Flash-induced oxygen evolution in photosynthesis: simple solution for the extended S-state model that includes misses, double-hits, inactivation, and backward-transitions

Flash-induced oxygen evolution in higher plants, algae, and cyanobacteria exhibits damped period-four oscillations. To explain such oscillations, Kok suggested a simple phenomenological S-state model, in which damping is due to empirical misses and double-hits. Here we developed an analytical solution for the extended Kok model that includes misses, double-hits, inactivation, and backward-transitions. The solution of the classic Kok model (with misses and double-hits only) can be obtained as a particular case of this solution. Simple equations describing the flash-number dependence of individual S-states and oxygen evolution in both cases are almost identical and, therefore, the classic Kok model does not have a significant advantage in its simplicity over the extended version considered in this article. Developed equations significantly simplify the fitting of experimental data via standard nonlinear regression analysis and make unnecessary the use of many previously developed methods for finding parameters of the model. The extended Kok model considered here can provide additional insight into the effect of dark relaxation between flashes and inactivation.     

On the O2 flash yields of two cyanophytes

We explored O₂ flash yield in two cyanophytes, Anacystis nidulans and Agmenellum quadruplicatum. On a rate-measuring electrode, a single flash gave a contour of O₂ evolution with a peak at about 10 ms which was maximum (100) for 680 nm background light. On 625 nm illumination the peak was smaller (62) but was followed by an increased tail of O₂ attributed to enhancement of the background. After a period of darkness, repetitive flashes (5 Hz) gave a highly damped initial oscillation in individual flash yields which finally reached steady state at 94% of the yield for 680 nm illumination. When O₂ of repetitive flashes was measured as an integrated flash yield the results was distinctive and similar to that for a continuous light 1 (680 nm). An apparent inhibition of respiration which persisted into the following dark period was taken as evidence for the Kok effect. With a concentration-measuring electrode, integrated flash yield vs. flash rate showed the same nonlinear behavior as O₂ rate vs. intensity of light 1. We draw three conclusions about the two cyanophytes. (a) The plastoquinone pool is substantially reduced in darkness. (b) Because of a high ratio of reaction centers, reaction center 1 / reaction center 2, for the two photoreactions, saturating flashes behave as light 1. (c) Because repetitive flashes are light 1, they also give a Kok effect which must be guarded against in measurements designed to count reaction centers.     

How fast can Photosystem II split water? Kinetic performance at high and low frequencies

Molecular oxygen evolution from water is a universal signature of oxygenic photosynthesis. Detection of the presence, speed and efficiency of the enzymatic machinery that catalyzes this process in vivo has been limited. We describe a laser-based fast repetition rate fluorometer (FRRF) that allows highly accurate and rapid measurements of these properties via the kinetics of Chl-a variable fluorescence yield (Fv) in living cells and leaves at repetition rates up to 10 kHz. Application to the detection of quenching of Fv is described and compared to flash-induced O₂ yield data. Period-four oscillations in both Fv and O₂, caused by stimulation of primary charge recombination by the O₂ evolving complex (WOC) within Photosystem II (PS II), are directly compared. The first quantitative calculations of the enzymatic parameters of the Kok model (α – miss; β – double hit; S-state populations) are reported from Fv data over a 5 kHz range of flash frequencies that is 100-fold wider than previously examined. Comparison of a few examples of cyanobacteria, green algae and spinach reveals that Arthrospira m., a cyanobacterium that thrives in alkaline carbonate lakes, exhibits the fastest water-splitting rates ever observed thus farin vivo. In all oxygenic phototrophs examined thus far, an unprecedented large increase in the Kok α and β parameters occur at both high and low flash frequencies, which together with their strong correlation, indicates that PS II-WOC centers split water at remarkably lower efficiencies and possibly by different mechanisms at these extreme flash frequencies. Revisions to the classic Kok model are anticipated.     

Effects of removal and reconstitution of the extrinsic 33, 24 and 16 kDa proteins on flash oxygen yield in Photosystem II particles

The effects of removal and reconstitution of the three extrinsic proteins on the flash O₂ yield were investigated and the following results were obtained. (1) Removal in darkness of the 24 and 16 kDa proteins affected neither the oscillation pattern nor the signal amplitude of the flash O₂ yield. However, the signal amplitude was reduced with a factor of 2 in the presence of EDTA and was restored by excess Ca²⁺. The EDTA treatment did not change the oscillation pattern of the flash O₂ yield, but considerably damped the oscillation pattern of thermoluminescence B band. These results suggest a heterogeneity among the centers in binding affinity for Ca²⁺, and that Ca²⁺ removal induces an all-or-none type inactivation of O₂ evolution but not in the thermoluminescence processes, indicative of an inhibition of the S-state turnover at a specific S-state. (2) Removal in darkness of the 33, 24 and 16 kDa proteins abolished the flash O₂ yield, but the inhibited yield was appreciably restored either by reconstitution with the 33 kDa protein or by inclusion of 200 mM Cl⁻ in the reaction mixture. The flash O₂ yield reconstituted by the 33 kDa protein exhibited a rather normal oscillation pattern accompanied by a slightly increased damping, which could be simulated by assuming a high miss factor (30%) for S₃ → S₀ transition. The Cl⁻-restored flash O₂ yield exhibited a strongly damped oscillation pattern with obscured maxima at the 4th and 8th flashes, which was simulated by assuming a much higher miss factor (70%) for S₃ → S₀ transition. It was indicated that the Cl⁻-restored O₂ evolution considerably differs from the 33 kDa protein-reconstituted O₂ evolution with respect to the mechanism of S-state turnover.     

Oxygen-evolving activity of thylakoids from barley plants cultivated on different concentrations of jasmonic Acid

The kinetics characteristics of oxygen evolution in thylakoids prepared from barley (Horeum vulgare) seedlings grown in the presence of different jasmonic acid (JA) concentrations were studied. In comparison to control preparations, 100 micromolar JA-treated samples show an inhibition of the Hill activity (46%) and of O₂-flash yields to above 70%. A damping in the oscillations of O₂ yields, induced by a flash train, increases with increasing growth regulator concentration. After these treatments, the value of the total number of oxygen-evolving centers (S₀ + S₁), estimated according to the Kok scheme, shows a considerable decrease. In 100 micromolar JA-treated preparations, the turnover half-time of S₁-states increases and the stability of the S₂- and S₃-states decreases.     

Interaction of N,N,N′,N′-tetramethyl-p-phenylenediamine with photosystem II as revealed by thermoluminescence: Reduction of the higher oxidation states of the Mn cluster and displacement of plastoquinone from the QB niche

The flash-induced thermoluminescence (TL) technique was used to investigate the action of N,N,N′,N′-tetramethyl-p-phenylenediamine (TMPD) on charge recombination in photosystem II (PSII). Addition of low concentrations (μM range) of TMPD to thylakoid samples strongly decreased the yield of TL emanating from S₂Q_B⁻ and S₃Q_B⁻ (B-band), S₂Q_A⁻ (Q-band), and Y_D⁺Q_A⁻ (C-band) charge pairs. Further, the temperature-dependent decline in the amplitude of chlorophyll fluorescence after a flash of white light was strongly retarded by TMPD when measured in the presence of 3-(3,4-dichlorophenyl)-1,1-dimethylurea (DCMU). Though the period-four oscillation of the B-band emission was conserved in samples treated with TMPD, the flash-dependent yields (Y_n) were strongly declined. This coincided with an upshift in the maximum yield of the B-band in the period-four oscillation to the next flash. The above characteristics were similar to the action of the ADRY agent, carbonylcyanide m-chlorophenylhydrazone (CCCP). Simulation of the B-band oscillation pattern using the integrated Joliot-Kok model of the S-state transitions and binary oscillations of Q_B confirmed that TMPD decreased the initial population of PSII centers with an oxidized plastoquinone molecule in the Q_B niche. It was deduced that the action of TMPD was similar to CCCP, TMPD being able to compete with plastoquinone for binding at the Q_B-site and to reduce the higher S-states of the Mn cluster.     

Interaction of N,N,N',N'-tetramethyl-p-phenylenediamine with photosystem II as revealed by thermoluminescence: reduction of the higher oxidation states of the Mn cluster and displacement of plastoquinone from the Q(B) niche

The flash-induced thermoluminescence (TL) technique was used to investigate the action of N,N,N',N'-tetramethyl-p-phenylenediamine (TMPD) on charge recombination in photosystem II (PSII). Addition of low concentrations (muM range) of TMPD to thylakoid samples strongly decreased the yield of TL emanating from S(2)Q(B)(-) and S(3)Q(B)(-) (B-band), S(2)Q(A)(-) (Q-band), and Y(D)(+)Q(A)(-) (C-band) charge pairs. Further, the temperature-dependent decline in the amplitude of chlorophyll fluorescence after a flash of white light was strongly retarded by TMPD when measured in the presence of 3-(3,4-dichlorophenyl)-1,1-dimethylurea (DCMU). Though the period-four oscillation of the B-band emission was conserved in samples treated with TMPD, the flash-dependent yields (Y(n)) were strongly declined. This coincided with an upshift in the maximum yield of the B-band in the period-four oscillation to the next flash. The above characteristics were similar to the action of the ADRY agent, carbonylcyanide m-chlorophenylhydrazone (CCCP). Simulation of the B-band oscillation pattern using the integrated Joliot-Kok model of the S-state transitions and binary oscillations of Q(B) confirmed that TMPD decreased the initial population of PSII centers with an oxidized plastoquinone molecule in the Q(B) niche. It was deduced that the action of TMPD was similar to CCCP, TMPD being able to compete with plastoquinone for binding at the Q(B)-site and to reduce the higher S-states of the Mn cluster.     

Thermodynamic limitations of photosynthetic water oxidation at high proton concentrations

In oxygenic photosynthesis, solar energy drives the oxidation of water catalyzed by a Mn(4)Ca complex bound to the proteins of Photosystem II. Four protons are released during one turnover of the water oxidation cycle (S-state cycle), implying thermodynamic limitations at low pH. For proton concentrations ranging from 1 nm (pH 9) to 1 mm (pH 3), we have characterized the low-pH limitations using a new experimental approach: a specific pH-jump protocol combined with time-resolved measurement of the delayed chlorophyll fluorescence after nanosecond flash excitation. Effective pK values were determined for low-pH inhibition of the light-induced S-state transitions: pK(1)=3.3 ± 0.3, pK(2)=3.5 ± 0.2, and pK(3)≈pK(4)=4.6 ± 0.2. Alkaline inhibition was not observed. An extension of the classical Kok model facilitated assignment of these four pK values to specific deprotonation steps in the reaction cycle. Our results provide important support to the extended S-state cycle model and criteria needed for assessment of quantum chemical calculations of the mechanism of water oxidation. They also imply that, in intact organisms, the pH in the lumen compartment can hardly drop below 5, thereby limiting the ΔpH contribution to the driving force of ATP synthesis.     

Evaluation of photosynthetic activities in thylakoid membranes by means of Fourier transform infrared spectroscopy

Light-induced Fourier transformed infrared (FTIR) difference spectroscopy is a powerful method to study the structures and reactions of redox cofactors involved in the photosynthetic electron transport chain. So far, most of the FTIR studies of the reactions of oxygenic photosynthesis have been performed using isolated photosystem I (PSI) and photosystem II (PSII) preparations, which, however, could be modified during isolation procedures. In this study, we developed a methodology to evaluate the photosynthetic activities of thylakoids using FTIR spectroscopy. FTIR difference spectra upon successive flashes using thylakoids from spinach exhibited signals typical of the S-state cycle at the Mn₄CaO₅ cluster and Q_B reactions in PSII with period-four and -two oscillations, respectively. Similar measurement in the presence of an artificial quinone as an exogenous electron acceptor showed features specific to the S-state cycle. Simulations of the oscillation patterns provided the quantum efficiencies of the S-state cycle and electron transfer in PSII. Moreover, FTIR measurement under continuous illumination on thylakoids in the presence of DCMU showed signals due to Q_A reduction and P700 oxidation simultaneously. From the relative amplitudes of marker bands of Q_A^? and P700⁺, the molar ratio of photoactive PSII and PSI centers in thylakoids was estimated. FTIR analyses of the photo-reactions in thylakoids, which are more intact than isolated photosystems, will be useful in investigations of the photosynthetic mechanism especially by genetic modification of photosystem proteins.     

Time-resolved X-ray spectroscopy leads to an extension of the classical S-state cycle model of photosynthetic oxygen evolution

In oxygenic photosynthesis, a complete water oxidation cycle requires absorption of four photons by the chlorophylls of photosystem II (PSII). The photons can be provided successively by applying short flashes of light. Already in 1970, Kok and coworkers [Photochem Photobiol 11:457-475, 1970] developed a basic model to explain the flash-number dependence of O2 formation. The third flash applied to dark-adapted PSII induces the S3-->S4-->S0 transition, which is coupled to dioxygen formation at a protein-bound Mn4Ca complex. The sequence of events leading to dioxygen formation and the role of Kok's enigmatic S4-state are only incompletely understood. Recently we have shown by time-resolved X-ray spectroscopy that in the S3-->S0 transition an interesting intermediate is formed, prior to the onset of O-O bond formation [Haumann et al. Science 310:1019-1021, 2005]. The experimental results of the time-resolved X-ray experiments are discussed. The identity of the reaction intermediate is considered and the question is addressed how the novel intermediate is related to the S4-state proposed in 1970 by Bessel Kok. This leads us to an extension of the classical S-state cycle towards a basic model which describes sequence and interplay of electron and proton abstraction events at the donor side of PSII [Dau and Haumann, Science 312:1471-1472, 2006].     

Anomalies in the kinetics of photosynthetic oxygen emission in sequences of flashes revealed by matrix analysis. Effects of carbonyl cyanide m-chlorophenylhydrazone and variation in time parameters

The model of Kok et al. (Kok, B., Forbush, B. and McGloin, M. (1970) Photochem. Photobiol. 11, 457–475) is considered the best kinetic explanation of the damped oscillations of O₂ evolution induced in higher plants by a sequence of brief saturating flashes. Matrix analysis applied to this model shows that the parameters involved (distribution of S states at zero time, probabilities of transition between states induced by a flash) cannot be completely known from the O₂ yield sequence, Y_n. However, four quantities, with limited content of information, are readily derived from data, without additional assumptions. They are σ₁, σ₂ and σ₃, three quasi-symmetrical functions of the transition coefficients, and $\text{Y}$, a weighed average of four consecutive Y_n values. The extent of misses and double hits and their variations can be qualitatively ascertained by inspection of the relative values of σ₁, σ₂ and σ₃. In a regular sequence (strictly obeying Kok's model), all four quantities should be constant along the time axis.It is shown that actual sequences are seldom regular, in particular in the following conditions: (1) variable flashing frequency, (2) addition of carbonylcyanide m-chlorophenylhydrazone, (3) incomplete deactivation, (4) change of flashing frequency at steady state.In order to account for these anomalies, it is proposed to modify Kok's model by introducing, in parallel to the four state storage entity (S states), a side carrier C, which can reversibly exchange a positive charge with it. In the new model, the transition coefficients are essentially time varying, thus producing a nonregular behaviour of Y_n sequences.     

Slow oxygen release on the first two flashes in chemically stressed Photosystem II membrane fragments results from hydrogen peroxide oxidation

Flash-induced amperometric signals were measured with a Joliot-type O₂ rate electrode in spinach Photosystem II (PS II) membrane fragments exposed to very low concentrations of added hydroxylamine or hydrogen peroxide. In both cases anomalous O₂ signals were observed on the first two flashes, and oscillating four-flash patterns were observed on subsequent flashes. The anomalous signals were eliminated in the presence of catalase but not EDTA. The rise times of the O₂-release kinetics associated with the anomalous signals were slow (ca. 20 ms with NH₂OH and ca. 120 ms with H₂O₂) compared to the kinetics of O₂ release on subsequent flashes and in control membranes (3–6 ms). It is proposed that when the intact PS II O₂-evolving complex is perturbed with small concentrations of added reductant, H₂O₂ can gain access and bind to the complex. Bound H₂O₂ can then reduce lower S states in some centers leading to anomalous O₂ signals on the first two flashes. A model is presented to explain both types of anomalous O₂ production. Oxygen observed on the third and subsequent flashes is due to the normal photosynthetic O₂-evolution process arising from the S₃-state. Anomalous O₂ production could be a protective mechanism in PS II centers subjected to stress conditions.Abbreviations DCIP 2,6-dichlorophenolindophenol - EDTA ethylenediaminetetraacetic acid - MES 4-morpholine-ethanesulfonic acid - OEC oxygen-evolving complex - PS II Photosystem II - Y_i O₂ flash yield on the i^th flash - Y_ss steady-state O₂ flash yield level in algae, chloroplasts, or thylakoids after flash-driven S-state oscillations have been damped Formerly, the Solar Energy Research Institute and operated by the Midwest Research Institute for the US Department of Energy under Contract DE-AC-02-83CH10093. Government and MRI retain non-exclusive, royalty-free license to publish or reproduce published articles, or allow others to do so for Government purposes.     

Flash-induced oxygen yield sequences during the life cycle of Chlorella

(i) The pattern of O₂ flash yields in the first 4 hours of the life cycle cannot be described by the simple Kok model without additional assumptions. (ii) The miss coefficient in the mature cells in significantly higher than that in the autospores, its change occurring at the expense of the single-hit coefficient . Computer simulation yielded values of 0.29 and 0.23 and values of 0.66 and 0.72 in the light and dark, respectively. (iii) The onset of light at the beginning of the cycle drastically changes the equilibrium distribution of the S states in the dark; the ratio S₀/S₁ increases from 30/70 to 50/50 in 1 h, and is restored not earlier than in the 6th hour. (iv) In the presence of 1 mmol/l p-benzoquinone, the alga shows pronounced and long-lasting oscillations in the O₂ yield sequences, independently of the time of the life cycle. This means that the O₂-evolving system itself is always present and equally efficient throughout the life cycle. Limits imposed on its activity (mainly in the first 4 hours) are clearly of an external nature. The redox potential of the inner thylakoid space is presumably involved.Abbreviations BQ p-benzoquinone - DCIP 2,6-dichlorophenolindophenol - OES oxygen-evolving system - PS photosystem     

Oxygen-evolution patterns from spinach Photosystem II preparations

Patterns of O₂ evolution resulting from sequences of short flashes are reported for Photosystem (PS) II preparations isolated from spinach and containing an active, O₂-evolving system. The results can be interpreted in terms of the S-state model developed to explain the process of photosynthetic water splitting in chloroplasts and algae. The PS II samples display damped, oscillating patterns of O₂ evolution with a period of four flashes. Unlike chloroplasts, the flash yields of the preparations decay with increasing flash number due to the limited plastoquinone acceptor pool on the reducing side of PS II. The optimal pH for O₂ evolution in this system (pH 5.5–6.5) is more acidic than in chloroplasts (pH 6.5–8.0). The O₂-evolution, inactivation half-time of dark-adapted preparations was 91 min (on the rate electrode) at room temperature. Dark-inactivation half-times of 14 h were observed if the samples were aged off the electrode at room temperature. Under our conditions (experimental conditions can influence flash-sequence results), deactivation of S₃ was first order with a half-time of 105 s while that of S₂ was biphasic. The half-times for the first-order rapid phase were 17 s (one preflash) and 23 s (two preflashes). The longer S₂ phase deactivated very slowly (the minimum half-time observed was 265 s). These results indicate that deactivation from S₃ → S₂ → S₁, thought to be the dominant pathway in chloroplasts, is not the case for PS II preparations. Finally, it was demonstrated that the ratio of S₁ to S₀ can be set by previously developed techniques, that S₀ is formed mostly from activated S₃ (S₄), and that both S₀ and S₁ are stable in the dark.     

EPR evidence for a modified S-state transition in chloride-depleted Photosystem II

The role of chloride on the S-state transition in spinach Photosystem II (PS II) particles was investigated by EPR spectroscopy at low temperature and the following results were obtained. (1) After excitation by continuous light at 200 K, chloride-depleted particles did not show the EPR multiline signal associated with the S₂ state, but only showed the broad signal at g = 4.1. The S₂ multiline signal was completely restored upon chloride repletion. (2) In the absence of chloride the S₂ multiline signal was not induced by a single flash excitation at 0°C. However, upon addition of chloride after the flash the signal was developed in darkness. (3) The amplitude of the multiline S₂ signal thus developed upon chloride addition after flash illumination did not show oscillations dependent upon flash number. These results indicate that the O₂-evolving complex in chloride-depleted PS II membranes is able to store at least one oxidizing equivalent, a modified S₂ state, which does not give rise to the multiline signal. Addition of chloride converts this oxidizing equivalent to the normal S₂ state which gives rise to the multiline signal. The modified S₂ state is more stable than the normal S₂ state, showing decay kinetics about 20-times slower than those of the normal S₂ state, and the formation of higher S states is blocked.     

In appreciation of Bessel Kok

This issue of Photosynthesis Research is dedicated to the memory of Bessel Kok, the discoverer of the photoactive reaction center pigment of Photosystem I, P700, and a pioneer in the field of biophysics of photosynthesis. We particularly salute his formulation of the 5-step S-state O₂ clock, based on the elegant experiments of Pierre Joliot. Pierre observed a characteristic period four oscillation of the O₂ yield when dark-adapted photosynthetic samples were illuminated with a train of single turn-over flashes. We honor Pierre by inviting him to write his personal perspective in which he discusses the events that led to this seminal discovery.     

Depletion of Photosystem II-extrinsic proteins. I. Effects on O2- and N2-flash yields and steady-state O2 evolution

Wheat O₂-evolving Photosystem II (PS II) membranes having a PS II unit of approx. 200 chlorophylls (Chl), approx. 4 Mn/200 Chl, less than 1 P-700/3000 Chl and an electron-acceptor pool of approx. 2.5 equiv./PS II were analyzed and compared with wheat PS II membranes depleted (at least 90%) of the 17 and 23 kDa proteins by NaCl extraction during Triton X-100 isolation of membranes. Extraction of these proteins caused approx. 50% decrease in O₂ evolution in any light regime and an increase of approx. 2 equiv./PS II of the electron-acceptor pool, but affected neither Mn abundance, photoreduction of DCIP by tetraphenylboron, or N₂ yield (from NH₂OH) from a single flash. Mass spectrometric analyses of O₂ flash yields in the presence of potassium ferricyanide showed that both chloroplasts and the unextracted PS II membranes yielded oscillations compatible with S₀/S₁/S₂/S₃ of 25:75:0:0 and α (0.1) and β (0.05). Depletion of 17 and 23 kDa proteins resulted in a two-fold increase in α, approx. 25–40% disconnection of the S state complex from the PS II trap complex but with no change in β. Preincubation of control or extracted PS II membranes with potassium ferricyanide permitted a significant double-hit on the first flash. In the absence of an added electron acceptor, N₂ flash yields were more sustained with 17 and 23 kDa depleted than with 17 and 23 kDa sufficient PS II membranes. In contrast, no significant O₂ flash yields were observed with extracted PS II preparations under these conditions (control PS II membranes showed a predictable O₂ pattern before damping after only 5–6 flashes). These results suggest that extraction of the 17 and 23 kDa proteins results in an increase of pool size on the PS II acceptor side (seen as unmasking ‘Component C’). ‘Component C’ can mediate electron transfer from Q⁻ to Z⁺ (S₂).     

Flash kinetics and light intensity dependence of oxygen evolution in the blue-green alga Anacystis nidulans

Patterns of oxygen evolution in flashing light for the blue-green alga Anacystis nidulans are compared with those for broken spinach chloroplasts and whole cells of the green alga Chlorella pyrenoidosa. The oscillations of oxygen yield with flash number that occur in both Anacystis and Chlorella, display a greater degree of damping than do those of isolated spinach chloroplasts. The increase in damping results from a two- to threefold increase in the fraction (α) of reaction centers “missed” by a flash. The increase in α cannot be explained by non-saturating flash intensities or by the dark reduction of the oxidized intermediates formed by the flash. Anaerobic conditions markedly increase α in Anacystis and Chlorella but have no effect on α in broken spinach chloroplasts. The results signify that the mechanism of charge separation and water oxidation involved in all three organisms is the same, but that the pool of secondary electron acceptors between Photosystem II and Photosystem I is more reduced in the dark, in the algal cells, than in the isolated spinach chloroplasts.Oxygen evolution in flashing light for Anacystis and Chlorella show light saturation curves for the oxygen yield of the third flash (Y₃) that differ markedly from those of the steady-state flashes (Y_s). In experiments in which all flashes are uniformly attenuated, Y₃ requires nearly twice as much light as Y_s to reach half-saturation. Under these conditions Y₃ has a sigmoidal dependence on intensity, while that of Y_s is hyperbolic. These differences depend on the number of flashes attenuated. When any one of the first three flashes is attenuated, the variation of Y₃ with intensity resembles that of Y_s. When two of the first three flashes are attenuated, Y₃ is intermediate in shape between the two extremes. A quantitative interpretation of these results based on the model of Kok et al. (Kok, B., Forbush, B. and McGloin, M. (1970) Photochem. Photobiol. 11, 457–475, and Forbush, B., Kok, B. and McGloin, M. P. (1971) Photochem. Photobiol. 14, 307–321) fits the experimental data.