Sources and sinks of light-evoked A[K+], in the vertebrate retina'

CHESTER J . KARWOSRI' AND LUIS M. PROEN ZA

Vision Research Lnhoratoq).., Departments c!f'Bsychokogy and ZooEogy, University ofGeorgia, Athens, GA, U.S.A. 30602

Received July 2 1, 1986

KARWOSK~, C. J . , and PROENZA, L. M . 1987. Sources and sinks of light-evoked A[K ' 1, in the vertebrate retina. Can. J. Physiol. Phannacol .65: 1009- 10 14.

In the vertebrate retina, recordings of light-evoked changes in extraccllular K ' concentration A ( K ' 1, are of particular interest because this tissue is coinplex and multilayered, yet can be activated routincly with its "natural" stimulias (i.c.. light). This review identifies the components of the spatiotemporal profile of retinal light-evoked A[K' 1, and then presents evidence concerning the specific neural origins of these con~ponents as well as the mechanisms by which these A[K 'I,, are dispersed from extracellular space. Finally, to gain improved resolution of K' sources and sinks, the technique of ion source density is introduced and applied to both nlodel and real spatistemporal distributions of ALK'],.

KARWOSKI, C. J . , ct PRQENZA, L. M. 1987. Sources and sinks of light-evoked A[K ' 1 , in the vertebrate retina. Can. J. Physiol. Pharmacol. 65 : 1009- 1017.

Bans la retine des vertkbrks, l'enregistrement des variations dvoquees par la lumiere de la concentration K t extracelIulaire A[K ' I , est particulikrement intkressant p a c e que ce tissu est complexe et en multicouche, et qu'il pcut justement etre activk par son stiinulus <( nature1 ,, (c.-a-d., la lumiere). Cette revision identifie les composantes du profil spatio-temporel de la AIK' 1,) rktinienne dvoqude par la lumiitre puis elle presente des faits concernant les origines neuroniques spdcifiques de ces com- posantes, ainsi que les nlkcanisrnes par lesquels ces A[K+], sont disperskes de 19espace extracellulaire. Enfin, pour obtenir une meilleure rksolution des sources et des puits de K ' . on introduit ct applique la technique de la densite de source ionique a des distributions spatio-temporelles modkles et viritables de A[K+ 4,.

[l'raduit par la revue]

Several reasons have made the vertebrate retina a useful focus of neurophysiological observations. First, it has served as a model for the cerebral cortex because the retina is of similar embryological origin and because it is sin~ilarly layered and has a rich complexity of cellular organization. Second, the anatomy and physiology of the retina is well known, in part because of its accessible location in the periphery of the organism and because the retina, and even its individual cells, can be isolated and studied in vitro. Finally, an important advantage is that the retina is easily stimulated with its "natural" stimulus, light. Thus, patterns of neural activity studied experimentally approach being identical to those naturally and normally occur- ring in the retina of animals, and it is this feature that sets the retina apart from most other CNS tissues studied with ion- selective microelectrodes (ISMS).

Light-evoked changes in extracellular K' concentration (A&+],) are now routinely measured with Kf ISMS. In the retina, in addition to such A[K+], providing a window with which to study the activity and function of neurons and glial cells, A[Kf], has been targeted as a link in the generation of several field potentials (AVO), some of which constitute major components of the clinically useful electroretinogram. This review will first identify the components of the spatiotemporal profile of retinal light-evoked A[K'], and then present evidence concerning the origin and Fate of these components. Finally, to gain improved resolution of K+ sources and sinks, the technique of ion source density analysis will be introduced and applied to both model and real spatiotemporal distributions of A[K' I , .

retina, a characteristic profile of light-evoked AVK+ (AVK + is the recorded difference between the two barrels of a K ' ISM and is logarithmically related to A[K+],) can be observed. The largest, easiest to record, and best-studied AVK+ is the K' decrease at light onset in the subretinal space (space between the photore- ceptor~ and the pigment epithelial cells). This response, first described by Oakley and Green (1 976), has since been studied by several researchers, most extensively by Oakley. It is seen in Fig. 1 (70-90% retinal depth) and can often be observed at a longer latency more proximally and as far as in the vitreous (Steinberg et al. 1980). Throughout the rest of the retina, a K ' increase can be observed (Fig. 1, depths 0-70%), which has maximum amplitude in the proximal retina at about the level of the inner plexiform layer, IPL (depth 33% in Fig. 1 ) .

An ongoing issue has been whether there is simply one K f increase that diffuses proximally and distally or whether distinct K+ increases exist at other depths. The latter is probably correct as there is evidence that K+ increases arise from at least three retinal layers. (i) A small KS increase can be detected relatively distal in the retina (Fig. 1 , 69% depth), a finding first noted by Dick and Miller (1978) and Kline et al. (1978). This K+ increase has separate components as both light onset and offset (Dick 1979; Karwoski et al. 198%); however, since little is known about the off increase, only the on increase is discussed here. It is unlikely that this distal on increase results from K+ diffusing from more proximal sites, because the K+ increase at this depth is larger (Kline et al. 1978; Karwoski et al. 1985b) and has shorter latency and rise time (Karwoski et d. 19856; Dick and Miller 1985) than K t increases recorded at adjacent depths and

Profile of light-evoked A[K'], in the retina because certain drugs enhance its amplitude, while depressing As a K+ ISM is moved through the various layers of the the resDonse more ~roximallv (Dick and Miller 1998. 1985: , -

h his paper was presented at the Ion-selective Microelectrodes and ~himaiaki et al. 19i4). The ietkal layer that gives rise to this

Excitable Tissue Symposium (Toronto, Ontario, July 8-1 1, 1986). a re"0nse has been 'pecified in the 'lice? where a K+ Satellite Symposiuln of the 3oth IUpS Congress, and has undergone the increase in this region is seen almost exclusively in the outer Journal's usual peer review. plexiform layer (OPL) (Fig. 2) and hence the term for this

' ~ u t h o r to whom correspondence should be addressed at the Depart- response, "OPL K+ increase" (Karwoski et al. 198%). ment of Psychology. Although the OPL K+ increase is a distinct response, it has been Prunted In Canada Irnynrrlc au Cdrlddd

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CAN. J . PHYSHOL. PHAXMACOL. VOL. 65. 1987

Percent Retinal Depth

FIG. 1. Depth profile of light-evoked A&'# t obtained by radially inserting K' ISM in retina of frog eyecup. Bnmer limiting membrane corresponds to 0% retinal dcpth and the pigment epithelium to IbBO%'/e. Resting VK+ corresponds to [K '1, of 2.9 mM. From Kamoski et al. 1985 reproduced from The Journab of Genercll Phj)sicrlogy , 1985, Vol. 86, p. 193, by copyright permission of the Rockefeller University Press.

difficult to study because all investigators find it is small and (or) recorded only erratically and because it is usually "cut into" by the subretinal space K+ decrease. (ii) The largest Kf increase in the retina lies more proximally at the Hevel of the IPk. This Kf increase also has separate OW and off components, the on re- sponse being first observed by Oakley and Green (19'76) and the off response by Karwsski and Broenza ( 1977). Experiments using extracellular dyes (Kawoski et al. 1978) and recordings in the retinal slice (Marwasski et al. I985b) show that this K+ increase is recorded maximally in the IPL, whereas the off increase peaks more distally than the on increase (Fig. 2). For these reasons, we have termed this K+ increase the "TPL K+ increase9' (Karwoski et al. 19856). (a'ii) Aia increase in the amplitude of the K+ increase relative to adjacent depths can sometimes be detected proximal to the IPL K+ increase (e.g.,

dist I NL

mid INh

prex 1NL

dist IPL

prox BPL

P 2 s FIG. 2. Depth profile of light-evoked AVK+ obtained by tangentially

inserting K' ISM into selected layers of slice of frog retina. Resting VK+ cornsponds to [K ' ] of 2.5 n N . ROS, rod outer segments: INL. inner nuclear layer; GCL, ganglion cell layer. From Karwoski et aI. 1985 reproduced frown The Journal qfGerler6al Physiology, B 985, Vol. 86, p. 200, by copyright pernlission s f ahc Roekcfeller University Press.

Fig. I , off response at depth 17%). When such a response is present, K+ increases at both light onset and offset generally show decreased latency and rise time relative to K + increases a8 adjacent depths. This response, which must arise at either the ganglion cell or optic nerve fiber layers, is r~aoi-c readily dis- cerned with ion source density analysis (see below) a i d has recently also been reliably observed in cat retina (L. 9. Frishrnan and R. H. Steinberg. personal col~~m~nication).

K' increases can also be observed in the vitreous hunnor near the retina (Karwoski and Proenza 1977; %. J . Frishman and R. H. Steinberg, personal com~nunication) and in thc inner nuclear layer (e.g . , Fig. I , depths 50-00%). 'Fhe latter response may be largely compcjsed of K+ diffusing from the increases found in the adjacent plexiforrn layers (Karwoski et al. 19855). ?he response in the vitreous is discussed in more detail below.

Neural origins sf A[K'], An important question concerning retinal A[K '1, is the

identification of their neural origins. In general. KS flux across the membranes of activated neurons will take one of two fornms: (i) K+ naay move across the me~a~brane via transport mecha- njisrns (active or passive) or (ti) K + rnay move passively through the membrane via K+-selective channels. In the lattcr case, if cell rne~labrane conductance does not change, then K ' flux will simply be apassive function s f the driving force csn K ' , i.e., the difference between transmembrane potential (V,) and the Mi equilibrium potential jEK ,). However, H(+ flux is also a function of the amount of time the cl-rannels are open, and this time usually depends upon suck parameters as synaptic transmitter,

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KARWOSKI AND PROENZA 101 1

transmembrane voltage, or [ ~ a " 1,. The observation that K' increases in the retinal slice are seen in plexiform, but not nuclear, layers (Karwoski et al. 19850) suggests that channels modulated by synaptic transmitter are of greatest importance. However, voltage- and ~ a ' + -dependent Kf channels should also be found in neuropil, and the following discussion assumes that any of these K ' channels could play a role in transmem- brane Kt flux. Another issue concerns results from isolated cells: channels in such cells may be relevant to the functioning of the cells in situ, but there are concerns that isolation procedures may induce new channels or alter existing ones. For example, E. A. Newman (personal communication) and P. A. Coleman (personal comnlunication) find that E3a2' blocks K ' channels of isolated Muller cells, but not of -!duller cells in situ.

The Kt decrease in the subretinal space is largely generated by photoreceptor activity and probably originates from the inner segments, where it has largest amplitude (Oakley and Green 1976; Oakley et al. 1979; Karwoski et al. 19850). Although rods are the major contributors to this Kt decrease, cone activity can be important in certain situations (Matsuura et al. 1978). The K t decrease is thought to arise because the light-evoked rod hyperpolarization causes decreased passive efflux of K + , while the active uptake of K' by the N ~ + - K + pump of the rods is initially unchanged (Oakley et al. 1979). Voltage-dependent K+ channels in rods (Bader et al. 1982) should also contribute to the K+ decrease.

For the A[K+j, in t h ~ ~ O X a t light orrset, neural origins are more difficult to specify, since the OPL contains postsynaptic processes of photoreceptors, horizontal cells, and depolarizing and hyperpolarizing bipolar cells, any of which may contribute to A [ K ~ , , . Little is known about the postsynaptic responses of the photoreceptors, but they are often depolarizing and thus might generate K+ efflux. Depolarizing bipolar cells could release K t and the data, though mixed, on balance support this idea: (k) Saito et al. (1979) report two types of depolarizing bipolar cells. one in which Kt conductance (gK+) actually decreases and another in which some K' efflux is a stronger possibility, because the response is due to Na t current; ( i k ) Kaneko and Tachibana (19856 have described a voltage- dependent K + current that will generate K + efflux in dcpolariz- ing bipolar cells; and (iii) Dick (1979) and Dick and Miller ( B 978, 1985) have argued that depolarizing bipolar cells are the source of the BPL K+ increase, since ethanol enhances the OPL K increase and the on responses of depolarizing bipolar cells but depresses horizontal and hyperpolarizing bipolar cell re- sponses. On the other hand. horizontal cells possess a transnnit- ter-sensitive channel and three voltage-dependent K + channels, all of which should contribute to decreased [K'],, during the hyperpolarizing light response of this cell (Tachibana 1983, 1985; Kaneko and Tachibana 1985). Likewise, hyperpolarizing bipolar cells possess a number of membrane csnductmces that should generate lowered ( K "1, (Kaneko and Tachibana 1 985), and their synaptic current is not cmied by K' (Sctito and Kaneko 1983). Dick (1979) raised the possibility that neurons proximal to photoreceptors contribute to the K + decrease in the distal retina, and the behavior of these hyperpolarizing neurons is compatible with this idea. In sum, there are good reasons to expect either a K + i~mcrease or decrease in the OPL at light onset: probably separate neurons simultancously generate in extraceHlulx ((EC) space K increases and decreases, which subtractively interact, and the small observed K" increase, followed by a decrease, is simply the remainder.

For the IPL Kt increase, candidate neural responses are the

postsynaptic potentials of bipolar, amacrine, interplexifom and ganglion cells. and the action potentials of amacrine and gan- glion cells. Interplexiform and bipolar cells will not be discus- sed since little is known about their postsynaptic activity within the IPL. A number of amacrine and ganglion cell types exist, and several observations are consistent with them contributing to the IPL K+ increase. (i) The depolarizing responses of these cells at light on and (or) off may be associated with KS flux because the difference between kTln and EK+ is increased. (ii) There is a bisublaminar organization within the IPL, with the processes that respond at light offset located distal to those responding at onset, a layering in agreement with that observed in the IPL K+ increase (see Karwoski et al. 1978 for references). (iii) For the on-off neurons of rnudpuppy (but probably not for on or off neurons), there are parallel changes in neural responses and the IPL K+ increase to various stimulus manipulations ( K m o s k i and Proenza 19801-8. I980h). However, on-off neurons are not always the major source of the IPL K' increase. since in cat, on-of neurons are found rarely, yet the IPL K+ increase is similar to that in mudpuppy (Frishrnan and Steinberg 1985). (iv) These cells exhibit somatic and dendritic action potentials, which are thought to be caused by Nat influx. Classically, such spikes should have an associated delayed K+ efflux; Belgum et al. (1983) show current-voltage relations consistent with the presence of a delayed rectifier in on-off ganglion cells. Furthermore, on-.-off amacrine cells possess a ca2+-dependent outward K' current, which is sustained during depolariaations of >30 mV (Barnes and Werblin 1986). Final- ly, the observation of Witkovsky et al. (1985), that tetrodotoxin decreases the depolarizing light responses of Miiller (glial) cells, suppoi-ts an amacrine-ganglion cell contribution to Ki increases in the proxirnal retina. Overall, amacrine and ganglion cell contributions to the IPL K+ increase are likely, but addition- al work needs to be done before quantitative statements can be made.

The K + increase in the ganglion cell and (or) optkc nsr~e~fib'ber layer is probably due to spike activity. Evidence for this, however, comes from intracellular recordings of glial cells, which can be considered only approximate indices of A[K+],. Specifically, cells presumed to be Miiller glial cells are depolar- ized by antidromic optic nerve stimulation (Miller et al. 1977), and light-evoked depolarizations have been found in cat astro- cytes, whose processes ramify only within the optic nerve fiber layer (Pflug and Nelson 1986).

The K+ incrcuse in the vitreous near the retinal surface has two possible origins: K+ that has been spatially buffered from the retina via Miiller cells or K+ that has simply diffused out of the retina. In amphibians, a K+ increase is seen in the vitreous during spreading depression (Mori et al. 1976) and during light stimulation, especially after drainage of the vitreous (Kmvoski and Proenza 1977). In cat, a K' increase, as well as the K+ decrease originating in the subretinal space, can be recorded in the vitreous (Steinberg et al. 1980; Frishman and Steinberg, personal coinmunication). However, in suanmary, although spatial buffering by Miiller cells is virtually certain (see below), there exists no evidence quantitatively examining what portion of these A[K+], in the vitreous is due to spatial buffering versus diffusion.

Mechanisms of dispersal of Bight-evoked A[K '1, A second general question concerns the mechanisms by

which retinal A[K+], are dispersed from extracellular space. We will explore this within the context of a framework pre-

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1012 CAN. J. BHYSIOL. PHARMACOL. VOL. 65, I987

sented by Gardner-Medwin (1980) for understanding mecha- nisms by which A[K'], moves across membranes and (or) through neural tissue. Gardner-Medwin described seven pro- cesses, four termed "space-dependent" and three "space- independent", with these terns referring to whether the process depends on the existence of a spatial gradient in EC ionic concentration. For each of these processes, we will assess to what extent it is known to be operative in the retina.

Space-clependent mechanisms Difu.siorz through EC space The concepts of EC space volume fraction ( a ) and tortuosity

(A) are now well known (Gardner-Medwin 1980) and critical to analyses of diffusion, as well as of other processes that might affect EC changes in ionic concentration. For a number of cations, the diffusion coefficient (D) in saline equals that within EC fluid (Nicholson and Phillips 198 1): but for macroscopic diffusion in neural tissue, path length must be considered and the apparent diffusion coefficient (D*) equals D/h2. At several sites in the nervous system, X - 1.55 (Nicholson and Phillips 198%) and this yields for KS a D* of 1 .O X lW5 cm2/s at 37OC and (4.8 X 1 W5 cm2/s at 20°C- Diffusion will also be affected by ol if a exhibits inhomogeneity (i.e., varies as a function of location), as it does across the different retinal layers (Kal-woski et al. 1985a).

Since the retinal A[K+], seem to originate from specific and rather thin layers, diffusicm should play some role in distributing it through EC space. In the retina, diffusion can be either radial (across the layers) or lateral (along a layer). For the IPL K+ increase in frog, Karwoski and Proenza ( 1980) used a D* of 2.3 x l V g cm2/s and calculated that radial diffusion could be an important dispersal mechanism; if they had used a higher D* (e.g., 0.8 x cm2/s as suggested above). the importance of diffusion would be increased. This conclusion is limited, however, since a and X were not considered; cu may be in- homogeneous, such that the low cx of the nuclear layers may "trap" A[K+], in the IBL where a is high, or a may be artificially homogeneous (and A decreased) owing to the ISM creating a cylinder of damaged tissue through the retinal layers (Karwoski et al. 1985~) . In cat, lateral diffusion in tl-ae subretinal space was found by Steinberg et d. (1980) to be an in~portant dispersal mechanism. However, if A is considered and equals 1.55 in the tangential direction, then their data are fitted by a high D* of 4 x l V 5 cm2/s. This could suggest a process in addition to diffusion, an intriguing possibility being lateral spatial buffering via Miil- ler cells and (or) pigment epithelial cells (see below).

IntrucelHular dijfsusion Since this mechanism comes into play only after solute has

already moved across cell membranes to create an intracellular gradient, its contribution to clearance of EC ionic changes is indirect. However, it could play a significant role in the retina; if K+ moved quickly into Muller cells (whose main stalk is rel- atively wide and straight), K+ could diffuse intracellularly faster than through the narrow and tortuous EC clefts.

Tran,sport by bulk flow This might play a significant role only during pathological

conditions such as retinal detachment (Steinberg 1986).

Spatial bufering In this process, a rise in A[Kt], in one reglon is dispersed by

current flow through cells to other regions. In the retina, both MuBler cells and pigment epithelial cells share two basic prere-

quisites for serving as spatial buffers: their membranes exhibit relatively high g ~ + and they view localized A[K+],. In addition, both are positioned to buffer A[K+], out of the retina to loca- tions where A[K+], have little effect on tissue function, into the vitreous humor in the case of hduller cells and into the subchor- oidal space in the case of pigment epithelial cells.

For Muller cells, observations of Newn-aan and co-workers (Newman 1980, 1985; Newman and Odette 1984) suggest a spatial buffer function, and Newnlan et al. (1984) showed directly that Kf ejected along the distal end of a Muller cell generates K+ efflux from the proximal end foot. Thus, spatial buffering by Miiller cells does occur, but its specibic contribu- tion to K' clearance is quantitatively less certain. Newman et al. (1984) developed a model showing that spatial buffering is the primary means by which light-evoked A[K '1, is dispersed, but Sardner-Medwin (8986) argues that buffering via cytoplasmic uptake (see below) is more effective.

For the isolated pigment epithelium, Immel and Steinberg (1986) showed that A[K+], in the apical (retinal) side is transfer- red to the basal (choroidal) side. For the retina in situ, this spatial buffering would contribute to the dispersal of light-evoked A[K+], occurring in the subretinal space, but its importance relative to other mechanisms has yet to be worked out.

Space-independent mechanisms Qfoplasmic uptake: active transport qf'K ' via the Ma -K'

Pump This may be stimulated by raised [ ~ a ' ] , or IK' j,, and it is

noteworthy that Stirling and Sarthy (1 985) localized appreciable Naf -K+ pumps only to those retinal layers at which light- evoked A[K+], is known to occur (i.e., inner segments, OPL, IPL, and optic nerve fibers). Anatomically, many of thesc pumps in the inner segment layer are in Miiller cells (Stirling and Sarthy 1985). Weichenbach et al. (1 986) present physiological evidence for an active pump in isolated Miiller cells, though its contribution to K+ clearance in whole retina is unknown. Kline et al. (1985) found that the IPL K' increase at light onset decays and that the off K+ increase is followed by a K+ decrease: they interpret this decay and off overshoot as being due to increased Na+-K+ purrkp activity. Kline et al. were unable to assess such activity in response to intense stimuli; however, with stimuli too dim to evoke a K+ decrease in the subretinal space, it appears to play a significant role only tens of seconds after light onset. Shimazaki et al. (1984) showed that, during maintained illu- mination, a progressive slowing of the Na-' -K' pump of rods leads to reaccumulation of [K + 1, in subretinal space. However, since they used isolated retinas (which possess no pigment epithelium and a greatly enlarged EC space around the outer segments), it is possible that pigment epithelium and (or) Miiller cells contribute to this reaccumulation in the retina in siru. In fact, pigment epithelial cells possess a N~'-K+ pump along their apical membranes (Steinberg 1985).

Cytoplusmic uptake: pass iv~ K' trtr~sport The time course of passive uptake of KC1 during attainment of

a new Donnan equilibrium has been estimated by Gardner- Medwin (1980) for cells with various ratios of gK+ and gel-. This ratio for Miiller cells is at least 100 (Newman 19859, which means the time constant for a A[K+], to approach equilibrium via Miiller cells alone would be approximately 24 s. The value of this ratio for the apical membrane of plgment epithelial cells and for retinal neurons is less certain, but probably less than 180, which would lead to shorter time constants.

When [Kf], is elevated, passive fluxes may also result In

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KARWCXKI AND PROENZA

FIG. 3. An ion sourcc distribution Q(.x, t ) exists (column 1) in a layer s anning 50 bm (-20 to + 20 pm). This source has a strength of 1.0 9 r n ~ - s - ' . c m - ~ , begins at 200 ms, and lasts 200 ms. Setting D = 1 .1 1 X 10- cm2is, h = 1.55, and a = 0.21, permits the concentration distribution c(x,t) expected from Q to be computed (column 2) (C. Nicholson. personal communication). Q may be recovered from c by subtracting the second spatial derivative (weighted by D h 2 ) of c (column 4) from the first time derivative of c (column 3) and coirecting for a (column 5 ) . For these calculations. each trace was digitized into 30 points. Then, dcldt was computed by (Ct+, - @!-,)/2~, where @, is the concentration at time t and T is the sampling increment of 20 ms. d2cldx2 was computed by (C, +,, - 2C, + G, - i1) /122, where G, is the concentration at depth x and h is the sample spacing of 10 pm. Scaling is the same for columns 1 and 5 and for 3 and 4.

Na+-K+ exchange across membranes, particularly in cells with a high ratio of [Na + I i to [K+J,, as is likely the case for many of the retinal neurons that have shallow membrane potentials. There is little data regarding the contribution of this process to the buffering of A[K+],, in the retina, or indeed anywhere in the nervous system; however, Gardner-Medwin (1986) has argued that it, in conjunction with the other types of cytoplasmic up- take, could be the most important of the buffering mechanisms, even for brief A[K+], as found in the retina.

paradoxical consequence of resulting in the undershoots of [K+], sometimes observed after neural activity, and this should thus be considered an alternative explanation for the undershoot observed by Kline et al. (1 985).

Ion source density analysis Another way to gain clues about the origins and dispersal

mechanisms of extracellular changes in ionic concentration is to identify the sources and sinks of the ion of interest (K+, in the present case). A source of K t exists if, in a unit volume of Exchange. across capillary walls (blood-brain burrier) tissue, K' is leaving intracellular space and entering EC space. This is not relevant for A[K ' 1 , occurring in isolated eyecups Conversely, there is a K + sink in regions where Kf is leaving or retinas, where most of the research has been done. It may play EC space and entering intracellular space. Sources and sinks of a role in dispersal of A[K+j, in retinas in vivo (see paper by K+ generate A[K'],, but the spatial and temporal characteris- Newman 1987) but the time course of its action is uncertain. tics of these source-sinks are obscured because of diffusion, as

Osmotic eflects Water movements across cell membranes in consequence of

ion fluxes would alter a and result in changes in the concentra- tion of EC ions, such as K t e Significant activity-induced shrink- age in cx has been reported in several nervous system sites (e.g., Orkand et al. 1984) and if occurring in the vertebrate retina, would lead to measured K+ increases. Also, Gardner-Medwin (1980) describes how such shrinkage could eventually have the

is apparent from all typical depth profiles obtained with K+ ISMS (Fig. I) . However, if a spatioternporal distribution of [K'], is known, as when measured with a K+ ISM, then the sources-sinks of Kf giving rise to this distribution can be calculated by solving the diffusion equation. Such a procedure might be termed ion source density (ISD) analysis, and we have been developing computational procedures for ISD in collabora- tion with Charles Nicholson. Our results to date are only pre-

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CAN. I. PHYSIBI,. PHARMACOL. VOI.. 65, 1387

--. -- -- - F-

- - - - SUBRETINAL

- S PAC E

r-,.-&-L-"-+--- 0 OPL K + SOURCE

r-r- -- . -..-- --

/------

percent 561 f l k - 4 - --- .-2----- -

P-.

Retinal 50 r--, --

b ~ k i ~ * W . - -h..&-d~..-,-

h _ J I ~ DISTAL I P L 11 MAXIMUM OFF K' SOLIRCE

~%+.+%\-w&.m; - ---7,-----

I i

iL++-%.-.&- .----- - PROXIMAL IPk I---------- F MAX lMUM ON K + SOLlRCE L+L&k-- _-,- 1-

r ~ ~ ~ L --- - GANGLBON C E L L P

1- - !L& OPTIC NERVE FIBER LAYER K + SOURCE

L-- -

FIG. 4. Depth profile (same serics as in Fig. I ) of light-evoked AVKi (left column) and computed K + HSD (right column). Calculations were done as an Fig. 3, except d2c/dx2 is computed as (C,,,, - 2C, + ~ ~ - , ~ ) / ( 2 h j ' , 11 = 1.85 X 10 cm2/s, and traces are digitized into 255 points Scaling is same for columns 2 and 3.

lirninaq but illustrate several features that are instructive and that suggest ]LSD can ultimately be a useful analytic tool.

To illustrate the general principles of HSD, we consider a spatiotemporal distribution of K i sources, calculate the ex- pected A[K+],, and then solve back to recover the original source distribution. In Fig. 3, there is an ion source distribution (Qcx, t ) , column 1) spanning a layer with a thickness of 50 yrn. This source begins at 200 ms and lasts for 200 ms. After setting D , a, and X, the concentration distribution cjx, t ) expected from & is computed (column 2) . Q anay be recovered Gom c by solving the diffusion equation. modified to include a and h

(Nicholson and Phillips 198 1):

Equation 1 is solved in steps in Fig. 3. where column 3 shows a ~ l a t , column 4 shows (~ iX~) ! (d~c ! idx?) , and column 5 the dafference, weighted by a, which yields Q(x,t). G c ~ l u n ~ n 2 (c.(x,~)) is analogous to a set of A[K+],, recordings made with a Ki ISM. At depths of the source (0 , * 10, and -+20 pin). c(.x, f )

rises and falls gradually. and at adjacent depths (e.g., .6 30 airad

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+ 40 pm), a K' increase owing only to diffusion is seen. The recovered Q(x, t) of column 5 has a similar shape and amplitude as the original Q , with slight distortions owing to the process of digital differentiation.

The depth profile of light-evoked AVK+ in Fig. 1 is repro- duced in Fig. 4 (column 1). For the levels of resting and light-evoked AVK- in this profile, [K+], is almost linearly related to VK+ , SO for ease of calculation, VK , is considered to equal c(x,t). Also, at all depths, we arbitrarily set A = 1.55 and a = 0.1. (The reason for setting a and A constant, along with a more detailed examination of the general procedures underlying the ISD technique, is presented in Appendix 1 .) The calculated distribution of source-sinks that gives rise to c(x,t) is shown in colunln 4. In the subretinal space, a K t sink. which spans the region from 78-89% retinal depth. is maintained at fight onset and decays slowly at offset. A small and transient Kt source at light onset is resolved at the OPL. Just proximally, at depths 56 and 62%, the light-evoked K+ increases (column 1) do not have associated sources, so may be due only to diffusion. At the IPL, K' sources are large and transient, with the source at light (?@set maximum at depths 39-45%, slightly distal to the source at onset (34%)). Smaller sources are seen more proxi~nally , with a relative increase emerging at depth 17%. It is interesting to note a similarity between the results obtained with ISD of standard radial penetrations (Fig. 4) and those with tangential penetra- tions from the retinal slice preparation (Fig. 2). In both, KS sources are localized to the inner and outer plexiform layers but are negligible in the inner and outer nuclear layers.

When interpreting profiles of Q(x,t), care must be taken in making inferences about mechanisms of the origin and dispersal

of A[K'],,. This is because a calculated Q(x.t) may represent K' directly released by neurons, but could also be due to K' dispersed from other loci via clearance mechanisms other than diffusion. Also, calculated Q(x, t) show net source-sinks and at any one time, a sink may subtract from a source. For example, during light onset at depth 34% in Fig. 4. there is only a transient K+ source, but this does not necessarily mean that K+ is released transiently from the neurons. Rather, K+ may be re- leased tonically, but sustained clearance mechanisms (sinks) could come into play with a short delay and sum with the source, resulting in no net source-sink at that time. Other considera- tions in interpreting Q(x, t ) are found in Appendix 1.

In summary, our preliminary attempts at ISD have localized K+ source-sinks in space and time, and they suggest properties that are not obvious from the relatively smooth profiles of AVK 1

recorded in standard radial penetrations. Thus, although the full potential of ISD must await the resolution of some general issues, the procedure promises to be a useful technique for analyzing extracellular changes in ionic concentration.

Acknowledgements Special thanks go to Dr. Roy H. Steinberg, who provided

C. J . Karwoski with a nurturing environment for his sabbatical year at the Department of Physiology, University of California, San Francisco, during which this manuscript was written. In addition, we sincerely thank Drs. Laura Frishman, Joe Immel, Jack Belgum, and David Copenhagen for helpful discussions and for their comments on earlier versions of the paper. The ISD research reported in this paper was supported by National Insti- tutes of Health grant EY 03526.

Appendix 1. Procedures underlying ISD $repal-trtion

Since the experiment to collect responses though the retina for ISD analy\is takes approximately 1-2 h. the preparation must be mechanically and physiologically stable for this time. With retinas of frog and mudpuppy, we Bind that only superfused eyecup preparations yield sufficient mechanical stability and that HCO? is necessary in the superfusate (Karwoski ct al. 19856).

'To keep ISD calculations manageable, there should be no net movement of ions laterally through the retinal layers. Thus, diffuse light stimulation should be used, and the ISM must bc positioned away fro111 the optic disc and from any cut or injured edgcs of the tissue.

E lectl-ode The K' ISM should have a h s t rise time. sinall differencing artifact. minimurn intrinsic noise, and good selectivity for K over

other biologically relevant ions, and it should create minimal tissue damage. Unfortunately. no one type of KI ISM be5t meets all these criteria. For example, large-tipped and bevelled electrodes optimize the first three criteria but create increased tissue damage. On the other hand, ionic selectivity is improved with ISMS containing the valinoniycin llquid membrane (see Karwoski et al. 198% for references), but these ISMS (compared with those made with the Cornlng K' exchanger) perform worse on the first three criteria. In practice, we feel that the only potentially serious problems in our experiments are tissue damage and electrode ribe tirne, and either of thesc could limit the rise tlme of hVK + and thus of calculated K ' source-sinks.

Yrqfili? qf X Neither the absolute value nor spatial profile of X in the retina is known. It is doubtful that the ionophoretic technique of

Nicholson and Phillips (198 1) could elucidate this because the retina and its layers are \o thin; thus, anatomical studies may prove rnost useful to characterize X. Presently. we assume that X in the radial direction through most of the retina is 1.55 (as in brain, IVicholson and Phillips 1% 8 B But decreases to I .2 in the subretinal space.

Prt$ke of r ~ s i . r t i v i ~ ( p ) ~znd oj W.

From the prc~file of p, cu of the various retinal layers can be estimated (Karwoski ct al. 1985~) . However, determination of p is fraught with difficulties. For example, a constant current (with a 4trcngth below that which directly activates photoreceptors) must be passeci through the retina, and the current density within the retiila muht be known, along with the percent of this current that travels extracellularly. Another problem rs that the effect of tissue damage on p profiles is not known. In co~nputing profiles of a , we have addressed these issues (Karwoski et al. 1985~~): however, some uncertairmties remain. Other technical considera- tions include ensuring that the electrode movcs a srmll, but known (e.g.. 10 p n ) , incremci~t relative to the tissue (even smaller incre~nents may be necessary to reliably resolve the OPL K ' Increase, Karwoski et al. 198550) and r~measuring p before and after determination of hVK + at each depth to ensure that recordings are stable. Activity-induced Aol also need to be specified before ISD results can be fully interpretable.

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CAN. J . PHYSIOL. PHARMACOE. VOL. 65, 1887

TABLE A1. Estimated resistivity (p) and tortuosity (X) in the radial direction and EC space volume fraction (a) of the

layers in frog retina* - - -

Layer P cm) X a

Superfusate GC/ONF IPL INL QPL 8 N L Subretinal space Pigmented

epithelium Very high ? Very small

MOTE: GC, ganglion cell; ONP, optic nerve fibers: IPL, inner plexiform layer; INL, inner nuclear layer: OPL, outer plexiform layer; ONL, outer nuclear layer.

*Resistivities were empirically determined, except for OPL; A's were assumed; a's were calculated from p and A. (Data from Karwoski et al. 1985a.)

Computation oflSD There are many possible formulas for computing the first time and second spatial derivatives. each incorporating various

degrees of slnoothing (temporal or spatial). Smoothing minimizes fluctuations owing to noise but also blurs the time course and spatial extent of source-sinks.

Inhomogeneity of a exists in the retina (Kanvoski et al. 1985a) and exerts a major effect in ISD calculations. Each measured c(x,t) should be multiplied by a prior to solving Eq. 1, thus yielding:

The practical result of such scaling by a is that bc at regions where CY is relatively high (i.e.. plexiform layers and subretinal space) beccdane larger, leading to larger Q at these depths. In Fig. 4 , this would result in the KS sink in the subretinal space and the K' sources in the OPL and IPL becoming at least three times inore prominent than source-sinks in the nuclcar layers, since u of the plexiform layers and subretinal space is at least t h e e times that of the nuclear layers (Table A l ) . However, it is also possible that because of electrode-induced tissue damage, a is locally homogeneous at all depths, and: thus, the data are accurate as presented in Fig. 4 .

Additional difficulties arise because of large discontinuities in a. Specificallyt a is negligible in the pigment epithelium ceil layer but high ( 1 .O) in the superfusate at the retinal surface. Two problems arise at these ciucial loci. First, electrode position must be known exactly relative to these boundaries so that artifactual source-sinks do not emerge. Second, artifactual source-sinks may still arise, even if electrode position is known exactly, because of the process of digitally taking the spatial derivative across a discontinuity. This latter phenomenon may be the origin of the K" sinks at depths 84 and 89% in Fig. 4 . Discontinuities also exist in X and are difficult to handle mathematically.

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