BY STEFANO FORTI*, ANNA MENINIt, GIORGIO RISPOLI§ AND ...

Journal of Physiology (1989), 419, pp. 265-2915 265With 9 text-figuresPrinted in Great Britain

KINETICS OF PHOTOTRANSDUCTION IN RETINAL RODS OF THENEWT TRITURUS CRISTA TUS

BY STEFANO FORTI*, ANNA MENINIt, GIORGIO RISPOLI§AND VINCENT TORREt

From the Dipartimento di Fisica, Universitd di Genova, Via Dodecaneso 33,16146 Genova, Italy and *IRST, 38050 Povo, Trento, Italy

(Received 9 March 1989)

SUMMARY

1. The kinetics of photoresponses to flashes and steps of light of rods, from theretina of the newt Triturus cristatus, were analysed by recording the membranecurrent with a suction electrode.

2. In dark-adapted conditions the relation between the normalized amplitude ofthe photoresponse at a fixed time 1 s after the onset of light and the light intensitycould be fitted by an exponential or a polynomial relation. In the presence of a steadybright light the same relation could be fitted by a Michaelis-Menten relation.

3. The kinetics of photoresponses to light stimuli was reconstructed using a modelin which: (i) three molecules of guanosine 3',5'-cyclic monophosphate (cyclic GMP)open a light-sensitive channel; (ii) light activates the enzyme phosphodiesterase,which hydrolyses cyclic GMP, thus closing light-sensitive channels; (iii) Ca2" ionspermeate through light-sensitive channels; and (iv) intracellular Ca21 inhibits, in aco-operative way, the enzyme cyclase, which synthesizes cyclic GMP.

4. The model reproduces the shortening of the time to peak of brief flashphotoresponses from about 1080 ms to about 690 ms with brighter lights. The modelalso explains the shortening of the time to peak to 350 ms observed in the presenceof a steady light and the lack of a further acceleration with brighter flashes of lights.

5. The presence in the model of an intracellular calcium buffer accounts for thepartial reactivation of the photocurrent following a step of light, lasting severalseconds. The time course of this reactivation is not accelerated by a steady brightlight both experimentally and in the model.

6. After the extinction to a long step of light the photocurrent showed a rapidpartial reactivation, which was followed by a slow component of the photoresponsewhich extinguished with a rate constant of about 0 05 s-'. The model explains theorigin of this slow component by assuming that the inactivation of excited rhodopsinis partially reversible.

7. The model is also able to explain the particular changes of kinetics when

t To whom correspondence and reprint requests should be sent.$ Present address: Istituto di Cibernetica e Biofisica, C.N.R., 16146 Genova, Italy.§ Present address: Department of Physiology and Biophysics, University of Washington,

Seattle, WA 98195, USA.MS 7567

S. FORTI, A. MENINI, G. RISPOLI AND V. TORRE

different amounts of exogenous calcium buffers are incorporated into rods (Torre,Matthews & Lamb, 1986).

INTRODUCTION

In recent years our understanding of mechanisms of phototransduction hassubstantially changed. We now know that guanosine 3',5'-cyclic monophosphate(cyclic GMP) is the internal transmitter of phototransduction (Caretta & Cavaggioni,1983; Fesenko, Kolesnikov & Lyubarsky, 1985; Yau & Nakatani, 1985b; Haynes,Kay & Yau, 1986; Zimmermann & Baylor, 1986) and that Ca21 is not a positivetransmitter (Matthews, Torre & Lamb, 1985; Lamb, Matthews & Torre, 1986) asoriginally proposed (Hagins, 1972) since its concentration falls during light (Yau &Nakatani, 1985a; McNaughton, Cervetto & Nunn, 1986; Ratto, Payne, Owen &Tsien, 1988). It is also well established that cyclic GMP controls the current inducedin excised patches from outer segments of photoreceptors in a co-operative way(Fesenko et al. 1985; Haynes et al. 1986; Zimmermann & Baylor, 1986).The purpose of this paper is to reconsider some aspects of phototransduction and

light adaptation within the framework of this new evidence and to attempt aquantitative reconstruction of phototransduction. First the role of diffusion inphototransduction is analysed, the relation between light intensity and amplitude ofnormalized photoresponse at different times, in the dark and during light adaptationis also studied. It is also argued that a parsimonious model of phototransduction canneglect effects due to diffusion of intracellular molecules and that intracellularuniformity can be initially assumed. Secondly, changes of the concentration ofintracellular Na+, Ca2+ and cyclic GMP are evaluated and their effects on lightadaptation are discussed, assuming the view that changes of intracellular Ca2" affectthe cyclic GMP metabolism, thus controlling sensitivity and light adaptation(Cervetto, Torre, Rispoli & Marroni, 1985; Torre et al. 1986; Matthews, Murphy,Fain & Lamb, 1988; Nakatani & Yau, 1988c). Finally, we attempt to reconstruct thetime course of photoresponses to flashes and steps of light using the availableknowledge of the cyclic GMP cascade. The proposed model is also able to account forthe remarkable changes of the kinetics of photoresponses observed by incorporatingcytoplasm Ca2+ buffers into the rod (Torre et al. 1986).The experiments were performed on rods of the newt (Triturus cristatu8) of

northern Italy to extend the analysis to a new animal, which could be found locallyand the circulating photocurrent was recorded with a suction electrode (Baylor,Lamb & Yau, 1979a).

METHODS

Recordings of suction-pipette current were made from rods of the dark-adapted retina of thenewt Triturus cristatus (supplied by Fauna Esotica, Bologna, Italy). Newts were decapitated underdim red light. The retina from an eyecup was gently removed under infra-red light and immersedin a Ringer solution, and was finely chopped on Sylgard using a small piece of razor blade. Noenzymes were used. An aliquot (240Qul) containing many cells and tiny pieces of retina was thentransferred to the chamber. It was rather difficult to obtain intact isolated rods from the newtretina with a mechanical dissociation, which had proved successful with the retina of the tigersalamander. The great majority of recordings were obtained from outer segments of rods fromsmall pieces of retina. The inner and outer segment have shape and dimensions similar to rods ofthe tiger salamander.

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KINETICS OF PHOTOTRANSDUCTION

The apparatus for suction-electrode recording and optical stimulation of rods was similar to thatdescribed by Menini, Rispoli & Torre (1988). Experiments were performed at room temperature(17-25 °C). Unpolarized light of wavelength 498 nm was used for all stimuli.

After allowing the cells to settle for a few minutes, slow perfusion was applied in order to removedebris from the chamber. In scanning the preparation for cells with the best appearance it proveduseful to monitor the microscope X-Y stage position using a pair of linear position transducers(LCPT- 100; Penny & Giles, Gwent). The outer segment of a rod was drawn into the suction pipette,and its light response tested. Provided the saturating response was sufficiently large ( > 20 pA) ondstable the experiment was started. The largest photoresponse was 45 pA, while using the retina ofthe tiger salamander it was common to record photoresponses larger than 50 pA (Menini et al.1988), using exactly the same experimental procedure. The methods associated with the suctionpipettes were similar to those of Baylor et al. (1979a). The pipettes were coated with silane toprevent cells sticking. The reference electrodes in the bath and in the suction-pipette holder weresilver wires coated with a Ag-AgCl matrix (E255, Clark Electromedical). The suction pipette signalwas stored on a magnetic tape (TEAC R-80) for back-up and digitized on line at about 50 Hzsampling rate by an A/D system kindly provided for us by Dr D. Bertrand. The digital data weresubsequently transferred to a computer (IBM AT) for the analysis, which was performed using theprogram DATAC kindly provided by Dr C. Bader & Dr D. Bertrand. The Ringer solution was thesame as used by Baylor et al. (1979a) and contained (in mM): NaCl, 110; KCl, 2-5; CaCl2, 1; MgCl2,1-6; HEPES, 3; EDTA, 0-1; glucose 5; buffered to pH 7.5 with TMAOH (tetramethylammoniumhydroxide).

LIST OF SYMBOLS

ARIR = normalized photoresponseI = light intensity (in arbitrary units)Io = light intensity producing a photoresponse of half amplitude (in arbitrary

units)J = photocurrent or cyclic GMP gated current in excised patches (pA)is = steady circulating photocurrent (pA)9 = concentration of cyclic GMP (,UM)go = steady-state level of cyclic GMP (,CM)K = half-activation of the cyclic GMP gated current in excised patches (,UM)imax = maximal cyclic GMP gated current in excised patches (pA)t = timehp = photonsYi = intermediate photo products of the absorption of a photonaIX = rate constant of the reaction YY-* Y,+1 (s-1)JNa = Na+ influx (,M s-1)F = Faraday constantv = rod volume (1)YNa = rate constant of Na+ extrusion mediated by the Na+-K+ pump (s-1)Jca = Ca2+ influx (glM s-1)YCa = rate constant of Ca2+ extrusion in the absence of Ca2' buffers mediated

by the Na+-Ca2+ exchanger (s-1)eT = low-affinity Ca2+ buffer concentration (,lM)c = intracellular free Ca2+ concentration (,am)Cb = intracellular Ca2+ concentration bound to the low-affinity buffer (,UM)kp k = 'on' and 'off' rate constants for the binding of Ca2+ to the buffer (s-i

tMm-1 and s-1 respectively)

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KD = k2/kl (ftM)0c = intracellular Ca21 concentration at the steady state (,tM)Vm = membrane potential (mV)A = guanylate cyclase activity (tmM s-1)V = cyclic GMP hydrolysis in dark (s-1)V = cyclic GMP hydrolysis (s-1)PDE* = activated phosphodiesterase (/#M)ct = proportionality constant (s-1 ftM-1)PDETot = phosphodiesterase (4ttM)a = proportionality constant between current and g'nb = proportionality constant between Ca2+ influx and photocurrent (,/M s-1

pA-1)Amax = maximal activity of guanylate cyclase (,#M s-1)

Kc = intracellular Ca2+ concentration halving the cyclase activity17 = 2FVYcaal = rate constant of Rh* inactivation (s-1)at2 = rate constant of the reaction Rh, -- Rh* (s-1)a3 = rate constant of the decay of inactive rhodopsin (s-')Rh = active rhodopsin (#M)Rhi = inactive rhodopsin (#tM)Rh* = effective photoisomerizationse = rate constant of T* activation (s-1 /M'))61 = rate constant of T* inactivation (s-1)Ti = rate constant of PDE activation (s-1 /M-1)Ir2 = rate constant of PDE inactivation (s-1)T = active transducin (#tM)TTot = total transducin (#tM)Jh (t) = theoretical flux of photoisomerization (Rh* s-1)h, h2 = 'on 'and 'off' rate constants for the binding of Ca2+ to the high-affinity

buffer (s-1 tM-1 and s-1 respectively)hb = intracellular Ca2+ concentration bound to the high-affinity buffer (#tM)hT = high-affinity Ca2+ buffer concentration (#tM)

THEORY

In this section we examine some quantitative aspects of processes involved inphototransduction. The conclusions of this section form the theoretical backgroundfor the parsimonious model of phototransduction, which is introduced at the end ofthe section.

The relation between light intensity and amplitude of photoresponseThe relation between light intensity I (assumed to be in arbitrary units) and the

normalized amplitude of photoresponse AR/R has been described for a long time bya Michaelis-Menten relation:

AR IR l+I0' (1)

268


where Io is the light intensity halving the photoresponse (in the previous section allsymbols used in the text and their meaning are reported).

Equation (1) was first proposed by Baylor & Fuortes (1970), who supposed theexistence of a positive transmitter whose concentration inside the photoreceptor wasuniform and which was able to block light-sensitive channels. It was later shown thatthe diffusion of excitation and therefore of the internal transmitter was ratherrestricted (Lamb, McNaughton & Yau, 1981), possibly just to a few discs. A morecareful analysis of the relation between normalized suppressed photocurrent AJ/Jsand I at fixed times showed that the experimental data were not fitted by equation(1), but better by

AJ=t1e-I. (2)Js

Equation (2) can be obtained assuming that diffusion of excitation is restricted andthat a photoisomerization completely blocked all channels within a narrow region(Lamb et al. 1981). When diffusion of excitation is restricted, in the presence of verydim lights, we expect the distribution of the internal transmitter along the outersegment to have many large minima and maxima. By increasing the light intensitythe number of minima increases and minima eventually will start to superimpose. Itis evident that under these conditions the spatial profile of the distribution of theinternal transmitter becomes more uniform and in the presence of a steady lightexciting many rhodopsin molecules or when light flashes producing thousands ofphotoisomerizations are used, the interior of the photoreceptor will appear as a well-stirred compartment which has an almost uniform distribution of the internaltransmitter. Consequently, during light adaptation there is no strong argumentsupporting eqn (2).

In the experimental section it will be shown that in dark-adapted rods, eqn (2) fitsthe experimental data reasonably well but does not fit the data obtained during lightadaptation. It is useful to consider theoretical relations between I and AJ/J, whichcould hold during light adaptation when the interior of the photoreceptor is wellstirred.

It is now well established that the light-sensitive channel is activated by cyclicGMP and experiments with excised patches have shown that the cyclic GMP-activated current J, does not increase linearly with the cyclic GMP concentration gbut as

J n

Jmax Kn+gn (3)

where Jmax is the maximal cyclic GMP-dependent current which can be recorded inan excised patch. Haynes et al. (1986) and Zimmerman & Baylor (1986) found a valueof n close to 3 and values for K, that is the cyclic GMP concentration opening halfthe channels, in the range between 10 and 50 fM. The cube law indicates that at leastthree cyclic GMP molecules must bind to the channel before opening it.

Now an equation is derived describing the relation between light intensity I of a flash andamplitude of photoresponse which assumes the co-operativity between cyclic GMP molecules anda uniform distribution of cyclic GMP inside a rod. Let go be the steady-state level of cyclic GMP

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S. FORTI, A. MENILVI, G. RISPOLI AND V. TORRE

in some light-adapted conditions. The simplest way to describe the decrease of cyclic GMP causedby the light I is an enzymatic cascade leading to a Michaelis-Menten relation:

fgiIoO (4)rJI+Io

where IO is the light intensity halving the steady level of cyclic GMP go. In darkness the resting levelof free cyclic GMP is only a few micromolar (Yau & Nakatani, 1985b; Stryer, 1986; Nakatani &Yau, 1988b) and it decreases during light adaptation; therefore go is much smaller than K. Fromeqn (3) we obtain that, during light adaptation or, in general, when g << K:

J , 9n (5)max

where n is close to 3. If Js is the circulating photocurrent during a steady light for which theconcentration of cyclic GMP is go, the fraction of current suppressed by a superimposed light I is

___-J= 70q (6)Js g

and, using eqn (4), we finally obtain

is 1 +Io (7)

which describes the dependence of AJ/Js on light intensity I.

Kinetics of phototransduction and diffusionIn a variety of photoreceptors (Fourtes & Hodgkin, 1964; Baylor, Hodgkin &

Lamb, 1974; Baylor et al. 1979a) the time course of the electrical response to a dimflash of light can be fitted by a Poisson equation:

tn e-at (8)

which can be explained by a chain of n+ 1 slow stages:

hp->y, Y2 ... Yn+1Scheme A

where yi are intermediates photo products of the absorption of a photon hp and Yn+1is a substance controlling the kinetics of phototransduction. Equation (8) reproducesthe time course of the photoresponse to a dim flash of light very well in severalamphibian rods with n = 3 and a around 3 s-'. As diffusion can play a relevant rolein shaping the relation between amplitude of photoresponse and light intensity, it isthen conceivable that longitudinal and radial aqueous diffusion contribute to theshaping of the kinetics of the light response and that some of the slow stages impliedby eqn (8) are simply caused by diffusion and do not represent independent chemicalreactions. The number of slow stages can be easily determined by looking to the slopeof the rising phase of photoresponses when displayed on a log-log plot (Fourtes &Hodgkin, 1964; Baylor et al. 1974, 1979a). As shown by Baylor & Hodgkin (1974)and Lamb (1984) with backgrounds of steady lights of different intensity the flashresponses begin rising along a common curve. In the newt retina collected data from

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eleven rods show that in dark-adapted conditions the value of n is 2-8 + 0.3 and in thepresence of bright steady lights is 2-6 + 04 (data not shown). The difference in thevalue of n from 3 does not appear to be signilicant and it is concluded that diffusioncan contribute to the shaping of the light response in darkness, but it is unlikely thattht number of delays is primarily controlled by diffusion.

Photoresponses to steady lightsWe now analyse the effect of prolonged illumination, which ultimately leads to

light adaptation. We discuss changes of intracellular Na+ and Ca2+ which occur whentheir influx through light-sensitive channels is decreased or blocked by the light. Weanalyse these changes assuming that the intracellular level of Ca2+ is involved in thecontrol of the cyclic GMP metabolism and therefore contributing to light adaptation(Torre et al. 1986; Sather, Rispoli & Detwiler, 1988; Matthews et al. 1988; Nakatani& Yau, 1988c). We also assume that the main site of action of intracellular Ca2+ isthe guanylate cyclase (Lolley & Racz, 1982; Pepe, Panfoli & Cugnoli, 1986; Koch &Stryer, 1988; Rispoli, Sather & Detwiler, 1988) and not on the phosphodiesterase asindicated by previous results (Robinson, Kawamura, Abramson & Bownds, 1980;Torre et al. 1986).

Changes of intracellular Na+The intracellular level of Na+ is unlikely to be buffered and its changes d[Na+]j/dt

can be described by its influx and its extrusion, assumed to obey a first-order kinetic:

d[Na ]i-=Na-YNa [Na ]i (9)

where F is the Faraday constant, v the rod volume, JNa the Na+ current entering intothe rod and YNa [Na+]i is the Na+ extrusion mediated by Na+-K+ pump. When theNa+ influx is abolished intracellular Na+ in toad rods is likely to decreaseexponentially with a rate constant of about 0 04 s-I (Torre, 1982). Assuming a similarbehaviour for newt rods, we have the value 0 04 s-' for YNa Since a large componentof the Na+ influx is through the light-sensitive channels we can expect significantchanges of [Na+]i within a couple of minutes when the photocurrent has been reducedby a steady light.

Changes of intracellular Ca2+Intracellular Ca2+, unlike Na+, is buffered (McNaughton et al. 1986) and its changes

e are controlled by the influx through light-sensitive channels (Yau & Nakatani,19$4 a; Hodgkin, McNaughton & Nunn, 1985; Nakatani & Yau, 1988 a; Menini et al.1988), by its extrusion by the Na+-Ca2+ exchange (Yau & Nakatani, 1984b;Hodgkin, McNaughton & Nunn, 1987; Lagnado, Cervetto & McNaughton, 1988) andby binding and unbinding to internal buffers. The equations describing thesemechanisms are:

c=2Fv-Ycac-kl (eT-Cb)C+k2Cb, (10)and

71= 7c

271

Cb = k1VT CO C k2 Cb) (I 1)

S. FOR TI, A. MENINI, G. RISPOLI AND V. TORRE

where JCa is the total Ca2" current, eT is the total buffer concentration, cb the Ca2+concentration bound to the buffer, YCa the rate of Ca2+ extrusion mediated by theNa+-Ca2+ exchange, k, and k2 the 'on' and 'off' rate for the binding of Ca2+ to theinternal buffer. In tiger salamander rods the ratio between bound and freeintracellular Ca2+ is at least 10 (MeNaughton et al. 1986) and there is evidence tosuggest the existence of low-affinity buffers which are not saturated under normalconditions (eT > Cb) and high-affinity buffers which are almost entirely saturated(eT - Cb) with a dissociation constant k2/kl - 30 nm (Hodgkin et al. 1987). Thesteady-state level of intracellular Ca2" c does not depend on the buffer concentrationand we obtain from eqns (10) and (11)

c= JCa (12)2FvyCa'

which depends only on the Ca2+ influx and its rate of extrusion.The total volume of the newt outer segment and inner segment is respectively

2-7 x 10-12 and 3 6 x 10-12 1. Assuming that the free volume is half of the total volume,the total free volume of the rod can be taken as about 3-5 x 10-12 1. The resting levelof free intracellular Ca2+ is about 300 nm (Ratto et al. 1988) and JCa is approximately1/4 of the total photocurrent (Menini et al. 1988). Since in newt rods the largestphotocurrent recorded with a suction electrode was 40 pA (giving a value of Jca/2Fv in darkness of about 15/M s-1), from eqn (12) Yca can be estimated to be about50 s-1. The rate constant of the electrogenic current carried by the Na+-Ca2+ on thetop of a bright flash response is about 1 s-1, a value significantly smaller than the rateconstant of Ca2+ extrusion Yca of the exchanger derived from eqn (12). As suggestedby Professor Alan L. Hodgkin, this apparent discrepancy can be accounted for bythe presence of a high-affinity Ca2+ buffer inside the rod which can prolong the timeconstant of the exchanger by even 100 times.

Equations (10 and 11) describe the Ca2+ extrusion through the Na+-Ca2+ exchangeby a simple first-order mechanism, neglecting the Ca2+ entry through the exchangeitself, which will be relevant when [Ca2+]i is very low. As pointed out by Blaustein& Hodgkin (1969), at equilibrium and when [Ca2+]i is entirely controlled by theactivity of the exchanger, the intracellular level of free Ca2+ co is set by

= [Ca2+]i = [Ca2]0 [Na+]i3 eVm FIRTCo=[Ca[Ca]03 e ~~~~~~~(13)taking [Na+]i = 12 mm (Torre, 1982) and Vm =-60 mV, a value of co equal to about100 nm is obtained.Consequently eqn (10) can be more appropriately rewritten as

JCac 2Fv= yca(C cO) kl(eT cb)c +k2 Cb (14)

Changes of intracellular cyclic GMPIn the dark cyclic GMP is continuously produced by guanylate cyclase at a rate

A and is hydrolysed at a rate V. The rate of cyclic GMP hydrolysis is increased by

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light proportionally to the activated phosphodiesterase PDE* (Liebman & Pugh,1982).Therefore we can describe changes of free cyclic GMP g as

g = A-g(V+ oPDE*), (15)

where o- is a proportionality constant, assumed for simplicity to be 1 s-1 M-1. Thefree cyclic GMP concentration in the rod outer segment in darkness is only a fewmicromolar (Yau & Nakatani, 1985b; Stryer, 1986; Nakatani & Yau, 1988b) andhere it is assumed to be 2 /tM. The rate of dark activity of phosphodiesterase V hasbeen estimated to be about 0 4 s-' by Hodgkin & Nunn (1988). The rate of synthesisof cyclic GMP A from eqn (15) at the steady state is equal to goV or 0-8 tM s-'.

It now seems to be well established that the activity of the cyclase is controlled byintracellular Ca2+ in a co-operative way (Lolley & Racz, 1982; Pepe et al. 1986; Koch& Stryer, 1988; Rispoli et al. 1988) and the simplest way to describe this effect is toassume that

A- Amax (16)

1+()where Amax is the maximal activity of the cyclase and Kc is the intracellular Ca21concentration producing half-inhibition of the cyclase activity and m is the numberof Ca2+ molecules necessary to inhibit a cyclase molecule. From Koch & Stryer (1988)m is close to 4 and Kc is about 0 1 /,M. Since the resting level of free intracellular Ca21in darkness is about 300 nm (Ratto et al. 1988), the modulating action of Ca2+ on thecyclase is expected to be high in darkness but, in the presence of steady bright lights,when intracellular free Ca2+ has substantially dropped, the activity of the cyclase isaffected to a lesser extent by intracellular Ca2 .

Let us examine the relationships between c, g and light intensity I at the steady state or nearequilibrium in two cases: when the resting level of intracellular Ca2` is high and its effect on thecyclase is fully active (c > K,) and when the intracellular level of Ca2+ is low (c < Kc). The first caseis likely to describe the dark-adapted condition better, while the second case is more appropriatein the presence of a bright steady light. The level of free cyclic GMP at the steady-state g dependsonly on the steady-state synthesis A and hydrolysis V:

A (17)V.

The simplest way to describe the activation of light on the phosphodiesterase is

V= 1V+dI, (18)

where V is the dark or basal activity of phosphodiesterase and d a proportionality constant. Asalready discussed we can assume that

J = ag', (19)

and if the Ca2` photocurrent is a fraction of the circulating current we have

Jca = bJ. (20)

From eqns (16)-(19) it is possible to obtain a relation between the fraction of suppressed currentAJ/Js and !. The value of b is likely not to be constant as it changes as cyclic GCMP increases in the

273

S. FORTI, A. MENINI, G. RISPOLI AND V. TORRErod (Cervetto, Menini, Rispoli & Torre. 1988). but in the present parsimonious model b is assumedfixed.

(i) Let uts coiisider the case when c > KC. The eqn (16) then simplifies to

A Am c (21)

at the steady state, from eqns (17), (18) and (21),

g = Amax( c) (22)

by usiig eqnIs (12), (19) anid (20) we have

c=-bag (23)

where y = 2FVy,a, and finally from eqns (22) and (23),

9n+l Amaxt ba )Zm (24)

then at the steady state from eqns (19) and (24) after some simple algebra we obtain

AJ 1.(V )n/(nm+l)4S fV+dj} (25)

which becomes

Js (Io +0 (26)

where Jl = V/d.(ii) Let us now consider the case when the intracellular Ca2+ is already well below K,. In this case

eqoi (16) simplifies to

A = Amax, (27)

and the relation between fractional suppressed photocurrent and light intensity is

Al = 1 - "0) (28)4S (o +1)(8

Mwhich is the same relation of eqn (7).Equation (26) suggests that when the intracellular level of Ca2+ is high, as in dark-adapted

conditions, the relation between suppressed photocurrent and light intensity, at the steady state(i.e. when intracellular Ca2+ has reached an almost stationary level) is flatter than aMichaelis-Menten. On the contrary during bright steady lights, when intracellular Ca2` is alreadylow, the relation between suppressed photocurrent and light intensity is steeper, as suggested byeqn (28).

-27I'l


The reconstruction of the kinetics of photoresponsesLet us now attempt to provide a kinetic scheme able to reproduce several aspects

of phototransduction. We will not discuss the very early events, occurring during theinitial 50 ms, because they have already been thoroughly discussed by Cobbs & Pugh(1987). Our aim is not to obtain a perfect fitting of the experimental recordings, butto explain the major features of the kinetics of phototransduction using aparsimonious model which considers the known biochemistry of the cyclic GMPcascade and of changes of intracellular Ca2 .

It is now useful to summarize some conclusions so far obtained:(1) Aqueous diffusion of the internal transmitter is not responsible for the existence

of the slow stages in the linear response to a flash of light. The main reasonsupporting this view is that four slow stages are still required to fit the linear responsein the presence of a bright steady light. Under these conditions, given the highnumber of photoisomerizations, the cell interior is likely to be well stirred and theconcentration of the internal transmitter can be expected to be homogeneous. In thisview diffusion may shape the time course of the photoresponse in darkness, but it israther unlikely to affect the kinetics during light adaptation. Moreover it has beenshown (Karpen, Zimmerman, Stryer & Baylor, 1988) that cyclic GMP opens channelsin excised patches within very few milliseconds. Therefore the binding of cyclic GMPto the channel is unlikely to contribute to the slow stages.

(2) It is now well established that intracellular Ca2+ falls during light (Yau &Nakatani, 1985a; McNaughton et al. 1986; Ratto et al. 1988) and that changes ofintracellular Ca21 contributes to light adaptation (Torre et al. 1986) by modulatingthe cyclase (Pepe et al. 1986; Koch & Stryer, 1988). The time course of changes ofintracellular Ca2+ are controlled by the many intracellular buffers, which differ bytheir speed and affinity (McNaughton et al. 1986; Hodgkin et al. 1987). Thisparsimonious model assumes only the existence of a low-affinity Ca2+ buffer insidethe rod with a KD = k2/l1 = 4 /tM and a total concentration of 500 jm. These figuresimply that the ratio between lightly bound Ca2' and free Ca2+ is about 115, a valuehigher than the estimate of 10-20 of McNaughton et al. (1986). In order to reproducethe time constant of the reactivation of the photocurrent observed with steps of light(see Figs 4 and 5) we have assumed k2 = 0.8 s-1 and k1 = 0-2 s-1 tM-1. The value of500 /zM for the total buffer concentration is necessary to reproduce in the model areactivation of the photocurrent of approximately the same size as experimentallyobserved in newt rods during light adaptation.

Origin of the slow stagesIn their seminal paper on the kinetics of light responses in Limulus photoreceptors

Fuortes & Hodgkin (1964) identified the slow stages as activations, but also asinactivations of the internal transmitter. Therefore a slow stage in phototransduction(Baylor et al. 1974; Cervetto, Pasino & Torre, 1977; Baylor et al. 1979 a; Lamb, 1986)of vertebrate rods could be a slow activation in the cyclic GMP cascade but could alsobe a slow inactivation. In the scheme B we have reported the known biochemicalevents involved in the control of free intracellular cyclic GMP.

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S. FOR TI, A. MENVINI, G. RISPOLI AiND V. TORRE

hp pRh -kRhi

a24- 4

T*

PDE*

AlA cyclic GMP V-- GMP

Scheme B

where hv is a photon, Rh and Rhi is the activated and inactivated rhodopsinrespectively. T* and PDE* are the active transducin and phosphodiesteraserespectively.The pathway for the activation of PDE* is known in great detail, but the values

of rate constants of different biochemical steps in the intact cell have yet to beestablished precisely. Light activates rhodopsin very quickly. Activated rhodopsin isinactivated by the encounter with the two proteins rhodopsin kinase and 48 kDprotein (Applebury & Chabre, 1986; Stryer, 1986). It is assumed that the inactivationof photoexcited rhodopsin Rh is reversible, thus giving origin to the late response.The inactivation of Rh is a rather slow stage and is likely to be one of the slow stagesin phototransduction.

It is well known that 1 activated rhodopsin is able to activate about 500transducins per second (Bennett, Michel-Villaz & Kuhn, 1982; Vuong & Stryer, 1984)and 1 transducins activates 1 PDE within 100 ms (Liebman & Evanzuk, 1982),therefore indicating that the activation of PDE by transducins is another slow stagein phototransduction. The only known pathway for PDE* inactivation is throughinactivation of transducin, which again could be another slow stage in photo-transduction (Applebury & Chabre, 1986; Stryer, 1986). From the scheme B weobtain the set of equations:

Rh = Jh,(t)- l Rh + a2 Rhi, (29.1)

Rhi = l Rh-(a2 + a3)Rhi, (29.2)

T* = cRh(TTOt- T*) -IA T* + T2 PDE* (29.3)

PDE* = zr T*(PDETot-PDE*)-r2PDE*, (29.4)

where Rh and Rhi are the photoexcited and inactive rhodopsin concentration, TTotand T* are the total and activated trasducin concentration, PDETot and PDE* arethe total and the active phosphodiesterase concentration and Jh,(t) the flux ofrhodopsin photoisomerizations. In eqns (29) we have assumed that the concen-trations of excitable rhodopsin are unlimited and that the maximal amount ofexcitable transducin TTot and phosphodiesterase PDETot are 1000 and 100 1uM re-

276


TABLE 1. Value and reason for choice of parameters used in computer simulationsValue

20 s-'

0 0005 s-10 05 s-

0.5 8-5',M-1000 ,UM10-6 s-'

0-1 s-',u

10 s-'

100/SM1 S5 J/M-50 s-'

100 nM

0-625 /,M s-1 PA-0.2 s' /Sm-0.8 s-1.500/SM04 s-'

65 6 SM S-1lOOnM

1000 /,M35040 pA

Reason for choiceTo fit the time course of photoresponses to dim flash of lightTo obtain the appropriate amplitude of the late response

To fit the time course of the late response

From Bennett et al. (1982)From Stryer (1986)To fit the time course of fast reactivation of the photocurrent atthe cessation of a step of lightTo fit the time course of photoresponse to dim flash of light

From Stryer (1986)Unitary proportionality constant

From eqn (12) and the value of resting free Ca2 of 300 nm(Ratto et al. 1988)From eqn (13)From eqn (14) and the value of yCaX cO and of resting free Ca2

To reproduce the kinetics of the reactivation of the photo-current with steps of light and to have an affinity buffer withKD close to 10/M (Hodgkin et al. 1987)From Hodgkin & Nunn (1988)To have 2,/M for the resting level of free cyclic GMPFrom Koch & Stryer (1988)From Zimmerman & Baylor (1986)From eqn (3) and to have 40 pA of resting current and a restinglevel of 2,/M of free cyclic GMP

spectively (see Stryer 1986 for a justification of these assumptions). The values of therate constants al, c2, cc3, %, T, and T2 were chosen to be equal to 20 S-1, 0 0005 s-1,005 s-', 10-6 S-1, 01 s-1 /M-1 and lOs- respectively. The values for c2 and a3were selected so as to reproduce the time course and amplitude of the late response

(see p. 283). The values for acl, f,l, r, and T2 were primarily selected so as to accountfor the kinetics of dim flash responses.

In order to have a full reconstruction of the kinetics of phototransduction the fourdifferential eqns (29) describing the activation of phosphodiesterase and thefollowing eqns (30)-(33) were solved:

c = bJ-yca (c-co)-kl(eTccb)c+k2cb,

Cb = kl(eT-Cb)C-k2 Cb,

(30)

(31)

9ax)4-g(V+oPDE*),

J g3ma=J.x 3 K3

(32)

(33)

Parameteral

aIX2C3

Ti

sT2

PDETot

YCa

Cobkk2eT

K'K3

Jmax

277


The values of different parameters and the reason for their choice are given inTable 1.The seven differential equations were numerically integrated using the routine

RKF45BC kindly provided by Dr Greg Bernstein, based on the method of Shampine(1977). The initial conditions were g(0) = 2 gM; c(O) = 300 nM; Cb(O) = 500/(1 +4/0 3)/aM = 34-9 /M; Rh(0) = 0; Rhi (0) = 0; T*(0) = 0; PDE*(0) = 0.

Before seeing the performance of the model and its comparison with theexperimental recordings it is important to stress that in eqn (29.3) we have assumedthat the rate of removal of activated transducin does not depend directly on thenumber of activated phosphodiesterase. When eqn (29.3) is substituted with theequation

T* = eRh(TTot -T*)- fBl T*- rlT*(PDETot-PDE*) +r2 PDE* (34)

where the subtraction of the term r1 T*(PDETot-PDE*) seems more in agreementwith the present view of the enzymatic cascade, the obtained scheme is able toaccount for many features of phototransduction but not as many as a scheme usingeqn (29.3). Therefore we are inclined to favour the use of eqn (29.3) instead ofeqn (34).

RESULTS

Responses to brief flashesFigure 1 illustrates four families of photoresponses to brief flashes of light in

darkness (A) and in the presence of a steady light equivalent to 120 (B), 1300 (C) and110000 Rh* s-1 (D). The circulating photocurrent was 30 pA in darkness and wasreduced to 26, 15 and 4 pA by the three steady lights. The flash sensitivity indarkness was about 0-28 pA (Rh*)-' and decreases to 0-07 pA (Rh*)-', and 5 and0-025 fA (Rh*)-' in the presence of the three backgrounds of light. In darkness thetime to peak of the dim flash response was 950 ms and decreases to 650 ms byincreasing the light intensity by 100 times. When flashes are superimposed onbackgrounds of steady light the time to peak of dim flash responses shortens to330 ms and the acceleration of the time to peak with brighter flashes is not observedwith the two brightest steady lights.At the top of the photoresponse to bright flashes a notch was present, very similar

to that described in toad rods (Yau & Nakatani, 1985a) and in salamander rods(Hodgkin et al. 1987). This notch is likely to represent the light-insensitive currentcarried by the electrogenic Na+{-Ca2+ exchange. The rate constant of extinction ofthis current is between 1 and 2 s-' and is likely to reflect the fast component of thedecline of intracellular Ca2+, caused by the suppression of the Ca2+ entry through thelight-sensitive channels (Yau & Nakatani, 1985a). This notch is not evident in thepresence of bright steady lights probably because it is obscured by the presence ofvoltage-sensitive conductances in the inner segment. These conductances cause aprominent relaxation from the peak to a plateau on the voltage response (Fain,Quandt, Bastian & Gershenfeld, 1978; Torre, 1982) and can drive some capacitativecurrent through the suction pipette.

In Fig. 2 some theoretical relations between normalized photoresponse AJ/J5 andlight intensity I are reproduced (A) and the experimental data obtained in darkness

278

KINETICS OF PHOTOTRANSDUCTION 279

(B) and in the presence of a steady light equivalent to 110000 Rh* s-1 (C) are shown.In Fig. 2A we have drawn the Michaelis-Menten relation (eqn (1), thin continuousline), the exponential relation (thick continuous line) and the relation described byeqn (7) with n equal to 2, 3 and 4 (dashed lines, see figure legend). These theoreticalcuirves are rather similar to those already proposed by Baylor et al. (1974) and Lambet al. (1981). As shown in Fig. 2B and C the experimental points at different timesappear just shifted and the same relation fits the experimental data obtained atdifferent times. In darkness (see Fig. 2B) the experimental points lie between the

A 08 0 2

c -10

o1 2 3 4~~~~~~L 0 1

c~~~~~~~~~~~~-20

-20-

-30~~~~~~~~~~~30 1 2 3 4 0 1 2 3 4

C

D

0 1 2 3 4 0 1 2 3 4Time (s) Time (s)

Fig. 1. Families of responses to brief flashes in darkness (A), superimposed on a steadylight equivalent to 120 Rh* 0I (B), to 1300 Rh* s-' (C) and to 10000 Rh*sb' (D). Flashintensities mA were: 3,6, 12, 25, 58, 115, 230, 600, 1150, 2350, 6100, 12.500, 24000 Rh*inB: 12, 25, 58, 115, 230, 600, 1150, 2350, 6100, 12500, 24000, 50000 Rh*; in C: 58, 115,230, 600, 1150, 2350, 6100, 12500, 24000, 50000 Rh*; inD: I1150, 2350, 6100, 12500,24000, 50000, 98000, 205000, 480000, 980000, 2050000 Rh*. Responses of amplitudleless than 5 pA were obtained as the average of at least eight responises.

exponential eqn (2) and eqn (7) with n = 4. In the presence of a bright steady lightequivalent to 110000 Rh* s- the experimental points are better fitted by theMichaelis-Menten eqn (1) or by eqn (7) with n = 2.

These results show that eqn (2) fits the experimental data obtained in darknessreasonably well, but not those obtained in the presence of bright steady lights. As aconsequence we do not expect diffusion to shape the photoresponse during lightadaptation, where different mechanisms, like those described by eqn (7), are likely tocontrol the relation between amplitude of photoresponse and light intensity.However, the exact value of n cannot be decided, because our data were not collectedunder voltage clamp conditions and voltage-dependent currents may have slightlyaffected the traces of most bright photoresponses (Baylor & Nunn, 1986; Cobbs &Pugh, 1987).


A 1i

0.8 _-

AJJs

0.6 _

0.4 _

0.2 _

o0

0.01 0.1 1log lo

B 1

10 100

0.8 _-

AJ0.6 _

0.4 _-

0.2 _-

I I I IL L .

0.01 0.1I a.||I I ..II . I.a.I a 1 a I1

1 10 100log 10

t I t I I fil a l

0.01 0.1 1log lo

I.I.a. .

10 100

Fig. 2. A, thick continuous line has been obtained with the exponential relation, eqn (2),thin continuous line with the Michaelis-Menten relation, eqn (1), the dashed lines havebeen obtained with eqn (7) with n = 2 ( ), n = 3 (--) and n=4 (-- --).

Theoretical curves have been shifted so to have the same rising phase for dim lightintetnsities. I0 is the light intensity causing a photoresponse of 05 with the relationdescribed by eqn (1). Comparison of the theoretical curves of panel A with theexperimental data from traces shown in Fig. 1 obtained in darkness at the followingtimes (s): 07 (A), 0-8 (U), 09 (O), 1 (O) and 1P1 (0) (B) and in the presence of a steadylight equivalent to 110000 Rh* s-I at the times (s): 0-275 (-), 0-3 (O), 0-325 (O') and 0 35(0) (0). The experimental points have been shifted so as to lie on the same curve.

C 1

0.8 _

0.6 _-AJ

0.4 _-

0.2 _-

0L

2980


D

CL

40

:

a)

E

Zi

a.)

0

1

oI I I

1 2 3 4

F

0.31

i

CU4co

I I I I I I I

0.21

I I

0 1 2 3 4

_

0.1 L0 1 2 3

Time (s)0 1 2

Time (s)Fig. 3. Theoretical curves obtained from eqns (29)-(33). A, theoretical photocurrentsobtained with pulses of JjV(t) of duration 10 ms equal to 0-2, 0-5, 1, 2, 5, 10, 20, 50, 100,500, 1000, 2000 Rh' s-'. B, theoretical changes of free cyclic GMP associated to curves

shown in A. C, theoretical changes of intracellular free Ca2' associated to curves shown inA. D, theoretical photocurrents obtained with pulses of JhV(t) of duration 10 ms, equal to2, 5, 10, 20, 50, 100, 1000, 2000 Rh; s-, superimposed on a steady light equivalent to 01Rh* s-'. Pulses of Jh,(t) were given 40 s after the onset of the steady light. E, theoreticalchanges of free cyclic GMP associated with curves shown in D. F, theoretical changes ofintracellular free Ca2' associated with curves shown in D.

A family of traces obtained by solving the set of differential eqns (29)-(33) in whichthe flux of photoisomerization Jh,(t) had a duration of 10 ms is illustrated in Fig. 3A.The associated changes of free cyclic GMP and of intracellular Ca2+ are shown in

Fig. 3B and C respectively. The theoretical curves have a time course rather similar

A

281

0.

-

4

0

B

2i

0

1

0L0

CrE1 .u 3I'r -

i

CU40

0.2 1

0.1 L

3 4

I

I4

S. FORTI, A. MENINI, C. RISPOLI AND V. TORRE

to the experimental traces shown in Fig. 1A. The time to peak of theoretical traces,which is about 1080 ms for dim lights, shortens to 690 ms for bright lights, similarlyto the experimental behaviour. The theoretical traces do not reproduce the notch (seeFig. 1) due to the Na+-Ca2+ exchange electrogenic current, because this current wasnot included in the model. The time to peak shortens because as intracellular Ca2+drops, the cyclase is stimulated, thus more efficiently counteracting the light-inducedphosphodiesterase activation. The traces shown in Fig. 3 C illustrate a basic featureof the proposed model: Ca2+ buffer inside the rod is assumed to be slow (k, = 0-2 s-I/m-1 and k2 = 0-8 s-1) thus causing changes of intracellular Ca2+ with a time coursein which a fast and a slow drop are present.The theoretical families of photocurrents, of changes of free cyclic GMP and of

intracellular Ca2+, obtained by simulating a pulse superimposed to a steady flux ofphotoisomerizations are shown in panels D, E and F respectively of Fig. 3. Inagreemnent with the experimental traces, the time to peak of the dim flash responseshortens to 450 ms and does not accelerate with brighter flashes (compare with theexperimental traces of Fig. 1 C and D). Observe also that in this case the cyclic GMPdrops only to about 0-2 /tM, although this causes a complete suppression of thephotocurrent. The co-operative action of cyclic GMP on the channel (see eqn (33)) isresponsible for the almost complete suppression of the photocurrent even thoughcyclic GMP is only reduced by 10 times. This feature is likely to be a remarkableproperty ofthe phototransduction machinery. The associated changes of intracellularCa2' are smaller and slower.The experimental traces obtained in response to bright flashes of light have a

longer plateau than the theoretical traces. This defect of the model is more severe indarkness than in the presence of a steady light.

Photoresponsees to lights of different durationsWhen a light is impinging onto a rod for a time longer than a second or so, the rod

changes its responsiveness to light and initiates light adaptation. Figure 4Areproduces photoresponses to a steady light equivalent to 4500 Rh* s-' of differentdurations (1, 2, 5, 10, 20, 30 and 40 s). The photocurrent, which initially is fullysuppressed, partially reactivates within 10 or 20 s. When the light is turned off, afterlonger exposures, the photocurrent recovers with a complex time course. The timecourse of the recovery of the photocurrent after a steady light of 5, 10 and 20 s isshown in greater detail in Fig. 4B.The photocurrent, following a flash of 5 s, remains saturated for an additional

2-5 s, while after longer illumination it promptly recovers as the light is turned off.However, the two traces cross because, with time, another late or slow component ofthe photoresponse is turned on. This component appears clearly only followingstrong lights.A full speeding-up of the recovery of the photocurrent, when the light is turned off,

is obtained with illuminations exceeding 10 s. When the same experiment is repeatedin the presence of a steady light equivalent to 1050 Rh* s-1 the late component of thephotoresponse is reduced or even abolished as shown in Fig. 4C. In this case whenthe test flash is terminated the experimental traces do not cross (see Fig. 4D).

It is of some importance to see whether the proposed model is able to account for

282


these aspects of phototransduction. Figure 5A reproduces theoretical curvesobtained by simulating photoresponses of different durations. In Fig. 5B thetheoretical curves at the cessation of the light are reproduced on an enlarged timescale to illustrate the time course of the reactivation of the photocurrent. Figure 5CandD reproduce similar theoretical curves obtained in the presence of a constant fluxof photoisomerizations.

IIIA 0

CL

0)

C-)

-10 _

-20

-30

B 0

. -10

40

-20 H

-30

0 40 80 120

111 1 i I

5~~~~~

1~~~~~~~~~~~~~~~~~~~~~~~

0 10

-ID O

a40.a-

-5 _

-10 F

-15 L

0 40 80 120 0 10Time (s) Time (s)

Fig. 4. Photoresponses to flashes of different duration. A, photoresponses to steps of lightequivalent to 4500 Rh* s-I of 1, 2, 5, 10, 20, 30 and 40 s of duration. B, the reactivationof the photocurrent following a step of light of 5, 10 and 20 s. Time 1 s coincides with theextinction of the light. Same experiment as in A. C, photoresponses to steps of lightequivalent to 4500 Rh* s-' of 1, 2, 5, 10, 20, 30 and 40 s of duration superimposed to a

steady light equivalent to 1050 Rh* s-1. D, the reactivation of the photocurrent followinga step of light of 5, 10 and 20 s. Time 1 s coincides with the extinction of the light. Sameexperiment as in C.

Most of the experimental features, shown in Fig. 4, are reproduced well by themodel: the shortening of the latency of the reactivation of the photocurrent withlonger lights and the progressive appearance of the slow response (Fig. 5A); thecrossing of the repolarization phase after a brief and a long step of light (Fig. 5B);the reduction or suppression of the late response and the absence of the crossing ofthe repolarization phase in the presence of a steady light (Fig. 5C and D).The two theoretical traces shown in the inset of Fig. 5A illustrate how the model

accounts for the late component of the photoresponse at the cessation of the light.

C

40.CG)C-L-

Or

-5 F

-10 H

-15 L

283

S. FORTI. A. MENVINI, G. RISPOLI AND V. TORRE

The theoretical curve indicated by the arrow has been obtained by simply imposing°2= 0 and in this case the late component completely disappears from the theoreticalcurve. Therefore the slow component originates from an assumed partial reversibilityof the inactivation of photoexcited rhodopsin.

A 0

:; -10

C -2016a)

) -30

-40

C o

Q-

ca)L-,

B 0O

CL

4,cL-4-

-10 -

-20 -10

-30 L

-40

D

;j -5a

-10

C-. -15

-5

-10o

-15 F

-20 L

L

0 10

, ~~-20 lllo -20

0 40 80 120 0 10Time (s) Time (s)

Fig. 5. Theoretical curves obtained with pulses of Jh,,(t) of different duration. A, pulsesof 1. 2. 5a 10. 20. 30. 40 s of Jh,(t) equal to 10 Rh* s-'. B, the reactivation of thephotocurrent following steps of 2. 5. 10 s ofduration Time 1 s coincides with the extinctionof the light. C. pulses of 1. 2, 5. 10. 20. 30 and 40 s of Jh,.(t) equal to 10 Rh* s-',superimposed on a steady light equivalent to 01 Rh* s-'. D, the reactivation of thephotocurrent following steps of light of 2, 5 and 10 s of duration. Time 1 s coincides withthe extinction of the light. The inset of panel A illustrates the origin of the slowcomponent in the model. Step of light of 40 s equivalent to 10 Rh* s-'. The trace indicatedby an arrow has been obtained by the model with the value a2 = 0. In this case the slowcomponent disappears because the inactivation of excited rhodopsin is completelyirreversible.

Responses to steps of lightPhotoresponses to steps of light of 60 s of increasing intensity are shown in Fig. 6.The low-frequency noise present with weak light is likely to be caused by quantum

fluctuation as in toad rods (Baylor, Lamb & Yau, 1979b). Photoresponses tointermediate and bright light intensities reach a peak within one or two seconds andat later times present a partial reactivation of the photocurrent. This delayedreactivation of the photocurrent is the major mechanism underlying light adaptation.When the step of light is switched off the photocurrent reactivates with a complex

time course. Following light intensities not fully suppressing the photocurrent, the

284

KINETICS OF PHOTOTRANSDUCTION2

current reactivates with a delay of less than 100 ms and with a time constant ofabout 08 s-1. In the presence of brighter lights the photocurrent remains fullysuppressed for a few seconds before commencing to reactivate. After a partial fastrecovery of the photocurrent a long-lasting component of the photoresponse isobserved, as shown in Fig. 6B. This component of the photoresponse, which isobserved in darkness and can be named the late response, extinguishes with a rateconstant of about 0 05 s-5. Following Lamb (1981) we attribute the origin of the lateresponse to the existence of a reversible step in the inactivation of photoexcitedrhodopsin or to a partial ability of inactive rhodopsin to activate transducin.

Photoresponses to steps of light of 60 s of increasing intensity, in the presence ofa steady light equivalent to 1050 Rh* s-1 are shown in Fig. 6B. The effect of thesteady light on the kinetics of photoresponses is mostly pronounced at the cessationof the steps of light where an overshoot can be observed and the kinetics of the lateresponse is slightly accelerated. The time course of the reactivation of thephotocurrent, observed with steps of light initially blocking a large fraction of thecirculating current, is not accelerated. Similarly the time course of reactivation of thephotocurrent at the termination of non-saturating steps of light is hardly affected.The time course of the reactivation of the photocurrent during a step of light is

better analysed in Fig. 6C and D, where traces are shown on a semilogarithmic scale.In C we have reproduced the time course of the reactivation of the photocurrentobserved with steps of light intensity equivalent to 1050, 2200, 4500 and 11500 Rh*s-1 respectively and suppressing initially 79, 94, 97 and 98% of the circulatingcurrent. The photocurrent reactivates with slower rate constants when the lightintensity is higher and for the four traces in Fig. 6C the rate constants are 0 33, 0f21,0-096 and 0-051 s-1. In the presence of a steady light equivalent to 1050 Rh* s-1 theserate constants are hardly affected. For steps of light equivalent to 2200, 4500, 11500and 22000 Rh* s-1, initially suppressing 63, 81, 91 and 94% of the circulatingcurrent, the rate constants of the reactivation of the photocurrent become 0-25, 041,0075 and 0037 s-' respectively. Therefore backgrounds of light do not accelerate thetime course of the reactivation of the photocurrent during steps of light while theyaccelerate the kinetics of flash responses (see Fig. 1).The normalized amplitude of suppressed photocurrents, 16 s after the onset of the

step of light in darkness and in the presence of different steady lights, is plotted inFig. 7. The dynamic range of the photoresponse to steps of light is broader than thedynamic range for brief flashes of light. This extension of the dynamic range is at thebasis of light adaptation and plays a crucial role in vision (Baylor & Hodgkin, 1974;Lamb, 1986).The dynamic range for steps of light is about 3 log units in darkness (see 0 in

Fig. 7) and in the presence of bright steady lights is decreased to about 2 log units (seeO in Fig. 7). Most of these effects can indeed be explained by the regulating effectof Ca21 on the cyclase activity: in a previous section we derived the two equations(26) and (28) describing the relation between amplitude of photoresponse and lightintensity when the resting intracellular Ca21 was above or below the value of K, Thecontinuous curve in Fig. 7, obtained by using eqn (26) with m = 1 and n = 3, doesnot fit the experimental points exactly, but clearly takes account of the broadeningof the dynamic range. The dotted line, obtained with m = 4 and n = 3 fits the

285


j 0a

o

I

0o

I I ~~~~~~~I

0 In 0 L

we~~nI

CI (Vd) luajjn:

A_

I

0 0 0 0

CX)

Q

I-.

(Vd) juaJJfn

000

0

qt

7

o0

,N

CC)

a

0

LU0

'ICK (Vd) ju3nJdU

0

0E

I o

D

C-

o

._

Eo -

286

(Vd) juaiino

KINETICS OF PHOTOTRANSDUCTION 287

0 v A d

A0-8 _- ,

A /0.6 0

AJ CJs A A /

0-4 _ 2 /

0-2 tA<[:1 ; -~- A

0

7.0 6.0 5.0 4.0 3-0log (M)

Fig. 7. The relation between normalized amplitude of photoresponse and light intensity,16 s after the onset of a step of light. The experimental data were obtained in darkness(0), and in the presence of a steady light equivalent to 1850 (El), 4000 (A), 8800 (A),19 000 (U) and 51000 Rh* s-1 (K). The continuous curve was obtained from eqn (26)with m = 1 and n = 3 and the dotted line with m = 4 and n = 3. The dashed line wasobtained from eqn (28) with n = 3. The intensity of the step of light is given in attenuatedlog units. Unattenuated light was equivalent to 48 x 106 Rh* s-1.

experimental points rather well only for dim and moderate steps of light, a rangewhere the assumption made in deriving eqn (26) is reasonable (c > Kc). Theinterrupted line obtained from eqn (28) fits reasonably well the experimental dataobtained in the presence of a bright steady light (O), when the resting level of freeCa21 is likely to be low and the derivation of eqn (28) is justified (c < K).A family of theoretical traces, simulating a flux of photoisomerizations of 60 s, is

shown in Fig. 8A. The associated changes of free cyclic GMP and of intracellular Ca21are shown in panels B and C respectively of Fig. 8. In agreement with the

Fig. 6. A, photoresponses to steps of light of 60 s of duration. The intensity of steady lightswas equivalent to 5, 11, 20, 45, 100, 210, 480, 1050, 2200, 4500, 11500, 22000, 45000,110000 and 220000 Rh* s-'. B, photoresponses to steps of light of 60 s in the presence ofa steady light equivalent to 1050 Rh* s-'. The intensities of steps of light were 480, 1050,2200, 4500, 11500, 22000, 45000, 110000 and 220000 Rh* s-i. Each trace is the averageof at least two responses. Responses to dim lights (amplitude < 5 pA) were obtained as theaverage of at least five responses. In C and D the time course of the reactivation of thephotocurrent during a step of light is plotted on a semilogarithmic scale. The zero levelof the photocurrent was taken as the average value reached at the steady state. Thecontinuous straight lines were obtained by a least-squares interpolation of theexperimental traces. C, the reactivation of the photocurrent during a step of lightequivalent to 1050, 2200, 4500 and 11500 Rh* s-' and the rate constants of thereactivation of the photocurrent were 0 33, 0-21, 0-096 and 0-051 s-' respectively. D, as inC but in the presence of a steady light equivalent to 1050 Rh* s-'. The intensities of stepsof light were 2200, 4500, 11500 and 22000 Rh* s-' and the rate constants of thereactivation of the photocurrent were 0-25, 0-11, 0-075 and 0-037 s-' respectively.

S. FORTI, A. MEIVINI, G. RISPOLI AND V. TORRE

D 0

CaTa)

E

_ i 22 K

::1.~z2 1 _tDn0

I I

0 40 80

C

0.3

a t=0-102 -,I

N~~~~~~~~~~~~~~~~~~~~~~

i~~~~~~~~~~~~~~~~

0.1

I)

0 40Time (s)

J

2 1

0 40 80

F0.3

02 F0-2

m

u-

0.80 0 40

Time (s)80

Fig. 8. Theoretical curves obtained from eqns (29)-(33) with steps of Jh,,(t) of 60 s ofduration. A, theoretical photocurrent obtained with Jh,(t) equal to 0-002, 0005, 0-01,0-02, 0 05, 0-1, 0 2, 0 5, 1, 2, 5, 10, 20, 50 Rh* s-'. Theoretical changes of free cyclic GMP(B) and of intracellular Ca2+ (C) associated to curves shown in A. D, theoreticalphotocurrents obtained with steps of Jh,(t) of 60 s of duration superimposed on a steadylight equivalent to 0-1 Rh* s-1. The intensity of Jh(t) was 0-05, 0-1, 0-2, 0 5, 1, 2, 5, 10,20 and 50 Rh* s-1. Theoretical changes of free cyclic GMP (E) and of intracellular Ca2+ (F)associated to curves shown in D.

experimental traces (see Fig. 6) the photocurrent, after a partial or completesuppression, reactivates with a delay. This reactivation is produced by the secondslow fall of intracellular Ca2+ (see Fig. 8 C), caused by the Ca2+ uptake by the internalbuffer. A noticeable feature of the proposed model is shown in Fig. 8B where the levelof free cyclic GMP during a steady light does not fall below the level set by themaximal activity of phosphodiesterase and cyclase. From eqn (30) intracellular Ca21cannot fall below 100 nm (i.e. the value of co) and from eqn (32) at the steady statethe lower level of cyclic GMP is

Amax

( 42C)(35)

288

A 0

<E -10a0.L-c -20

) -30

-40

B


which from the values of Table 1 is 0 33 /SM. Consequently at the steady state thelevel of free cyclic GMP decreases by a factor of only 6, while acting as an internaltransmitter able to transduce light intensity over 4 log units.At the termination of the light the theoretical curves show almost the same

behaviour as the experimental traces, where the photocurrent reactivates with a fastand a late or slow component. The fast reactivation of the photocurrent is due to thesubstantial depletion of intracellular Ca2 , which activates the cyclase (Hodgkin &Nunn, 1988). This enzyme remains activated even during the 2 or 3 s of the fastreactivation, because the influx of Ca2 , through light-sensitive channels, is absorbedby the intracellular Ca2+ buffer. The slow component (see previous section) isprobably caused by the reversible inactivation of photoactivated rhodopsin.A defect of the model evident in the traces shown in Fig. 8 is the almost

instantaneous reactivation of the photocurrent at the cessation of the step of light.A more complex scheme for the enzymatic cascade is likely to remove this defect.

Figure 8D, E and F reproduces theoretical traces simulating a step of light of60 s but in the presence of a steady light. The theoretical traces reproduce the timecourse of the experimental recordings shown in Fig. 6B quite well. The presence ofa steady light in the model does not accelerate the time course of the reactivation ofthe photocurrent, in agreement with the experimental observation (see Fig. 6).Similarly to the experimental traces of Fig. 6B, a rebound of the photocurrent isobserved at the cessation of the step of light. In the model the rebound is accountedfor by a faster deactivation of transducin and phosphodiesterase in the presence of asteady light and by the presence of the Ca2+ buffer. This rebound, caused by a steadylight, could not be obtained by a model using eqn (34) instead of eqn (29.3), withouthaving a rebound also in the absence of a steady light.

The effect of trapping BAPTAWhen a photoreceptor is loaded with the Ca2+ chelator 1,2-bis(o-amino-

phenoxy)ethane-N,N,N',N'-tetracetic acid BAPTA (Tsien, 1980), the time course ofphotoresponses is significantly affected (Lamb et al. 1986; Torre et al. 1986). A furthertest of the proposed model is to see whether introducing into the model a high-affinity Ca2+ buffer with the 'on' and 'off' rates h, and h2 equal to 100 s-1 UM-1 and10 -1 as for BAPTA (Tsien, 1980) reproduces the changes of the kinetics ofphotoresponses experimentally observed by infusing BAPTA into the rod. Thetheoretical model is accordingly changed by substituting for eqn (30) the twoequations:

zFV-Yca (c-co) -kl(CT-Cb)C+k2Cb-hl(hT-hb)C+h2hb, (36)

and hb = hl(hT-hb)C-h2hb, (37)where hT is the total concentration of the high-affinity buffer, hb is the Ca2*concentration bound to the high-affinity buffer.

Families of theoretical photoresponses and of changes of iintracellular Ca2+,obtained by simulating the infusion of 1000 /LM of BAPTA, are shown in panels A andB respectively of Fig. 9. Figure 9C compares three traces (thin traces) generated bythe model without the high-affinity buffer and three traces (thick traces) obtained

PH Y 419

289


with a model including 1000 ,tM-BAPTA. Figure 9D reproduces theoretical tracesobtained after the cessation of bright lights of different durations (2, 4, 8, 16, 32 and64s).The theoretical curves reproduce quite actcurately the experimental recording

obtained by Torre et al. (1986) after trapping I3APTA into a rod (see Figs 2 and 3 ofTorre et al. 1986). The increase of sensitivity, the rebound at the termination of the

A 0

< -20a)4-

.) -40

0

B

i(U

0

s

0 5 10 15

I II

1 2 3Time (s)

4

D 0

-20.

c -40

0u -60

-801

0 5 10 15

64\

I

0 2 4 6 8Time (s)

Fig. 9. A, theoretical curves obtained with eqns (29), (32), (33), (36) and (37) simulatingthe infusion of 1000 /M-BAPTA and pulses of J,,(t) of duration of 10 ms equal to 1, 2, 5,10, 20, 50, 100, 200 Rh* s-'. B, theoretical changes of intracellular free Ca2+ associated tocurves shown in A. C, superimposed traces obtained with (thick trace) and withoutinfusion of BAPTA (thin trace) and pulses of Jh,(t) equal to 2, 20 and 200 Rh* s-1. D,family of theoretical traces obtained simulating the infusion of BAPTA and illustratingthe time course of the reactivation of the photocurrent following pulses of J",(t) ofdifferent duration (2, 4, 8, 16, 32 and 64 s). Jh,,(t) was 10 Rh* s-'. Time zero coincides withthe cessation of the pulse of JAP(t).

photoresponse, the lengthening of the photoresponse, the lack of the acceleration ofthe time to peak with flashes of increasing intensity and the increased size of therebound after longer illuminations, are features shared by the experimental tracesand the theoretical curves.

The remarkable agreement between the theoretical curves of Fig. 9 and of theexperimental recordings of Torre et al. (1986) represents a good test for the proposedmodel of phototransduction.

C Or

CL

a)Q,-

-10 F

-20 F-30

_40 L -

0O

290


DISCUSSION

Photoresponses of rods from the retina of the newt Triturus cristatus are verysimilar to photoresponses already described in many amphibians and reptiles (Bayloret al. 1979a, b; Lamb et al. 1986).

In this paper a quantitative reconstruction of the kinetics of phototransductionhas been attempted, obtaining a satisfactory agreement between theoretical andexperimental curves. A noticeable feature of the proposed model is the relativelysmall modulation of internal messengers, while preserving the ability of thephotoreceptor to transduce light intensity over a 4 log unit range. As shown in Fig. 8,during steady bright lights, the intracellular cyclic GMP decreases from 2 to about0-3 /M and free Ca21 from 300 to 100 nm. This ability to modulate the response overa rather wide range of light intensity, with small changes in the concentration ofinternal transmitters, is due to the co-operative action of cyclic GMP on the channeland of Ca21 on the cyclase activity. These observations may suggest that anytransduction mechanism is unlikely to require large changes of internal secondmessengers, such as a rise or a fall of free Ca2+ by several log units, and so,consequently, the obvious design to increase the operating range of the transductionprocess would be to use highly co-operative mechanisms.The model is able to account for many features of the kinetics of photo-

transduction, but not all the details, as discussed in the experimental section.

DiffusionIn the equations used to obtain the theoretical curves, the concentration of

different substances has been assumed to be uniform, thus highly simplifying themodel. It is well known, however, that internal diffusion inside a photoreceptor isrestricted (Lamb et al. 1981) and the concentration of the internal transmitter is notexpected to be uniform when just a few photons are absorbed in a second.The main reason for making this simplifying assumption is the observation that in

the presence of steady bright lights, producing several tens of thousands ofphotoisomerizations per second, the kinetics of phototransduction is accelerated, butthe number of slow stages required to fit the time course of the rising phase ofphotoresponse in the linear range is not changed. Since, under these conditions, giventhe high number of photoisomerizations, the cell interior is expected to be almostuniform, it is concluded that while internal diffusion could shape the time course ofthe photoresponse in dark-adapted conditions, it does not in the presence of brightsteady lights. The understanding of photoresponses to dim or moderate flashes indark-adapted conditions can be refined by introducing longitudinal diffusion into themodel.

The role of Ca21Calcium permeates through light-sensitive channels (Yau & Nakatani, 1984a;

Hodgkin et al. 1985; Nakatani & Yau, 1988a; Menini et al. 1988) and controls lightadaptation (Torre et al. 1986; Matthews et al. 1988; Nakatani & Yau, 1988c) byinhibiting the activity of the cyclase (Lolley & Racz, 1982; Pepe et al. 1986; Koch &

10-2

291


Stryer, 1988). Internal Ca2+ is extruded by Na+{Ca2+ exchange and can be bound byinternal buffers (Hodgkin et al. 1987). If the role of internal Ca2+ now seems to berather well understood, there are still some open questions, relevant to a quantitativeanalysis of its role in phototransduction. In the proposed model we have assumedthat the internal low-affinity buffer was slow, that is the 'on' rate was well below thelimit set by diffusion of 100s-5 /LM-1. The main reason for this assumption is basedon computer simulation in which the presence of fast Ca2+ buffers, such as BAPTA,caused the appearance of rebounds as those observed by trapping BAPTA inside arod (Torre et al. 1986). Therefore it is concluded that the existence of large amountsof fast Ca2' buffers inside a rod gives rise to an unusual time course of photoresponses.In this model only one kind of internal Ca2+ buffer has been considered at aconcentration significantly higher than the one estimated from experimentalmeasurements (McNaughton et al. 1986). Additional evidence indicates the existenceof a high-affinity buffer (Hodgkin et al. 1987) and the agreement with theexperimental data can be expected to improve by including a second Ca2+ buffer inthe model.The proposed model assumes a fast action of Ca2+ on the cyclase and an almost

instantaneous equilibrium between active and inhibited cyclase. The effect of Ca21 onthe cyclase does not seem to be direct, but to require a soluble component (Koch &Stryer, 1988), which is not considered in the model. The argument in favour of a fastaction of Ca2+ on the cyclase is the rapid blockage of the photocurrent whenintracellular Ca2+ rises (Hodgkin et al. 1985) and the rapid activation whenintracellular Ca2+ falls (Lamb & Matthews, 1988). Finally it is useful to rememberthat while biochemical evidence strongly supports an action of Ca2+ to inhibitguanylate cyclase, Ca2+ may also exert effects on other sites within the transductionmechanism. The proposed parsimonious model cannot exclude additional effects of

2+Ca

The activation of transducin and phosphodiesterase

The activation of transducin and phosphodiesterase are assumed to be describedby scheme B. The removal of transducin is assumed not to directly depend on theactivated phosphodiesterase and is described by eqn (29.3). When eqn (34) is usedinstead of eqn (29.3) several features of phototransduction are not reproduced, forexample the presence of the rebound when steps of light are superimposed to steadylights (see Fig. 6) and some effects observed with flashes of light of different duration.The reason for the better performance of eqn (29.3) can be seen by considering the rateof removal of T* + PDE* which is speeded up in the presence of a steady light, whilstwhen eqn (34) is used the rate of removal of T* + PDE* is unaffected by a steadylight.The model also assumes that the inactivation of rhodopsin is slightly reversible,

thus giving origin to the late response (Lamb, 1986). It is also possible to account forthe late response by supposing that inactive rhodopsin is still able to activatetransducin with a much lower efficacy than activated rhodopsin. The large bufferingof cyclic GMP has not been included in the model, and this could be relevant and playa role in light adaptation. The reason for not including the cyclic GMP buffering isessentially one of parsimony and uncertainty of its kinetic properties. The model is

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KINETICS OF PHOTOTRANSDUICTION

not very critical with respect to the values of the rate constants, but is sensitive totheir order of magnitude. Biochemical measurements of these rate constants,possibly in situ, will provide good tests for this model.

It is a pleasure to acknowledge many useful discussions with Professor L. Cervetto and thecritical reading of the manuscript by Professor A. L. Hodgkin. D. A. Bavlor. L. Strver. T. D. Lamband G. Owen. The experimental part of this work was made possible by the help and advice ofmany people: Dr D. Bertrand supplied us with all the computing programs and gave of his timeto ex)lain many details of his program DATAC; Dr T. D. Lamb gave us the schemes of manycircuit diagrams and very helpful technical advice; Mr G. Franzone built all the mechanical partsof the experimental set-up; Mr E. Gaggero built manv electronic circuits for the apparatus. Specialthanks are due to Dr Franco Gambale for his continuous encouragement and helpful advice. Weappreciate the help of Miss C. Rosati who kindly typed the manuscript many times and preparedthe illustrations. Clive Presst checked the English.

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