Durham, NC 27710, U.S.A

Joural of Physiology (1988), 403, pp. 439-471 439With 17 text-fijure8Printed in Great Britain

CONTROL OF LIGHT-SENSITIVE CURRENT IN SALAMANDER RODS

BY A. L. HODGKIN AND THE LATE B. J. NUNN*From the Physiological Laboratory, Downing Street, Cambridge CB2 3EG

and the Department of Physiology, Box 3709, Duke University Medical Center,Durham, NC 27710, U.S.A.

(Received 2 December 1987)

SUMMARY

1. The exponential decline of light-sensitive current seen after a switch fromNa+ to Li+ in the presence of Ca2+ probably depends on the activity of thephosphodiesterase (PDE) which hydrolyses cyclic GMP.

2. This probability is supported by experiments with suction electrodes whichshow that in toad and salamander rods the rate constant, b, of the exponentialdecline of current was increased at least 10-fold by moderate light intensities anddecreased about 10-fold by 3-isobutyl-1-methylxanthine (IBMX), an inhibitor ofPDE.

3. The rate constant b is about 3 times more sensitive to weak lights or to IBMXthan the membrane current. This may be explained by a feed-back involving calciumions which tends to hold current constant, perhaps by calcium inhibition ofguanylate cyclase.

4. The time course of b, which probably represents the changes in PDE activity,was measured by switching from Na+ to Li+ at various times after a flash. The resultssuggest that a moderate flash (140 Rh*) increased b about 7 times in 0-5 s and thatb then declined with a time constant of 1-5-2 s.

5. Extrapolated values of the parameter b suggest that strong flashes (5000-10000Rh*) increased b from 1 s-1 in the dark to perhaps 60 s- and that b continued toincrease with flash strength for several log units after the current had reachedsaturation.

6. The observations in 4 and 5 fit well with the idea that b is related to PDEactivity and that changes in the latter are sufficient to account for the rising phaseof the flash response.

7. After a flash the light-sensitive current recovers much more rapidly than thetime constant b-1, a discrepancy which is explained if a light flash causes a delayedincrease in guanylate cyclase activity.

8. The apparent delayed increase in cyclase activation is consistent with aninhibitory effect of [Ca2+]i which is reduced when calcium is pumped out during theplateau of the response.

* To the deep regret of his colleagues, Dr B. J. Nunn died on 18 September 1987, about twomonths after completing the first version of this paper.

A. L. HODGKIN AND B. J. NUNN

9. Experiments in which pulses of IBMX were applied at different times during aflash response support the idea that a flash causes a delayed increase in the rate ofsupply of cyclic GMP. Quantitative analysis of these and other tests with IBMX gaverate constants similar to those obtained by the Na+ -> Li+ method.

INTRODUCTION

Control of light-sensitive currents in salamander rodsThere is now strong evidence that ionic channels in vertebrate photoreceptors are

kept open by cyclic GMP and that light closes channels by interacting with aphosphodiesterase (PDE) which hydrolyses cyclic GMP (Fesenko, Kolesnikov &Lyubarsky, 1985; for other references see Stryer, 1986, Pugh & Cobbs, 1986). Thesequence of events after absorption of a quantum of light by rhodopsin is theactivation of several hundred molecules of G-protein in a cyclical reaction involvingexchange of GTP for GDP. The active G-protein then interacts with thephosphodiesterase and greatly accelerates the hydrolysis of cyclic GMP, with theresult that after a strong flash free cyclic GMP falls to a low value in about 100 ms.The present experiments deal mainly with the recovery phase of the response to

a flash and suggest that the recovery of inward current depends partly on the declinein phosphodiesterase activity and partly on the increase in the supply of cyclic GMPassociated with the transient decrease in [Ca2+]i that follows a strong flash. Ourexperiments are indirect but several of the conclusions from them agree with thoseof Miller (1982) and Kawamura & Murakami (1986) who investigated PDE activityby measuring the rate of repolarization after injecting cyclic GMP into Geckophotoreceptors.Our method of estimating PDE activity depends on the observation that after

exchanging Na+ for Li' with Ca2+ in the external solution the light-sensitive currentfirst increases suddenly and then declines exponentially with a rate constant of about1 s-1 in darkness (Hodgkin, McNaughton & Nunn, 1985). The initial increase isattributed to the light-sensitive channel having a greater permeability to Li+ thanNa+ and the subsequent decline to a blockage of guanylate cyclase by the rapid risein CaW+ that occurs when Na+ is removed from the external medium.An experimental justification for taking the rate constant /? with which cyclic

GMP is destroyed to be related to the rate constant b with which light-sensitivecurrent declines in lithium is that b is doubled by very weak lights (25 Rh* s-1) andhalved by low concentrations (10 #M) of IBMX, an inhibitor of PDE (Hodgkin et al.1985).The last part of the experimental section deals with results obtained with an

alternative method involving sudden application ofIBMX which provides a differentway of measuring b and other rate constants. The results were in general agreementwith those obtained by the Na+ -+ Li+ method.A preliminary account of the variation of f, during the recovery phase of a flash

response was given by Hodgkin, McNaughton & Nunn (1986a).

440

CONTROL OF CURRENT IN RODS

METHODS

The experiments were carried out on isolated rods of Amby8toma tigrinum by the methodsdescribed by Hodgkin, McNaughton & Nunn (1985, 1987). The Ringer solution contained (in mM):NaCl, 110; KCl, 2-5; MgCl2, 1-6; CaCl2, 1D0; HEPES, 10; pH 7 5, and glucose, 3.

In addition to the light-sensitive current j, the main experimental variable was the rate constantb with which current declines after replacing Na+ by Li' in the presence of Ca . Under theseconditions our experiments show that the current is given by

-bt

where b is about 1 s-1 when Li+ replaces Na+ in the Ringer solution in darkness but is increased atleast 10-fold (and probably much more) by light and decreased 10-fold in 05 mM-IBMX. Asexplained on p. 443, b is considered to be proportional to the rate constant t6 with which cyclic GMPis hydrolysed.Two methods of estimating b were employed: (1) the computer was programmed to calculate and

plot lnj, giving the type of trace shown in Fig. 1B; b was given by the slope at time t' namely-d lnj/dt; (2) the computer calculated b as:

1 Ajj At'

where At is a time interval of 0 05 s centred on the time t' at which j was measured. Examples ofthe two types of record are given in Fig. 1. When b was plotted as a function of time measurementsare given at the moment when b was determined, which was usually about 0 5 s after switchingfrom Na+ to Li+.

Flash intensities are given in isomerizations (Rh*) per rod using an estimated collecting area of20 /m2 based on a mean outer segment diameter of 11 um and length of 20 sm (see Lamb,Matthews & Torre, 1986; value for unpolarized light).

THEORY

In analysing the experiments we have used a scheme similar to that adopted byKawamura & Murakami (1986) or Pugh & Cobbs (1986).

a

GTP-cGMP GMP, (1)

where a and /6 are rate constants determined by the activity of guanylate cyclase andPDE respectively.

In this system a possible differential equation is

V d[tGMP] = a[GTP] -,f[cGMP], (2)

where t is time and the parentheses denote the concentration of free GTP or cyclicGMP (cGMP). If all the cyclic GMP were free, or so tightly combined that the boundfraction remained constant over the range of concentrations considered, y would beunity, as in eqn (4) of Kawamura & Murakami (1986). The more general case iscovered by eqn (2) provided y is defined as dy/dx where y is total cyclic GMP and xis free cyclic GMP. It seems necessary to assume binding by high-affinity sites inorder to explain the relatively small loss in total cyclic GMP after exposure to stronglights (Cote, Biernbaum, Nicol & Bownds, 1984). These high-affinity sites mayperhaps be identified with the two non-catalytic binding sites of PDE which havedissociation constants of 160 and 830 nm respectively (Yamazaki, Sen, Bitensky,

441


Carnellie & Greengard, 1980). Binding by the catalytic site can almost certainly beignored as PDE has a Michaelis constant of 0-5-1-4 mm which is much higher thanany concentration of cyclic GMP likely to be encountered in the present work(Robinson, Kawamura, Abramson & Bownds, 1980; Pugh & Cobbs, 1986; Barkdoll,Sitaramayya & Pugh, 1986; Sitaramayya, Harkness, Parkes, Gonzalez-Olivia &Liebman, 1986). The same argument justifies the assumption implicit in eqn (2) thatthe rate of hydrolysis of cyclic GMP is proportional to the concentration of cyclicGMP.

Previous workers have found a sigmoid relation between current and [cGMP] inisolated patches ofrod outer segment membrane with a Hill coefficient, N, that seemsto vary between 1P8 (Fesenko et al. 1985) and 3 (Haynes, Kay & Yau, 1986;Zimmerman & Baylor, 1986). Kawamura & Murakami (1986) consider N = 2appropriate for intact rods in Ringer solution and a value near 2 fits the results onperfused outer segments obtained by Sather & Detwiler (1987). Since the light-sensitive currents in Ringer solution are small compared to those seen after removingdivalent ions or after adding IBMX, procedures likely to increase cyclic GMP, itseems reasonable to assume that the light-sensitive current in Ringer solution isproportional to [cGMP]N. Hence,

j = A[cGMP]N, (3)

where A is a constant which disappears when the variables are normalized by writingJ = j/j. and [cGMP]r = [cGMP]/[cGMP]n where the suffixes r and n stand for'relative' and 'normal' respectively. Since jn (the normal dark current) is givenby

= A[cGMp]N X (4)

we obtain J = [cGMP]N, (5)

a relation which is probably established within 1-2 ms (Pugh & Cobbs, 1986). Thenext step is to divide both sides of (2) by [cGMP]n giving

d[cGMP]r = a'-f[cGMP]r, (6)dt

where a' stands for a[GTP]/[cGMP]n. This can be transformed into an equation fornormalized current by substituting from eqn (5), thus

V-= a',iI (7)

In the steady state this reduces to

J= (a'/f)N (8)

Our first method of estimating fi is to switch from Na+ to Li+ in the presence ofCa2+. This leads to a rapid build-up of internal calcium (Hodgkin et al. 1985, 1987)

442


which is assumed to inhibit guanylate cyclase and thus lead to an exponential declineof current as cyclic GMP is hydrolysed by the phosphodiesterase. Under theseconditions the light-sensitive current is observed to decline as

j =jo e-bt (9)where the rate constant b is of the order of 1 s-1 in the dark. Provided ?/ remainsconstant over the range considered and a[GTP] is small compared to ,[cGMP] onewould expect from eqns (2) or (6) that [cGMP] would decline as

[cGMP] = [cGMP]0 e-ft/8, (10)

so that the current would bej=jo e-N/8lV )

On comparing eqns (9) and (11)

fi = Ib/N. (12)Plausible assumptions are that v is not much greater than unity and that N is

about 2; this makes the rate constant ofPDE about half the electrical rate constantb that is observed on switching from Na+ to Li+ in the presence of Cao

It is convenient to express rate constants as fractions of their normal value indarkness, i.e. fir = fl/fln and br = b/bn from which it follows from eqn (12) thatflr = br; eqn (8) can, therefore, be rewritten

a-= b JulN (13)This relation, which does not involve j, is helpful in pointing to qualitative

conclusions about the way in which the rate of supply of cyclic GMP seems to varyafter applying flashes or steps of light. If a[GTP] remains constant ac equals unityand the steady-state eqn (13) becomes

JlN = b-1, (14)

or J1/N = Tr (15)

where T = b-1 (16)

These relations are used in connection with Figs 6 and 8 to show that a' does notremain constant after a flash response.Our evidence, like that of Kawamura & Murakami (1986), is consistent with the

idea that the rate constant fi, which depends on the activity of PDE, increasesrapidly during a flash of light and then decreases with first-order kinetics, a possibledifferential equation being

dt8 +(fi-fin)m = c'I, (17)

where fin, the value of f in Ringer solution in the dark, is about 0-8 S-1; m is a rateconstant which determines the decline of f during the falling phase of a flash responseand is about 05 s-1, I is the light intensity and c' is a constant of the order of0-02 s-1/Rh*. The biochemical implications of these numerical values are discussedon p. 468.

443


If eqn (12) holds, b should obey the equation

ldb (8-&+(b-bn)m=cI, (18)

where c = c'N/1q.The constant m is the same in both eqns (17) and (18) so that our estimates of the

rate constant with which b declines can be compared directly with those ofKawamura & Murakami (1986) based on the rate of disappearance of the electricaleffects of injected cyclic GMP.

Estimates of rate constants from experiments with IBMX

A useful method of checking the estimates of the rate constants , and a' wassuggested by P. A. McNaughton.

In the Na+ Li+ method we assume that the rise in internal Ca2+ leads to a rapidand substantial fall in the supply of cyclic GMP, represented by the term a[GTP] ineqn (2). Hence the initial rate of change of cyclic GMP is

(dtcGMP) * -g]cmr]. (19)dt 0

When 0 5 mM-IBMX is suddenly applied the rate constant of PDE, fi, is quicklyreduced to a low value, so

(d[cGIMP]a).n[GTP]. (20)k dt 0

But an[GTP] = /i&[cGMP], so the initial rates of change of cyclic GMP in the twocases should be equal and opposite. A similar conclusion applies to the current,provided allowance is made for the greater permeativity of Li+ than Na+ in the light-sensitive channel.The basis of the IBMX method of estimating rate constants is as follows.Equation (7) may be rewritten

dJ aNJ-11N /jN. (21)

dt

If a' and f are constant for t < 0 and a' is zero for t > 0, as assumed in the Na+ -Li+ method,

dJ-= fl J=-bJ, (22)dt 1y

1dJfor t > 0. Hence b=--

In the IBMX method, with 0 5 mm-IBMX applied suddenly at t =0, we assume,B-*0 at t = 0. So for times slightly greater than zero we have

(dJ aNI'N(23)kdt/0 - j11N(23)

444


But for t < 0 the system is in a steady state with a' = fiJi/N. Hence

td~ _flNJ= J (24)( dt )o+ 71 *(4

In the simplest case where there is no significant binding of cyclic GMP (y = 1) andno co-operativity (N = 1), oc' equals dJ/dt and / = J-'dJ/dt. Equation (24) showsthat the rate constant b can in principle be obtained as J-ldJ/dt without a knowledgeof y or N. In practice unless N = 1, it is better to use a method like that describedon p. 462.

Validity of a8sumptionsThe lithium method of estimating the rate constant of PDE is based on the following

assumptions. (1) In toad and salamander rods internal calcium is maintained at a low level byNa+-Ca2+ exchange. (2) On switching from Na+ to Li+ (or some other cation) in the presence of

2+ internal calcium rises and reduces the light-sensitive current to less than about 5% of itsnormal value within 05 s. (3) The reduction of current associated with the rise of internal calciumis brought about by a fall in cyclic GMP resulting from a decrease in the rate at which cyclic GMPis supplied rather than by an increase in its rate of destruction: i.e. by a decrease in a' rather thanan increase in f.

Evidence for the first two points has been summarized by Yau & Nakatani (1984), Hodgkin etal. (1985) and Hodgkin & Nunn (1987). A particularly strong argument is the close correlationbetween the time taken to restore light-sensitive current after a period in a sodium-free solutioncontaining calcium with the time taken to pump out most of the calcium load, which time may varybetween about 0-2 and 30 s (Hodgkin et al. 1987). The criticism that the argument depends onelectrical rather than chemical evidence can now be met by experimental results with aequorinsuch as those described by McNaughton, Cervetto & Nunn (1986 a, b) which demonstratequantitative agreement between the aequorin response and the rise in internal calcium deducedelectrically. The assumption that the rise in calcium acts within less than 0 5 s is supported by ourunpublished measurements of the calcium-pumping transients which show that internal calciumreaches a blocking concentration in roughly 0-2 s.There is now such strong evidence that light-sensitive channels are kept open by cyclic GMP that

it seems reasonable to identify the reduction of current resulting from the increase in internalcalcium with a reduction in [cGMP]. The debatable point in our third assumption is whether thedecrease in cyclic GMP is caused by a decrease in a' reflecting reduced cyclase activity or anincrease in fl reflecting increased PDE activity. The latter seems unlikely because large changes inexternal calcium which appear to alter internal calcium have little effect on the rate constant b withwhich current declines in lithium (Hodgkin et al. 1985). This leaves a depression of cyclase activityby the rise in internal calcium as the most likely cause of the decrease in current in sodium-freesolutions.

Biochemical tests of the effects of Ca2+ on guanylate cyclase in retinal homogenates givesomewhat confusing evidence, perhaps because the incubating media are deficient in some essentialcomponent such as calmodulin. Thus Lolley & Racz (1982) found a marked inhibitory effect ofCa2+ on guanylate cyclase in homogenates of rat retinae at concentrations of 10-8 to 10-6 M, whereasPepe, Panfoli & Cugnoli (1986) found that toad rod cyclase was only inhibited by suchconcentrations if the cyclase activity had first been enhanced by a strong flash.The lithium method can probably not be used at concentrations below 10 4M-Ca2+ because

guanylate cyclase is not adequately blocked by calcium entry when the external calciumconcentration is as low as that.The main assumptions in the IBMX method of measuring a' and hence b are that 0-5 mM-IBMX

reduces b to a relatively small value within about 0 5 s and that it has no other significant effectat that time. These assumptions seem justified by the general agreement between the values of bobtained by the lithium and IBMX methods. The IBMX method may give a large errorimmediately after strong flashes (> 104 Rh*), partly because the remaining light-sensitive currentis too small to measure quantitatively, and partly because it is uncertain whether 0 5 mM-IBMXdoes reduce PDE activity to a sufficiently low value under these conditions.

445

446 A. L. HODGKIN AND B. J. NUNN

Light: 10 Rh* s-1 (2) or 45 Rh* s-1 (3)

Na+A Li+

0 3iO(pA) 3_

-201_ 2.1, dark

-40 L

B

JI0-3 -

0.1 F

0-03 L

4

Time (s)

Fig. 1. Records illustrating effect of weak light on b, the rate constant for decline ofcurrent after switching from Na+ to Li+, and two methods of measuring b. The externalsolution was switched from Na+ to Li+ (with 1 mM-Cal+) either in the dark (1) or 6 s afterapplying a weak step of light of intensity 10 (2) or 45 Rh* s-' (3). Panel A gives recordsof the light-sensitive current j obtained by subtracting a record in a bright light (the'junction' current) from one obtained in darkness or with a dim light (Hodgkin et al.1985). B gives J (logarithmic scale), as a function of time, which was found to be a straightline with slope b. J is the normalized current, i.e. j/jn where jn is the current in Ringersolution in the dark. C is a plot ofj-' Aj/At with At = 0 05 s. The estimated value of therate constant is shown by the horizontal lines with the value of b corresponding to theslope in the middle panel. Further data from this experiment are given in Fig. 2.

RESULTS

Effect of weak lights on rate constant and currentFigure 1 illustrates the effect of a step of dim light on the rate constant b with

which current declined when Na+ is switched to Li+ in the presence of Ca . Panel Agives the light-sensitive current obtained in the usual way by subtracting a record ina bright light from one obtained in darkness. Panel B shows lnJ as a function of time,which is found to be a straight line with a slope - b. Panel C gives j-1 Aj/At. Thevertical position of the horizontal line through the trace provided an estimate of bwhich agreed with that obtained from the slope of the line in the middle panel.

Curve 1 in Fig. 2 shows the relation between light intensity I and the rate constantb. For weak light intensities the slope of the curve at the origin was 0-08 (Rh*)-', avalue close to the mean of 0-058 (Rh*)-'. The mean value of b in the dark in Ringer

CONTROL OF CURRENT IN RODS 447

A 10

I 108

2,~~~~~~~~~~~~~~~~~~~~~~~tr Or2 Zt

B

*-06 b

0- - or0-4~~~~~~~~~~~~~*

0 100 200 1300

/ (Rh* S-')

Fig. 2. Effect of steady light intensity on the rate constant b, normalized light-sensitivecurrent J and derived quantities; from Fig. 1 and other records from the sameexperiment. Curve 1 (panel A) shows the variation of b, the rate constant for decline ofcurrent with light intensity, and curve 6 (panel B) shows the variation of the normalizedrate constant T where T = b-l and Tr = T/IT (rn = time constant in dark). Curve 5 showsthe variation of J, i.e. normalized light-sensitive current in Ringer solution, with lightintensity. If /J, the rate constant of PDE, were the only variable, curve 6 for Tr shouldcoincide with either curve 4, J2, or curve 5, J, depending on whether a square or a linearrelation between [cGMP] and current is assumed. Curves 2 and 3 show how the rate ofsupply of cyclic GMP would have to vary with light intensity in order to explain theresults. The scales on the right-hand side of the top panel give fr, the relative value of ,(curve 1), and also show how a' defined in eqn (13) would have to vary with light intensityon the basis of a square (curve 2) or linear (curve 3) relationship between current and[cGMP].

solution, bn was 1-54 s-' in these experiments (see Table 1 legend, p. 456, for furtherdetails).

It follows from the simple scheme summarized in eqns (1) and (2) that in the steadystate the rate of supply of cyclic GMP which is a[GTP] should equal the rate ofhydrolysis of cyclic GMP which is fl[cGMP]. If a[GTP] were constant then theconcentrations of cyclic GMP should be inversely proportional to b and hencedirectly proportional to its reciprocal denoted by Tb. If current is proportional tocyclic GMP the normalized current J should equal the normalized time constant Trwhere J = j/jn and Tr = T/Tn (eqn (15), N = 1); jn and Tn are the values of thevariables in Ringer solution in the dark. A comparison of curves 5 and 6 in Fig. 2shows that this prediction is not fulfilled and that the variation of steady-state


Na+m Li+

T- -

0 IBMX

3 pM-IBMX

30 ,LM-IBMX

500 $AM-IBMX

-100 F

-2001

0*90 (3,uM-IBMX)

0-37 (30 AM-IBMX)

L I

0 10 20Time (s)

Fig. 3. Demonstration of the slower decline of current in a solution containing Li++IBMX. In each case the Li+ current declined exponentially with a rate constant b(= j-1 dj/dt) which varied from 1P48 s-' (0 IBMX; A and E) to 0-09 s-5 (500 ,SM-IBMX; Dand E). Records measured in darkness. Same experiment as rod 1 in Fig. 4. The rod wastransferred to Ringer solution +IBMX for 10-20 s before switching to Li++ IBMX.

current with light intensity is much less than that expected from the change in timeconstant. The discrepancy becomes worse if current is assumed to vary as [cGMP]2in which case there should be agreement between Ji and Tr (eqn (15), N = 2). But as

can be seen from Fig. 2 the difference between J2 and Tr is greater than that betweenJ and Tr

The discrepancy between Tr and J was present in all experiments. For weak lightsAJI/ATr was 0O33+±006 (s.E.M., n = 8). A simple explanation of the discrepancy isthat light closes channels and reduces the influx of calcium so that Ca2+ falls and

448

A

B

pA

pA_

D 0

pA

E1-5

1 Ai (s') 1X0

0*5

30

a

I I


inhibition of guanylate cyclase is reduced. Curves 2 and 3 in Fig. 2 show how the rateof supply of cyclic GMP would have to increase in order to reconcile the variation ofcurrent with the observed changes in time constant. Curve 3 gives bJ for the linearcase and curve 2, which is considered more appropriate, assumes J cc [cGMP]2.

52

IL\Dim light

b WIl)\ Dark

0-1

0-01 L0 0.3 1 10 100 1000

[IBMX] (WM)

Fig. 4. Effect of concentration of IBMX (abscissa) on the rate constant b in dark (curve1) and weak light (curve 2); both scales are logarithmic. Symbols 0 and O give b in thedark for rods 1 and 2 respectively; * for rod 1 and * for rod 2 show b -0-06 s-1 where0-06 s-1 makes allowance for a small fraction of PDE not inhibited by IBMX (see text).Triangles show b in dim light (43 Rh* s-1) for rod 2; the light was turned on about 20 sbefore application of Li+; IBMX was added to the Ringer solution after 10 s in light. Thesmooth curves 1 and 2 are given by eqns (25d) and (26a) respectively, with KIBMX = 9/UMin both curves.

Quantitative effect ofIBMX on the rate constant bThe rate constant for the decline of current in different concentrations of IBMX

was measured by switching from Na+ to Li+ after equilibrating in IBMX Ringersolution for 10-30 s. Sample records of the current j, and j-1 dj/dt are given in Fig.3 from which it can be seen that the current declined exponentially both in thepresence and absence of IBMX. This was true at all concentrations of IBMX and isto be expected because the concentration of free cyclic GMP in a normal rod isprobably of the order of a few micromolar which is small compared to the Michaelisconstant of the phosphodiesterase (0-5-1-4 mm, Robinson et al. 1980; Sitaramayyaet al. 1986; Barkdoll et al. 1986).The graphs in Fig. 4 summarize the results obtained in two experiments in which15 PHY 403

449


both bw, the rate constant in Ringer solution in darkness, and KIBMX, the inhibitoryconstant of IBMX in darkness, were very similar, i.e. bn = 15 S1 and KIBMX = 9 ,UMfor both rods. The experimental points in darkness are shown by the open symbols,O for rod 1 and Cl for rod 2. The deviations from a reciprocal relationship at100-500 /LM-IBMX suggest that some 4% of the PDE may not have been inhibitableby IBMX. The filled symbols, 0 and * in Fig. 4, are the experimental values of bminus 0-06 s-1, i.e. minus 4% of the dark value without IBMX present. The filledtriangles which were obtained on rod 2 show the effect on the rate constant atdifferent [IBMX] of applying a background light of intensity 43 Rh* s-1. It can beseen that IBMX increases the ratio b (light)/b (dark) but decreases the absoluteincrement b (light) - b (dark). This result might be explained qualitatively if IBMXhindered but did not prevent the GOa-protein from activating the phosphodiesterase.Curve 1 in Fig. 4, which is a reasonable fit to the corrected points in the dark, was

calculated from standard enzyme kinetics by assuming that the velocity ofhydrolysis of cyclic GMP is given by

V [cGMP]/Km (25a)Vmax 1+ [cGMP]/Km + [IBMX]/KIBMX'

where Km is the Michaelis constant for cGMP, [IBMX] is the concentration ofIBMXand KIBMX the inhibitory constant for IBMX. According to Pugh & Cobbs (1986) theKm of the phosphodiesterase is 0-5-1A4 mm whereas free cyclic GMP is not likely tobe present at more than about 10 tM (see Pugh & Cobbs, 1986) so the term [cGMP]/Km in the denominator of eqn (12) may reasonably be neglected. Hence the rateconstant fin for destruction of cyclic GMP in the absence of IBMX should be

fln =Vmax/Km (25b)fi 1

50ofi - 1+ [IBMX]/KIBMX (25c)Since b/b. = fl/f,n the equation for b in the dark is

b ~~bnb + [IBMX]/K ' (25d)

and for curve 1 in Fig. 41@35b = 1+', (25e)

where x = [IBMX]/KIBMX. The average value of KIBMX in eight experiments was7-0+ 0-9 #m (S.E .M.) .

To describe the effect ofdim light, we assume that a light intensity which increasesthe rate constant by Ab in the absence of IBMX will increase it by pAb at highconcentrations of IBMX, when all the PDE is combined with IBMX. Curve 2 wasobtained on this assumption which leads to

b(L) = bn + Ab +pxAb (26a)1+x

450


and b(L) = 4+07x (26b)1+x'(2b

if Ab is taken as 2-65 s-1 and p as 0-26; as in curve 1, bn was taken as 1-35 s-1. Twosimilar experiments gave values of p of about 0 4 and 0 9 but the constant is hard tomeasure and it does not seem safe to go beyond the qualitative conclusion thatIBMX may hinder but does not prevent the activation of phosphodiesterase bylight.

A Na+ B

O~~~~_3 _D -J rrLr.

00

1*0

0*3

0.03

0 5 0 5 10 15 20Time (s)

Fig. 5. Increase and subsequent decline of rate constant b during response to 20 ms flashdelivering 5700 photoisomerizations (given at arrow). Part A shows the exponentialdecline ofdark current seen on switching from Na+ to Li+ with 1 mM-Ca2+ on a linear scale,above, and logarithmic scale, below. The right-hand panel (B) shows the effect ofrepeating the same change at different times on the falling phase of the response. At timesearlier than 3 s the rate constant was too rapid to measure. For further analysis of thisexperiment see Figs 6 and 10.

The experiments with IBMX show the same type of quantitative discrepancybetween current and rate constant as that described for steady light. Thus 10,UM-IBMX, which on average reduced the rate constant br from 1 to 0 40 s-1, increasedJ from 1 to 1X18. Such behaviour is explained if IBMX increased internal calcium andthus inhibited guanylate cyclase. In 10 #,M-IBMX the apparent rate of supply ofcyclic GMP changes from 1 to 0 47 when calculated as Jbr and from 1 to 0 43 whencalculated as J-lbr. The standard errors of these estimates of ar are + 0 04 and + 0 03respectively (n = 7). The explanation seems plausible since there is evidence thatIBMX increases internal calcium (Yau & Nakatani, 1984; Cervetto & McNaughton,1986; McNaughton et al. 1986 a, b) and that a rise in calcium blocks guanylate cyclase(Lolley & Racz, 1982).

15-2

451


Increase and subsequent relaxation of rate constant after flashThe left-hand part (A) of Fig. 5 shows the exponential decline of dark current seen

on switching from Na+ to Li' in the presence of Ca"+; the current was recorded ona linear scale in the upper panel and on a logarithmic scale below. From the slope ofthe log plots the rate constant b with which the dark current declined in lithium wasfound to be about 1 s-1. The right-hand part of the figure shows the effect ofrepeating the same solution change at various times during the falling phase of aresponse to a 20 ms flash of strength 5700 Rh*. The family of curves shows that the

A 0

.-d 05

I-0B 100 r Dark

10-

0-1 -

L0

0

I10

Time (s)

J20

Fig. 6. A, comparison of recovery of light-sensitive current after a flash (5700 Rh*) withthe recovery of the time constant Tr (= 1/br). Note that the period of reduced timeconstant outlasts the period of reduced current. Comparing Tr with J2 or JP rather thanwith J makes the discrepancy worse. The values of Tr were obtained from the slopes of thestraight lines in the lower part of Fig. 5B. The time course of the rate constant b is shownon a logarithmic scale in B. The straight line through these points and the curve forTr= brb in A are drawn from b = 0-95+ 70 et-12 1. A linear plot of b(t) is shown in Fig. 10.

decline of current gets progressively faster at earlier times, until at about two-thirdsof the way up the response the rate constant reached the limit of resolution of themethod - about 20 s-1.From the lower part of Fig. 6 it can be seen that the rate constant b declined

exponentially with a time constant m-1 of about 2-0 s. An experiment with a weakerflash (Figs 7, 8 and 11) indicated that the rate constant b reached its maximum atabout 0 5 s after the flash. If the straight line in Fig. 6 is extrapolated to this time,b is found as 55 s-1. A reason for choosing 0-5 s rather than some other time is thatfor flashes of moderate intensity which gave responses like that in Fig. 11 the area

II

452

-0

-0

1


under the experimental curve for b equals (bo.5 -bn)/m. This enables a prediction tobe made about the expected value of Ab/AI for weak steady lights (p. 445). Theexperiment of Fig. 6 suggests that a flash of 5700 Rh* rapidly increased theactivation of PDE some 50-fold and that after about 2 s the concentration of activePDE declined exponentially to its dark value with a time constant of about 2 s.During the falling phase, the rate constant b, and probably ,1 too, is so high that thesystem must be fairly close to the equilibrium condition defined by fl[cGMP]=a[GTP].

A BNa'

0.2-0L4

04 }W

0.8-

1.0 0

1.2-

8

6

4-b (WI)

0 2*5 0 5 10

Time (s)

Fig. 7. Estimation of b during response to a medium flash (140 Rh*). A, current (top) andrate constant b (= j-'Aj/At, lower panel) of current decline in Li+ in the dark(bn = 1-3 s-1). B, Li+ current decline is speeded (top) and b is rapidly increased (below) bydim flash. The points in the lower panel show values of b estimated from these records;values from these and other records are shown in Fig. 11 A. The measurements show thatthe flash raised b to 6-8 s-' in about 0-5 s. The smooth curve drawn through the points inB (lower panel) and in Figs 8B and I IA has the form expected for a chain of threereactions with two having equal rate constants of 4 0 s-1 and the third a smaller rateconstant of 0-635 s-' (Baylor, Hodgkin & Lamb, 1974, eqn (45)). Dark currentn = -35 pA at the start of the experiment.

As shown on p. 443 if the inward current is proportional to [cGMP] and a[GTP]remains constant, the inward current should recover along the same curve as thetime constant Tb(= b-1). The upper part of Fig. 6 illustrates the comparison betweennormalized current J and normalized time constant Tr, with both variables plotteddownwards, and shows that the decrease in time constant lasts much too long for theprediction to be true. The discrepancy is slightly increased by removing the steady-state approximation and becomes much worse if current is assumed proportional to


the square or cube of [cGMP] rather than to its first power. In the case of a squarerelation the correct comparison would be between J2 and Tr, which differ more thanJ and Tr, as illustrated in Fig. 6.

This discrepancy was also present in experiments with weak flashes (Figs 7 and 8).In the case of medium flashes the time course of b(t) could be followed throughout theresponse by applying the flash during the exposure to Li+ as well as beforehand asshown in Fig. 7. In this experiment Tr again recovered more slowly and reached ahigher peak than the normalized current J (Fig. 8).

A0 _

J,Trr

B10 _

b-bn (s-1)

0.1L I I I I0 5 10

Time (s)

Fig. 8. Comparison of recovery of Tr (= /br) and normalized current J after a medium,143 Rh* flash. Note that rr came closer to zero and recovered more slowly than J. Pointsin A and B from measurements of b in Figs 7 B and 11 A. The logarithmic plot of b -bin B demonstrates that b recovers exponentially with a time constant of 1-57 s.

Kinetics of activationFigure 9 gives the relation between the increase in peak rate constant Ab and flash

strength in Rh*; A is on linear and B on logarithmic co-ordinates. The relation islinear up to about 400 Rh* per rod but above that the rate constant increased lessrapidly with the number of photoisomerizations. However, there was no sign of anydefinite upper limit or saturating level for the rate constant b. This is to be expectedas the rate constant of fully activated PDE, about 500 s-5 (Pugh & Cobbs, 1986), isfar beyond anything that can be resolved by our method.From Fig. 9 and Table 1 it is clear that the behaviour of the rate constant b under

the influence of illumination is much more linear than that of the light-sensitivecurrent. This indicates that phosphodiesterase activity continues to increase withflash intensity long after the light-sensitive current has saturated. If the kinetics of

454


the release and decay of the activating G-protein are reasonably linear it should bepossible to predict the effect of weak steps of light on b from data based on flashes.Thus a steady light of intensity I in Rh* s-1 should increase b by IfJ Ab'(t) dt whereAb'(t) is the transient increase in rate constant produced by one photoisomerization.Hence under steady conditions

Ab = J|(b-bn)dt) (27 a)

A 20 - 32

Ai (pA)==

">10 -16/

200 400 600 800 1000B Rh*

10~~~~~~~~~~~~~~

Ca 4 -

.< -,

10 100 1000 10000Rh*

Fig. 9. Relation between strength of 20 ms flash (Rh*) and the increase in rate constantAb measured at the peak of the b(t) curve (circles). Triangles show the peak change incurrent Aj. In A both co-ordinates are linear, and in B, which covers a wider range, bothare logarithmic. Note that Aj saturates above 700 Rh* whereas Ab is not saturated at thehighest intensity. Filled circles for measurements made early in the experiment areconsidered to be more precise than later measurements (open circles). The dashed portionof the Aj curve in the lower panel is an extrapolation based on the linear behaviourdemonstrated for dim flashes in many other rods.

where Q is the strength of the flash used to increase b from its dark level bn. It wasfound empirically that the integral of the response of b to a medium flash, such asthat in Fig. 11, was close to the area under an exponential fitted to the falling phaseand extrapolated back to 0 5 s: that is

C0 r0J (b- bn)dt = (bO.5-bn)J e-m(t-05)dt (27b)

0 0-0.5-b~)/m.(5= (bo-5 -b.)Im. (27 c)


But the constant c in Table 1 was defined as (bo- 6b)/Q, where Q is the strengthof the flash in Rh*, so

Ab c (27d)

Ten experiments with weak steps of light gave a mean value of 0-058+0-009(S.E.M.) (Rh*)-f for Ab/AI which may be compared with the mean value ofc/rn = 0-049 +0-007 (s.Em.) (Rh*)-1 in the three experiments with 140 Rh* flashes inTable 1. A direct comparison on rod 4 gave 0-035 for Ab/AI and 0-045 for c/m. The

TABLE 1. Parameters determining effect of flashes on apparent activation and relaxation of PDE

Flashstrength Q bn bo55. m c

Rod (Rh*) (S-') (S-') (S-1) (s-r/Rh*)1 11400 1-7 104 0-40 0-0092 7200 1-8 45 0-55 0-0063 7200 1-3 36 0-58 0-0054 7200 1-6 59 0-48 0-0085 5700 0-95 56 0-48 0-010Mean 7700 0-52 0-0083 750 1-3 9 0-48 0-0104 750 1-6 13 0-54 0-0156 750 1-5 10 0-44 0-0117 750 2-4 14 0-67 0-016Mean 750 0-53 0-0132 140 1-3 5-9 0-85 0-0334 140 1.1 4-8 0-57 0-0268 140 1-3 6-8 0-64 0-039Mean 140 0-69 0-033

b is the rate constant with which current declines in lithium: bn in the dark, bo.5 at 0-5 s after a20 ms flash of strength Q, given in second column (b,., was extrapolated). m is the rate constantwith which b declined; c is (bo.5-bn)/Q. Results for rod 5 shown in Figs 5, 6 and 10 and for rod 8in Figs 7, 8 and 11. The mean value of bn in seventeen rods was 1-54 s-' (S.D. = 0-36). The meanvalue of Ab/Al for weak steps of light (< 50 Rh* s-1) was 0-058+0-009 (s..M.) (Rh*)-1 in tenexperiments.

possible biochemical implication of the values found for the parameters 6, c and m areconsidered on p. 467.Table 1 indicates that m decreased from 0-69 to 0-52 s-' when the flash strength

was raised from 140 to about 8000 Rh*. This effect, which is small, does not requireany special explanation as one would hardly expect the mechanism responsible foreliminating the active G-protein to be strictly linear over a very wide range ofconcentrations.

Evidence for a delayed activation of guanylate cyclaseThe discrepancy between the recovery of current and of the time constant Tb can

be explained by accepting the strong evidence that [Ca2+]i declines during the

456


plateau of a flash response and assuming that this decline activates guanylatecyclase, so increasing the rate of supply of cyclic GMP.The argument is illustrated in Fig. 10. Here curve 1 in the lower panel gives the

normalized current J, plotted upwards, as a function of time. Curve 2 in the upperpanel is a smooth curve fitted to the experimental points for the rate constant b (seelegend to Fig. 6). Curves 3 and 4 show how a4, the relative rate of supply of cyclic

60 -12bJ+,bJ 4 6012r

b.}i-,~1-

8

bJ+ b,

b SX40 8 / \ 40 8b (s'1)

20 4 2 -4

0 -01*0

J,CarOS X 00

0 10 20Time (s)

Fig. 10. Analysis of response to strong flash (5700 Rh*) illustrated in Fig. 6. Curves are: 1,normalized current J as a function of time; 2, smooth exponential curve fitted toexperimental values of b (filled circles) by method of Fig. 6B; 3, bJ giving a' as a functionof time assuming Joc [cGMP]; 4, bJI giving 2a' assuming Joc [cGMP]2; 5, relative calciumcontent Car calculated by eqn (28c) in text with rp = 1-6 s. The right-hand scales in theupper panel are for the normalized quantities br and a'.

GMP, would have to vary in order to reconcile the curves for current and rateconstant; the two curves correspond to different assumptions about the relationbetween current and the concentrations of cyclic GMP.

In curve 3 current is assumed proportional to [cGMP] and ar was calculated asJSfr where ir, assumed equal to br, is the normalized value of the rate constant ofhydrolysis of cyclic GMP. In curve 4, current is assumed proportional to [cGMP]2 soar is calculated as Jl1?r. Both curves 3 and 4 have been magnified 5 times as can beseen from the different numbers on the vertical scales. The result which wasconfirmed in seven experiments is clearly consistent with the idea that the flash oflight evokes a sudden increase in PDE activity which rapidly increases the rate ofhydrolysis of cyclic GMP and causes the current to fall to zero within 0 5 s or less.Recovery is partly due to the decline of the activity of PDE, which decays with a

457


time constant of 21 s and partly to the delayed increase in the variable a' whichcharacterizes the rate of supply of cyclic GMP from GTP.

In order to explore the possibility that the increased rate of supply of cyclic GMPis caused by a fall in internal calcium, we calculated the time course of theexchangeable calcium content Ca on the assumption that calcium influx is a constantfraction of the inward light-sensitive current j' and that the efflux is proportional toCa. These assumptions lead to

dCadt +IT-Ca =yj, (28a)

which reduces to Tr1 an = yj, (28b)

for the steady state in the dark. Hence

dt+Cara=J (28c)

where Tr is the pumping time constant, Car = Ca/Can and J = j'/j'. Note that theconstant y disappears when the normalized variables in eqn (28c) are employed.Curve 5 in Fig. 10 was calculated from J with rp = 1-6 s. This is the average value

of the time constant of the final decay of the Na+-Ca2" exchange current measuredin bright light after a period of darkness spent in Ringer solution or in Li+ to increasethe Ca2+ load (see Hodgkin et al. 1987). As can be seen from Fig. 10 a pumping timeconstant of 1-6 s gives a minimum calcium content at the time of 3 s which is closeto the peaks of a' in curves 3 and 4. However, this argument is clearly speculativeand the only safe conclusion from Fig. 10 is that it seems qualitatively consistentwith the idea that a fall in internal calcium may be responsible for the delayed risein a'.

Experiments with weaker flashes showed that a' reached a lower maximum at anearlier time as shown in Fig. 11 (curve 3). In this experiment the exchange currenton turning on a bright light was too small to be seen and the value of Tp was takento be 0-5 s, which is at the lower end of the range measured by Hodgkin et al. (1987).Again the results are consistent with the idea that a' is increased by a fall in Cat'.Validity of steady-state approximationA simple check of the validity of this approximation is to assume that the

constants y and N in eqn (7) are both unity. In that case b = fln and eqn (7)becomes

dJ+bJ = a', (28d)dt

during the falling phase.In Fig. 10 we calculated a' in curve 3 as bJ. If eqn (28d) is used the curve for a'

reaches a maximum that is 4% higher and 4% earlier than bJ and then declines inmuch the same way. The correction becomes more important when considering theeffect of weaker flashes and more complicated ifN > 1. Equation (28d) was used incalculating a' in Fig. 11.

458


A 8

6

b (sr1)4

2

01

- t

2

Dark

'5

4

3oa,b,

2

1

0

B FOr

J, Car0*8 F

0-6 I

/4Car

JiL0 5

Time (s)10

Fig. 11. Analysis of response to medium flash (140 Rh*) illustrated in Figs 7 and 8. Curvesare: 1, normalized current J as a function of time; 2, smooth curve fitted to experimentalpoints (circles) giving rate constant b as a function of time (the basis of the smooth curveis given in the legend to Fig. 7); 3, bJ+dJ/dt giving a' as a function of time assumingJa[cGMP]. The right-hand scales are for the normalized quantities a' and b,. Curve 4shows relative calcium load Car calculated by eqn (22) in text with rp= 05 s.

The effect of sudden application ofIBMX during the flash responseThe conclusion that the increased activation of PDE after a flash, which initially

reduces free cyclic GMP to a low level, is followed by a rise in the rate of supply ofcyclic GMP is supported by experiments with pulses of IBMX applied at varioustimes during the response to a strong flash.IBMX appears to cross the surface membrane rather easily and its electrical effects

suggest that under most conditions an external concentration of 500 FM gives asubstantial inhibition of PDE within 0-5 s or less. When the destruction of cyclicGMP is suddenly blocked the rate of rise of inward current should provide aqualitative index of the rate at which cyclic GMP is supplied from GTP throughguanylate cyclase.

Figure 12 illustrates one of these experiments. In the dark a 5 s pulse of 500 #m-IBMX gave a large increase in inward current but the maximum rate of rise ofinward current was small compared to that seen if the same pulse was applied at the

459


A

j (pA)

0.5 mM-IBMX0 IBMXYSFIFJ-7 iz rOr v.r x I T,

-1001-

-200 L

B0

d/ (pA s')dt

-200 _

-400 _

C

-400

i(pA s')dt-200

0

% dj/dt

D_"I

0

j (pA)

-20

-40

0 10 20Time (s)

Fig. 12. Rate of increase of light-sensitive current on application of 0-5 mM-IBMX indarkness and at various times after a 100 ms flash (40800 Rh*). A, current records in darkand after flash; B, rate of current increase in IBMX. C, comparison of form of flashresponse (continuous trace) with maximum rate of rise of current after applying IBMX( and broken curve), which reached a peak about 8 s after the flash. Dashed curve drawnby eye. The current in IBMX could be suppressed almost entirely by very brightlights.

end of the plateau of the flash response. In Fig. 12 the inward current increased atan initial rate of 75 pA s-1 in the dark but the rate rose to a maximum of 490 pA s-'at 7 s after the flash. This is consistent with a 6-fold increase in guanylate cyclaseactivity if current is assumed proportional to [cGMP].The effect of a wide range of flash strengths is illustrated in Fig. 13 from which it

can be seen that for flash strengths < 104 Rh* the general form of the curve for theinitial dj/dt is similar to those deduced for cyclase activity (a') from the lithium data(Figs 10 and 11). There are various complications and uncertainties. Immediatelyafter a strong flash the initial rate of rise of current in IBMX was less than the valuein the dark, and fell to near zero with flash intensities greater than 20000 Rh*. Thismight result from an early inhibition of guanylate cyclase, but it seems more likely

460


that sufficiently high concentrations of the active G-protein prevent IBMX blockingthe phosphodiesterase. This explanation is supported by the observation that therewas no decrease in dJ/dt after a weak flash of 50 Rh* and hardly any after a mediumone of 5600 Rh*. The suppression after the flash became conspicuous at 24000 Rh*and was more complete and more prolonged at 101000 Rh*. With such strong flashesit seems likely that the PDE is incompletely blocked at early times and that thisaccounts for much of the apparent delay in the onset of increased cyclase activity.

A _j-4, 1 s step

400

-di (pA/s)dt

200-

0

B 1*0F

054

0I I II

0 10 20Time (s)

Fig. 13. Comparison of normalized current J with (- dj/dt)m.X on applying 05 mM-IBMX at different times after brief exposure to light. Light durations were 20 ms forcurves 1 and 1 s for curves 2-4; Rh* was 50; 5600; 24000 and 101000 in curves 1-4respectively. Same rod as in Fig. 12.

However, this complication should be much less serious with flashes weaker than104 Rh*.The prominent overshoot seen when IBMX is applied at the end of the plateau or

early in the falling phase (Fig. 12A) probably occurs because when channels open,calcium ions rapidly enter the rod, and then inhibit the cyclase, thus reclosing abouthalf the newly opened channels. This idea was supported by the observation thatapplying 0 Ca2W, 0 Mg2' Ringer solution, with BAPTA and IBMX, gave no overshootbut increased the current monotonically to values of several hundred picoamperes,both in darkness and after a flash.

461


Use ofIBMX to determine rate constantsQuantitative analysis of the IBMX experiments gave rate constants similar to

those obtained by the Na+ -- Li+ method. To illustrate the analysis, considerevaluation of bn, the value of b in the dark. In Fig. 12, panel A gives the dark currentas -50 pA and panel B gives dj/dt as -75 pA s-' for the maximum rate of changeof current immediately after applying IBMX in the dark. By definition J is unity inthe dark, so from eqn (24), p. 445, bn is found as dJ/dt = 1-5 s-1. The average valueof bn obtained by this method in eight rods was 1P46+ 0-23 (s.E.M.) s-1 compared with1-54+0-1 (S.E.M.) s-1 in seventeen rods studied by the Na+-* Li+ method. Thedifference is clearly not significant. If the action of IBMX were instantaneous thecalculated value of b should be independent of the co-operativity number N.However, unless N is unity, which seems unlikely, it is better to use the methodoutlined in the next section. If current is proportional to [cGMP]2 use of eqn (29b)(below) gives values of b about 5-15% less than those obtained above.

Evaluation of rate constants during falling phase of flash response by IBMX methodUse of the simple method outlined in the previous sections may lead to large errors

if the normalized current J is small. To illustrate an alternative and probably morereliable method we assume that I = 1, i.e. there is no significant binding of cyclicGMP and that the current is proportional to [cGMP]2. For the reasons given onp. 458 the system is considered to be in a steady state during the falling phase of theresponse to a strong flash. Just before applying IBMX the normalized current J1 isgiven by

= [cGMP]l = (az'/fl)2. (29a)With v = 1 and N = 2, eqn (7) becomes

VI=a-,J (29b)dt

After applying 0 5 mM-IBMX, fl-'->0 and a' = dJIdt, so it seems reasonable to obtainan approximate estimate of oc' from the maximal rate of rise of Ji, which occurredabout 0-2 s after applying IBMX. Provided that PDE was blocked sufficientlyrapidly and completely a' and , can then be obtained from

,(dti)m (29c)

and alJt=ca', (29d)

where J1 is the current when IBMX is applied.The method is illustrated by Fig. 14. In the upper panel the broken curve gives the

normalized current J for a test in which 0 5 mM-IBMX was applied at 9-2 s after astrong flash (40800 Rh*). Plotting this curve required a knowledge of the zero levelat which there is no light-sensitive current and the dark current before the flash. Thefirst quantity was obtained by averaging a suitable section of the plateau, and thesecond by averaging the initial part of the trace, in this case from -1 s to zero. The

462


continuous trace, in the upper panel, which became very noisy as the currentapproached zero, gives the square root of the current J2, with imaginary quantitiesequated to zero. The records in the lower panel show dJ2/dt for application of IBMXat different times and the trace marked with the vertical line is the one correspondingto the curves in the upper panel; this had a peak of 6-4 s-' at 9-3 s after the flash andgives a' at that time. On the assumption that the same value holds 0-1 s earlier whenIBMX was applied and Jl = 0-55, eqn (29d) gives ,8 as 11-6 s-'. The values of the rateconstants in the dark obtained from the left-hand record in the lower panel werea' =t=0 75 s-1.

A,if2 1A /

IX /

1 -0_

djA 6 -Darkdt 4(s1) 2

0

0 3 0 5 10 15Time (s)

Fig. 14. Method of obtaining a' and f during recovery from strong flash (40800 Rh*).Current is assumed proportional to [cGMP]2. The upper panel shows the normalizedcurrent J and its square root J2; 0-5 mM-IBMX was applied at 9 s after the flash. Thelower panel shows dJ2/dt for IBMX applied in the dark (left) and at 3, 5, 7, 9, 11, 13, 15and 17 s after the flash. The rate constant a' (supply of cGMP) and ft (hydrolysis ofcGMP) are given by dJi/dt and J-2dJ2/dt respectively. Same experiment as Fig. 12. Thedark current, -jn, in the upper panel was 44 pA and varied between 44 and 46 pA in thelower panel.

In Fig. 15 a' and ft are plotted on a log scale against time. At 7-2 s after the flasha was close to its maximum value of 7-4 s-1 and , was 30 s-5. Thereafter , declinedexponentially to its dark value of 0-8 s with a time constant of 2-45 s which is similarto that obtained by the Na+-+ Li' method. As explained on p. 461 the long delay inthe rise of the calculated value of a' to its maximum may occur because PDE is notcompletely blocked by IBMX after such a strong flash (40800 Rh*) as that used inthis experiment. Another test made on the same rod showed that the peak value ofa' (7 5 s-1) was reached at 3-3 s after the end of a 1 s pulse of strength 5700 Rh*. Thisis similar to the estimate obtained by the Li' method in Fig. 10 where curve 4 showsthat for N = 2, a' (= WJi/2) reached a maximum of 5 s-1 at 3 s after a 20 ms flash ofstrength 5600 Rh*.

463

464 A. L. HODGKIN AND B. J. NUNN

1.0 r .

J J

0- d- * - 05

30 -30

10 10

all (S-,1)3 3

1 1

0*3 0I30 5 10 15 20 100

Time (s)Fig. 15. Top, normalized current J after strong flash (40800 Rh*). Circles show value ofJ used in lower panel. Lower panel, rate constants a' (A) and 3(0) Rlotted on logarithmicscale against time after flash (linear scale). a' was calculated as (dJ'/dt)max and /3 as J- a'(see Fig. 14 and text). The curve through the open circles (,/) is 0-8 + 30 exp [-(t -7)/2 45]. The curve through the triangles (a') is arbitrary.

100

2 34

10

j3 -j3n(s1)

0.

0 5 10 15Time (s)

Fig. 16. Exponential decline of rate constant /3 after flashes of different intensity. Theordinate is the increment in /3, i.e. /3-,8n, on a logarithmic scale, where /3n, which variedbetween 0-6 and 0-8 s-1, is the dark value of /3. The abscissa is time from the beginning ofthe flash. O, line 1, 20 ms flash, strength 51 Rh*. A, line 2, 1 s flash, strength 5620 Rh*.0, line 3, 0 1 s flash, strength 41000 Rh*. *, line 4, 1 s flash, strength 101000 Rh*. Theslopes of the lines correspond to m-l of about 2 s, line 1; 2-2 s, line 2; 2-45 s, line 3; 3 0 s,line 4. A 1 s flash of strength 24000 Rh* gave a line (not plotted here) of slope 2-4 sabout 1 s to the left of line 3. Rate constants obtained by the method of Fig. 14; originalrecords in Fig. 12, line 3, and Fig. 13, other lines.


The rate constant m, with which /J, the rate constant ofPDE, declined after a flash,was estimated by plotting the increment of fi, on a logarithmic scale, against time.Figure 16 illustrates such plots for flashes of strength 51, 5600, 41000 and 101000Rh* applied to the same rod. In each case , declined exponentially with a timeconstant m-1 which seemed to increase slightly from about 2 s with 51 Rh* to 3 s

A

d 2 -

dt(S-)

0-5p0L

Jl

)O 400/ (Rh* s-')

-00 1 2 3 4 5log1o (/)

B

Fig. 17. Effect of t s step of light on dJ2/dt following sudden application of 0 5 mM-IBMX;J is the normalized current. A, 1 and 2 are examples of records of dJ2/dt: 1, in dark with0 5 mM-IBMX applied at 1 s; 2, 0 5 mM-IBMX again applied at 1 s but with step of lightof strength 110 Rh* S-1 switched on at time zero. B, rate constants a' and /B versus lightintensity with both scales linear. The rate constants were calculated from eqn (29c, d), i.e.N1Ji = ac' = (dJ/dt)m^, where J1 is the current just before IBMX was applied. C,normalized current J1 and rate constants a' and fi versus log1O of intensity of light stepapplied 1 s before IBMX. A light step of strength 1100 Rh* s-1 which reduced thenormalized current J to 0 03 increased fi to 21 s-5 but uncertainty as to J makes this valueunreliable. The dark current in varied between -38 and - 38-7 pA. The initial slope A,8/Al in B is 0-03 (Rh*)-. IBMX was applied for a nominal period of 1 s, but in the dark orwith a weak background its effect outlasted the pulse by several seconds.

with 101000 Rh*. This and similar values in two other rods agree reasonably withresults obtained by the Na+-+ Li' method (Table 1).

Figure 17 shows the effect on the rate constants of switching on steps of light ofdifferent intensities at 1P2 s before applying 0 5 mM-IBMX. The record in Al givesdJi/dt as a function of time for application of a pulse of IBMX in the dark. Theincrease of dJ2/dt to 0-7 s-' gives this as the dark value of the rate constants a' and

465


,. In A2 a light of 110 Rh* s-' was switched on at time zero, about 1X2 s beforeapplying IBMX. The step of light gave a negative displacement of d12/dt which hadlargely subsided by the time IBMX was applied. The effect of this weak light was toincrease dJ2/dt after IBMX from its peak value in the dark of 0 7 s-' to about2-5 s-' which gives the new value of oc'. The record of the square root of the currentindicated that Ji was 0-63 when IBMX was applied so the new value of , was foundas 4s-.

Repetition of this procedure with lights of different strength gave the relationbetween the rate constants oc' and /3 and light intensity. In Fig. 17B both co-ordinates are linear and in C the abscissa is log10 of the light intensity in Rh*s-* .The rate constant /3 continues to increase with light intensity up to 1000 Rh* s-' butcannot be calculated for stronger lights because J2 is too small to measure. Theapparent rate constant a', calculated as dJ2/dt, declined to a small value as the lightintensity was increased from 103 to 105 Rh* s-l. This phenomenon is almost certainlyrelated to the initial decrease in dJ/dt produced by very strong flashes (Fig. 13) andmay occur because sufficiently strong lights counteract the effect of IBMX inblocking phosphodiesterase.

Results similar to those in Fig. 17 were obtained in another experiment in which5 s pulses of IBMX were applied at 2-5 s after the step of light instead of 1-2 s as inFig. 17. The ratio A,8/AI was found to be 003 (Rh*)-' in one experiment, whereSn was 0-7 s-5, and 0-016 (Rh*)-' in the other experiment, where /n was 0 34 s-1. Sincethese values were obtained from VJ on the assumption that current is proportionalto [cGMP]i they should be multiplied by 2 before they are compared with the ratioAb/AI obtained by the Na+ Li' method. On this basis Ab/AI was 0-06+ 0-01(S.E.M.) (Rh*)-1 on the Na+ Li+ method and 0'03-0-06 (Rh*)-' on the IBMXmethod.

DISCUSSION

The results of our experiments are reasonably compatible with those obtained byKawamura & Murakami (1986) on Gecko photoreceptors using a more direct methodof assessing the activity of PDE. To judge from the inset records of their Fig. 2, thein situ hydrolysis time of cyclic GMP (measured by their subtangent method) wasapproximately 1-3 s in the dark, 0-6 s with a steady light of 24 Rh* s-1 and 0-2 s with120 Rh* s-1. The differences in preparation and method clearly invalidate any exactcomparison but the general similarity between their results and our Fig. 1 supportsthe assumption that the rate at which current declines in lithium is determined bythe rate at which cyclic GMP is hydrolysed. In Kawamura & Murakami's experimentsthe activity of PDE was increased markedly by a bright flash and then returned toits resting level with a time constant of 10-20 s which increased with the strength ofthe flash. This result is qualitatively similar to ours but the time constant was 5-10times longer and varied more with flash strength than in our experiments onsalamander rods.Kawamura & Murakami showed that photoreceptor sensitivity and PDE activity

returned to their dark value with approximately the same time constant, 8 s for thedecline of PDE activity and 7 s for the recovery of photoreceptor sensitivity. In asingle experiment of the same general type, we found that the reciprocal of the

466


sensitivity (SF) and the rate constant b both declined with a time constant ot about1P8 s. The product SFb was approximately constant during the whole of the recoveryphase; SF was defined in the same way as in Kawamura & Murakami's analysis butusing current instead of voltage. It would seem highly desirable to compareKawamura & Murakami's method with ours on the same preparation.The most interesting aspect of our experiments is the conclusion that recovery of

light-sensitive current after a flash is brought about partly by the decline in PDEactivity (,J) and partly by a delayed rise in cyclase activity, or by something elsewhich increases a', the rate at which cyclic GMP is supplied from GTP. The timingis important because if /1 and a' increased simultaneously there would be little changein the concentration of cyclic GMP and a wastefully large breakdown of GTP.The parallel with the nerve action potential is striking. In nerve the rising phase

of the action potential is generated by the rapid rise in sodium permeability whichmay be regarded as analogous to the rapid rise in the activity ofPDE brought aboutby the active G-protein. The recovery of light-sensitive current depends partly on thedestruction of active G-protein, equivalent to sodium inactivation, and partly on thedelayed rise in the rate of supply of cyclic GMP which is analogous to the delayed risein potassium permeability. The analogy is, of course, not complete because activityof PDE* leads to a suppression of sodium current and a hyperpolarization, theseeffects being the opposite of those of excitation in nerve. Another difference is thatin the mechanism controlling light-sensitive current in rod outer segments there isnothing equivalent to the regenerative increase in sodium permeability in nerve.The delayed increase in the rate of supply of cyclic GMP helps to explain the

observations of Goldberg, Ames, Gander & Walseth (1983) whose elegantexperiments show that light increases the rate of supply as well as the rate ofhydrolysis of cyclic GMP, with little or no alteration in cyclic GMP. There certainlyshould be some transient decrease in [cGMP], but as other authors have pointed outthis might be hard to detect in the presence of bound cyclic GMP (Pugh & Cobbs,1986).

It seems possible that the delayed increase in the supply of cyclic GMP inferredfrom our experiments occurs because internal calcium falls when ionic channels closeand there is a net outward movement of calcium through the Na+-Ca2 exchangesystem. There is also the possibility suggested by two lines of enquiry that reductionof internal calcium might shorten the life of transducin and thus acceleraterepolarization (Hodgkin, McNaughton & Nunn, 1986b; Torre, Matthews & Lamb,1986). We hope to describe these two aspects in a subsequent paper. Anotherimportant line which should be followed up is the effect of light and calcium onguanylate cyclase (see Lolley & Racz, 1982; Pepe et al. 1986).

Biochemical interpretation of parameters m, b and cTable 1 shows that the rate constant b, which may be proportional to the activity

of PDE and hence to the concentration of active G-protein, decays with a timeconstant m-1 of 1-4 s after moderate flashes (140 Rh*) and with one of 2 s after strongflashes (8000 Rh*). These values are one-quarter to one-half of the 5 s obtained forthe decline of PDE velocity after a flash applied to fractured toad rods in thepresence of 1 mM-ATP (Fig. 9 of Liebman, Mueller & Pugh, 1984).

467


To take the argument further we shall assume a Hill coefficient ofN = 2 in eqn (5)and no significant binding of cyclic GMP (y = 1, in eqn (6)) from which it follows fromeqn (12) that the rate constant of PDE, designated by /3, is b/2. The mean value ofbn, the value of b in the dark, was 1-5+0X1 (S.E.M.) S-1 (n = 17) so an estimate of/8n is 0-8 s-' which is similar to the value of 0-5 s-' found by Goldberg et al. (1983) forthe rate constant of PDE in rabbit rods in the dark.Next we consider the constant c' = A/J/Q which gives the rise in rate constant per

photoisomerization and is taken as half the constant c in Table 1. For moderateflashes (140 Rh*) c' was 0-016 s-l/Rh* and for strong flashes (8000 Rh*) it was004 s-'/Rh*. From such values, the concentration, or number per rod of PDEmolecules activated by one photoisomerization, may be calculated in the followingway.

If all the PDE molecules were activated the maximum rate constant would begiven by an equation similar to eqn (25b) i.e.

fimax = [PDE] k3/Km, (30a)

where k3 is the turnover number of PDE in reciprocal seconds, [PDE] is the totalconcentration of PDE in number of molecules per rod, and Km is the Michaelisconstant of PDE, in the same units as [PDE]. Iff is the fraction of PDE moleculesactivated by one photoisomerization, it follows that the constant c' which determinesthe increment in /8 per Rh* is given by

C' =f[PDE] k3/Km, (30b)

from which we obtain the number of PDE molecules activated by one photo-isomerization as

N(PDE*) =CKm/k3, (30c)

where the Michaelis constant Km should be expressed in number of molecules per rod.From Pugh & Cobbs (1986) the turnover number of PDE, k3, is taken as 2000 s-' andKm as 0 5 mm or 3 x 108 molecules per rod. With these numbers, c' = 0-016 s-1, thevalue for moderate flashes of 140 Rh* gives 2400 activated PDE molecules perphotoisomerization whereas c' = 0 004 s-1, obtained for stronger flashes of 8000 Rh*,corresponds to 600 activated PDE molecules per photoisomerization. According toStryer (1986) one photoisomerization activates about 500 molecules of G-protein, sothe number of activated PDE molecules should be somewhat less than this. It willbe seen that our estimates ofN(PDE*) do not involve a precise knowledge either ofthe total concentration ofPDE or of the concentration of cyclic GMP. However, theydo depend on [cGMP] being less than the Km of PDE, an assumption which seemsjustified by the values mentioned in Pugh & Cobbs (1986), i.e. 5-10/LM for [cGMP]and 0-51-4 mm for the Km of PDE.On p. 456 it was shown that for weak lights the step sensitivity of the rate constant

b agreed roughly with the theoretical equation

Ab cAIm' (27d)

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and further that Ab/AI was about 0-06 (Rh*)-1. The assumptions of a Hill coefficientof 2 for the interaction of cyclic GMP with ionic channels and no significant bindingallow Ab to be replaced by 2A/ and eqn (22) by

Afl 2 (30d)AI 2m

so M = 0'03 (Rh*)-'.

An approximate estimate of the total hydrolysis of cyclic GMP resulting from aflash is fJ> [cGMP] (/3-f,b) dt where fl& is the dark value of the PDE rate constant /8.For a single photoisomerization the average value of [cGMP] should be nearlyconstant at about 5/M, so from the definition of c' and the argument on p. 455 wehave

C,A[cGMP] = --[cGMP] =- [cGMP]

m 2

=-003 x 3 x 106 -105 molecules per rod per Rh*. (31)

This is in reasonable agreement with the order of magnitude usually quoted(105_106, Stryer, 1986).In the experiment of Fig. 1 where A//AI was close to 0 03 (Rh*)-' the average

electrical effect of a single photoisomerization was calculated as a decrease of inwardcurrent of amplitude 0 33 pA with an integration time of about 1 1 s, assuming afactor of one-half for the collecting efficiency of the suction electrode. Hence thecalculated decrease in the number of ions moving inwards was about 2-3 x 106 for onephotoisomerization. The amplification through the cascade in this experiment wasthen roughly

1 Rh* -- N active G-protein -* 2500 PDE*-105 cyclic GMP -2 x 106 Na+ ions,

where N > 2500.Apart from the indirect nature of the evidence, two reservations must be made

about these numbers. In the first place, isolated salamander rods have only aboutone-quarter the flash sensitivity of toad rods so the reduction in the number of ionsmoving per photon is less than the usual figure of 107 ions. The second reservationis that the calculated decrease in cyclic GMP represents the total number hydrolysedas a result of the flash and cannot be converted into a real decrease in concentrationwithout knowing more about the way in which a', the rate of supply of cyclic GMP,varies with time after a weak flash. It is also possible that the argument leading toeqn (31) may be upset by a highly localized depletion of cyclic GMP in the regionwhere a photon is absorbed (Lamb, McNaughton & Yau, 1981).

We are very much indebted to Dr Peter McNaughton for help with the early experiments. Wethank him and Dr T. D. Lamb for reading the manuscript and for much helpful discussion. B. N.was a Lister Institute Research Fellow.

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