on visual adaptation: i. photochemistry

BULLETIN OF MATHEMATICAL BIOPHYSICS

VOLUME 24, 1962

ON VISUAL ADAPTATION: I. PHOTOCHEMISTRY*

HAROLD WHITE~ COMMITTEE ON MATHEMATICAL BIOLOGY

THE UNIVERSITY OF CHICAGO

Quantitative aspects of the photochemistry of visual adaptation are considered. A simplified model is given that fits data on changes of rhodopsin concentration during and following strong illumination. A variation on Wald~s compartment hypothesis is shown to fit the quasi~ linear dependence of log threshold upon pigment concentration. Finally~ there is a brief review of pertinent data on cone pigments.

A recent experiment, to be d i s cus sed below, has confirmed that the change in concentrat ion of v isual pigments is the principal factor determining the threshold change that occurs in visual adaptation. In this paper we consider quanti ta t ive aspec ts of these photochemical changes.

I. The l l - c i s isomer of vitamin A aldehyde (retinene) combines with a protein (opsin) to form rhodopsin, the visual pigment of the retinal rods. Rhodopsin absorbs light and is spli t into opsin and all-trans ret inene. The opsin is apparently fixed but trans vitamin

A diffuses out of the rods and into the epithelium that l ies behind the r e t i n a . Here some vitamin A is es ter i f ied. This seems to be a

mechanism by which the epithelium lowers the mobili ty of the vitamin and accumulates it from the choroidal blood. (Dowling,

1960. A general re ference is Brindley, 1960.) Some vitamin A is isomerized to the cis form and t ravels back into a rod. This

*This research was supported in part by the United States Air Force through the Air Force Office of Scientific Research of the Air Research Development Command under Contract No. AF(638)-414~ and in part by the United States Public Health Service Training Grant 9G-833.

?Present Address: Department of Mathematics~ The University of Hawaii~ Honolulu~ Hawaii.

351

352 HAROLD WHITE

combines with opsin. So combining Dowling's discovery with the older data, we get the following diagram:

t ran s vitamin A ~ in rods ~ f r e e

rhodopsin opsin - - v i t a m i n A : :

~ c i s j i n epithelium

vitamin A j 5 in rods

esterified 3

�9 vitamin A 4 in epithelium

There are three possible complications to this scheme. First, isomerization of vitamin A is catalyzed directly by light, so that under strong illumination it might not be necessary for the vitamin to travel to the epithelium and back before it can recombine with opsin. However, retinene absorbs weakly except in the ultraviolet, and there is direct evidence that this mechanism is not important physiologically (Rushton, 1957). Second, although vitamin A must be in the aldehyde form to combine with opsin, most free vitamin A in the body is in the form of an alcohol. The aldehyde-alcohol equilibrium is known to be catalyzed by DPN and has been carefully studied in vitro (Bliss, 1951). The rates in vivo are probably much greater than the rates for the processes diagramed above, so that this does not affect the bleaching-resynthesis kinetics. Third, it is possible that vitamin A must diffuse longitudinally through the rod to get back and forth between the inner parts of the outer segment and the epithelium. If so, the time taken for this diffusion will affect the kinetics. The rod contains thousands of transverse membrane-like discs, through which there are only small channels available for diffusion (Fernandez-Moran, 1961).

Now we ask whether there is a simplification of the diagram that gives an easy determination of the rhodopsin concentration in various stages of adaptation. From Dowling's data (op. cit.) on rats, we see that ordinarily there is much less free vitamin A in the rods than the amount bound in rhodopsin or the amount in the epithelium. Processes 2 and 6 in the above diagram are fast, relative to i and 5, under most conditions. (This would not be true

ON VISUAL ADAPTATION 353

under weak illumination, for then the amount of free opsin would limit process 6.) As an approximation, we set the rate constants for processes 2 and 6 equal to infinity. Now consider the six quantities that appear in the diagram above. Since the total amount of protein and the total amount of the vitamin are each unchanged by the processes illustrated, four of these quantities are independent. If processes 2 and 6 are very fast and the amounts of trans and of eis vitamin A in the rods are negligible, then there are only two independent quantities. Therefore we can get two first-order differential equations from the diagram. Eliminating one of the variables between the two equations, we get a single second-order differential equation. Letting r be the ratio of the actual amount of rhodopsin to the amount present in the dark- adapted state and I be the intensity of illumination, the following is the equation we obtain:

dr d 2 r + ( k l l + k 3 + k 4 + k s ) - ~ + k l l ( k ~ + k 4 ) + k 4 k s r = k 4 k s . (1) dt ~

Campbell and Rushton (1955) have measured, by means of light reflected out of the eye, the bleaching of rhodopsin in the human. (That they were in fact measuring this has been confirmed by Rushton, 1956.) Their data are adequately fit by this equation (see Figure 1). The only significant discrepancy is that the resynthesis of rhodopsin lags behind the theoretical curve in the early minutes of dark adaptation (the rising curve of Figure 1). It is here that Dowling's data show a surprising feature. The cessation of bleaching shuts off one of the two sources of free vitamin A in the rods. One would expect, therefore, that the amount of this vitamin A would decrease. In fact, there was more free vitamin A found in the rods after a few minutes of dark adaptation than there was at the end of the preceding light adaptation. Possibly this is due to the third "complication" mentioned above. If longitudinal diffusion is a factor, then under strong illumination most synthesis and bleaching takes place in the very outermost portion of the rod, which lies in closest conjunction with the epithelium. In dark adaptation, the free opsin there would be quickly exhausted and the amount of free vitamin A might increase while it is diffusing to the inner parts of the rod.

Equation (1) is not applicable to conditions of weak illumination, when the rods are functionally most important. For then proc-

354

g

U

HAROLD WHITE

1.0

�9 5 �9

0 2 4 6 8 10 12

t. (MINUTES)

I I I 14 16 18

F I G U R E 1. R h o d o p s i n c o n c e n t r a t i o n in the human e y e , from Camp-

b e l l and R u s h t o n (1955). T h e d e s c e n d i n g l i g h t a d a p t a t i o n p o i n t s w e r e r e c o r d e d unde r s u c c e s s i v e i n t e n s i t i e s of 2 • 104, 105 and 2 • 108 t ro - l a n d s . T h e a s c e n d i n g cu rve w a s r e c o r d e d dur ing dark a d a p t a t i o n . A l l o f the c u r v e s were c a l c u l a t e d from e q u a t i o n (1) wi th k 1 -- 2.1 x 1 0 - 7 / t r o -

l a n d - s e c . , ks • 2.1 x 1 0 2 / s e c . , k 4 = 9.7 • 1 0 - 3 / s e c . and k 5 = 4.1 x 1 0 - 3 / s e o .

ess 6 is limited by the amount of available opsin and is not rela- tively fast. We return to this topic below.

The parameter k l , the rate constant for the bleaching process, can be estimated from different kinds of data. According to both H. J. A. Dartnall et al. (1938) and E. Schneider et al. (1939) it has a value in vitro of 9 • 10 -1~ cm2/quantum, which equals 5.5 x 10-8/troland-sec. An experiment by G. Wald (1954) yields the figure 5.7 • 10-S/troland-sec. Such close agreement is not found among the data measured from the living human eye. The experiment illustrated in Figure 1 gives kl = 21 x 10-S/troland-sec. Using a relationship (discussed below) between the threshold and the rhodopsin concentration, we obtained the following estimates of k l from four standard dark-adaptation experiments: Craik (1941), 8 x I0-8; Haig (1941), 2 x 10-s; Crawford, (1946), 15 x 10 -8 and Wald (1954), 8 x 10 -8. There are three reasons for this wide scat- ter. First, different photometric techniques seem to give some- what different results. Second, basic to the conversion of other units to " t rolands" is the assumption that the intensity of the illumination upon the retina is simply proportional to the pupillary


area~ but this may not be strictly true and the pupillary area is not always carefully controlled. Third~ early in the course of dark adaptation the simple relation between threshold and pigment concentration does not hold (for reasons to be discussed in a following paper), but later one is measuring only a small increment of the threshold and the relative error is necessarily great. There is one experiment (Rushton~ 1956) in which the value of this parameter in viq)o was deliberately sought. Careful photometry indicated that in the absence of regeneration 3.4 • 10-15 quanta/cm 2 are required to bleach half of the rhodopsin. Hence kl = In 2/(3.5 • 10 -15 ) = 2 • 10-18 cm2/quantum ___ 12 • 10-S/troland-sec. This is greater than the value in vitro by a factor of 2.2. At least part of this increase can be attributed to molecular orientation. Polarized light is absorbed most strongly when its electric vector is perpendicular to the orientation vector of the molecule and shows negligible absorption when they are parallel. The molecules are oriented within the rod so as to achieve maximum absorption (Denton, 1954). It has been estimated that this should increase the absorption by a factor of 1.5~ but this figure is calculated from the untested assumption that the absorption of polarized light is proportional to the square of the sine of the angle between the vectors; it is con- ceivable that it might be increased by a factor of 2.2. Rushton (op. cir.) proposed that the inner segment of the rod focuses light into the outer segment; this would increase the bleaching rat% but it is questionaSle whether the geometry of the rod is adapted to this.

II. Formerly it was supposed that visual sensitivity and the concentration of visual pigments are related in a simple way, that the threshold is inversely proportional to pigment concentration. Then it was repeatedly shown that vast threshold changes are as- sociated with very small changes in concentration. There was some speculation (e.g., Granit~ 1955) that there is no direct dependence of threshold upon concentration. However~ Dowling and Wald (1960) have shown that in the rat there is such a dependence. Two groups were used. One group consisted of normal rats~ light adapted to various degrees. The other consisted of rats deprived of vitamin A and dark adapted. Thresholds were measured by means of electroretinograms, the animals killed and the rhodopsin measured. On a graph showing thresholds vs. pigment concentra-

356 HAROLD WHITE

tion, the points for the two groups fell on the same curve (lower curve of Figure 2). In this c a se , threshold was a function only of pigment concentration.

Since a small change in concentration produces a great change

in threshold, it seems that the integrity, not only of the absorbing molecule, but of its neighbors as well , is required for the absorption of a quantum to trigger s ignif icant activity. The rhodopsin in the outer segment of the rod is not in solution but is bound in a solid state. Wald (1954) suggested that the rhodopsin is arranged into compartments such that an absorption by a molecule can result in activation of the rod only if no molecule in its compartment is bleached. If there are n molecules per compartment and a propor- tion r of the opsin molecules are united with retinene, then the probabil i ty of a compartment containing i t s full quota of rhodopsin is r ~, indicating that it takes 1 / r ~ t imes as much light to get the same effec t as in the dark-adapted s tate . So letting 0 be the loga- rithm of the relat ive threshold,

: E t -

..$ I

2 o o w

0 I I I I I 1.0 .8 .6 .4 .2 0

r CREtAT~VE CONCENTRATION OF RHODOP$1N)

F I G U R E 2. T h r e s h o l d a s a f u n c t i o n of p i g m e n t c o n c e n t r a t i o n . Open c i r c l e s : l i g h t - a d a p t e d r a t s ( D o w l i n g and Wald~ 1960). F i l l e d c i r c l e s : v i t a m i n - A - d e p r i v e d r a t s (ibid). T r i a n g l e s : human r e d m o n o c h r o m a t (Rushton~ 1961). C u r v e s c a l c u l a t e d from e x p r e s s i o n (3). U p p e r c u r v e (human): a--- 9 i n = 25. L o w e r c u r v e (rat) : a : 1% n : 2.


0 = n log ( l / r ) . (2)

For any posi t ive value of n, this gives a curve which goes con- cave upward as r drops from one to zero, and it cannot fit the points of Figure 2. This ra ises the question: is it poss ib le for a model, based on considerat ions such as the above, to yield a curve which is almost linear from r - - 1 . 0 to r = 0.05 and then asymptotic to a vert ical line at r = 0? (Presumably the threshold would be infinitely great if there were no rhodopsin left at all.) The following example shows that this is poss ib le .

Suppose that rhodopsin is arranged in units , each of which con- s i s t s of a rows, each row having n molecules . Next to the first row of each unit is a sens i t ive s i te . If a molecule in the ruth row absorbs a quantum of light, the energy can be transported to the sens i t ive s i te only if the f irs t m rows are entirely composed of unbleached molecules . The probabil i ty of this is r ran. Averaging over all the rows that the light quantum may hit, the probability that the energy can be transported to the s i te is

1 a rn -- ra n a E rmn = 1

a 1 - r n ' (3)

and the relat ive threshold is the reciprocal of this. The curves of Figure 2, ca lcula ted from this express ion, fit the points well.

The upper curve of Figure 2 represents Rushton ' s (1961) data for a human who had no cones in her retina. Pigment concentration was measured by means of ref lected light. In this experiment, the thresholds may have been influenced by adaptational changes other than pigment concentration.

III. L e s s is known about the pigments of the cones. They are composed of the same form of vitamin A but of different proteins than in the c a s e of rhodopsin. Rushton (1958) has shown that the kinet ics of two of these cone pigments obey the same empirical equation:

ds d-i+ (k l l + k2) s -- k2 (4)

where s is the normalized pigment concentration, k l - - 2 • 10 -7 / t roland-sec. , and ku = 7.7 • 10 -S / sec . This simple behavior sug- ges ts that there is a lways a sui table surplus of l l - c i s vitamin A

358 HAROLD WHITE

within the cone so that the syn thes i s of pigment is limited only by the amount of protein. (It may be that something like (4) descr ibes

the kinet ics of rhodopsin under weak illumination; Dowling (op. cir.) found a surplus of vitamin A in the rods of dark-adapted rats . )

In vitro experiments on the photopigments of a fowl give a lower

figure for the bleaching rate of a cone pigment than for rhodopsin

(Wold, Brown and Smith, 1955). On the other hand, a cone seems to focus light into its small outer end, and this increases the rate.

The figure for kl above is vir tual ly the same as we found in fitting the points in Figure 1, and the experimental set-ups were similar:

this indicates that the two factors balance out and the in vice b leach ing rate of the cone pigments is about the same as that for

rhodopsin. According to Rushton (1961) the re la t ive threshold for cone vi-

sion is roughly e x p [ 4 ( 1 - s)], where s is the normalized pigment concentra t ion.

LITERATURE

Bliss, A. F. 1951. "The Equilibrium Between Vitamin A Alcohol and Aldehyde." Arch. Biochem. Biophys., 3i, 197-204.

Brindley, G. S. 1960. Physiology of the Retina and the Visual Pathway. London: Edward Arnold (Publishers) Ltd.

Campbell, F. W., and W. A. H. Rushton. 1955. "Measurement of the Scotopic Pigment in the Living Human Eye ." J. Physiol., 130, 131- 147.

Craik, M. Vernon. 1941. '~The Nature of Dark Adaptation." Brit. J. Psychol., 32, 62-81.

Crawford, B . H . 1946. "Photochemical Laws and Visual Phenomena." Prec. Roy. Soc., 133B, 63-75.

Dartnall, H. J. A., C. F. Goodeve, and R. J. Lythgoe. 1938. "Photo- chemical Bleaching of Visual Purple Solutions." Prec. Roy. Sac. London, A, 164, 216-230.

Denton, E . J . 1954. "A Method of Easily Observing the Dichroism of the Visual Rods." J. Physiol., 124, 16P.

Dowling, J. E. 1960. ~The Chemistry of Visual Adaptation in the Rat ." Nature, 188, 114-118.

Dowling, J. E., and G. Wald. 1960. "The Biological Function of Vita- min A Acid." Prec. Nat. Acad. Sci. U.S., 46, 587-607.

Fernandez-Moran, H. 1961. "The Fine Structure of Photoreceptors." In The Structure of the Eye, G. Smelser, ed. New York: Academic Press.

Granit, R. 1955. Receptors and Sensory Perception. New Haven: Yale University Press.

Haig, C. 1941. "The Course of RodDark Adaptation." J. Gen. Physiol., 24, 735-751.


Rushton, W. A.H. 1956. "The Difference Spectrum and the Photosensi- tivity of Rhodopsin in the Living Human Eye." J. Physiol., 134, 11-29.

. 1957. " B l u e Light and the Regenera t ion of Human Rhodopsin in s i tu . " J. Gem Phys io l . , 41, 419-428.

- - . 1958. " K i n e t i c s of Cone P igments Measured Objec t ive ly on the L iv ing Human F o v e a . " Ann. N .Y . Acad. Sai., 74, 291-304.

1961. " T h e In t ens i ty Fac to r in Vis ion . ~' In Light and Li fe , W. D. McElroy and B. Glas s , eds . Balt imore: Johns Hopkins P r e s s .

Schneider , E . , C. F . Goodeve~ and R. J . Lythgoe. 1939. " T h e Spectral Var ia t ion of the P h o t o s e n s i t i v i t y of Visua l P u r p l e J ~ Proc. Roy. Soc. London A, 170, 102-112.

Wald, G. 1954. " O n the Mechanism of the Visua l Threshold and Visua l Adap ta t ionJ ~ Science, l l 9 , 887-892.

Wald, G., P . K. Browne and P. H. Smith. 1955. " Iodops in . ~ J. Gen. Physiol.~ 38, 623-681.

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