- Email: [email protected]
The role of restricted extracellular compartments in vision
THE ROLE OF RESTRICTED EXTRACELLULAR COMPARTMENTS IN VISION’
W.
KREBS.’
Institut
fir Neurobiologis.
C. S. HELRICH and V. J. \VCLFF
KFA. 517 Jtilich. German) and The Llason~c Llcdical Resexch
Laboratory. L’tica. New York 13501. C.S.X.
model is proposed N hich su,,mwsts rhat the narro\\ sxtrucellular cleft adjacent to photorsceptar cells constitutes a distinct compartment capable of regulating the ionic environment of ths sensor) cells. This model postulates a system of sodium pumps maintainin, *a rclati~ei~ high sodium concrntratlon in the vicinity of the photorrcrptor cells even in the case of \er) IOU [.Ua’] in the bathing fluid. The puzzling fact that rhe photoreceptor potential cannot be abolished bk loibcring the sodium content of the bathing medium can be readill explained b) the proposed model.
Abstract-A
INTRODUCTION
Considerable indirect evidence (summary. Wulfl’. 1973) exists indicating that the inward Bus of Na- is chief? responsible for the generation of the receptor potential in sense cells in the eyes of invertebrates. Although it had been thought that Ca” could participate in the inward current (Lisman and Brown. 1972: Broken and Lisman. 1972). recent evidence argues against this idea (Lisman and Brown, 1974; Brown. 1974; Broivn and Mote. 1973). It is, however, a puzzling fact. well estab-
’ This study was aided in part by Grant 5 ROI EY 00236 from the National Eje Institute. National Institutes of Health, Public Health Service. Dept. of Health. Education and Welfare. ’ W. Krebs. member of SFB 160 of the Deutsche Forschungsgemeinschaft
lished b> a number of investigators (Stieve. 1964; FuIpius and Baumann, 1969: Millecchia and Mauro. 1969: Brown. Hagiwara, Koike and >Isech. 1970: Gaube and Stievs and LVirth. 1971: Stieve. Pvlalinoa-ska. 1971: Wulff. 1973) that the sense cells of several invertebrates still depolarize following a light flash after prolonged exposure to environments containing little or no sodium chloride. Particularly. the receptor potential elicited from LinAs lateral eye rstinular cells dark adapted in such sodium deficient environments is about as large as that obtained under similar conditions in an en\-ironment normal with respect to KaCl (Wulff. 1973; Wulff. Stieve and Fahp. 1975; Fig. I, left and middle columns. upper oscillograms): i.2. the receptor potential elicited from a dark adapted eye is virtually independent of the C;VaCI],,,. The response to the second light flash (lo-set interval) is markedly attenuated (Fig. 1. middle column), but
SECONDS AFTER DARK ADAPTATION
10
20
Fig. 1. Oscillograms of receptor potentials elicited from a dark adaptsd Lmrrhs lateral eke retinular cell by a 20-llsec light flash (IO?-gWsec cm’ at the cornea) coincident uith rhe onset of each tract. Prior to the first responses (upper roa) the preparation was dark adapted for 30 min in environments 435 and 50 mat with respect to sodium chloride and (right column) 10 +I ouabain. After the tirst stimulus. liyht Rashes \\ere delivered 767
at lo-s-c intervals.
subsequent responses increase to a stable magnitude that is lower than that of the initial response (stcadq state after about -@sect. TO explain these observations. Stieve I 1964) and FL& pius and Baumann (1969) and others have suggested that. in sgite of prolonged exposure of isolated photoreceptors to sodium deficient environments, sufficient sodium rsmuins in the vicinity of the light-activated photoreceptor membrane to produce an attenuated receptor potential. Fulpius and Baumann further suggested that. in the eye of ths honey bee drone. pigment cells or land) the extracsllular compartment of the rhnbdome possibly constitute sodium reservoirs from which sodium is excreted or diffllses into the extracelMar space adjacent to the sense cell. However. these authors presented no detailed model. The results ofelectron microscopic investigations indicate that it is a common feature of arthropod photoreceptors that the extracellular space surrounding the sense cells is reduced to a small cleft approx 100 A wide. This cleft is either between the photoreceptor and glia cells (barnacle-Fahrenbach. 1965). or between photoreceptor and pigment cells (Litmrius --MiIler. 1957; Fahrenbach. 1969; honey bee drone -Perrelet. 1970: and Musa+Boschek. 1971) or between neighboring photoreceptor cells (&racus--Krebs. 1972).The membranes of these cells often interdigitate extensively. It seems that each photoreceptor cell is shielded from the external environment. consisting either of blood in ciao or a bathing medium irl citro. by other cells. The existence of such a cleft. acting as a finite sodium reservoir, has already been proposed by Krischsr (1972) to sxplain the transient phase of the receptor potential of the barnacle. Here Evepropose a model. schematically illustrated in Fig. 2. which suggests that the strict limitation of the extracellular space encircling the cell bodies of ths photoreceptors of arthropods (and. perhaps, other invertebrat? photoreceptors as well) plays an important physiological role. This model extends the hypothesis of Fulpius and Baumann I 1969). THE MODEL
The esistence of a system of sodium pumps bound to the membranes is postulated as shown in Fig. 2. The role of the system pl is simply to maintain the glia cell sodium concentration at a sufficiently low level by pumping sodium back into the bathing medium. We choose the activity of this system. i.e. its contribution to the current. ill, to be proportional to the sodium concentration in compartment (2). That is (j2 I Ipump= KrJ[Na12.
(1)
The function of pump system p2 is to maintain a relatively high sodium concentration in the extracellular cleft compartment (E.C.). We choose the activity of this system to be inversely proportional to the concentration in the E.C.. so that li2Jpump = Kb?i PaI3 (ii3)pump= Kk”,!ma],.
13) (3)
Such a pump system. which functions to establish and maintain a concentration gradient of sodium across 3 layer of cells is. for example. k;noLvn to exist in ths frog skin (Damson. 19701.
:z------,,
?3-
-
,31
_.
jJ_.----_ ---
:i
Fia=. 2. Schematic diagram of the model. t.4) membrane separating compartments I (bathing medium) and 2 (glin cell/. Contains pump pi.(B) Membrane sepamting compartments Z tglia cell) and 3 (E.C.. extracellular sieft compartment). Contains pump ~2. (0 Membrane qarating compartments 3 (E.C.) and 4 (Receptor cell). Conrains pump ~2. jmnis the sodium current flowing from compartment m into
compartment n. We assume all further contributions to the currents j,, to be diffusion currents. These we express as Omnhilf
=
LPaL
(4)
in which kmn is the diffusion coefficient for the membrane separating compartments rn and )I. Since the pumping systems pl and p:! are different it may be expected that the structure of the corresponding membranes is different, resulting in different diffusion coeficients. We shall write the diffusion coefficients for the membranes A. B. and C of Fig. 2 as k.,, k,, and k, respectively. That is. k,? = k?, = k,<. etc. ,\ccordinglq. the currents are then given bq ;,2 = k,,[Na],
(5)
jzI= k,r[Na]z + KF’[Na]l
(61
jz3 = k*[Na], + KF’![Na], j3? = k,[Na],
i71
i3& = kCNa13 jl3 = kc[Na], + K’,” [NalJ.
19)
(8) (IO)
From these, the sodium concentrations in the various compartments may be calculated from the mass conservation equation (written here for compartment h) dCNa],/dt=
(lll’):Vmh + jnh) -i;!+,, -I- ihn)l (Ill
in which tn and n are the compartments bounding h and I/ is the volume of the compartment /I. Experiments are normally performed on partially light adapted excised eyes. With respect to the analytical formulation. this is a state of equilibrium specified by the conditions
imn= inm
(12)
produce three equations relating the equilibrium concentrations, [Na]‘,“‘, nz = 2. 3. 4. for a given bathing medium concentration. [Na]‘Io’. for all jn and n. These conditions
+ k-f) [Na]P
0 = ~IISa]‘lO’ - pa]:“‘, 0 = X-&[&i]\”
- [Na]l;OI) f K;” [Na]\“‘.
(11)
[Na]>” = ( I 2) {[Nn]‘:’
- , i[Nu]‘P’)’ - 4iKb” kBj.
( 15) (23)
In vvhat iolloas. vve shall assume that k, = kc. That is. ue assume that the structure of membranes B and C 1s the same and that their areas do not differ apprsciably from one another. This is true if the E.C. volume is small. From equations (13)-(15). one then obtains for the squilibrium concentrations
The concentration proportional to
gradient across membrane
C is then
If pump sjstsm pl remains active. the concentration gradient across membrane C is proportional to
The positive square root has been chosen in equation I LY)as the only physically acceptable solution. PKEDICTIOSS
From equations I 16t( IS). some conclusions may be drawn regarding the equilibrium configuration of the system. (I) Combining equations (16). (17) and (1s). [Na]\O’ = (k,,‘(b, + Ky’))[Na]‘,“’ [Na]\O’ = ( I I)(b,
(k, f A$“))
i
09)
[Na]‘,” t
The sodium concentration in the receptor cell is. then. proportional to that in the bathing medium. [Sal’:‘. and is louver than that in the bathing medium. Also. the concentration in the E.C. varies with [Na]‘,” and. dependin? on the magnitude of the term K\” (k,, + A’;[‘) k,,kB. may exceed [Sal’,“. This latter term increases vr,ith increasing activity of pump sqstsm ~2. Therefore. as this activity increases. the concentration in the E.C. increases. (2) From equations (19) and (20). we obtain d[Xa]\”
d[Na]‘y’
d[Sa];O’ d[Na]‘y’
d[Na]\”
d[Na]‘y’
d[Na]y
d[Na]‘y’
That is. the concentratton gradient in fact increases if the activit! of pump system pl is inhibited. Such a selective inhibition of the pump system pl could occur during the earl) stages of ouabain intoxication. since ouabain is known to inhibit Xa-K activated ATPase. The oscillograms in Fig 1. right column, demonstrate the results of an ssperiment in vvhich the excised Lirmhs lateral eve was dark adapted for 30 min in an environment 50 rn>r with respect to NaCl and containing 10 j*41ouabain. The magnitude of the initial response (upper oscillogram) is significnntlq larger than that in the middle column as nell as that in the left column. which is predicted above. Stieve. Bollmann-Fischer and Braun (1971) also observed transitory enhancement of the response mayituds of craqfish photoreceptors during the earl) stages of ouabain intoxication. (4) ;\s stated above. if the sense cell is subjected to a series of flashes (in the experiment of Fig. I the flash interv-al vvas 10s~~) while immersed in a bathing medium deficient in ?JaCl. a response of a non-decreasing magnitude is elicited from each of an indeiinite number of flashes. That is. provided the time interval between fashes is long enough. the cell system is able to recover to a state in which the Na concentrations in the E.C. and sense cell are such that the cell will fire in spite of the lo\\ [NaCI] in the bath. The squations (16t(lS1 show that the steady state concentrations [Ya]i,“. . [Na]:” are uniquely determined bq‘ the bath concentration [-\;a]‘,@. That is. the state to which the svstem will recover is unique and identical with the initial state. Since the system u-as responsive in its initial state. it will then also be responsive to ail subsequent Rashes. DISCL SSIOS
< ’
which is to say that with a decrease in sodium concentration in the bathing medium. the corresponding decrease in concentration in the receptor cell is greater than that in the E.C. Therefore. the sodium concentration gradient across the membrane C increases. When these conditions prevail. a sizeabkresponse to a light flash. even n-hen the sodium concentration in the bathing medium is considerably reduced. is possible. Figure I shovvs this to be the tax (3) Removing the pump system yl is tantamount to setting h’b!’ = 0 in equations (19) and (20). Doing so. we have [Xl]:“’ = [Na], 101 (22)
To obtain a clear quantitative picture of the behavior of the concentrations [Na],,,. 1~1 = 2. 5. 4. as the concentration of the bathing medium is changed. we integrated equation (11) on a digital computer for step changes in the bathing medium sodium concentration. [Na],. The results of these calculations are presented in Fig. 3. Concentrations normalized to the value of [Na], before the step change are plotted against the time normalized to the diffusion time through membrane .-I. The step change was introduced at time : = 0. The equilibrium concentrations in all compartments before the step change were assumed as indicated in the legend of Fig. 3. From this unttal equilibrium state and the equations I 13t(I5). th? nscessarq
:
:
. l
:
.
.
.
.
.
.
l
.
.
.
.
.
l
l
l
.
.
l
Broun H. XI.. Hagiwara S.. Kotke H. an.2 !4erch R. 51. I lY_01!4embrancproperties ci? i?arnx:~ photoreceptor cuJmincd by the voltage clamp tcchniqc f. Physif~i.. L0!fd. 208. 3854ij. Broun J. E. I 1971) Inrracsllular cak:_n and light :idapration in invertebrat: phatorecz;:ors labstmct~. Spring Meeting of “The .%ssociation %r Research in Vision and Ophth~~lmolog~‘.. Sarasota. Florida. Brown J. E. and L&man f. E. i 19731.4n elcctrogenic sodium pump in Lrn~titfs %entrai photoreceptor &Is j. gm. PhrjlO/ 39. -N-77?
.
41) 3;
Fig. 3. Sodium concentrations in compartmenrs 3. 3, and 4 normalized to initial bathing medium sodium concentration. [Na]$. presented as functions of time normalized to the ditfusion time for membrane A. The curves represent the responses of the respective compartmrnts to a step decrease in [Na],. Curve parameter, p. is the ratio of [Ka], after the step change to its value before the step change. Assumed initial conditions are: [Na],(normalizedl = (~1, fNa],(normalized) = 05. (~a]~(nor~~iz~d) =I O.OYS. coefficients for the differential equations were calcula ted. The conclusions (1) and (2) above are reflected in the
curves of Fig. 3. That is. it is easily seen that step decreases in [Na]l produce proportional changes in [Na], and [??a]., and that the change in [Na], exceeds that of (?%a],. We make no pretence regarding the correctness of our model in all details; i.e. the system we have arbitrarily called pZ may not be a simple ATPase system. but a more complicated regulatory system. The oniy property of this system that has been of interest to us has been its pumping capacity. The model described above explains some of the puzzling observations regarding the behavior of some invertebrate photoreceptors in low sodium environments. Therefore, it can be suggested that the extremely narrow extracellular cleft surrounding the photosensitive ceils plays an important physiological role in maintaining an ionic environment of these cells which enables them to function even when the bathing medium deviates from the normal ionic composition. ,Ickflovviedgement--We wish to express our appreciation to Dr. G. B. Arden for suggesting that a mathematical analysis of the model be attempted. This was achieved and signifi-
cantly changed the nature of the presentation. REFEREXCES
Boschek C. B. (1971) On the fine structure of the peripheral retina and lamina gan@ionaris of the Hy Muscn dornestica Z. Zdlforsch. 118, 369409.
fulpius B. and Baumann F. I 1369)EtYectj/I( Gddium. pdtassium xnd caloiu.m ions on slow and shim: potentials in single photoreceptor cells. J. J+K Pl~ys~l 53, S-tl-561, Krebs Q’. (1972IThe fine structure of the r~mula of ,~S~~IZUS fitrriciriiis. 2. Ztififnrsch. 133. ?99-414. Krischer C. C. I 19’2) On the mschanisr:: .:‘t elect&i rcsponsc of the photoreceptors of the ba-zz~le and other animals. Z. .\‘imrrf: 76, 109~At 2. Lisrnan J. E. and Brown J. E.I 19121The eK::r, of mtra;ci[uktr C,t _ _ on the light response 2nd i>c .:&: ddap&ttion in Liof~ii~sventral photoreceptor. .-ldr. 2-:: if&. BbI. 25. 2: ~5.:. Listnan J. E. and Brown J. E. I 13”41Ette~:~oi calcium an adaptation and excitation in Lirttilir~ vent:11 photorrccptori (abstract). Spring Meeting of “The kjjociation for Rsxsarch in Vision and Ophthalmolo~!Sarasota. Florida. Mitlscchia R. and Mauro A. 41969)The ve~zll photorec~ptor ceils of Lin~rl~r.~.Il. The basic phot~~:e-;ponsr. J. +,n. Ph~sid. 54, 310-330.
Pzrrefet A. 11970) The fine structure of rh rsrina of the hone> bee drone. Z. Z~~~~~~~~.$08, S?p-563. Stisks H. ii964 Das Belichtungspot~ntiai ;it: isoiiertzn Retina des Einsiedlerkrebses (Eqqtrru.: ?<~hnizkrs L.I in ;\bh2ngigkeit van den cutrazellu~ren l,?nenkonzentrationen. Z. cqqi. P!~rs~i~.47. 457-493. Stie:\: H., Bollmann-Fischer H. and Braun B.f i971) The significance of metabolic energ) and thr :i‘: ?ump for the receptor potrnriaf of the cra\;fIsh phor,~~eptor ceil. 2. .t-rrntrj: 26, 131l-1321. Stievc H.. Gaube H. and Maiinowska T. : .Q-_‘i The e&t of some sodium substitutes on the rece?rcr potentiai of ths crayfish photoreceptor cell. Z. .l-cmcr-:17. 153_~1516. Stie\e H. and %‘irrh Chr. (19il1 cbrr die Icnsn-Xbhkv&kit dzs Rszeptorpotentials der Rztina :<‘I?.-lsroc~s Irpfo&N&S. Z. .VutttrJI Xb, 43%4% Wulif V, _i,i 1973)The effect of sodium. possum and calcium on Lirrnfirrslattral e>s rctinular ceil. i isinn Re.s. 13, 2X9-2326. WulRV. J.. Stieve H. and Fahq, J. L. t 19751Dark adaptation and sodium pump actlvlt], in Limxk lateral :ye retinular cells. C’isior~Rer. 15. 759-‘65.
W.
KREBS.’
Institut
fir Neurobiologis.
C. S. HELRICH and V. J. \VCLFF
KFA. 517 Jtilich. German) and The Llason~c Llcdical Resexch
Laboratory. L’tica. New York 13501. C.S.X.
model is proposed N hich su,,mwsts rhat the narro\\ sxtrucellular cleft adjacent to photorsceptar cells constitutes a distinct compartment capable of regulating the ionic environment of ths sensor) cells. This model postulates a system of sodium pumps maintainin, *a rclati~ei~ high sodium concrntratlon in the vicinity of the photorrcrptor cells even in the case of \er) IOU [.Ua’] in the bathing fluid. The puzzling fact that rhe photoreceptor potential cannot be abolished bk loibcring the sodium content of the bathing medium can be readill explained b) the proposed model.
Abstract-A
INTRODUCTION
Considerable indirect evidence (summary. Wulfl’. 1973) exists indicating that the inward Bus of Na- is chief? responsible for the generation of the receptor potential in sense cells in the eyes of invertebrates. Although it had been thought that Ca” could participate in the inward current (Lisman and Brown. 1972: Broken and Lisman. 1972). recent evidence argues against this idea (Lisman and Brown, 1974; Brown. 1974; Broivn and Mote. 1973). It is, however, a puzzling fact. well estab-
’ This study was aided in part by Grant 5 ROI EY 00236 from the National Eje Institute. National Institutes of Health, Public Health Service. Dept. of Health. Education and Welfare. ’ W. Krebs. member of SFB 160 of the Deutsche Forschungsgemeinschaft
lished b> a number of investigators (Stieve. 1964; FuIpius and Baumann, 1969: Millecchia and Mauro. 1969: Brown. Hagiwara, Koike and >Isech. 1970: Gaube and Stievs and LVirth. 1971: Stieve. Pvlalinoa-ska. 1971: Wulff. 1973) that the sense cells of several invertebrates still depolarize following a light flash after prolonged exposure to environments containing little or no sodium chloride. Particularly. the receptor potential elicited from LinAs lateral eye rstinular cells dark adapted in such sodium deficient environments is about as large as that obtained under similar conditions in an en\-ironment normal with respect to KaCl (Wulff. 1973; Wulff. Stieve and Fahp. 1975; Fig. I, left and middle columns. upper oscillograms): i.2. the receptor potential elicited from a dark adapted eye is virtually independent of the C;VaCI],,,. The response to the second light flash (lo-set interval) is markedly attenuated (Fig. 1. middle column), but
SECONDS AFTER DARK ADAPTATION
10
20
Fig. 1. Oscillograms of receptor potentials elicited from a dark adaptsd Lmrrhs lateral eke retinular cell by a 20-llsec light flash (IO?-gWsec cm’ at the cornea) coincident uith rhe onset of each tract. Prior to the first responses (upper roa) the preparation was dark adapted for 30 min in environments 435 and 50 mat with respect to sodium chloride and (right column) 10 +I ouabain. After the tirst stimulus. liyht Rashes \\ere delivered 767
at lo-s-c intervals.
subsequent responses increase to a stable magnitude that is lower than that of the initial response (stcadq state after about -@sect. TO explain these observations. Stieve I 1964) and FL& pius and Baumann (1969) and others have suggested that. in sgite of prolonged exposure of isolated photoreceptors to sodium deficient environments, sufficient sodium rsmuins in the vicinity of the light-activated photoreceptor membrane to produce an attenuated receptor potential. Fulpius and Baumann further suggested that. in the eye of ths honey bee drone. pigment cells or land) the extracsllular compartment of the rhnbdome possibly constitute sodium reservoirs from which sodium is excreted or diffllses into the extracelMar space adjacent to the sense cell. However. these authors presented no detailed model. The results ofelectron microscopic investigations indicate that it is a common feature of arthropod photoreceptors that the extracellular space surrounding the sense cells is reduced to a small cleft approx 100 A wide. This cleft is either between the photoreceptor and glia cells (barnacle-Fahrenbach. 1965). or between photoreceptor and pigment cells (Litmrius --MiIler. 1957; Fahrenbach. 1969; honey bee drone -Perrelet. 1970: and Musa+Boschek. 1971) or between neighboring photoreceptor cells (&racus--Krebs. 1972).The membranes of these cells often interdigitate extensively. It seems that each photoreceptor cell is shielded from the external environment. consisting either of blood in ciao or a bathing medium irl citro. by other cells. The existence of such a cleft. acting as a finite sodium reservoir, has already been proposed by Krischsr (1972) to sxplain the transient phase of the receptor potential of the barnacle. Here Evepropose a model. schematically illustrated in Fig. 2. which suggests that the strict limitation of the extracellular space encircling the cell bodies of ths photoreceptors of arthropods (and. perhaps, other invertebrat? photoreceptors as well) plays an important physiological role. This model extends the hypothesis of Fulpius and Baumann I 1969). THE MODEL
The esistence of a system of sodium pumps bound to the membranes is postulated as shown in Fig. 2. The role of the system pl is simply to maintain the glia cell sodium concentration at a sufficiently low level by pumping sodium back into the bathing medium. We choose the activity of this system. i.e. its contribution to the current. ill, to be proportional to the sodium concentration in compartment (2). That is (j2 I Ipump= KrJ[Na12.
(1)
The function of pump system p2 is to maintain a relatively high sodium concentration in the extracellular cleft compartment (E.C.). We choose the activity of this system to be inversely proportional to the concentration in the E.C.. so that li2Jpump = Kb?i PaI3 (ii3)pump= Kk”,!ma],.
13) (3)
Such a pump system. which functions to establish and maintain a concentration gradient of sodium across 3 layer of cells is. for example. k;noLvn to exist in ths frog skin (Damson. 19701.
:z------,,
?3-
-
,31
_.
jJ_.----_ ---
:i
Fia=. 2. Schematic diagram of the model. t.4) membrane separating compartments I (bathing medium) and 2 (glin cell/. Contains pump pi.(B) Membrane sepamting compartments Z tglia cell) and 3 (E.C.. extracellular sieft compartment). Contains pump ~2. (0 Membrane qarating compartments 3 (E.C.) and 4 (Receptor cell). Conrains pump ~2. jmnis the sodium current flowing from compartment m into
compartment n. We assume all further contributions to the currents j,, to be diffusion currents. These we express as Omnhilf
=
LPaL
(4)
in which kmn is the diffusion coefficient for the membrane separating compartments rn and )I. Since the pumping systems pl and p:! are different it may be expected that the structure of the corresponding membranes is different, resulting in different diffusion coeficients. We shall write the diffusion coefficients for the membranes A. B. and C of Fig. 2 as k.,, k,, and k, respectively. That is. k,? = k?, = k,<. etc. ,\ccordinglq. the currents are then given bq ;,2 = k,,[Na],
(5)
jzI= k,r[Na]z + KF’[Na]l
(61
jz3 = k*[Na], + KF’![Na], j3? = k,[Na],
i71
i3& = kCNa13 jl3 = kc[Na], + K’,” [NalJ.
19)
(8) (IO)
From these, the sodium concentrations in the various compartments may be calculated from the mass conservation equation (written here for compartment h) dCNa],/dt=
(lll’):Vmh + jnh) -i;!+,, -I- ihn)l (Ill
in which tn and n are the compartments bounding h and I/ is the volume of the compartment /I. Experiments are normally performed on partially light adapted excised eyes. With respect to the analytical formulation. this is a state of equilibrium specified by the conditions
imn= inm
(12)
produce three equations relating the equilibrium concentrations, [Na]‘,“‘, nz = 2. 3. 4. for a given bathing medium concentration. [Na]‘Io’. for all jn and n. These conditions
+ k-f) [Na]P
0 = ~IISa]‘lO’ - pa]:“‘, 0 = X-&[&i]\”
- [Na]l;OI) f K;” [Na]\“‘.
(11)
[Na]>” = ( I 2) {[Nn]‘:’
- , i[Nu]‘P’)’ - 4iKb” kBj.
( 15) (23)
In vvhat iolloas. vve shall assume that k, = kc. That is. ue assume that the structure of membranes B and C 1s the same and that their areas do not differ apprsciably from one another. This is true if the E.C. volume is small. From equations (13)-(15). one then obtains for the squilibrium concentrations
The concentration proportional to
gradient across membrane
C is then
If pump sjstsm pl remains active. the concentration gradient across membrane C is proportional to
The positive square root has been chosen in equation I LY)as the only physically acceptable solution. PKEDICTIOSS
From equations I 16t( IS). some conclusions may be drawn regarding the equilibrium configuration of the system. (I) Combining equations (16). (17) and (1s). [Na]\O’ = (k,,‘(b, + Ky’))[Na]‘,“’ [Na]\O’ = ( I I)(b,
(k, f A$“))
i
09)
[Na]‘,” t
The sodium concentration in the receptor cell is. then. proportional to that in the bathing medium. [Sal’:‘. and is louver than that in the bathing medium. Also. the concentration in the E.C. varies with [Na]‘,” and. dependin? on the magnitude of the term K\” (k,, + A’;[‘) k,,kB. may exceed [Sal’,“. This latter term increases vr,ith increasing activity of pump sqstsm ~2. Therefore. as this activity increases. the concentration in the E.C. increases. (2) From equations (19) and (20). we obtain d[Xa]\”
d[Na]‘y’
d[Sa];O’ d[Na]‘y’
d[Na]\”
d[Na]‘y’
d[Na]y
d[Na]‘y’
That is. the concentratton gradient in fact increases if the activit! of pump system pl is inhibited. Such a selective inhibition of the pump system pl could occur during the earl) stages of ouabain intoxication. since ouabain is known to inhibit Xa-K activated ATPase. The oscillograms in Fig 1. right column, demonstrate the results of an ssperiment in vvhich the excised Lirmhs lateral eve was dark adapted for 30 min in an environment 50 rn>r with respect to NaCl and containing 10 j*41ouabain. The magnitude of the initial response (upper oscillogram) is significnntlq larger than that in the middle column as nell as that in the left column. which is predicted above. Stieve. Bollmann-Fischer and Braun (1971) also observed transitory enhancement of the response mayituds of craqfish photoreceptors during the earl) stages of ouabain intoxication. (4) ;\s stated above. if the sense cell is subjected to a series of flashes (in the experiment of Fig. I the flash interv-al vvas 10s~~) while immersed in a bathing medium deficient in ?JaCl. a response of a non-decreasing magnitude is elicited from each of an indeiinite number of flashes. That is. provided the time interval between fashes is long enough. the cell system is able to recover to a state in which the Na concentrations in the E.C. and sense cell are such that the cell will fire in spite of the lo\\ [NaCI] in the bath. The squations (16t(lS1 show that the steady state concentrations [Ya]i,“. . [Na]:” are uniquely determined bq‘ the bath concentration [-\;a]‘,@. That is. the state to which the svstem will recover is unique and identical with the initial state. Since the system u-as responsive in its initial state. it will then also be responsive to ail subsequent Rashes. DISCL SSIOS
< ’
which is to say that with a decrease in sodium concentration in the bathing medium. the corresponding decrease in concentration in the receptor cell is greater than that in the E.C. Therefore. the sodium concentration gradient across the membrane C increases. When these conditions prevail. a sizeabkresponse to a light flash. even n-hen the sodium concentration in the bathing medium is considerably reduced. is possible. Figure I shovvs this to be the tax (3) Removing the pump system yl is tantamount to setting h’b!’ = 0 in equations (19) and (20). Doing so. we have [Xl]:“’ = [Na], 101 (22)
To obtain a clear quantitative picture of the behavior of the concentrations [Na],,,. 1~1 = 2. 5. 4. as the concentration of the bathing medium is changed. we integrated equation (11) on a digital computer for step changes in the bathing medium sodium concentration. [Na],. The results of these calculations are presented in Fig. 3. Concentrations normalized to the value of [Na], before the step change are plotted against the time normalized to the diffusion time through membrane .-I. The step change was introduced at time : = 0. The equilibrium concentrations in all compartments before the step change were assumed as indicated in the legend of Fig. 3. From this unttal equilibrium state and the equations I 13t(I5). th? nscessarq
:
:
. l
:
.
.
.
.
.
.
l
.
.
.
.
.
l
l
l
.
.
l
Broun H. XI.. Hagiwara S.. Kotke H. an.2 !4erch R. 51. I lY_01!4embrancproperties ci? i?arnx:~ photoreceptor cuJmincd by the voltage clamp tcchniqc f. Physif~i.. L0!fd. 208. 3854ij. Broun J. E. I 1971) Inrracsllular cak:_n and light :idapration in invertebrat: phatorecz;:ors labstmct~. Spring Meeting of “The .%ssociation %r Research in Vision and Ophth~~lmolog~‘.. Sarasota. Florida. Brown J. E. and L&man f. E. i 19731.4n elcctrogenic sodium pump in Lrn~titfs %entrai photoreceptor &Is j. gm. PhrjlO/ 39. -N-77?
.
41) 3;
Fig. 3. Sodium concentrations in compartmenrs 3. 3, and 4 normalized to initial bathing medium sodium concentration. [Na]$. presented as functions of time normalized to the ditfusion time for membrane A. The curves represent the responses of the respective compartmrnts to a step decrease in [Na],. Curve parameter, p. is the ratio of [Ka], after the step change to its value before the step change. Assumed initial conditions are: [Na],(normalizedl = (~1, fNa],(normalized) = 05. (~a]~(nor~~iz~d) =I O.OYS. coefficients for the differential equations were calcula ted. The conclusions (1) and (2) above are reflected in the
curves of Fig. 3. That is. it is easily seen that step decreases in [Na]l produce proportional changes in [Na], and [??a]., and that the change in [Na], exceeds that of (?%a],. We make no pretence regarding the correctness of our model in all details; i.e. the system we have arbitrarily called pZ may not be a simple ATPase system. but a more complicated regulatory system. The oniy property of this system that has been of interest to us has been its pumping capacity. The model described above explains some of the puzzling observations regarding the behavior of some invertebrate photoreceptors in low sodium environments. Therefore, it can be suggested that the extremely narrow extracellular cleft surrounding the photosensitive ceils plays an important physiological role in maintaining an ionic environment of these cells which enables them to function even when the bathing medium deviates from the normal ionic composition. ,Ickflovviedgement--We wish to express our appreciation to Dr. G. B. Arden for suggesting that a mathematical analysis of the model be attempted. This was achieved and signifi-
cantly changed the nature of the presentation. REFEREXCES
Boschek C. B. (1971) On the fine structure of the peripheral retina and lamina gan@ionaris of the Hy Muscn dornestica Z. Zdlforsch. 118, 369409.
fulpius B. and Baumann F. I 1369)EtYectj/I( Gddium. pdtassium xnd caloiu.m ions on slow and shim: potentials in single photoreceptor cells. J. J+K Pl~ys~l 53, S-tl-561, Krebs Q’. (1972IThe fine structure of the r~mula of ,~S~~IZUS fitrriciriiis. 2. Ztififnrsch. 133. ?99-414. Krischer C. C. I 19’2) On the mschanisr:: .:‘t elect&i rcsponsc of the photoreceptors of the ba-zz~le and other animals. Z. .\‘imrrf: 76, 109~At 2. Lisrnan J. E. and Brown J. E.I 19121The eK::r, of mtra;ci[uktr C,t _ _ on the light response 2nd i>c .:&: ddap&ttion in Liof~ii~sventral photoreceptor. .-ldr. 2-:: if&. BbI. 25. 2: ~5.:. Listnan J. E. and Brown J. E. I 13”41Ette~:~oi calcium an adaptation and excitation in Lirttilir~ vent:11 photorrccptori (abstract). Spring Meeting of “The kjjociation for Rsxsarch in Vision and Ophthalmolo~!Sarasota. Florida. Mitlscchia R. and Mauro A. 41969)The ve~zll photorec~ptor ceils of Lin~rl~r.~.Il. The basic phot~~:e-;ponsr. J. +,n. Ph~sid. 54, 310-330.
Pzrrefet A. 11970) The fine structure of rh rsrina of the hone> bee drone. Z. Z~~~~~~~~.$08, S?p-563. Stisks H. ii964 Das Belichtungspot~ntiai ;it: isoiiertzn Retina des Einsiedlerkrebses (Eqqtrru.: ?<~hnizkrs L.I in ;\bh2ngigkeit van den cutrazellu~ren l,?nenkonzentrationen. Z. cqqi. P!~rs~i~.47. 457-493. Stie:\: H., Bollmann-Fischer H. and Braun B.f i971) The significance of metabolic energ) and thr :i‘: ?ump for the receptor potrnriaf of the cra\;fIsh phor,~~eptor ceil. 2. .t-rrntrj: 26, 131l-1321. Stievc H.. Gaube H. and Maiinowska T. : .Q-_‘i The e&t of some sodium substitutes on the rece?rcr potentiai of ths crayfish photoreceptor cell. Z. .l-cmcr-:17. 153_~1516. Stie\e H. and %‘irrh Chr. (19il1 cbrr die Icnsn-Xbhkv&kit dzs Rszeptorpotentials der Rztina :<‘I?.-lsroc~s Irpfo&N&S. Z. .VutttrJI Xb, 43%4% Wulif V, _i,i 1973)The effect of sodium. possum and calcium on Lirrnfirrslattral e>s rctinular ceil. i isinn Re.s. 13, 2X9-2326. WulRV. J.. Stieve H. and Fahq, J. L. t 19751Dark adaptation and sodium pump actlvlt], in Limxk lateral :ye retinular cells. C’isior~Rer. 15. 759-‘65.