Step-up photophobic responses of the unicellular alga Haematococcus pluvialis and their interpretation in terms of photoreceptive apparatus characteristics

ffom'anlof

AND B:~OLOGY

ELSEVIER

Journal of Photochemistryand PhotobiologyB: Biology33 (1996) 201-209

Step-up photophobic responses of the unicellular alga Haematococcus pluvialis and their interpretation in terms of photoreceptive apparatus characteristics Ciro Cecconi *, Cesare Ascoli, Donatella Petracchi lstituto di Biofisica del CNR, Via S. Lorenzo 26, 56127 Pisa, Italy

Received20 February 1995;accepted 11 October 1995

Abstract

This paper reports a systematic study of the step-up photophobic responses exhibited by the unicellular alga Haematococcus pluvialis when s:imulated unidirectionally or bidirectionally. The stimulus-response curves, obtained at four different wavelengths, are interpreted in terms ;~ the structure of the photoreceptive apparatus. In addition, an indirect method to obtain information about the stigma and photoreceptor(s) i~ reported. This method is based on the interpolation of experimental with simulated data. Our results confirm the widely accepted view that tie photoreceptors are located in the stigma region, and suggest the presence of two photoreceptors. A ~ywords: Photophobic responses; Haematococcus pluvialis; Photoreceptor; Stigma

I, Introduction

It is essential for photosynthetic organisms to find the best li ght conditions to carry out their vital functions, first of all photosynthesis, and to avoid excessive light intensities or potentially harmful wavelengths (UV). In order to perform this task, they possess photoreceptive and transduction-effecr.~,r systems which enable them to modify their behaviour in r,.'sponse to external stimuli. Unicellular algae represent clear e ~amples of this ability to adapt to the environment. Depend~r~gon the light conditions, these microorganisms can exhibit 1:ght-oriented movement (phototaxis), sudden and transient ~hanges in locomotion (photophobic responses) and varia~ons in steady state swimming velocity (photokinesis) [ 1,2]. The study of the mechanisms underlying these motile phot ~responses not only increases our knowledge of the micro~rganisms involved, but may also reveal primordial ,:haracteristics of our more complex visual system. The biflagellated alga H a e m a t o c o c c u s p l u v i a l i s [3,4] has quasi-spherical shape with a diameter of about 20/zm. It antains one large cup-shaped chloroplast closely surrounded t.y the cell membrane (Fig. 1). A red--orange spot, with a ,:urface area of about 2 / z m 2, is visible with an optic micro~.cope on the cellular surface of the flagella-beating hemi* Corresponding author. ]011-1344/96/$15.00 © 1996 Elsevier Science S.A. All rights reserved :'~D1101 1 - 1 3 4 4 ( 9 5 ) 0 7 2 5 3 - 5

\

f, m

/

Chl. C.w.

Fig. 1. Schematic drawing of Haematococcus pluvialis; the inset shows the eyespot region. N., nucleus; Chl., chloroplast; C.w., cell wall; FI., flagellum; I.m., inner membrane of the chloroplast envelope; O.m., outer membrane of the chloroplast envelope; P., plasma membrane; S.g., stigma granule.

sphere, near the equator. Various electrophysiological studies [5-9] have indicated that the photoreceptor(s) responsible for phototaxis and photophobic responses is located in this small, coloured area called the "eyespot region". Electron microscopy [ 10] clarified the ultrastructure of this region, showing a row of spherical granules (Fig. 1, inset), whose diameters range between 70 and 140 nm; they are located on the internal side of the inner membrane of the chloroplast envelope. These granules together constitute the eyespot or

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stigma. According to this electron microscopy study, the photoreceptor(s) is probably located in the membranes adjacent to the stigma, possibly in the inner membrane of the chloroplast envelope. In this study, we aim to obtain further information on the photoreceptive apparatus ofH. pluvialis by analysing its stepup photophobic responses.

2. Rationale

H. pluvialis slowly rotates around its longitudinal axis while it swims. Therefore, when a cell population on a microslide is stimulated by a short light flash from one side (unidirectional stimulation), in a fraction of this population (50% on average) the photoreceptor is directly reached by the light stimulus (with various incidence angles), whereas in the remaining cells the photoreceptor is shaded by the stigma and by the cell body. This type of stimulation thus reveals in the population two differently responding groups schematically represented by cells a and b in Fig. 2. However, when the light stimulus consists of two simultaneous flashes from opposite sides (bidirectional stimulation), in every cell the photoreceptor is reached directly by the light from one lamp and indirectly (through the stigma and the cell body) by the light from the other. In this case, the whole cell population will behave as a single group. Therefore the geometry of stimulation is expected to influence strongly the behavioural response of a population of H. pluvialis. This motivated us to study the photophobic

9

=,

G

Fig. 2. Schematic representation of the two groups of cells in a sample under unidirectional stimulation. The photoreceptor in cell b is directly reached by the light stimulus, whereas that of cell a is shaded by the stigma. S., stigma; Ph., photoreceptor(s).

responses of this alga using both unidirectional and bidirectional stimuli in order to compare the two sets of data. We also managed to obtain stimulus-response curves with flashes of different wavelengths in order to correlate their varying shapes with known properties of the stigma and photoreceptor, which are dependent on the wavelength of the light stimulus. Furthermore, a computer program was implemented to simulate the experiment. This allowed us to vary certain parameters representing certain properties of the stigma (e.g. absorbance) and photoreceptor (e.g. cross-section). Basically, it was assumed, as experimentally proven [ 11 ], that in this alga a photophobic response occurs when the number of absorbed photons exceeds a threshold value. For a single cell (either a or b), the response is a step function whose position on the fluence axis depends mainly on geometrical factors and on the individual features of the cell. The gradual slope of the stimulus-response curve in a population is due to the spread in the population of the individual stepwise responses. We used different values of the stigma absorbance and photoreceptor cross-section and employed the program to study the dependence of the experimental output on the features of the photoreceptive apparatus. By fitting simulated doseresponse curves to the experimental data, we obtained bestfit values of the parameters which give reliable information on the spectroscopic features of the stigma (or whatever screens the photoreceptor) and photoreceptor.

3. Description of the method

3.1. Set-up Fig. 3 shows a scheme of the set-up used. The non-actinic IR component of the microscope illumination was focused onto the sample by a dark-field condenser. Only the light scattered by the sample was collected by the microscope lens and detected by the photocell placed at the output pupil of the eyepiece. The power spectrum of the photocurrent was obtained through a computer program using fast Fourier transform (FFT). The population of microorganisms was stimulated by light flashes lasting 20 ms. For such a short duration, the photophobic responses are only affected by the light dose (intensity × time interval) and not by other phenomena such as the regeneration of the pigment [ 11 ]. Unidirectional stimulation was carried out using one lamp and bidirectional stimulation using two identical lamps facing each other. The light rays from each lamp formed an 18° angle with the horizontal plane and were focused in a light cone with an aperture of 30°. Fig. 4(a) shows a typical power spectrum of a non-stimulated population ofH. pluvialis. The band around 0 Hz (not shown for scale reasons) is caused by several factors: (i) body rotation during swimming; (ii) fluctuation in the number of microorganisms in the illuminated field [ 12]; (iii)

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C. Cecconi et al. / Journal of Photochemistryand Photobiology B: Biology 33 (1996) 201-209

a)100 AO

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=ig. 3. Schemeof the experimentalset-up. T., telecamera;E.p., eyepiece; 3.s., beamsplitter;O, objective;S, sample;D, dark-fieldcondenser;I.f., IR liter; H.p.f., heat protectionfilter; ln.f., interferencefilter; N.d.f., neutral ~ensityfilter. Brownian movement. In addition, there is a peak at about 32 Hz which can be ascribed to the flagellar beating frequency. The photophobic response exhibited by a single microorganism, as observed visually on the video, is characterized by the interruption of movement followed by a short backward motion and, finally, by a forward motion in another direction. Using high-speed cinematography on a wild-type strain of Chlamydomonas reinhardtii, it was observed [ 13] that stimulation with a light flash causes an increase in the frequency of flagellar beating. The same phenomenon also happens in H. pluvialis: indeed, light stimulation causes a peak in the spectrum at about 47 Hz. The area of this peak (A1) is proportional to the number of cells showing a photophobic response on the video, and widens as the flash intensity increases. At the same time, the area A0, due to non-responding cells, decreases (Fig. 4 (b)). Each experimental value of the photophobic response was obtained using the following protocol. The sample was stimulated with a series of 20 flashes of the same spectral composition and light intensity, at intervals of 30 s. After each flash, a power spectrum of the photocurrent signal was made in the interval between 380 and 780 ms. The 20 power spectra were then averaged in order to obtain more stable values and to increase the signal/noise ratio. Finally, the percentage of photophobic responses was calculated on the average spectrum using the expression: [ A 1 / ( A 1 +A0)] × 100. Fig. 4 shows four averaged power spectra. 3.2. Simulation program

The simulation was carried out by considering each individual cell in a population of N cells. The orientation of each

, 50

75 0

25 f(Hz)

50

75 0

25 50 f (Hz)

75

Fig. 4. Fourtypicalaveragepowerspectra (each obtainedby averaging20 individualspectra) for a populationof Haematococcuspluvialis: (a) average power spectrum of a non-stimulatedpopulation; (b) three different average powerspectraof populationsstimulatedwith differentlight intensities; fromleft to right: 0.24 mW cm-2, 0.4 mW cm-2, 3.9 mW cm-2. In all threecases,the stimuluswavelengthis 500 + 25 nm. individual cell relative to the light source was extracted at random by a suitable algorithm (see Appendix A). If the flash light impinges directly on the photoreceptor, the number of photons Q absorbed by the photoreceptor of that cell is computed as follows Q = CphLdAt

( 1)

where Ld is the intensity of light falling directly on the photoreceptor, A t is the flash duration and Cph = Cphm ( Cph is the cross-section of a single photoreceptor molecule and m is the number of photoreceptor molecules). Since we assumed a gaussian distribution of the m values in the cell population (with standard deviation O'm), we also assumed the same type of distribution for the Cph values, with a mean value of Cph (a function of the wavelength of the light stimulus) and a standard deviation of trChh. The standard deviation, when given as a percentage of the average as shown below, is a function of only trm. Photoreceptor molecules were assumed to be oriented in such a way that their electric dipole is randomly oriented in the plane of the cell membrane [ 14,15 ]. Therefore we treated Cph as a function of the incidence angle of the light rays (Appendix A, Eq. (A6)). Ld (direct light) is the overall flux of photons reaching the photoreceptor, i.e. those coming directly from the lamp plus those reflected by the stigma, when the latter does not shade the photoreceptor from light. If the cell receiving the flash has the stigma interposed between the light source and the photoreceptor, then

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Cecconi et al. / Journal of Photochemistry and Photobiology B: Biology 33 (1996) 201-209

Light r a y

Incidentlight

Reflectedlight

/

S,

~ / /

\\//

\\//

Cell

,

r

Microslide wall Transmittedlight

Fig. 5. Schematic drawing of the eyespot region. Ph., photoreccptor( s); S., stigma; 4, incidence angle; 8, refractive angle.

Q = CphLtAt

Fig. 6. Schemeof the grid used to take into accountthe light coneof the flashes. 8i, incidenceangleof the centralray.

(2)

where Lt (transmitted light) is the light intensity transmitted by the stigma. The stigma is considered as a dielectric thin film and its reflectivity and transmittance are calculated accordingly (Appendix A, Eqs. (A1) and (A5) respectively). More than one variable affects these two parameters, among them the incidence angle of the light stimulus and the absorbance A. As reported above for Cpb values, in the cell population a gaussian distribution has also been adopted for the A values, with a mean A and a standard deviation O'a. When the experiment with two lamps is simulated, Q is calculated for each lamp and the two values are summed. The main steps in the simulation program are described below and shown in the flow chart in Fig. 7. The simulation program initially requests six parameters: Cph, O'Cph,fi', O'A,the number of microorganisms in the sample N and the wavelength A. It then begins to run. The value of the light intensity I is increased step by step, and for each value the percentage of photophobic responses is calculated as follows. The orientation of each cell with respect to the lamps is extracted at random using a suitable algorithm. If the incidence angle of the flash light on the stigma (~i in Figs. 5 and 6) lies between 0 ° and 89 °, the cell belongs to the b cell population, and so Q is calculated using Eq. (1); if the incidence angle lies between 90 ° and 180°, the cell is an a cell, and so Eq. (2) is used. For each cell, the values of A and Cph are extracted at random, using a suitable algorithm, from the respective gaussian distributions. If the value of Q is higher than a threshold value Th, which is maintained constant for all wavelengths, the cell is assumed to have responded photophobically. It has been proven [ 11 ] that the photophobic response, in this alga, occurs when the number of absorbed photons exceeds a threshold value. Once the Q value of each microorganism has been compared with Th, the percentage of photophobic responses is calculated.

:

Request for parameters:

"~

~lnitialization of the flash light intensity I ) (~Randomextraction of~l

1 (

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Random extraction of A and Cph

alculation of the photons absorbed Q using equation 1 if ~ < 90° or uation 2 if ~1,~90°. J¢

J

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--Qf (o > Th)

~ Nr (number of photophobic responses) = Nr +1

photophobic response = (NdN) * 100

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Fig. 7. Flowchartof the one-lampsimulationprogram. Finally, the percentages obtained at each value of/are plotted. By varying the values of the parameters Cph, O'Cph,-4 and ~ra, representing the properties of the photoreceptive apparatus, the shape of the simulated stimulus-response curves change and a match with experimental values can be reached. The best-fit values are reported in Table 1. 4. Materials and techniques

H. pluvialis was supplied by Sammlung von Algenkulturen, Pflanzenphysiologisches Institut der Universit~ Gottin-

C. Cecconi et al. / Journal of Photochemistry and Photobiology B: Biology 33 (1996) 201-209 Table 1 Best-fit values ofthe parameters ofthe simulation program

l°°1o[ ) ~ soi

Parameter

?~ rcp~ rA

A (nm) 400

450

500

550

14 0.15 0.92 0.11

31.6 0.5 0.61 0.14

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25 0.09 0.54 0.12

~ o J~ o

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205

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gen (SAG). Algae were grown at 2 0 + 2 °C in 125 ml :otton-plugged flasks containing 50 ml of medium which was ~terilized by filtration. The composition of the medium was as follows: 2 mM KNO3, 0.8 mM CaCI2, 0.6 mM MgSO4.7H20, 1 mM KH2PO4, 0.5 mM K2HPO4" 3H20, 10 rnM HEPES, 1.48 mM vitamin B1, 0.003 mM vitamin B12, 2.5 mM FeSO4 •7H20, 2.5 mM sodium EDTA and a standard ~olution of trace elements. The pH was adjusted with NaOH r~o6.85__+0.1 [16]. Cultures were subjected to a 14 / 10 h dark/light cycle using fluorescent daylight lamps with an intensity of about 1 mW 2 m - 2.

The experiments were carried out on 8-10-day-aged non~ynchronized cultures, and thus with algae at the beginning of the stationary phase. During the experiments, the cells were kept on microslides (length, 40 mm; path length, 0.4 mm; width, 4.0 mm) supplied by Vitro Dynamics, Inc. The microslides were placed on a microscope stage maintained at 23 °C by a Peltier device. Light flashes were obtained from a halogen lamp ( 100 W Osram, Germany) in line with an electronically controlled shutter (Uniblitz, Vincent'Associates, Rochester, NY) triggered by the computer. The light was filtered appropriately to obtain: (i) four different wavelengths (400 ___25 nm, 450 + 25 nm, 500 + 25 nm, 550 + 25 nm) using Balzers K filters; (ii) different light intensities using Balzers neutral filters; (iii) cut-off of the IR component using Balzers Calflex B 1/K1 filters and Balzers DT-Cyan. In order to prevent the photocell (Hamamatsu, Japan) from collecting the stimulus, a filter (Kodak, Rochester, NY) that cut off UV and visible light was placed in front of the photocell. The photocurrent was fed to an IBM 386 personal computer supplied with an analogue-to-digital and digital-to-analogue converter and a digital input--output interface. The computer performed the spectral analysis by FFT in real time. The swimming behaviour of the microorganisms was observed by a video system (Nical, Italy). The simulation program was implemented and run on an IBM 486 personal computer. 5. Results and discussion

5.1. Experimental results Fig. 8 plots the percentage of photophobic responses against the light intensity for unidirectional (large filled cir-

0.2

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Fig. 8. Stimulus-response curves: large filled square, mean values of 7-9 experimental data obtained with two lamps; large filled circle, mean values of 7-9 experimental data obtained with one lamp; bar, standard error of the averages; small filled square, values obtained using two-lamp simulation program; small open circle, values obtained using one-lamp simulation program. Stimulus wavelengths: (a) 400_+25 nm; (b) 450_+25 nm; (c) 500+25 nm; (d) 550+25 nm.

cles) and bidirectional (large filled squares) light stimulation. Each point represents the average of several experimental values obtained as explained in Section 3. The low values of the standard deviation demonstrate the good stability and reproducibility of the results, which were obtained on different samples on different days. Before examining these curves, we discuss qualitatively how the presence of a shading body (the stigma) on one side of the photoreceptor(s) can affect the shape of the stimulusresponse curves. Let us consider separately three different ranges of values of stigma transmittance. (1) High value of stigma absorbance. In this case, the stigma significantly reduces the intensity of light falling on the photoreceptor of the a cells in Fig. 2. As a consequence, when stimulated unidirectionally with increasingly higher light intensity, the type b cells will respond first. If the stigma absorbance is very high, the photophobic response of the a cells will begin after the response of the b cells has reached saturation. Therefore in curves such as those shown in Fig. 8 there will be a plateau at around 50% of the photophobic response. The photophobic response occurs gradually it, both b cells and a cells because there is a variability in the features of the photoreceptive apparatus, and because the orientation of each cell with respect to the flash light direction can be more or

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C. Cecconi et al. / Journal of Photochemistry and Photobiology B: Biology 33 (1996) 201-209 1.0

0.8

L

L

L

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I

I

I

400

450

500

550

Wovelength

600

(nm)

Fig. 9. Graphic representation of values in Table 1: I , ,~; [3, trA; O, Cph/ 100; ©, O'cph.

less favourable. These different cell conditions cause a gradual rise in photophobic response. The slope of the curve before the plateau is related to the variability in the b cells, while the slope of the curve after the plateau is related to the variability in the a cells: the greater these variabilities, the lower the slopes of the curve. When the absorbance of the stigma is high, the transmitted light will strongly depend on the incidence angle 6i (see Appendix A, Fig. 10). As a consequence, the variability of the photophobic response in a cells will be higher than in b cells and the portion of the curve after the plateau will have a lower slope. Under bidirectional stimulation, the photoreceptor of each cell will be illuminated directly by one lamp and indirectly (through the stigma) by the other. When the stigma absorbance is high, up to a certain value of the light intensity, the stimulus from one lamp will be almost completely removed by shading. Consequently, for the same light intensity of one lamp, each cell will exhibit the same photophobic response as that shown by the b cells under unidirectional stimulation. In plots such as those shown in Fig. 8, in which the abscissa reports the light intensity of one lamp on a logarithmic scale, the curves obtained with the two stimulation methods should begin at the same point and then diverge. The two-lamp curve should have a slope twice that of the other curve, and reach saturation at about the abscissa value where the plateau of the one-lamp curve begins. No change in slope is expected. (2) Low value of stigma absorbance. In this case, the photoreceptor will practically no longer be shaded. Consequently, even under unidirectional stimulation, the number of photons which fall on the photoreceptor(s) of b cells and a cells will be almost the same. The photophobic responses of the two populations will then begin and reach saturation almost together. In the stimulus-response curve, no change in slope is expected.

Under two-lamp stimulation, the number of photons which fall on the photoreceptor(s) of each cell will be doubled. In this case, the important factor is the total intensity of the light falling on the sample and not the light intensity of a single lamp. In graphs such as those shown in Fig. 8, the curve obtained with bidirectional stimulation is expected to be shifted to the left by a factor of two, and to have the same slope as the onelamp curve, (3) Intermediate absorbance value. In this case, under unidirectional stimulation, the b cells will begin to respond before the a cells, but the saturation will occur after the beginning of the a cell photophobic response. In this case, no plateau is expected, but the slope of the curve will change. The general shapes (starting point and slope) of the twolamp and one-lamp curves will be halfway between those described in cases ( 1) and (2). Within this conceptual framework, we can now interpret our experimental data. The stimulus-response curve obtained with one lamp at 450 nm shows, if not exactly a plateau, a strong slope change at around 50% of the photophobic response which begins at the same point as the two-lamp curve: the two curves then diverge. The slope after the plateau is less than the slope before. All these features agree with the predictions for case (1), and thus with a high absorbance of the stigma at this wavelength. The stimulus-response curves obtained at 400 nm and especially at 550 nm do not show slope changes, and the twolamp curves present a shift to the left but with the same slope as the one-lamp curves. All these features are consistent with case (2), and thus with a low absorbance of the stigma. Finally, the stimulus-response curve obtained with one lamp at 500 nm presents a change in slope at around 60% of the response. In addition, the general shapes (starting point and slope) of the two-lamp and one-lamp curves are halfway between the values observed at 450 nm and 550 nm. These results are consistent with a stigma absorbance value as in case (3) above. In summary, from our experimental data, the stigma absorbance appears high at 450 nm, low at 400 nm and especially at 550 nm, and intermediate at 500 nm. These results are consistent with a microspectrophotometric study [ 17] showing that the stigma presents an absorption spectrum typical of carotenoids: maximum absorbance at 450 nm, slightly lower value at 500 nm, and low absorbance at 400 nm and 550 nm. 5.2. Simulation results

The best-fit values of the four parameters Cph, O'Cph,t~ and Ora are reported in Table 1. Many different combinations of the four parameters were used for each wavelength, but only those reported in Table 1 gave a good fit to the experimental data. When carrying out the interpolations, we noticed that the values of ~-'phchiefly affected the starting point of the

C. Cecconi et al. / Journal of Photochemistry and Photobiology B: Biology 33 (1996) 201-209

curves, the values offi, the presence or not of the plateau, and the values of O'Cphand cra the slope of the curve before and after the plateau respectively. The best-fit values do not have absolute meaning; however, they represent a relative evaluation of the parameters. Thus it is of interest to compare the best-fit values of each parameter ~t the four different wavelengths. It is easy to see that the best-fit values of the ,4 parameter tre proportional to the typical absorbance values of caroteaoids (and thus of the stigma) at the same wavelengths (see Zig. 9). This supports the reliability of the simulation program and, consequently, the hypotheses on which it is based, irst of all those concerning the structure of the photoreceptive tpparatus. Even more interesting are the best-fit values of the standard .teviations: the era values are very similar at different wavelengths, whereas the CrCphvalues show relevant variations. In order to appreciate this point, we first discuss the meaning of these parameters. From the definition of ~Cph, this parameter is a function of the variability, between different cells, of the number of photoreceptor molecules, but not of A. Therefore if, at different wavelengths, light is absorbed by the same type of photore~eptor, the O'Cphvalues should be the same. From Table 1, it ~an be seen that this parameter has similar values at 500 nm and 550 nm, while it increases slightly at 450 nm and is clearly higher at 400 nm. This suggests the presence of two photoreceptors (thisexplains the " s " in parentheses after "photoreceptor" throughout this paper), one absorbing at 550 nm, 500 nm and partly at 450 nm and the second at 400 nm and partly at 450 nm. The increase in O'Cphwith decreasing wavelength can be accounted for by assuming that the variability between cells in the number of molecules of the second photoreceptor is greater than that of the first photoreceptor.

1

207

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I

lo °

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Fig. 10. Reflectivity(full lines) and transmittance (broken lines) of the stigma vs. the incidence angle. Thickercurves are calculated for a high absorbance,thinnercurvesfor a low absorbance. Sineshchekov [9] analysed the photoreceptor sensitivity by using electrophysiological methods on single H. pluvialis cells, and found that it reached a maximum at 500 nm, was slightly lower at 450 nm, low at 550 nm and lowest at 400 nm. These results are consistent with our Cph best-fit values. More importantly, the action spectrum of the photophobic responses obtained by Sineshchekov shows a number of bands, which substantiates the claim that more than one photoreceptor is probably involved in light absorption [9]. The same conclusion is suggested by our best-fit values of ~rcph. The similarity between the simulation results and the experimental data proves that the simulation model is based on reliable assumptions.

Acknowledgements 6. Conclusions Two main conclusions emerge from the discussion of the experimental results. (i) The shape of the stimulus-response curves can be explained by assuming that the structure of the photoreceptive apparatus shown in Fig. 6 is valid. This further confirms the widely accepted view that the photoreceptor(s) responsible for the photophobic response of H. pluvialis is concentrated in the stigma region and shaded, on one side, by the stigma itself [ 6,8,18 ]. (ii) This kind of photoreceptive apparatus means that the characteristics of the stimulusresponse curves shown in Fig. 8 will be affected both by the features of the stigma and the photoreceptor(s). We attempted to obtain independent information about the stigma and photoreceptor by fitting a mathematical model to the experimental data. As this is an indirect method, the results should be considered with caution. Nevertheless, the values shown in Table 1 are in keeping with the experimental results obtained by other techniques.

We are grateful to S. Lucia for helpful suggestions on the cell cultures, F. Dinelli for help with the optical equations reported in Appendix A and M. Barbi and G. Cercignani for critical reading of the manuscript.

Appendix A In this section, the following details of the simulation program are described: (i) the equation used to calculate the absorbance and reflectivity of the stigma; (ii) the equation used to take into account the dependence of the cross-section on the incidence angle; (iii) the method used to take into account the shape of the light flashes; (iv) the algorithm used to extract at random the orientation of the cells; (v) the equation used to calculate the intensity of the light falling on the photoreceptive apparatus. The stigma was considered to be a homogeneous dielectric thin film (its thickness being about one-quarter of the wave-

C. Cecconi et al. /Journal of Photochemistry and Photobiology B: Biology 33 (1996) 201-209

208

length used), and its reflectivity (reflected light/incident light) and transmittance (transmitted light/incident light) were calculated accordingly [ 19]. The reflectivity (R) is given by R=

r 2 ( . 1 + k2 - 2k cos 2fl__ .I 1-1-k2r4 -- 2kr2 cos 2/3]

(A 1)

where r is the refractive coefficient at the stigma/surrounding medium boundary; /3= (21r/a)n,dcos t5r (phase shift between two successive reflected rays), where a is the wavelength of the incident light, nr is the refractive index of the stigma, d is the stigma thickness and 6r is the refractive angle of the incident light on the stigma (Fig. 5); k = 10 -zaL/d, where A is the stigma absorbance when the optical path is d and L is the path through the stigma for any incidence angle 6i. L is given by Snell's law L=

d

(A2)

1/1 - (hi sin t~i/nr) 2 where ni is the refractive index of the surrounding medium and 6i is the incidence angle of the light falling on the stigma. The refractive coefficient r depends on the polarization of the incident wave. For TE waves (electric field perpendicular to the plane of incidence), r is r± =

n i COS 6 i - - n r COS 6 r

(A3)

n i COS ~ i - nr COS t~r

while for TM waves (electric field parallel to the plane of incidence), r is r, =

n~ cos 6 i - ni cos 6~ n rcOS ~+n

(A4)

i c O S t~i

We carried out our experiments using non-polarized light. The reflectivity was thus calculated as Ref= (Ref± + Refit) / 2, with Ref± = TE wave reflectivity and Ref, = TM wave reflectivity. Eq. (A1) gives the reflectivity as the sum of all the consecutive reflections occurring in a thin film with an infinite width. When the width is finite, as in the case of the stigma, Eq. (A1) gives values in excess. However, we calculated this error to be lower than 1% for incidence angles smaller than 86 °, and about 4%-5% for higher incidence angles; this neglects the absorbance inside the stigma, which further reduces the error. Thus the values given by Eq. (A1) are rather good approximations. The transmittance of the stigma was calculated as follows a2t2 Ts= 1 + ot4rn-2ra,2 cos 2fl

(A5)

where a = 10 -aUd and t=~/(1 - r 2 ) . As discussed above for the reflectivity, the total transmittance was assumed to be T=(T± +Tu)/2, with T± = T E wave transmittance and TII = TIVI wave transmittance. The values of d, n~and nr were kept constant: n~= 1.33 (the refractive index of water), nr = 1.55 [ 18] and d = 100 nm.

Fig. 9 shows the transmittance and reflectivity of the stigma as a function of the incidence angle of the light, for high and low stigma absorbance. By considering that the electric dipole of the molecules of the photoreceptor lies in the plane of the membrane [ 14,15], the effective value of Cph can be calculated as

Cph(•i) : Cph ( 1 - ½ sin

t~i2)

(A6)

We considered that the photoreceptor molecules are spaced out in such a way that screening between them does not occur at any incidence angle of light. To take into account the cone of lamp light, we schematized each lamp as a flat grid which has the same area as the light cone base (Fig. 7). The grid was divided into 25 equal quadrants, each representing the source of a light ray. The intensity of each ray was equal to 1/25 of the flash intensity. The rays converge on the microslide surface with an angle equal to/3 in Fig. 3. The incidence angle of the central ray (represented by a continuous line in Fig. 6) is equal to 90 ° - a (Fig. 3). The incidence angles of the other rays were calculated accordingly. In order to calculate the incidence angle of each light ray on the stigma ( ~i in Fig. 6), we chose a Cartesian reference system with the x-y plane parallel to the wall of the microslide in contact with the Peltier device. Then, using Snell's law, we calculated the direction of each light ray inside the microslide (the refractive index of the light propagation medium (air) was considered to be equal to unity, and the refractive index of the suspension solution of the algae was assumed to be equal to 1.33). We then extracted at random the direction of the unit vector perpendicular to the stigma. The unit vector is defined when its projection on the z axis and the qb angle, which its projection on the x-y plane forms with the x axis, are known. Both • and the z component were extracted at random in a uniform manner, in the ranges between 0 and 2~and between + 1 and - 1 respectively, using a suitable algorithm. Once the direction of the light ray and that of the unit vector are known, 8i is calculated. Single light rays fall on the microslide surface with different incidence angles and undergo different reflections at the air/glass boundary and then at the glass/water boundary. They thus reach the photoreceptive apparatus with different intensities. These intensities can be evaluated by calculating the transmittance at the above-mentioned boundaries: T= 1 - r 2, with r 2= [(r±2-krll2)/2]. The refractive index of the microslide walls (borosilicate glass) was considered to be np= 1.52. The thickness of the walls is much greater than the wavelengths used, and so they were not considered as thin films. The program also takes into account the reflections and refractions undergone by the single light rays inside the microslide. The most important is the reflection on the internal surface of the wall which is in contact with the Peltier device. The reflections on the other surfaces have negligible intensities.

C. Cecconi et al. / Journal of Photochemistry and Photobiology B: Biology 33 (1996) 201-209

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