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MS 10682 Received 4 February 2000; accepted after revision 10 July 2000.
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ABSTRACT |
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5 mechanism gave analogous results.
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INTRODUCTION |
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Dark adaptation describes the recovery of the visual system after exposure to light. The classical dark adaptation curves of Hecht (1921) showed two separate regions of recovery: an initial rapid component due to cones followed by a slower component due to rods.
Exposure of the photoreceptors to light results in photolysis of their photopigment. This reduces the number of photopigment molecules available to absorb quanta, and therefore decreases the effectiveness of light. This effect, called photopigment depletion, was originally thought to account for sensitivity losses observed during dark adaptation (Hecht et al. 1937). However, the decrease in sensitivity predicted from photopigment depletion dramatically underestimates the threshold elevation measured during dark adaptation. In fact, sensitivity is approximately logarithmically related to the remaining photopigment concentration (Dowling, 1960; Rushton, 1961). The discrepancy between the prediction from photopigment bleaching and the data indicates that there must be at least one other adaptation mechanism responsible for the observed thresholds (Geisler, 1978, 1979). It has been proposed for the rod system that the identity of this mechanism is an 'equivalent background' produced by the presence of photoproducts generated by a bleach (Lamb, 1981; Leibrock et al. 1998).
The similarity between desensitisation after exposure to bright light and during the presentation of steady backgrounds led Stiles & Crawford (1932) to postulate that a bleached 'photochemical substance' may cause a reduction in sensitivity by producing an equivalent background light. The idea is that this substance may act in a similar manner to true light, and as this substance is regenerated, the intensity of the equivalent background slowly fades until the photoreceptors return to their dark-adapted sensitivity. It is now known that the elevation of visual threshold arises from events occurring within the rod photoreceptors themselves, and the underlying molecular basis of these events is becoming clearer (Leibrock et al. 1998).
While rod dark adaptation has been widely explored, studies of cone dark adaptation are relatively rare. There are at least two obstacles to the study of this system during dark adaptation. The first is that the cone system recovers far more rapidly than the rod system, making it difficult to obtain reliable estimates of thresholds during dark adaptation. This problem was overcome by Mollon & Polden (1980) with the implementation of an elegant psychophysical procedure they called the 'Method of a thousand staircases', a modification of which is used in these experiments. The second obstacle is that the cone system is more complex because it involves interactions between the three cone types (Hering, 1878; Hurvich & Jameson, 1957). The typical approach to this problem is to attempt to study a single cone type or a single cone mechanism in isolation.
In this paper we develop a model of dark adaptation for the photopic luminance mechanism, based on the equivalent background principle. This model enables us to relate dark adaptation to our current understanding of the molecular mechanisms involved in cone phototransduction. The data presented are consistent with the idea that the equivalent background is produced by photoproducts generated by bleached cone photopigment, and that the decline in the equivalent background is due to removal of these photoproducts. The likely identity of these photoproducts is discussed.
In this section, a model is developed to provide a theoretical link between psychophysically measured desensitisation and the photoproduct concentration during dark adaptation. It is based on a sequence of explicit assumptions (using reasoning similar to that of Lamb, 1981) that culminate in the prediction that measured threshold elevation should be directly proportional to photoproduct concentration.
Correction for photopigment depletion
The first stage of the analysis involved correcting the psychophysical threshold for photopigment depletion. In our data, the depletion effect was accounted for by expressing the threshold in terms of effective absorbed quanta. The relationship between relative threshold in quantal absorptions V/V0 and relative threshold in quantal flux U/U0 is given by:
| V/V0 = (1 - q)U/U0, | (1) |
where q is the proportion of photopigment bleached. Using eqn (1), the depletion effect can be taken into account if q is known. The proportion of photopigment bleached as a function of time in the dark can be derived from Rushton's differential equations, which are based on first-order kinetics (Rushton, 1958, 1961; Rushton & Henry, 1968). This equation, combined with the Dowling-Rushton equation (Dowling, 1960; Ruston, 1965a), gives log desensitisation as a function of time. We combined the standard Dowling-Rushton equation and the Hollins & Alpern (1973) modification with Rushton's photopigment regeneration equation and fitted these equations to the raw threshold data by adjusting the parameters to minimise a 
2 merit function. They appeared to provide a reasonable fit. However, on closer inspection, the goodness of fit of these equations was often not acceptable, with Q values frequently less than 0·1. (A Q value indicates the probability that the observed minimum 2 is as large as it is, purely due to chance effects. Therefore, these values provide a quantitative measure of the goodness of fit of a model. Q values greater than 0·1 are generally taken as a good fit; Press et al. 1992.) Furthermore, examination of the residuals revealed a systematic and recurring pattern, indicating that these equations were an inappropriate description of the data. Instead, the model (eqn (10)) was fitted to the raw data in the same way. This equation gave better Q values, and the pattern in the residuals was greatly reduced. The log of the best-fit equation was then scaled so that immediately after extinction of the adapting field (t = 0) it has a value of q0 (the initial proportion of pigment bleached), and at t >> 0 it approaches a value of zero (see Fig. 1A). In equation form, the proportion of pigment bleached at any time during dark adaptation q(t) is given by:
| q(t) = q0logD(t)/logD(0), | (2) |
where logD(t) is the log desensitisation (or log relative threshold) during dark adaptation, and log D(0) is the log desensitisation at t = 0. Note that this equation is simply a form of the Dowling-Rushton equation (Dowling, 1960; Rushton, 1965a), with the constant of proportionality 
= logD(0)/q0. The values of q calculated from eqn (2) were used in eqn (1) to correct the data for photopigment depletion.
The initial proportion of pigment bleached was calculated from an equation proposed by Reeves et al. (1998). This equation is an analytical expression based on recent experiments using colour matching at high light levels which have shown that steady-state bleaching curves are generally steeper than the solution of Rushton's first-order kinetic equation. The form of the equation is:
p = k/ (W2 + k2),
| (3) |
where p is the proportion of pigment present at equilibrium (note that p = 1 - q), k is a constant related to the half-bleaching constant W0·5 by W0·5 = k3, and W is the adapting field radiance (see Fig. 1B). This function has no theoretical basis, but it shares with Rushton's function the property that W × p tends to a constant k as W grows large. Analysis of the data using Rushton's steady-state bleaching equation did not significantly alter the pattern of results. The value for logW0·5 of 4·3 log Trol is used for all calculations of pigment bleached at equilibrium (Rushton & Henry, 1968).
The model
At any time, the 'total light' (Wt), experienced by the visual system comprises three components: (1) the 'absolute dark light' (W0), which is experienced after complete dark adaptation and is presumed to be due to internal noise in the photoreceptors (Barlow, 1957); (2) the 'equivalent light' (We), which is experienced during dark adaptation following bleaching of a significant proportion of the photopigment (this component is also called the 'equivalent background', Stiles & Crawford, 1932); and (3) the 'real light' (W) which is the actual amount of physical light present in the adapting field. Expressed algebraically,
| Wt = W0 + We + W. | (4) |
The 'dark light' (Wd) present during incomplete dark adaptation is the sum of the absolute dark light and the equivalent light (Barlow & Sparrock, 1964),
| Wd = W0 + We. | (5) |
Figure 1D shows a typical cone increment threshold function. The threshold elevation, or desensitisation D(W), caused by this background field can be described by:
 | (6) |
where U(W) is the increment threshold for background radiance W, U0 is the absolute test threshold measured with no background field after complete dark adaptation, W* is the field threshold (the background field radiance that raises test threshold to 10 times its absolute level), and n is the slope of the upper linear region of the function when plotted on log-log co-ordinates. This equation is similar to that used by Sigel & Brousseau (1982) to model cone adaptation functions. The field threshold W* is the abscissa chosen by Stiles (1978) to indicate the position of the function relative to the background radiance axis, and is used in the calculation of field sensitivity S, where S = 1/W*. However, the value traditionally taken as the absolute dark light, or Fechner's (1860) Eigengrau, is not the same as the field threshold. The relationship between these two parameters is shown in Fig. 1D, and derivation of one from the other is simple. Given n,
| logW0 = logW* -1/n. | (7) |
Note that for n = 1 and W >W*, Weber's law is attained and the Weber fraction k is given by:
| k = U0/W0. | (8) |
Cone increment thresholds measured under achromatic conditions generally obey Weber's law (Shapley & Enroth-Cugell, 1984). Adherence to Weber's law means that during light adaptation the measured threshold elevation is directly proportional to the real light. This is the conventional meaning of Weber's law. However, from this we can infer that during dark adaptation, in the absence of real light, it is likely that the measured threshold elevation is directly proportional to the equivalent light.
Lamb (1981) accounted for rod dark adaptation by proposing that equivalent light is produced by the presence of photoproducts produced in the chain of photopigment bleaching steps. It is assumed that the photoproducts generate events indistinguishable from real photon hits and the rate of occurrence of these events determines the equivalent light. A similar assumption for cone dark adaptation seems reasonable given the psychophysical (Williams & MacLeod, 1979) and physiological (Fain et al. 1996) evidence that sensitivity losses during cone dark adaptation are caused by signals originating in the cones themselves. Therefore, to a good approximation, equivalent light during dark adaptation should be directly proportional to photoproduct concentration.
Combining the inference that desensitisation during dark adaptation is directly proportional to the equivalent light (Weber's law) with the assumption that equivalent light is directly proportional to photoproduct concentration implies that the measured threshold elevation should be directly proportional to photoproduct concentration (as proposed for the rod system by Lamb, 1981).
If the removal of a photoproduct is first order, its concentration will decay exponentially with time and, given the above logic, the desensitisation caused by the photoproduct will decline exponentially. On a plot of log threshold against time this type of decay will appear as a straight line. Decay through two removal steps with different exponential time constants will give rise to asymptotic behaviour toward two straight lines with appropriate slope, although some rounding will occur near the intersection of the lines. In the following analysis it will be shown that cone dark adaptation is well described by a linear combination of straight-line asymptotes and that it is possible to infer the kinetics of the photoproducts from these asymptotes.
Figure 1C shows threshold estimates obtained during cone dark adaptation (large open circles), and after correction for photopigment bleaching (small filled circles). The horizontal dashed line asymptote indicates the dark light, and is at the level of zero desensitisation or absolute test threshold. The other dashed line asymptotes represent two additional components. The linear sum of these asymptotes, indicated by the continuous curve through the filled symbols, provides a good fit to the corrected data. The equation for the early asymptote, in linear and log terms, is:
D1(t) = U(t)/U0 = D1exp(-t/ 1),
| (9a) |
or
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logD1(t) = logD1 - t/(1ln(10)),
| (9b) |
where U(t) is the increment threshold at time t after extinction of the adapting field, U0 is the absolute test threshold measured after complete dark adaptation, D1 is the initial desensitisation caused by this early component, and 1 is the exponential time constant for the decay of this component. On linear-log co-ordinates, the asymptote has slope -1/(1ln(10)). The equation for the late component is of the same form as the early component, but with initial desensitisation D2 and exponential time constant 2.
The rounding near the intersection of the asymptotes (at 43 and 120 s in Fig. 1C) occurs because, at these times, the two mechanisms cause equal desensitisation (i.e. double the desensitisation) which increases the combined desensitisation by 
0·3 log units. The data should approach a mechanism's asymptote only at times where the other mechanisms cause much less desensitisation. The sum of these separate components describes the desensitisation during dark adaptation, so that:
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D(t) = U(t)/U0 = 1 + D1exp(-t/1) + D2exp(-t/2).
| (10) |
The decline of the equivalent background as a function of time can be calculated by what has become known as the Crawford transformation (Crawford, 1947). Substituting the dark adaptation model (eqn (10)) into the inverse of the increment threshold model (eqn (6)) gives,
 | (11) |
Fitting these equations to psychophysical data enables us to characterise the dark adaptation that occurs in cone pathways and to make inferences about the underlying molecular mechanisms of cone phototransduction.
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A, the continuous curve indicates the proportion of photopigment bleached as a function of time after extinction of the adapting field, calculated from eqn (2). For comparison, the curve measured by Hollins & Alpern (1973) is indicated by the dashed line (calculated from their eqn (2)b with t0 = 105 s). The curves are similar in shape, and with t0 = 70 s they are almost identical. B, the proportion of photopigment bleached as a function of steady adapting field level (eqn (3)), with logW0·5 = 10·47 log quanta s-1 deg-2. C, threshold estimates as a function of time after extinction of the adapting field ( | ||
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METHODS |
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Apparatus
Stimuli were generated using a simple two-channel Maxwellian view optical system, illustrated in Fig. 2. The test and background channels shared a common light source (LS; 24 V, 250 W tungsten-halogen projector bulb, driven by a current stabilised power supply). Lens L11 imaged the source onto a 0·5 mm diameter aperture-stop AS at pupil-conjugate plane P6. A diffuser covering AS improved field quality. Light from AS passed through a heat-rejecting filter IRF, lens L10 collimated the beam, and beam splitter BS2 divided the collimated light into test and background channels.
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Stimuli were presented using a two-channel Maxwellian view optical system. A single light source LS is split by beam splitter BS2 to form the background (dashed lines) and test (dotted lines) channels. Beam splitter BS1 recombines the two channels. Fixed neutral density filters ND3-ND1 and circular neutral density wedge W1 (and wedge W2 for the dark adaptation and spectral sensitivity experiments) control the intensity of the test field. Fixed neutral density filters ND6-ND4 (together with the circular neutral density wedge W1 for the increment threshold experiments) control the intensity of the background field. A monochromator controls the wavelength of the test field and interference filter IF controls the wavelength of the background field. The photometer head was fixed in position throughout these experiments, and was used to adjust the calibration prior to an experiment. Further details are provided in the text. | ||
Light entering the test channel passed through a field-stop FS2 that, combined with lens L5, matched the numerical aperture of the beam to the input aperture required by the monochromator. Neutral density wedge W1 was positioned near the entrance slit of the monochromator, and shutter S1 was positioned near the exit slit. Lens L4 collimated the output of the monochromator, mirror M1 reflected the beam through 90 deg, and neutral density filters ND3-ND1 attenuated the beam. Lens L3 created an image of the source at pupil-conjugate plane P1 where neutral density wedge W2 further attenuated the beam. W2 was positioned in this channel for the dark adaptation experiments. Lens L2 collimated the light and field-stop FS1 positioned at retinal-conjugate plane R1 controlled the angular size of the test field.
The background channel was of similar construction to the test channel. Lens L9 formed an image of LS at pupil-conjugate plane P5. Shutter S2 and neutral density wedge W2 were set near this plane. W2 was positioned in this channel for the increment threshold experiments. Lens L8 collimated the light, mirror M2 reflected the beam through 90 deg, and neutral density filters ND6-ND4 attenuated the beam. Lens L7 formed another image of LS at pupil-conjugate plane P4. After collimation by lens L6 the light passed through interference filter IF and field-stop FS3, positioned at retinal-conjugate plane R2, which controlled the size of the background field.
Finally, beam splitter BS1 combined the test and background channels, and lens L1 (the Maxwellian lens) formed an image in the plane of the pupil of the eye P0. All lenses were achromatic doublets, except the collection lens L11, which was a large diameter plano-convex lens. The exit pupil of the system was 2·0 mm diameter, which was smaller than the observers' natural pupil.
Calibration
Three instruments were used for the calibration of this system. A Pritchard Model 1980B Spectroradiometer (S1480, Photo Research, Chatsworth, CA, USA) measured the relative spectral composition of the stimuli and a calibrated silicon photodiode detector (SED033/Y/L30, International Light, Newburyport, MA, USA) measured the absolute light level. Relative retinal illuminance calibration was performed prior to each experiment using a digital luxmeter (EC1-X, Hagner, West Sussex, UK).
Stimuli
A circular test field of 0·8 deg diameter was presented in the centre of a circular adapting field of 8·0 deg diameter. The adapting field was continuously present during increment threshold experiments but was present only during preadaptation for the dark adaptation experiments. The test flash had a duration at half-height of 202·5 ms, with a very rapid rise and fall. Four small, deep-red fixation lights helped maintain central fixation. They were mounted in the plane of test field-stop FS1 (see Fig. 2), and were positioned just beyond the edge of the adapting field. The intensity of these lights was adjustable by the observer; they were kept as dim as possible, while maintaining clear visibility.
The purpose of these experiments was to investigate dark adaptation in the photopic luminance mechanism. To increase the likelihood of detection by the luminance mechanism, the test and adapting fields were monochromatic with the test wavelength 
closely matched the to background wavelength µ. This type of stimulus modulates long wavelength-sensitive (L) and middle wavelength-sensitive (M) cones in an equal ratio (i.e. a stimulus vector close to 45 deg in the first quadrant of cone-contrast space; Stromeyer et al. 1987; Kalloniatis & Harwerth, 1990, 1991). Three wavelengths were used: 541, 579 and 621 nm. The spatial and temporal stimulus configuration also facilitated detection by the luminance mechanism.
Stimulus intensity is expressed as photon flux irradiance (in quanta s-1 deg-2). For monochromatic stimuli, intensities expressed in quanta s-1 deg-2 can be converted to photopic trolands using:
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T = 4·454 × 10-13V()N/,
| (12) |
where T is the intensity in Trol, N is the intensity in quanta s-1 deg-2, V is the photopic luminosity function, and is the wavelength of the stimulus in metres. The following conversion factors simplify the task of converting from log quanta s-1 deg-2 to log Trol - simply add the appropriate factor to the log quanta s-1 deg-2 value to find the corresponding log Trol value: -6·10 for 541 nm, -6·17 for 579 nm and -6·56 for 621 nm.
Observers
Observers participating in these experiments had normal colour vision, as assessed by Nagel anomaloscopy, Ishihara plates and the Farnsworth-Munsell 100-hue panel test. Observers used their habitual refractive corrections during testing and had visual acuity better than 6/6. MJP is an author; LKM was naive. Informed consent was obtained in writing, and the study was performed according to the Declaration of Helsinki, and was approved by the University of Melbourne ethics committee.
Threshold determination
Increment detection thresholds were measured in the dark and over a six log-unit range of adapting field intensity (up to the maximum attainable) in 0·25 log unit steps. This range ensured that the dark light and Weber's law regions could be well characterised. The observer was exposed to a series of increasingly intense adapting fields and sensitivity was probed at each level. A separate method of adjustment and ZEST (King-Smith et al. 1994) were performed at each adapting field level. The setting made in the method of adjustment became the mode of the initial probability density function for the ZEST. Test radiance was then varied according to the previous responses using the ZEST framework.
Before the experiment, dim test and background fields were displayed for the observer to align the bite bar. The fields were then turned off and the observer dark adapted for at least 10 min. The initial run was the zero background condition. For each run thereafter, there was a minimum adaptation period of 90 s, which was followed by the method of adjustment. The test field was flashed repeatedly (with a 1·2 s inter-stimulus interval) and by pressing buttons the observer adjusted the radiance of the test field so that it was just barely detectable. Once the observer indicated a satisfactory setting, a self-paced ZEST method was initiated. After a brief ready signal, the test flash was presented. After each presentation the observer pressed a button to indicate whether or not the flash was seen (i.e. a yes/no task). The stimulus radiance presented on each trial was the current mean of the posterior probability density function generated by the ZEST. The final threshold estimate was the mean of the posterior probability density function after a set number of trials had been completed (from 16 to 24). This sequence of adaptation, method of adjustment and ZEST was repeated at each adapting field level.
During the early phase of dark adaptation sensitivity changes substantially and, under certain conditions, non-monotonically. Since the rate of change of threshold may exceed 0·3 log units s-1, it is not feasible to track the changing sensitivity by means of a conventional psychophysical procedure. To overcome these difficulties, we have turned to a modified version of the 'Method of a thousand staircases' (Cornsweet & Teller, 1965; Mollon & Polden, 1980; Mollon et al. 1987). In this method the observer was repeatedly exposed to the same sequence of stimulation (adaptation and recovery), and in each pass sensitivity was probed at a fixed set of time points after extinction of the adapting field. On the first pass, the observer tracked their threshold using a method of adjustment and their threshold setting was sampled at each time point. The value obtained for a particular time point sets the mode of the initial probability density function for a ZEST specific to that time point. This ZEST controls the test radiance presented at this time point on all subsequent passes. Thus, each ZEST should converge on an estimate of the observer's sensitivity at a particular time after extinction of the adapting field. We call this procedure the 'Method of a thousand ZESTs'.
Before the experiment the observer aligned the bite bar while viewing dim test and background fields. The sequence of 120 s preadaptation and 360 s recovery was then repeated 17 times. It is assumed that equilibrium is reached after 120 s preadaptation, based on the data of Rushton & Henry (1968, their Fig. 5). During recovery, threshold estimates were sampled every 6·0 s, beginning 1·0 s after the extinction of the adapting field. During the method of adjustment pass the test field was flashed repeatedly (with a 1·2 s inter-stimulus interval) and the observer adjusted the radiance of the test field so that it was just barely detectable, thereby tracking their threshold as a function of time. For the subsequent ZEST passes, the test field was presented at each sampled time. After each presentation the observer pressed a button to indicate whether or not the flash was seen (i.e. a yes/no task). The stimulus radiance presented at each time was the current mean of the posterior probability density function generated by the ZEST operating at that time. The final threshold estimate was the mean of the posterior probability density function after the set number of passes had been completed.
Experiments were performed in 3 h sessions that were generally conducted on different days. Each session comprised the measurement of either two increment threshold data sets or one dark adaptation data set (for a single preadaptation level).
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RESULTS |
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Dark adaptation and increment threshold results are plotted in Fig 4 and Fig 4. In each row the left panel shows dark adaptation data and the right panel shows increment threshold data. For each data set, the ordinates are the log quantal flux of the test flash at threshold, estimated from a ZEST method; error bars show 95 % confidence intervals for the estimate. Each panel indicates the observer and the test and background wavelengths. The scales are consistent within (and between) figures to facilitate comparison of results across different experimental conditions and observers.
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The front plane (pass 0) indicates data collected using a method of adjustment, with each data point representing the test field radiance at that time after extinction of the preadapting field. Planes parallel to the front plane represent subsequent passes with each data point indicating the test field radiance presented based on the ZEST framework. The receding lines represent the progress of individual ZESTs operating at various times after extinction of the preadapting field (for clarity, only every fifth ZEST is indicated in this way). The continuous line on the back plane is the model fit to the final ZEST data. | ||
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Test and background fields were always the same wavelength, and were either green (541 nm, A and B), yellow (579 nm, C and D) or red (621 nm, E and F). Error bars represent 95 % confidence limits for the threshold estimates. A, C and E, dark adaptation threshold estimates (open symbols) as a function of time after extinction of adapting fields that elevated increment thresholds to the levels indicated by the filled symbols. The continuous curves indicate the best-fit models to the raw data; the dashed curves show the best-fit models for the data after correction for pigment depletion. Increasingly intense preadaptation levels have been translated along the time axis for clarity; dotted vertical lines indicate the time of extinction of the preadaptation field. Thresholds and models have been translated along the log U axis to equate dark adaptation and increment threshold absolute test thresholds. B, D and F, increment threshold estimates (open symbols) as a function of steady adapting field level. The continuous curve shows the best-fit model, with the parameters indicated in each panel. | ||
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Increment threshold
The increment threshold data follow the classical pattern, showing a dark light region, a Weber's law region, and a transition zone in between. For each data point, the abscissae give the log quantal flux of the steady background field. The continuous line drawn through the increment threshold data is the model represented by eqn (6), with the three free parameters adjusted to minimise a 2 merit function. Q values for these fits were always greater than 0·1 (with range 0·12 to 0·94). The best-fit parameters are indicated on each panel; they generally had small confidence intervals, indicating that they are well constrained by the data, although logW* was the least well determined.
Absolute test thresholds tended to be higher for LKM, and the average Weber fraction was also slightly higher for LKM (MJP, 0·0195; LKM, 0·0250). The slope parameter n is consistently close to 1·0 for both subjects and for all wavelengths tested, indicating adherence to Weber's law.
Dark adaptation
The dark adaptation data display the classical sensitivity increase with increasing time in the dark, reaching the final dark-adapted level after 1 to 5 min. The abscissae give the time in the dark (in s), while the ordinates indicate the log quantal flux of the test field at threshold (on the same scale as the increment threshold data). The filled symbols indicate the predicted threshold for the test field if presented on the steady preadapting field (calculated from the increment threshold model fit). Results for increasingly intense levels of preadaptation have been translated along the time axis for clarity, with the dotted vertical lines marking the extinction of the preadaptation field.
The dashed lines indicate fits of the model (eqn (10)) to the dark-adaptation data after correction for photopigment depletion, with the five free parameters adjusted to minimise a 2 merit function. Q values were generally greater than 0·1 (with range 0·06 to 1·0). Plotted dark-adaptation thresholds and model fits have been translated along the log U axis to equate the absolute dark-adaptation test thresholds with the absolute-increment threshold (the translation required was never greater than 0·2 log units). This manipulation acted to minimise the effects of sensitivity fluctuations between sessions and facilitated the generation of the equivalent background functions. The generally high Q values suggest that eqn (10) is a likely candidate for the underlying model. This model is based on a two-stage exponential decay, and the best-fit model parameters provide insight into the characteristics of the two components.
Figure 6 plots the level of threshold elevation caused by these components immediately after extinction of the adapting field (the initial desensitisation is reflected in the parameters D1 and D2). For both components, these parameters increase as the level of preadaptation increases. In fact, the increase is directly proportional to the preadaptation level (slope of unity on log-log co-ordinates), indicating that the initial desensitisation follows Weber's law as a function of preadaptation level. The reliability of determination of the parameters is poor at low preadaptation levels because there is less desensitisation caused at these levels and therefore fewer data to constrain the parameters. The vertical spacing between the two components indicates that for any of these preadaptation levels, the initial desensitisation caused by the early component is greater than the late component. The separation is 0·64 log units for MJP and 0·79 log units for LKM. The abscissa of the line at log U = 0 for the early component indicates the preadaptation level that should elicit no desensitisation. The corresponding value for the late component indicates preadaptation levels below which only the early component is responsible for threshold elevation. These values are approximately independent of wavelength when expressed as photopic trolands.
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Early and late components are indicated by filled and open symbols, respectively. Test and preadaptation wavelength and the observer are indicated in each panel. Symbols match those used in Figs 4 and 5 and show the best-fit initial threshold elevation estimates for each component; error bars indicate 95 % confidence intervals for the estimates. A line of unit slope has been fitted to the data from each component. The initial threshold elevation appears to follow Weber's law for each component, for both observers, and for all wavelength conditions. | ||
In the analysis of Lamb (1981), the initial desensitisation for two components was plotted as a function of the fraction of bleached photopigment (Lamb, 1981; his Fig. 3). Both components displayed direct proportionality between initial desensitisation and log fraction bleached for small bleaches. However, for higher bleaches the second (and possibly the first) component deviated towards higher levels of desensitisation. Figure 7 plots the data from Fig. 6 with the horizontal axis converted to log proportion of pigment bleached, calculated from eqn (3), with W0·5 = 4·3 log Trol (Rushton & Henry, 1968). The pattern of results is similar to those of Lamb (1981) for both components.
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Early and late components are indicated by the filled and open symbols, respectively. Test and preadaptation wavelength and the observer are indicated in each panel. The symbols match those used in Figs 4 and 5 and show the best-fit initial threshold elevation estimates for each component; error bars indicate 95 % confidence intervals for the estimates. The proportion of pigment bleached is calculated from eqn (3), with logW0·5 = 4·3 log Trol (Rushton & Henry, 1968). Both components display near direct proportionality between initial desensitisation and proportion bleached for small bleaches (indicated by the continuous lines). However, for higher bleaches, both components deviate towards higher levels. | ||
The exponential decay time constants (the parameters 1 and 2) are plotted in Fig. 8. The reliability of determination of the parameters is again poor at low preadaptation levels. Horizontal lines indicate the weighted average for each component, and it is evident that there is no significant dependence on preadaptation level since the 95 % confidence intervals overlap this average. In addition, there is no significant dependence on wavelength, although there may be slight differences between observers (with LKM's time constants slightly faster). The average magnitudes are 19 s and 51 s for the early and late components, respectively.
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Early and late components are indicated by the filled and open symbols, respectively. Test and preadaptation wavelength and the observer are indicated in each panel. The symbols match those used in Figs 4 and 5 and show the best-fit time constant estimates; error bars indicate 95 % confidence intervals for the estimates. The continuous horizontal lines indicate the average time constant for each component within each condition. The time constants for the three wavelength conditions are similar. In addition, they appear to be similar for the two observers. | ||
The best-fit parameters from the dark adaptation and increment threshold analyses can be used to generate an equivalent background function (eqn (11)). These are plotted in Fig. 9. These plots highlight the different rates of decay of the equivalent background for each component. It can be seen that the decay of both components is faster for LKM than MJP. It is also clear that for either observer, apart from a few exceptions, the form of the equivalent background functions is similar, so that in general they may be superimposed by translation along the logWe axis.
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These curves were plotted substituting the increment threshold and dark adaptation best-fit parameters into eqn (11). For each observer, the equivalent background functions are similar in shape and, apart from a few exceptions, the curves may be superimposed by translation along the logWe axis. For both components the rate of decay of the equivalent background is clearly evident and it is slightly faster for LKM than for MJP. The dotted line indicates the dark light value W0. | ||
The data of Hollins & Alpern (1973)
As a test of the generality of the model, it was applied to the results of Hollins & Alpern (1973). These data represent foveal test thresholds (1 deg diameter, 675 nm) measured during dark adaptation after exposure to a white preadaptation field (7 deg diameter, xenon) that bleached 10 to 100 % of the cone photopigment. Their Fig. 4 was scanned at high resolution and the data were extracted using a custom-built software package for analysing previously published data (Cuckoo). These data are plotted in Fig. 10. The abscissae give the time in the dark (in seconds), while the ordinates indicate log Trol of the test field at threshold. Hollins & Alpern (1973) did not specify the intensity of their preadaptation fields, only the proportion of photopigment bleached. To obtain an estimate of preadaptation field intensity, we used the inverse of the steady-state bleaching formula presented in their paper. For the 100 % bleach, this calculation gave the nonsensical value of +
Trol for the preadaptation field, so this condition was excluded from the rest of the analysis. The ordinates of the filled symbols show the predicted log Trol of the test field log U' that would be at threshold when presented on the preadapting field (calculated from the assumed increment threshold function shown in Fig. 10B). Results for increasingly intense levels of preadaptation have been translated along the time axis for clarity, with the dotted vertical lines marking the extinction of the preadaptation field. The continuous lines indicate fits of the model (eqn (10)) to the raw dark-adaptation data, and the dashed lines show model fits after correction of the data for pigment bleaching. The absolute dark-adaptation test threshold was fixed at -1·0 log Trol.
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5 dark adaptation dataThe raw data are indicated by the open symbols for observer MH from the study of Hollins & Alpern (1973). The test field was deep red (675 nm) and the background field was white (xenon). A, the symbols indicate threshold estimates measured during dark adaptation after extinction of the adapting field (from left to right, the proportions of photopigment bleached were: 0·10, 0·15, 0·20, 0·30, 0·40, 0·50, 0·60, 0·70, 0·80, and 1·00). The continuous curves indicate the best-fit models for the raw data; the dashed curves show the best-fit models for the data after correction for pigment depletion. During curve fitting, absolute threshold was fixed at -1·0 log Trol. Increasingly intense preadaptation levels have been translated along the time axis for clarity; dotted vertical lines indicate the extinction of the preadaptation field. Best-fit model parameters (for the dashed curves) are plotted in Fig. 11. B, theoretical increment threshold function. | ||
The best-fit parameter estimates and × 2 standard errors are plotted in Fig. 11. The pattern of results is very similar to those found for the photopic luminance mechanism. For each component, desensitisation follows Weber's law, and the exponential decay time constants appear to be independent of preadaptation (although the early component may be an exception).
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5 data
Early and late components are indicated by the filled and open symbols, respectively. Symbols match those in Fig. 10; error bars indicate × 2 standard error. A, initial desensitisation as a function of preadaptation level (with the preadaptation level calculated from eqn (3), with logW0·5 = 4·3 log Trol. A line of unit slope has been fitted to the data for each component. The initial threshold elevation appears to follow Weber's law as a function of preadaptation level for both components. B, the data of panel A plotted as a function of the proportion of photopigment bleached. Both components displayed near direct proportionality between initial desensitisation and fraction bleached for small bleaches (continuous line). However, for higher bleaches, both components deviate to higher levels. C, time constants as a function of preadaptation level. The continuous line indicates the weighted average time constant for each component ( | ||
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DISCUSSION |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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Human psychophysical experiments have shown that the threshold elevation during dark adaptation is equivalent to the desensitisation produced by a steady stabilised background field, called the equivalent background. This equivalent background gradually decreases in strength with increasing time in the dark, until only the absolute dark light remains.
In rod vision, it has been argued that following a bleach the equivalent background decays in three separate components, and that these components are due to the presence of photoproducts that cause events indistinguishable from those triggered by photoisomerisation (Lamb, 1981). The results presented here for the photopic luminance mechanism and for Stiles' 5 mechanism (Hollins & Alpern, 1973) provide evidence that the decline of equivalent background following a bleach can be accounted for by two separate components. The behaviour of the two components during dark adaptation is similar. The amount of initial desensitisation caused by each component follows Weber's law as a function of preadaptation level, but the early component causes greater initial desensitisation. In addition, both components show exponential decay, but with different time constants (with the early component faster).
Validity of correction for photopigment depletion
One conclusion of this paper is that there is a linear relationship between dark-adaptation thresholds and the concentration of the photoproducts generated by bleaching cones. This is at odds with the exponential relationship originally proposed by Dowling (1960) and Rushton (1965a), but is similar to the relationship found by Lamb (1981) for rods. Based on this result, the correction we have used for photopigment depletion cannot be correct since it relies on the Dowling-Rushton equation. Despite this, our estimate of the proportion of photopigment bleached as a function of time after extinction of the adapting field is probably reasonable. The continuous curve in Fig. 1A is an example of q(t) calculated from eqn (2). For comparison, the dashed curve indicates the q(t) measured by Hollins & Alpern (1973), calculated from their eqn (2b) with t0 = 105 s (the largest discrepancy is 0·14 at 70 s). The two curves are similar in shape, and with t0 = 70 s the curves are almost indistinguishable (the largest discrepancy is then only 0·013 at 60 s). Therefore, the q(t) we have used is likely to be a close approximation of the true q(t).
Luminance mechanism
The test and background field wavelengths are as closely matched as possible to increase the likelihood of detection by the luminance mechanism. This configuration corresponds to a +45 deg stimulus vector in (
L/L, M/M) cone contrast space and, equivalently, to the deepest part of the Sloan notch in spectral sensitivity data (Kalloniatis & Harwerth, 1990, 1991; Calkins et al. 1992; Chaparro et al. 1995).
There is no guarantee, however, that the luminance mechanism is responsible for detection of these flashes during dark adaptation. Several theoretical and empirical lines of argument strongly suggest that the luminance mechanism is responsible for detection of these stimuli during dark adaptation. (1) It is generally accepted that cones adapt independently, making their contrast contributions free from the influence of the spectral nature of the illuminant (Ives, 1912; Chaparro et al. 1995). This effect is known as von Kries adaptation (von Kries, 1877) and is thought to prevent response saturation of the cones or subsequent neural stages (Purpura et al. 1990). Moreover, the L- and M-cone pigments have been shown to regenerate at the same rate (Rushton, 1963, 1965b). These concepts, taken together, suggest that the relative adaptive state of the L and M cones that is set by the preadapting field is maintained during dark adaptation. Consequently, during dark adaptation the test flash is likely to be detected by the luminance mechanism, just as it is on the steady background. (2) The L and M cone weights to the red-green (RG) colour-opponent mechanism are of opposite sign and are nearly equal (Cole et al. 1993). This suggests that detection contours in the (L/L, M/M) plane of cone contrast space will have a slope close to unity. Therefore, the stimulus vectors used here are almost parallel to the RG colour-opponent mechanism detection contours, making it extremely unlikely that the RG colour-opponent mechanism is responsible for detection of these stimuli. This is true regardless of the fact that the RG colour-opponent mechanism is 10-fold more sensitive than the luminance mechanism (Cole et al. 1990; Chaparro et al. 1993). (3) For any of the conditions, the appearance of the stimuli did not change during dark adaptation. (4) There are no obvious breaks in the dark-adaptation curves, which would generally indicate the intrusion of another mechanism (see Du Croz & Rushton, 1966).
Evidence for the equivalent background hypothesis
The analysis in this paper relies on the equivalent background hypothesis: that the effects of bleaching observed during dark adaptation are equivalent to those obtained by presenting a continuous stabilised background of light that has the same spatial configuration and retina locus as the bleaching field. A large body of evidence supports this hypothesis for human rod vision (Crawford, 1937, 1947; Barlow & Sparrock, 1964; Blakemore & Rushton, 1965; Lamb, 1981). In contrast, there have been few tests of the equivalent background hypothesis in cones. Attempts to extend the classical studies of Crawford (1937, 1947) to cones have led to conflicting results. Rinalducci et al. (1970) found that the equivalent background hypothesis failed drastically for test field diameters that varied between 8 to 20 min of arc, whereas Geisler (1979) found that the equivalent background held for test field diameters of 3·5 to 50 min of arc. Neither of these studies used stabilised backgrounds, but Geisler (1979) argues that the earlier study failed to support the hypothesis because pigment depletion was not taken into account.
No attempt has been made here to measure dark adaptation with steady background fields in conjunction with bleaches. However, the additivity of real and equivalent background light is implicit in the model. Therefore, at any fixed time during dark adaptation, the predicted variation of threshold with real background light will be based on the dark-adapted increment threshold function, but with dark light given by the appropriate equivalent background light. Evidence for this type of behaviour has been found for both rods (Blakemore & Rushton, 1965) and cones (Du Croz & Rushton, 1966).
Identity of photoproducts
To account for the dark adaptation in the rod system, Lamb (1981) proposed a scheme in which the equivalent background was produced within rod photoreceptors by the presence of photoproducts of pigment bleaching. This paper proposes a similar scheme for the cone system. This seems reasonable given that cone and rod phototransduction is probably similar (Koutalos & Yau, 1996).
In this scheme, Rh is activated by light to form Rh*, which then decays through a series of intermediate forms, each capable (to a different extent) of mimicking light (Leibrock et al. 1998). These intermediates generate the equivalent background either by re-forming Rh* (via reverse reactions) or by acting directly on the G-protein cascade. Figure 12 illustrates the likely pathways, and they are discussed separately below. Note that in this discussion, the rod-specific terms rhodopsin (Rh) and activated metarhodopsin II (Rh*) are used for clarity, but they also refer to their cone counterparts.
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Rhodopsin (Rh) is transformed into activated metarhodopsin II (Rh*) either by photon absorption (light) or occasionally by thermal activation (heat). Rh* catalyses the activation of G protein to G*, which subsequently leads to the generation of the light response. Rh* is rapidly inactivated by phosphorylation and arrestin binding to form Mii-P-Arr (Rh* has been identified as metarhodopsin II, or Mii). This reaction exhibits a small degree of reversibility, so that Mii-P-Arr occasionally reverts to Rh* (indicated by A). In addition, Mii-P-Arr can directly activate the G-protein cascade, since the inactivation of Rh* by phosphorylation and arrestin binding is not total (indicated by B). Eventually, the all-trans retinoid is hydrolysed off, leaving the opsin. Opsin can also activate the G-protein cascade (indicated by C). Finally, opsin recombines with 11-cis retinal to reform rhodopsin. (Reproduced from Leibrock et al. 1998, with the addition of pathway C.) | ||
Reversion of Mii-P-Arr to Rh*. Rh* is rapidly inactivated by phosphorylation and arrestin binding to form Mii-P-Arr. However, this reaction exhibits a small degree of reversibility, so that Mii-P-Arr occasionally reverts to Rh*. This pathway will generate events indistinguishable from real photon hits (because the photoreceptor cannot distinguish the source of Rh*), and will generate photon-like fluctuations. The degree of reversibility required to explain the observed fluctuations in rods is extremely small (Lamb, 1981; Leibrock et al. 1994). This pathway is indicated by A in Fig. 12, and occurs at a rate of 2 × 10-7 Rh* s-1 (molecule of Mii-P-Arr in rods)-1 (Leibrock et al. 1994). The difference between the efficacy of transduction for rods and cones suggests that this value may be approximately two log units faster for cones (Fain et al. 1996).
Activation of the G-protein cascade by Mii-P-Arr. It appears that the ability of Mii to activate the G-protein cascade is not entirely removed by phosphorylation and arrestin binding (i.e. Mii-P-Arr can directly activate the phototransduction mechanism). This pathway will generate steady activation of the G-protein cascade, but will cause negligible fluctuations (because G* will be activated in the form of individual molecules, rather than in bursts as occurs with Rh*). In Fig. 12, B represents this pathway, which has an efficacy of 10-5 to 10-7 that of Rh* in rods (Leibrock et al. 1994; Cornwall & Fain, 1994); this value is 10-4 to 10-5 in cones (Cornwall et al. 1995).
Activation of the G-protein cascade byopsin. Opsin is also capable of activating the G-protein cascade in both rods and cones (Cornwall & Fain, 1994; Cornwall et al. 1995). The action of this pathway will be indistinguishable from the direct action of Mii-P-Arr. It is indicated by C in Fig. 12 and has an efficacy of 10-7 that of Rh* in rods (Cornwall & Fain, 1994).
From the data presented here, it is not possible to unequivocally identify these mechanisms with the components of photopic dark adaptation. However, the early (faster) component of photopic dark adaptation is likely to be due to the photon-like events generated by reversion of Mii-P-Arr to Rh* and/or the steady action of Mii-P-Arr directly onto the G-protein cascade. The later (slower) component could be due to opsin directly activating the G-protein cascade. Application of this model to pathological conditions that affect visual adaptation may provide insights into the nature of the deficiency.
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We wish to thank the anonymous referees for their comments on an earlier version of this paper. This work was supported in part by a National Health and Medical Research Council grant (980668) to Dr M. Kalloniatis.
Corresponding author
M. Kalloniatis: Department of Optometry and Vision Sciences, The University of Melbourne, Victoria 3010, Australia.
Email: m.kalloniatis{at}optometry.unimelb.edu.au
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); the continuous curve through this data is the best-fit eqn (10). The continuous line in A is the same curve scaled to range from the initial proportion of photopigment bleached q0 at t = 0 through to zero at t > > 0. The continuous curve below the data points represents the function that would be obtained if the only source of sensitivity loss were photopigment depletion, i.e. U/U0 = 1/(1 - q). The small filled symbols indicate the thresholds after correction for this photopigment bleaching effect; the continuous curve through these data is the best-fit eqn (10). The horizontal asymptote (dashed line) represents the absolute threshold U0. The other asymptotes (dashed lines) indicate exponential decay with time (on these log-linear axes, exponential decay becomes a linear decrease). The early and late components cause desensitisation at t = 0 of D1 and D2, and have exponential time constants of 
) is the theoretical threshold measured on the adapting field W'. D, increment threshold estimates as a function of steady adapting field level (