O a k ley, 1990). F o r the electrode with the smaller tip (Fig. 3A), the light-evoked increase in V K h a d a r a p i d onset a n d r e a c h e d a p e a k a m p l i t u d e of 1.6 mV, - 520 ms after flash onset. This increase in V~ c o r r e s p o n d e d to an increase in [K+]o of 0.27 m M . F o r the e l e c t r o d e with the larger tip, the light-evoked increase in V K h a d a m u c h slower onset and r e a c h e d a p e a k a m p l i t u d e of o n l y 0.8

mV, - 1.11 s after flash onset. This increase in V K c o r r e s p o n d e d to an increase in [K+]o of 0.13 m M . W e o b s e r v e d responses similar to those ill u s t r a t e d in Fig. 3 in m a n y o t h e r experiments. In o u r first a t t e m p t s to m e a s u r e a light-evoked increase in [ K + ] o n e a r the OPL, we used electrodes with tips that were 1 . 5 - 2 . 0 /~m in diameter. In these e x p e r i m e n t s , the [K+]o responses were difficult to detect, a n d never were larger than that shown in Fig. 3B (8 retinas). W e s u b s e q u e n t l y b e g a n to use electrodes with smaller tips (estim a t e d to be 0 . 5 - 1 . 0 / ~ m in diameter), a n d we then r o u t i n e l y o b s e r v e d responses similar to that in Fig. 3 A (18 retinas). W e c o n c l u d e that small changes in tip d i a m e t e r p r o d u c e significant changes in the m e a s u r e d l i g h t - e v o k e d increase in retinal [K+]o n e a r the O P L . T h e e l e c t r o d e s with the r a p i d tapers a n d fine tips h a d excellent m e c h a n i c a l stability within the retina, since the a m p l i t u d e of the lighte v o k e d K ÷ increase n e a r the O P L was often constant for p e r i o d s of > 30 rain (Wen+ 1989); this r e s p o n s e a m p l i t u d e c a n c h a n g e significantly with e l e c t r o d e m o v e m e n t s of only 1 ~tm ( W e n and Oakley, 1990).

Discussion In this p a p e r , we have p r e s e n t e d techniques for f a b r i c a t i n g ion-selective m i c r o e l e c t r o d e s with fine tips a n d r a p i d r e s p o n s e times. These electrodes, which were d e s i g n e d to sense r a p i d changes in retinal [K+]o, are quite different t h a n the finet i p p e d ion-selective m i c r o e l e c t r o d e s for which detailed f a b r i c a t i o n techniques have been p u b l i s h e d p r e v i o u s l y (e.g., K a r w o s k i et al., 1985; D j a m g o z a n d D a w s o n , 1986). T h e features of our electrodes that a p p e a r to i m p r o v e their p e r f o r m a n c e in the retina are all r e l a t e d to their small tip d i a m e t e r c o m b i n e d with their low resistance; these features result from the e x t r e m e l y r a p i d taper, the theta c o n f i g u r a t i o n , a n d the new p r o c e d u r e of d r y - b e veling after silanization. By the a p p r o p r i a t e choice of ion sensor (liquid i o n - e x c h a n g e r or neutral ligand), this t y p e of e l e c t r o d e c o u l d be m a d e to sense the e x t r a c e l l u l a r c o n c e n t r a t i o n of a n y ion of e l e c t r o p h y s i o l o g i c a l i m p o r t a n c e ( A m m a n n , 1986). Such e l e c t r o d e s s h o u l d have general a p p l i c a t i o n s

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in all tissues where rapid, transient changes in extracelhilar ionic concentration occur. We have shown that in the vertebrate retina, small changes in the tip diameter of a K+-selective microelectrode can make significant differences in the waveform of the measured light-evoked increase in [K+]o near the OPL. This effect is likely due to changes in the amount of damage to cells as a function of tip geometry. This damage will create a dead space through which K + must diffuse to be sensed. In fact, Newman and Odette (1984) simulated how increasing the dead space at the electrode tip would cause the measured increases in [K+]o to become smaller and to peak at a later time. In a previous study, Karwoski et al. (1985) used K+-selective microelectrodes to make careful measurements of the light-evoked increase in [K + ]o in the frog retinal slice preparation. Their electrodes had tips that were broken to 0.5-1.5 /~m, DC resistances of 8 - 5 0 GO, and electrical time constants ranging from 50 to 200 ms. They measured an increase in [K+]o in the OPL that peaked 0.75-1.0 s from stimulus onset and was as large as 0.13 m M (very similar in waveform to the response shown in Fig. 3B that we recorded with a microelectrode having a relatively large beveled tip). We now have found that the measured increase in [K+]o near the OPL can become much larger and faster if the K+-selective microelectrode tip is made smaller (Fig. 3A), providing that the electrode still has a low resistance and a rapid response time. It was our impression that microelectrodes with smaller, unbeveled tips had significantly higher resistances and much slower response times, but we did not investigate this systematically. Although these unbeveled electrodes might have caused less tissue damage, their slow response times made them less useful in the retina. It seems that in or near the OPL, the retina is especially sensitive to damage by even moderately small microelectrode tips, and in using K+-selec tive microelectrodes to sense the light-evoked increase in [K+]o at this depth, there is a trade-off between tissue damage and electrode response time. For a given tip diameter, a beveled electrode will have a sharper tip and a lower resistance

(Brown and Flaming, 1979), and therefore will be preferable to an electrode with a broken tip (Karwoski et al., 1985). The electrodes we used in the retina responded to step changes in [K+]o with a time constant of 70-95 ms. This electrode characteristic acts as a low-pass filter, and slows and attenuates rapid changes in [K+]o . Thus, it is likely that the actual increase in retinal [K+]o is larger and faster than the responses we have recorded (Wen and Oakley. 1990). The K + exchanger that we used (Coming ~477317) is much more sensitive to quaternary a m m o n i u m ions than to K + (e.g., Karwoski et al., 1985). However, K+-selective microelectrodes based upon a valinomycin sensor (Ammann, 1986) have much greater resistances and correspondingly slower response times (Karwoski et al., 1985), which would be a disadvantage when trying to measure rapid changes in [K ~ ]o. A direct comparison of the light-evoked changes in retinal [K + ]o made using the two different types of K ~-selective microelectrodes found no evidence to suggest that the responses of the Corning-based electrodes were contaminated by a response to an interfering ion (Karwoski et al., 1985). We also have used the technique described in this report to fabricate p H electrodes for the measurement of rod intracellular p H (Wen and Oakley, 1989). These electrodes were dry-beveled for a much briefer time, and had smaller tip sizes than the electrodes used extracetlularly. These electrodes had lower resistances and more rapid response times than electrodes we made using more conventional means.

Acknowledgements We thank Dr. Bret Hughes for showing us how to clamp t h e t a tubing during the silanization process. We thank Yiwen Li and Jeffrey Tucker for expert technical assistance. This work was supported by grant EY04364 f r o m the National Eye Institute, U.S. Public Health Service.

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References

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Kline, R.P., Ripps, H. and Dowling, J.E. (1978) Generation of b-wave currents in the skate retina, Proc. Natl. Acad. Sci. USA, 75: 5727-5731. Miller, R.F. and Dowling, J.E. (1970) Intracelhilar responses of the Mtiller (glial) cells of mudpuppy retina: their relation to b-wave of the electroretinogram, J. Neurophysiol., 33: 323-341. Newman, E.A. and Odette, L.L. (1984) Model of electroretinogram b-wave generation: a test of the K + hypothesis, J. Neurophysiol., 51: 164-182. Oakley II, B. (1983) Effects of maintained illumination upon [K+ ]o in the subretinal space of the isolated retina of the toad, Vision Res., 23: 1325-1337. Oakley II, B. and Wen, R. (1989) Extracellular pH in the isolated retina of the toad in darkness and during illumination, J. Physiol., 419: 353-378. Odette, L.L. and Newman, E.A. (1988) Model of potassium dynamics in the central nervous system, Glia, 1: 198-210. Vogel, D.A. (1980) Potassium release and ERG b-wave current flow in the frog retina, Ph.D. Dissertation, University of Michigan, Ann Arbor, MI. Wen, R. and Oakley II, B. (1989) Direct measurement of intracellular pH in vertebrate retinal rods, Invest. Ophthalmol. Visual Sci., 30 (Suppl.): 61. Wen, R. and Oakley II, B. (1990) K+-evoked Miiller cell depolarization generates b-wave of electroretinogram in toad retina, Proc. Natl. Acad. Sci. USA, in press. Wen, R. (1989) Mechanisms of pH regulation and the generation of the electroretinogram b-wave in the toad retina, Ph.D. Dissertation, University of Illinois at UrbanaChampaign, Urbana, IL.