New trends in photobiology: Intracellular processing of a spatially non-uniform stimulus: Case study of phototropism in Phycomyces

J. Photochem. Photobiol. B: Biol., 19 (1993) 161-186 161

New Trends in Photobiology (Invited Review)

Intracellular processing of a spatially non-uniform stimulus: case study of phototropism in Phycomyces

Leonid Fukshansky Institute of Biology 2, University of Freiburg Schaenzlestrasse 1, D-7800 Freiburg i. Br. (Germany)

(Received February 9, 1993; accepted March 30, 1993)

Abstract

The phototropic reaction is manifested in asymmetrical (non-vertical) growth caused by unilateral irradiation in organs which under symmetrical irradiation (or in darkness) grow vertically. Thus, the spatial non-uniformity of both stimulus and response is the core of this phenomenon. A comprehensive theory should, therefore, treat phototropic signal processing as a sequence of pattern formations. Some steps toward such a theory have been carried through recently in the study of phototropism of giant sporangiophores (fruit bodies) of the lower fungus Phycomyces. Among other spatial factors, this classic phototropic object is also characterized by dichroism of the non-uniformly spaced membrane bound photoreceptor(s). Quantitative treatment of the spatial aspects - light pattern, pattern of excitation (energy absorbed per second on the site of photoreceptor location), pattern of adaptation - revealed some previously ignored general problems of spatially distributed signal processing. Among these are severe restrictions of the conventional interpretation of the action spectra, as well as of the purely temporal experimental kinetics of response and adaptation. Furthermore, this approach has provided new information about the location of the photoreceptor(s) and about the mechanism of negative tropism. New effects have been predicted and confirmed experimentally, and the physiological and genetic dissection of the presumably branched phototropic transduction chain now appears feasible. An intriguing question now is whether the following combined problem can be approached: on the basis of theoretical calculations, and measurements under incident light of varying polarization states, of the phototropic responses of sporangiophores immersed in media with varying refractive index, can one find both the in situ orientation of the receptor molecules (more exactly, their transition dipoles) and the spatial perceptivity of the phototropic mechanism? Some general aspects of spatially distributed signal processing and adaptation are also discussed.

Keyworak Directional growth, Lens effect, Symmetry breaks, Pattern of excitation, Adaptation, IJV-receptor.

1. Introduction

The giant single-celled sporangiophore of the fungus Phyco~yces is an object of notable interest for the study of phototropism - directional growth in response to asymmetrical irradiation [l]. Both the light-induced responses of the sporangiophore (phototropism) - and transient changes in the vertical growth rate due to changes in intensity of the symmetrically applied light (photomecism) operate in the enormous intensity range between 10m9 and 10 W mm2. The diversity of features of this presumably simple mechanism of signal pro-

cessing, including stimulus perception, signal am- plification, adaptation and response (growth), all confined to a single cell, prompted workers in the field, firstly Max Delbriick the brilliant leader of Phycomyces research in the 1960s and 197Os, to view it as a model object for the entire sensory physiology which might facilitate insights into the general principles obscured in more complex organisms [2]. Today we must admit that despite many achievements [3-161, the phototropism of Phycomyces cannot be seen as such a paradigm for two reasons. First, most of the new results have revealed an unexpected complexity of the

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162 L. Fukshansky I Phototropism in Phycotnyces

Phyccmyces transduction chain. Second, our current knowledge of light-induced signal processing in higher organisms, e.g. vision, is in many ways more advanced than our knowledge of the phototropism ofPhycomyces, especially the biochemical and molecular biological aspects [17, 181.

In the last five years a novel approach emerging in phototropic studies on Phycomyces has been to assign again a model character to this object. However, this time it is not in the broad scope of sensory physiology but in the limited area of spatially distributed signal processing in aneural organisms. Of course, spatial heterogeneity is an intrinsic property of practically all processes in highly structured and compartmentalized living cells and organisms. We will distinguish, however, the cases where the spatial structure of the signal must be processed by the transduction chain. Pho- totropism is a typical example of such a phenomenon. It appears owing to spatial non-uniformity of the light intensity and results in spatial non- uniformity of the growth rate. The entire signal processing is essentially a sequence of pattern formations.

Clearly, a quantitative analysis of single patterns and their transformations should give valuable information about the transduction chain. Con- versely, there is a danger of erroneous concepts and overinterpretation when the spatial aspects are neglected [19]. The last two statements are by no means new revelations; they were always acknowledged. However, they could only really be applied on the basis of a quantitative treatment of spatial factors. Such treatment is greatly fa- cilitated here by the physical nature of the phototropic stimulus and the special shape of the sporangiophore.

This is the first summary of the methods used and the information they have provided. Hopefully, some of the conclusions and ideas can be trans- ferred to other objects where such quantitative analysis is less feasible. This is the hope behind my. remark above on the possible role of the Phycomyces sporangiophore as a model object for a limited research area.

The next section (Section 2) contains a con- densed survey of phototropism in Phycomyces. This is not a review of the entire field but rather a compendium necessary for the subsequent introduction of the quantitative description of the spatial aspects (Section 3). Also summarized are some of the results obtained on this basis (Section 4). The concluding part (Section 5) contains a discussion of the constraints on the application of spatial analysis. Some problems arising when the

spatial factors are neglected as well as future applications of the spatial methods are envisaged.

2. General background

2.1. The specimen and basic responses The structurally simple cylindrical cell (diameter

about 100 pm) consists of the cell wall, the plasma membrane adjoining it, cytoplasm and an axial vacuole which is separated from the cytoplasm by a tonoplast and forms an internal cylinder (diameter 50 pm). A symmetrical light stimulus, administered as unilateral irradiation on the rotated (4 rev min-l) sporangiophore (Fig. l(A)) or as bilateral irradiation of a resting sporangiophore (Fig. l(B)), causes a transient increase (Fig. 2(A)) or decrease (Fig. 2(B)) in the growth rate, owing to an increase or decrease in light intensity respectively. The light-sensitive zone (which is also approximately the growing zone) begins immediately below the spherical sporangium and is about 2 mm long [l].

Under unilateral irradiation with blue light (Fig. l(C)), two strong focal bands occur on the non- irradiated (distal) side of the cylindrical boundary.

Fig. 1. Light-induced growth and phototropism, basic treatments. (A) Symmetrical stimulus due to unilateral irradiation of the fast rotating (4 rev min-‘) sporangiophore. (B) Phototropic balance under bilateral irradiation, I, and I, are intensities of the reference and testing light respectively. (C) Positive bending under unilateral irradiation with blue light. (D) Negative bending under unilateral irradiation with UV light.

L. F&handy I Phototropism in Phycomyces 163

GI. J

IO 1 3

‘1 1 if I

---TV-- I I

Fig. 2. Light-induced growth, basic protocols (above) and responses (below). Photomecism and test of symmetrical adaptation with symmetrical testing stimulus: G, growth rate; t, time; Z.. Z,, intensities of the adapting and testing light respectively; 7, latency.

Fig. 3. Light-induced growth and phototropism, basic protocols (above) and responses (below). Test of the symmetrical adaptation with asymmetrical testing stimulus: B, angle of bending; r, phototropic latency; r,,, intrinsic latency. Other designations as in Fig. 2.

This lens effect somehow increases the growth rate on the distal side to a level higher than that on the proximal side, which results in a bending toward the light source (positive tropism). The kinetics of the positive tropism induced through

Since light generally enhances the growth rate (Fig. 2) and the internal light flwr through the

the transition from symmetrical to unilateral ir-

proximal part exceeds that through the distal part, the positive tropism implies that it is not the total

radiation of the same intensity (by stopping the

radiation but rather the shape of the light distribution induced by the lens effect which is es-

rotation) are shown schematically in Fig. 3(A) [l].

sential for phototropism. The decisive role of the lens effect has been proved by immersing sporangiophores in media with different refractive indices [20]. With increasing refractive index, the lens effect and the phototropic bending decrease until the so-called compensation point is reached. At this critical value of refractive index (slightly below the refractive index of the sporangiophore), the residual lens effect is counterbalanced by attenuation within the sporangiophore and phototropic bending ceases. Any further increase in

refractive index results in a negative bending response.

As found by Curry and Gruen [21], in the far UV below 305 nm, even sporangiophores placed in air show negative tropism (Fig. l(D)). At A = 305 nm no bending occurs (the natural compensation point). This switching to negative tropism has been explained [2] as being due to the strong UV absorption by gallic acid concentrated in the vacuole (attenuation hypothesis).

2.2. The measured features With the basic set-up in Fig. l(A) the light

growth response (photomecism) is studied according to the protocols shown in Fig. 2(A) (step- up) and Fig. 2(B) (step-down) as well as more complex treatments such as pulses or intensity oscillations. Several parameters of the responses shown in Fig. 2 can be measured. The threshold is about lo-’ W rnm2. The amplitude depends strongly on the intensity range. It can reach 50 pm min-l. Reciprocity holds between 0.06 and 64 s. For definite fluence levels the light growth response shows optima at different pulse durations, indicating complexity of the initial steps of the transduction chain [22]. The latency T varies between 3 and 9 min, increasing at small intensities. Fluence-response curves and an action spectrum of the light growth response have been constructed [231.

The set-up in Fig. l(B) permits phototropic balance studies. The test intensities It at different wavelengths A, which counterbalance the opposite fixed stimulus (definite reference wavelength A,, fixed intensity IX) should be determined. Action spectra of the phototropic balance have been constructed for different A, and different intensity ranges [21, 241.

The set-up in Fig. l(C), (D) permits the study of phototropic bending. For bending caused by changes from symmetrical to unilateral irradiation with the same intensity, the kinetics of bending are shown in Fig. 3(A). For positive tropism the intrinsic latency 7. is about 6 min. The threshold (10T9 W mT2), bending rate and intrinsic latency of positive tropism have been measured for different wavelengths [2,25]. For the less investigated UV-induced negative tropism, shorter latencies and faster kinetics have generally been found. This has been explained on the basis of the contribution of the distal part to the directional growth being nullified as a consequence of the strong attenuation in the UV range.

The set-up in Fig. l(C) also permits measurement of the photogravitropic equilibrium. In a

164 L. Fukshansky / Phototropkn in Phycomyces

unilaterally irradiated sporangiophore the light signal is counteracted by the gravitropic stimulus, resulting in an intensity-dependent equilibrium angle of bending. Based on the light intensities at different wavelengths necessary to establish a fixed equilibrium angle, an action spectrum has been constructed [26, 271.

2.3. Adaptation of photomecism tests and theory The light growth response is governed not only

by the applied light intensity but also by the internal state - adaptation state - of the specimen, which in its turn changes upon light action. The adaptation changes are delayed with respect to the growth response (otherwise the adaptation could not be differentiated from the growth measurements). Figure 2 shows the basic experiment: the specimen preadapted to intensity 1, responds after delay T to the increased (Fig. 2(A)) or decreased (Fig. 2(B)) symmetrically applied intensity It with an increase or decrease in the growth rate G; the growth rate then returns to the previous level because the sporangiophore becomes adapted to the new intensity level It. Further step-up of the light intensity would effect the same sequence of events: transient growth response and readapta- tion. It is this feature which enables the sporangiophore to maintain its enormous adjustment range (1O-g-1O W m-*).

The time course of dark (& <Ia) and light (1* > la) adaptation can be tested by measuring the growth rate response to standard pulse stimuli at different times after the onset of the new intensity level It as described below. As shown experimentally, the growth rate G responds to the ratio of the pulse intensity IP to the intensity I,=A to which the sporangiophore has been preadapted at the moment of pulse application. This leads to the notion of the subjective stimulus S, i.e. the absolute stimulus I,At (At is the pulse duration) corrected by a factor representing the current adaptation state A:

S = (I* -A)At,‘A

This equation yields the adaptation level A of the sporangiophore (specified in the units of light intensity to which it would become adapted at equilibrium to possess this level); S is found from the standard plots G(S) constructed for different S values in experiments in which the adaptation changes have been saturated to different actual equilibrium levels A = It. For the measured growth rates G at different times, one can read from these plots the values of S and estimate the current adaptation levels. The adaptation kinetics found

in this way are approximately exponential:

d/f/& = (It -A)/b

with AO=Ia, A, =It and the adaptation-rate constant b=6 min.

This elegant description introduced by Delbrtick and Reichardt [3] combines both light-induced kinetics, i.e. those of response and adaptation. Later experiments demonstrated limitations of this theory [28] and revealed contributions to adaptation from different parts of the transduction chain (sensory z)s. effector adaptation 183). Note that the quantity A characterizes vertical growth under symmetrical irradiation and is outside the scope of analysis of spatially non-uniform stimulus and response.

2.4. Phototropic bending never adapts If a special arrangement (tropostat) ensures for

a long time the incidence of a unilateral light beam normal to a bending sporangiophore, it bends into a helix of arbitrary complexity, i.e. it never adapts [29]. This is a paradox (often called the main paradox of phototropism) because the non- uniformly distributed light within the sporangiophore should in the long run be adapted in every point and the bending should cease. The following results and considerations are connected to this problem. Growth is accomplished by stretching of the growing zone. The growing zone does not become longer because for every amount of length increase, a corresponding amount of length at the bottom is converted into secondary wall. It does not become thinner either because for every amount that it becomes thinner, new wall material is interpolated along the helically arranged mi- crofibrils. This results in a “spiral growth” [30]. Dennison and Foster [31] suggested that the plasma membrane with the receptor molecules located on it also rotates clockwise, thus providing stimulus variations for the receptor molecules and pre- venting their adaptation (merry-go-around hypothesis). By bilateral irradiation with unequal intensities (1:0.61) and a counter-rotation of 10” mm-‘, the bending can be reduced ahnost to zero [31]. This was interpreted as evidence for a rotating photoreceptor population. There are, however, strong objections to this interpretation (see ref. 32). First, spiral growth of the wall does not imply that the plasma membrane grows in the same way. Second, the bending results from the distal vs. proximal growth difference, predominantly at the bottom of the growing zone where the rotation ceases. Third, negative bending under UV stimulus could not be reduced by the counter-rotation.

L. Fukshansky / Phototropkm in Phycomyces 165

Medina and Cerda-Ohnedo [33] treated the merry- go-around hypothesis quantitatively to predict fluence rate-response curves for photogravitropic equilibrium.

Although phototropic bending does not adapt, it can be used to test the adaptation of the light growth response (Fig. 3). The experiments shown in Figs. 3(A) and 3(B) differ only in the relationship between the adapting 1. and testing It intensities. For It=l, the intrinsic phototropic latency r. elapses before the onset of bending. For It<l., a larger latency, T= r. + AT, appears because the specimen needs time to adapt to the lower intensity It (dark adaptation). Also light adaptation (& > la) causes an increase in T. One can use a sequence of such experiments with different It to plot T as a function of It/I,. This does not give the real kinetics of adaptation changes as in the case of probing the adaptation state with testing pulses (Section 2.3). Like &/I,, the quantity r is a char- acteristic of the adaptation states, but it is not the time variable. However, one can make a plau- sible assumption that the delay AT is equal to the time the system needs to cross the distance between the two adaptation states involved. Only on the basis of this assumption can we compare the adaptation kinetics obtained from the two different methods.

Another important point is that during a phototropic latency test the changes in adaptation state take place under a non-uniform pattern of light, which itself prevents adaptation of the phototropic response.

In addition to the two protocols of the adaptation tests described above (symmetrical adaptation symmetrically tested, symmetrical adaptation asym- metrically tested), studies of the so-called phototropic inversion present the case where both light patterns - that for establishing and that for testing the adaptation state - are asymmetrical [29, 34, 351. Both step-up and step-down of the light intensity elicit a transient reversal of a steady- state phototropic bending under unilateral irradiation. Furthermore, large increases in light intensity applied from any direction also cause a transient reversal of the bending direction, but it always remains within the pre-established bending plane.

2.5. Genetics, transduction-chain assay and photoreceptor infonna tion

Studies of Phycomyces have been greatly facil- itated by the isolation and characterization of many behavioral mutants, including those affecting the phototropic reaction (mad mutants). A tentative

scheme ascribing different types of phototropic mutants to particular pathways between stimuli and responses is shown in Fig. 4 [32, 361. The mad mutants form two classes: class 1 (mad A, B, C, I) contains mutants with no effect on the other two tropisms (avoidance of obstacles and gravitropism). Mutants from class 2 (mad D, E, F, G, H) have all three tropic responses abnormal. In contrast to the gene products A and B, the gene products D, E, F, G, H and C do not affect other light-induced responses. For the best studied mad A, B and C mutants, an elevated threshold (lo3 to lo6 fold) in the blue spectral range, longer latency, defects in growth regulation at higher intensities and abnormal adaptation kinetics have been reported. The abnormal action spectra of the photogravitropic equilibrium indicate that mad B and C mutants have defects in the photoreceptor [37]. Since these mutants also show the strongest deviations from the wild-type in their adaptation kinetics, it was further inferred that sensory adaptation is mediated by the phototropic receptor system [32].

Among the assays used to approach the intracellular events are the light-induced absorbance changes (LIAC). Such changes, manifested as an increase in absorbance at 460 nm relative to that at 345 nm in response to near UV irradiation, regenerate in subsequent darkness in the wild- type but not in the mad C mutant [38, 391. Also, light-induced fluorescence changes (excitation 345 mn, emission 450 nm) have been found [38]. Both flavins and pterins come in question as the photoreceptors for LIAC. However, there is no evidence that these effects are connected with phototropic reception or transduction.

A specific assay for kinetics in the transduction chain is to apply intermittent light pulses separated by a short variable time interval and to study the phototropic response as a function of the spectral and temporal characteristics of this treatment [9, 401. It was shown that two unilateral pulses (first

Gravity

Obstacles mod D,E,F,G,H tropirms mrcirms

Light - mod1

Fig. 4. Ascribing the phototropic mutants to the different pathways between the stimuli and responses. After Cerdi-Olmedo and Lipson [l] (modified).

166 L. Fukshansky / Phototropism in Phycornyces

blue, second red) given periodically every 30 s cause a photogravitropic response which is dependent on the time interval At between the first and second pulses and which is generally lower than the response to the first pulse alone. The counteraction between the first and second pulses is preserved even if both pulses are blue. For a longer interval (50 s) three At values can be found where the inhibiting effect of the second pulse has maxima; one of these disappears when the second pulse is red.

By analogy with other light-induced sensory responses, the electric-field changes due to ion- channel activity and the possible role of second messengers in signal transduction have been investigated by several groups. The comprehensive study by Weiss and Weisenseel [ll] shows that blue light induces hyperpolarization of the hyphal membrane potential in the wild-type and to a lesser degree in single mutants (double mutants show no effect). Calcium ion affects the chitinase activity in Phycomyces, which is light regulated through certain calmodulin-dependent and calmodulin-independent processes [41,42]. Also, evidence for calmodulin action in phototropism (in state-l sporangiophores) has been obtained [19]. Recent important results by Sineshchekov and Lipson [16] demonstrate the participation of Ca2+ in the dark adaptation. The adaptation kinetics studies by the phototropic latency method as described above (Section 2.4) were combined with the immersion of sporangiophores in solutions of CaCl,, LaCl, (a Ca2+ channel-blocker), MgCl, and the Ca2+ chelator EGTA. The latency was decreased by CaCl,, increased by LaCl, and (to a lesser extent) by EGTA and was not affected by MgC12.

The phototropic photoreceptor has not been identified. However, studies at different levels have provided valuable photoreceptor information. Meistrich et al. [43] attempted to localize the photoreceptor by using a laser microbeam (4 pm width) to irradiate a sporangiophore immersed in a fluorocarbon with a refractive index matching that of the cytoplasm. They found phototropic bending at different positions of the microbeam, including near the outer wall. It has been concluded that some photoreceptor molecules are located in the vicinity of the plasma membrane, but that most of them are located between the plasma membrane and the tonoplast. The second conclusion was based on a rather speculative model and is in contradiction with the notion of a membrane-bound photoreceptor established by Jesaitis [41-

Jesaitis compared the changes in growth rate due to intensity variations with those due to variations in the polarization of light. Using different species of Phycomyces with different light attenuation, he was able to exclude multiple internal reflections and dichroic attenuation of light within the sporangiophore as a presumable cause of the stronger action of transversely polarized light compared with longitudinally polarized light. In this way the existence of a preferable orientation of the photoreceptor and its association with a membrane have been proven.

It is widely accepted that the photoreceptor or at least an essential component of the photoreceptor system must be a flavoprotein. This was conjectured first of all from the shape of different action spectra and then strongly supported by several other findings. Substitution of riboflavin by roseoflavin [6] caused a corresponding shift in the blue-light action spectrum. Flavin inhibitors also affect some blue-light-induced responses [44]. Specific riboflavin-binding sites with a concentration above 10e6 M have been isolated from the membrane fraction of Phycomyces [7]. Delbriick estimated theoretically the minimal receptor concentration necessary to ensure the tropic signal on the background of statistical fluctuations as being equal to 10m6 M [2]. Although the required flavoprotein concentrations have not been found, in situ the binding sites may well be in constant interaction with free flavin molecules. In fact the concentration of free flavin is high enough to ensure a dynamic steady state in this interaction with most of the binding sites occupied by flavin molecules. Apparently, the blue-light receptor in Neurosporu functions in this way [45].

Along with many lines of evidence indicating a complex photoreceptor, arguments have been advanced in favor of a pterin as part of this system [46]. After the first detection of pterins in Phy- comyces (IIPLC with a fluorescence assay [47]), different patterns of both flavins [14] and pterins [15] relative to the wild-type have been discovered in mad mutants. The question of whether these pigment patterns have a connection with the phototropic reception is, however, still open. The nature of the photoreceptor has been discussed in detail in a recent review [48].

2.6. Compltx-ity of the photoreceptor (survey of evidence in favor)

The most frequently claimed result concerning photoreception is the statement of the multiplicity of photoreceptors, based on the phenomenological evidence summarized below:

L. Fukshansky / Phototropism in Phycomyces 167

(a) Irradiation with periodic pulses to produce the photogravitropic response shows that some light-sensitive processes (in the red and blue spectral areas) occur in the early transduction steps between 1 s and 1 min after light absorption ([9, 403 see Section 2.5).

(b) The reciprocity failure for the light-growth response at definite fluence levels shows that some changes in the state of the photoreceptor system and/or early transduction steps occur in the mil- lisecond range after light absorption ([22] see Section 2.2).

(c) Fluence rate-response curves of the bending rate for light-grown sporangiophores have different slopes at different wavelengths. The corresponding action spectrum of photogravitropic equilibrium deviates from that for phototropic balance ([27] see Section 2.4).

(d) The action spectra of phototropic balance depend critically on the reference wavelength and on the intensity range ([24] see Section 2.4).

(e) The fluence rate-response curves of the bending rate and the corresponding action spectra obtained for the two consecutive stages of bending of the dark-grown dark-adapted sporangiophores (i.e. for two parts of one bending curve) are different. These two stages - earlier bending and later bending - are separated in this case by a period of no bending. The later bending ceases for lower intensities. The conclusion was made that two photoreceptor systems, optimized for lower and higher intensity ranges, operate in phototropism ([25] see Section 2.4).

(f) Dark-adaptation kinetics measured with the phototropic latency method are wavelength dependent [49]. Furthermore, interposition of a period of irradiation with low-intensity light during the adaptation process accelerates the adaptation. This acceleration shows a wavelength dependence different from that of phototropism [50, 511. This led to the conclusion that some light-dependent reactions with their own photoreceptors affect the dark adaptation process.

(g) Mutants mad B and mad C both lack two of the blue-light photogravitropic action maxima, at 414 nm and 491 mrr ([27, 371 see Section 2.5).

3. Quantitative description of spatial factors

3. I. Light pattern As mentioned before, neither perception nor

transduction of a phototropic stimulus is concentrated at a point or spread uniformly. Every stage appears to have a spatial pattern, and any kinetics

are spatiotemporal. The first pattern is that of the light; this is brought about by several partial effects accompanying light propagation: light focusing or a lens effect (which plays the dominant role), light attenuation due to absorption and scattering, multiple internal reflections, the state of polarization of the incident wave and interference effects.

The theory which accounts for all these effects (see ref. 52 for details) is restricted to the case of a planar wavefront entering a cylinder orthogonal to the cylinder axis (Fig. 5(A)). A cross-section of a sporangiophore is considered as being divided into two concentric areas: the external ring (bounded by the plasma membrane and the cell wall) containing the cytoplasm and the internal circle (bounded by the tonoplast) containing the vacuole (Fig. 5(A)). The particular geometry of the cylinder causes the refracted rays to concentrate at the non-illuminated (distal) half of the cylinder (lens effect), forming a caustic. In that domain an intersection of differently refracted rays occurs (Fig. 5(A), (B)). Using simple differential-geometry methods, formulae for the caustic and the wave- fronts have been derived. Based on this, the focusing properties of the differential rays (Fig. 5(B)) were described. Superposition of the crossing rays incorporates interference. The resulting intensity distribution is calculated on a lattice which is also used in calculating the intensity distribution due to multiple internal reflections.

The following parameters have been measured and used in the calculations [54]: refractive indices of the cell wall, cytoplasm and vacuole, extinction (i.e. sum of absorption and scattering) coefficients of cytoplasm and vacuole. A three-dimensional light pattern is shown in Fig. 5(C). In Fig. 6(a) a typical light profile on the plasma membrane (on the cylinder boundary) is plotted as intensity VUS. azimuthal angle cp. The azimuthal range is from 0” to 180” (the same as given in Fig. 5(A)), which corresponds to the proximal side of the sporangiophore. The dashed line presents the proximal part of the light profile. The continuous line presents the distal part mapped into the proximal side so that the ordinate of the continuous curve at a point cp shows the intensity at point 360”- cp, i.e. at the corresponding point on the opposite side of the sporangiophore.

There are three sources of error in a theoretical profile like that shown in Fig. 6(a): (i) inaccuracy in measurements of the optical parameters; (ii) errors due to the idealized model of the sporangiophore (optical properties fluctuate, the shape of the cross-section deviates from a circle); (iii) errors due to neglecting scattering gain - an

168 I. Fukshhnmky I Phototropism in Phycomyces

(4 180"

Fig. 5. Light propagation in Phycomyces. (A) Cross-section of a sporangiophore. The outer circle represents the plasma membrane and the inner circle represents the tonoplast. The arrow marks the direction of the illumination. The azimuth scale is given relative to this direction. (B) Ray crossing and focusing of ray bundles - two contributions to the lens effect. (C) Three- dimensional plot of fluence rate at the cylinder boundary. After Fukshansky and Steinhardt [19] and Fukshansky and Richter [53] (modified).

additional amount of radiation redistributed into an area of interest owing to scattering (in the calculations only attenuation due to scattering, i.e. scattering loss, has been taken into account, since multiple scattering in a transparent sporangiophore is negligible). It was possible to verify the cal-

culations on the basis of the recent measurements by Dennison and Vogelmann [56]. They succeeded in measuring light immediately outside the distal side of a sporangiophore with a thin (4 = 5.5 pm) fiber optic probe. Figure 7(B) shows their experiment performed on a sporangiophore and Fig. 7(A) shows the same experiment on a water-filled glass vial (+= 14.5 mm) used as an optical model. The geometry of the experiments is shown in the insets. The tip of the probe was positioned in physical contact with the sample and the light source was rotated azimuthally. Curves a and b present light intensity as a function of azimuth, measured during rotation. Curve b shows measurements conducted with the probe oriented normally to the sample surface; curve a shows measurements with the probe tilted at 47” to normal. The resulting profile (curve c) is the sum of curves a and b. This approach was necessary because the rather small acceptance angle of the probe does not permit all the incoming rays to be collected at a given location of the probe. Thus, curves a and b give the intensity as measured in the two portions.

While the profile in Fig. 7(B) strongly deviates from the theoretical profile in Fig. 6(a) (the positions of focal bands coincide but the band heights and the contrast ratios differ markedly), the profile measured on the glass vial corresponds exactly, except that the thoeretical peaks near 10“ and 170” due to internal reflections are not measurable with an external optical probe. We could show, however [53], that the discrepancies between the experimental (Fig. 7(B)) and theoretical (Fig. 6(a)) profiles correspond to the intrinsic instrumental error of measurements arising from the low azimuthal resolving ability.

Consider the relationships between the size of the optical probe and the sample in both geometries (see insets in Fig. 7(A), 7(B)). In the case of the glass vial, the probe covers an azimuthal angle CX= 2.58’ on the periphery of the sample. This means that the radiative Aux measured at a “point” is in reality the integral over an azimuthal range of 2.58’. This region is small enough to be viewed as a point, and one can expect that in moving along the profile the probe will then give the true fine structure of the profile. However, the diameter of a sporangiophore is a factor of 150 less than that of the glass vial. Accordingly, on its periphery the azimuthal region of the same probe is 150 times larger, i.e. a= 620’.

The vertically shaded belt represents such a region in both Fig. 7(A) and 7(B). By taking measurements with such a large probe one ascribes

L. Fukshansky I Phototropism in Phycomyces 169

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Fig. 6. (A): cartoon illustrating the formation of an excitation profile on the boundary of the cylinder populated by oriented photoreceptor molecules (each of these is represented by a man with radially oriented nose). The energy absorbed per second at each azimuthal point depends on the angle between the E-vector of light (arrow) and the transition dipole (the left and right hands represent dipoles at different wavelengths). (B): unilateral light and excitation profiles for A = 480 nm. Optical parameters as measured by Steinhardt et al. [54]. Capture cross-sections of a flavoprotein (d-amino acid oxidase) are taken from Massey et al. [55]; (a) light profile; (b) excitation profile, randomly oriented receptor; (c) excitation profile, radially oriented receptor; (d) excitation profile, tangentially oriented receptor.

to a single azimuthal point (in our illustration this is the central point of the belt) the entire radiation contained within the shaded region. This quantity is proportional to the average flux in the shaded region. Obviously, such a measurement will yield distorted images of all the details which are smaller than or equal to the shaded region. It smooths sharp edges, lowers thin peaks and converts sin- gularities into sloping curves.

Figure 8 shows the quantitative effect of this “smoothing” on the measured profile. The profile from Fig. 7(A) is digitized with the azimuthal size of the probe being equal to 2.58’. Then it was calculated how this profile would be “seen” by a probe with an azimuthal size of 3” (Fig. 8(b)), 6” (Fig. 8(c) and 10” (Fig. 8(d)). Thus the measured data on the sporangiophore profile (Fig. 7(B)) represent fairly well the theoretical profile from

170 L. Fukshansky / Phototropism in Phycomyces

A \fiber optics / Fig. 6(a). However, in the shaded area a very low

01s vial

Azimuth (degrees)

B 1 fiber optic

40 60 80 100 120 140

Azimuth (degrees)

Fig. 7. Measurement of light intensity with a fiber-optic probe (+=5.5 pm) as published by Dennison and Vogelmann [56]. The geometry of the measurement is shown schematically in the insets. The shaded belt represents an optical resolution of 6”. (A) Measurement outside a water-filled glass vial (c#J= 15.4 mm). (B) Measurement outside a sporangiophore of Phycomyces (q5=100 pm). After Fukshansky and Richter [53].

6O I00

/+&k&%%L M /v 80 100 120 140

Fig. 8. (a) Digitized profile of Fig. 7(A) used for computer simulation of “smoothing”. (b)-(d) Different areas of integration of the profile shown in (a). Integration values a are given above the graphs. After Fukshansky and Richter [53].

level of scattered light was detected, in contrast to the theoretical value of zero (for details see refs. 53 and 56).

3.2. Ekcitation pattern on the plasma membrane The actual input of signal processing is, however,

not the light profile but the excitation profile (profile of energy absorbed per second). Its shape depends on the light profile as well as on the location and orientation of the photoreceptor. The cartoon in Fig. 6(A) illustrates the origin of an excitation profile on the plasma membrane. The man with the radially directed nose represents the orientated pigment molecule; his hands represent the transition dipoles at two different wavelengths. The energy absorbed by a population of dichroic molecules depends on the angle between the transition dipole and the E-vector of light (shown as an arrow). In the cartoon the E-vector is fixed, but for non-polarized light its direction changes randomly, remaining, however, in a plane directed normally to the wave vector of light. Owing to a lens effect the real picture is more complicated, but two basic features of the excitation profiles can be derived from this cartoon: the shape of an excitation profile does not coincide with that of an underlying light profile and it is wavelength dependent. This is illustrated in Fig. 6(B) on the basis of realistic calculations. One light profile (Fig. 6(a)) is shown together with three different excitation profiles emerging on the basis of this light profile for different orientations of the transition dipole: radial transversal (Fig. 6(c)), tangential transversal (Fig. 6(d)) and random (Fig. 6(b)). Note that, as can be seen on the ordinate, even the order of magnitude of the total absorbed energy is different for different dipole orientations. As one might expect, the randomly oriented (non- oriented) dipole gives the coincidence between the shapes of the light and excitation profiles. The theory of excitation profiles is given in refs. 19 and 57.

3.3. Spatial factors - an overview It is instructive to summarize here the spatial

aspects which underlie specific features of phototropic signal processing. First is the non-uniform light pattern as described above. At the place where the photoreceptor is located we have the pattern of energy absorbed per second (excitation pattern). Both the total absorbed energy and the shape of the excitation pattern depend on the light pattern as well as on three photoreceptor parameters, namely the absorption coefficient, the

L. Fukshansky I Phototropism in Phycomyces 171

polar angle (angle between the transition dipole and the vertical axis), and the azimuthal angle (angle between the transversal projection of the transition dipole and the radius of the vertical sporangiophore at the location of the photoreceptor molecule). All three photoreceptor parameters are wavelength dependent. For this reason alone, any phototropic action spectrum considered as a function of the absorption coefficient alone (i.e. as compared with the absorption spectrum of the same but non-oriented photoreceptor) is a @on’ arbitrarily distorted (an example is given in Fig. 15, Section 5.2).

Before proceeding to the subsequent patterns, a general statement about pattern transformations should be formulated. At least some of these transformations involve non-local signal processing, i.e. a local azimuthal value of the emerging pattern is not a function of the value of the preceding pattern at the same locus (as it is when the light pattern is transformed into the excitation pattern) but of the values of many loci, maximally of the entire preceding pattern [19]. Non-local processing is implied by the main paradox of phototropism (see Section 2.4) - “adapting mecism VUS. non- adapting tropism” - and is the only way to resolve this paradox. (In the case of a local processing each local value of excitation will sometimes be adapted and the bending of a sporangiophore mounted on a Dennison’s tropostat [29] will stop.) Therefore, it is not merely a hypothesis but a proven direct consequence of the experimental findings. Only the candidates for the physical mechanism providing the non-local processing are still hypothetical: rotation of the plasma membrane (merry-go-around hypothesis [31, 321, see Section 2.4), diffusible participants of the transduction chain discussed by Castle [58], Hertel [5] and Poe et al. [57], and electrophysiological mechanisms involving ion fluxes and ion channels.

Obviously, non-local processing must appear before the formation of the adaptation pattern, which should not match the pattern of excitation. This discrepancy was implicitly assumed by Del- briick and Reichardt [3] when they postulated an average constant adaptation level over the cross- section of a unilaterally irradiated sporangiophore.

Further spatiotemporal transduction steps lead to a non-uniform pattern of the light-induced potential growth rate which persists because of the lasting discrepancy between the patterns of excitation and adaptation. The actual directional growth results from the superposition on the potential growth-rate pattern of the constraints arising from the topological properties of the sporan-

giophore (non-disrupting cylinder), the structure of the growing zone (directional growth appearing not along the entire zone but only at the bottom of it) and the elasticity of the cell wall.

The interaction between the pattern of potential growth rate and the constraints ensures that bending occurs in a fixed plane approximately normal (under unilateral irradiation) to the plane separating the illuminated from the non-illuminated side. As this light-induced subdivision of the cross- section of the sporangiophore into the proximal and distal sides appears, a one-dimensional profile of azimuthal phototropic sensitivity becomes established on the boundary of the cylinder before any bending begins. This profile (which as yet has not been approached either by theory or by experiment) is defined operationally and is connected to the question of how the subsequent transduction steps evaluate the shape of the excitation pattern. There are two aspects contained in the notion of azimuthal sensitivity. First, some characteristics of the excitation pattern (for example the contrast ratio between the focal bands and the central well) may be more effective in enhancing growth than the total flux value. Second, a fixed growth enhancement in the center of either the distal or proximal side will contribute much more to bending than the same enhancement near the boundary between these sides.

The excitation is in the form of a function (not just a number!) which should be evaluated by the subsequent transduction steps. This precludes the conventional interpretation of the action spectra (independently of the exclusion by receptor orientation as mentioned above), because the basic equation of action spectroscopy can only be derived for numbers, not for functions (for details see ref. 19). This can be illustrated by the following example. Assume that several properties of the excitation pattern (e.g. contrast ratios, excess of scattered light over the phototropic threshold in the shade region and others) provide weighted contributions to the phototropic input to be processed. If this input is not proportional to the incident intensity (why should it be?), then the relation between the ratio of the intensities providing equal responses at two different wavelengths and the corresponding absorption coefficients of the photoreceptor are arbitrarily distorted (i.e. the conventional interpretation of an action spectrum is impossible).

All the phototropic kinetics, including those of response and adaptation, are spatiotemporal. For their characterization (remember the non-local signal processing!) partial differential equations

172 L. Fukshansky I Phototropiwn in Phyconzyces

containing the excitation pattern as a source term are connected by a non-branched section of the should be written. Since this pattern varies for transduction chain, any of our experimental or different receptor orientations (e.g. different wave- theoretical studies should yield the conclusion that lengths), the adaptation kinetics under unilateral a third pattern located between them is also sym- irradiation (during phototropic latency tests) are metrical. If this appears not to be the case, then wavelength dependent. They can also have different either there is an additional, still obscure, signal rates for symmetrical and asymmetrical irradiation input into this section or some other assumption of the same intensity. Thus, even use of the excess underlying our conclusion is wrong. The same of phototropic latency r-r0 (see Section 2.4) as consideration is, of course, applicable for asym- a measure of the rate of symmetrical adaptation metrical patterns or for symmetry breaks resulting may be questioned. from stimulus changes.

The same arguments are valid for the bending rate. In addition, during bending the orientation of the transition dipoles with respect to the electric vector of the light changes continuously. This complication is also present in studies involving photogravitropic equilibrium.

Thus the spatial factors bring severe compli- cations. Fortunately, they also open new possi- bilities, as discussed in the next section.

4. Spatial analysis: methods and results

4.1. Analysis of symmetry and symmetry breaks As discussed above, conventional studies of re-

sponse, adaptation and other measurable quantities as functions of time (purely temporal kinetics) and as functions of stimulus-parameters (fluence-response curves and action spectra of pho- toresponses) are subject to severe limitations when the stimulus is to be processed as a spatial pattern. An appropriate generalization of such studies necessary to overcome these limitations (treatment of the spatiotemporal kinetics and spatial functions of parameters) is not feasible, at least not until the information required for comprehensive math- ematical modeling of the transduction chain has been accumulated.

However, the quantitative treatment of spatial factors provides new approaches and relatively simple tools which can be applied to dissection and characterization of a transduction chain. In the case of asymmetrical growth in response to an asymmetrical stimulus one can expect that one of these tools may be the symmetry and symmetry break of a spatial pattern. The use of symmetry analysis of a transduction chain is based on the following postulate: a transduction chain or a part of it by itself can neither create nor abolish any asymmetry of a pattern. Of course, this is true only for asymmetry exceeding the resolving ability of the chain.

The following example shows how this postulate can be applied. If two symmetrical spatial patterns

Proceeding along these lines, we can consider the symmetry of patterns as being dependent on internal parameters such as photoreceptor orientation or adaptation state. This substantially expands the scope of the analysis. We can, for example, then predict the phototropic balance spectrum for a photoreceptor with known or assumed localization, orientation and absorption cross-section (see Fig. 15 and Section 5.2). This can be done by calculating the pattern of excitation under bilateral irradiation, for a chosen reference wavelength and intensity, with variable intensities of light at the testing wavelengths. The maximal possible distal-proximal symmetry (the absolute distal-proximal symmetry for a photoreceptor located on the plasma membrane corresponds to the complete matching of the dashed and continuous curves in Fig. 6(a)) should be achieved each time by varying the testing intensity. The values of the testing intensities providing maximal symmetry are used to construct the action spectrum. This procedure is called direct pattern adjustment since it simulates the experiment directly: the symmetry is achieved by varying the light intensity while the photoreceptor parameters are fixed. One can also proceed in the opposite way: consider the testing intensities as fixed and establish the symmetry by varying the photoreceptor parameters. This inverse pattern adjustment can, in principle, be used to derive information about the photoreceptor if the fixed testing intensities have been taken from a real balance spectrum. The inverse pattern adjustment is, however, hardly feasible in this straightforward way. Even if the photoreceptor in the spectral and intensity range of interest is a single molecule (which of course is not guar- anteed), there are still too many parameters to be estimated from one measurement. Therefore, the simulation of a phototropic balance experiment can only be viewed as an auxiliary means of analysis in a complex investigation combining many tools affecting the symmetry of a pattern: polarized light, immersion in media with variable refractive indices, time averaging of stimulus (see Section 5.3).

L. F&handy / Phototropism in Phycomyces 173

The results presented in the subsequent sections illustrate these general considerations.

4.2. i%e blue-light photoreceptor cannot be located on the tonoplast

As presented in Section 2.5 the dichroic blue- light photoreceptor is membrane bound; therefore, it should be located either on the plasma membrane or on the tonoplast. These two working hypotheses have been tested [12] by analysis of symmetry breaks occurring in the excitation profiles owing to changes in the refractive index of the external medium in the course of immersion experiments (see Section 2.1). The experiments [20] were carried out as follows. A unilaterally irradiated sporangiophore immersed in media of different refractive indices (various mixtures of fluorocarbons) shows decreased bending as the external refractive index n, approaches the value of the refractive index of the cytoplasm Iti. At some critical value of the external refractive index, n, =nC <ni, zero bending occurs. At higher values of n, (n, >n,, supercritical indices), negative bending occurs.

Obviously, at the point n,=n, the excitation profile weighted by the profile of azimuthal phototropic sensitivity (see Section 3.3) is perceived by the subsequent stages of the transduction chain as the maximally symmetrical stimulus and is transformed into a symmetrical pattern of growth rate. Where the variable n, crosses the point It,, a symmetry break occurs. For n, <n,, the excitation profile has positive asymmetry (i.e. asymmetry which produces positive bending). For n, > n,, the profile has negative asymmetry. To test the two working hypotheses one should analyze changes in the excitation profile in the vicinity of the symmetry break at both possible locations of the photoreceptor. Since the receptor orientation is unknown, three extreme orientations of the transition dipole - longitudinal, transversely tangential and transversely radial - should be studied simultaneously. Only if the same result is obtained for all three dipole directions can it then be accepted, because any dipole direction can be represented as a sum of three orthogonal components along these extreme directions, and hence the corresponding excitation profile can be represented as a sum of three profiles calculated for these three directions.

Figure 9 shows the excitation profiles calculated for longitudinal (A), transversely tangential (B) and transversely radial (C) directions of the transition dipole for the receptor molecule located at the plasma membrane. The left-hand column presents the results for n, = 1 (sporangiophore in air),

A 12.3376

c

0 45 90 135 180

Azimuth Azimuth

Azimuth Azimuth

Fig. 9. The receptor is assumed to be located at the plasma membrane. Comparison of excitation profiles in a sporangiophore placed in air (left) and in fluorocarbon medium with the critical refractive indexn, = ni = 1.306 which results in zero bending (right). Panels (A), (B), (C) represent longitudinal, transversely tangential and transversely radial orientation of the transition dipole respectively: - --, proximal part of the profile; -, distal part. Calculation carried out for A=495 nm. After Steinhardt et al.

WI.

and the right-hand column for n, = n, = 1.306 (non- bending sporangiophore in fluorocarbon). The calculations are performed for A =495 nm. Panel A shows the actual light profile, which is, however, proportional to the excitation profile for a longitudinal dipole, i.e. has the same shape. As one can easily see, the shape of the excitation profile is dramatically changed at the compensation point compared with that in air. For all dipole directions the profiles are highly symmetrical, and the focal bands are either abolished or shifted to the bound-


ary between the distal and proximal sides where they cannot contribute to directional growth.

Figure 10 presents the same information as Fig. 9 but for a receptor molecule located at the tonoplast. Even for a specimen in air, the lens effect at the tonoplast is strongly reduced. There are no focal bands and the degree of asymmetry is rather small. It disappears completely at the compensation point. The question arises whether a photoreceptor at the tonoplast can sense a change in refractive index producing the symmetry break which in the experiment is then transformed into a change in bending direction.

The answer is given in Fig. 11, and the answer is no. The middle column here is the same as the right-hand column in Fig. 10; it describes the profiles at the critical value II,. The left-hand

A 2.2116 1.12607

0 45 90 135 180 Azimuth

Z 16.5843

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2

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0 45 90 135 180 45 90 I35 180

--. /I\. :

45 90 I35 I80 Azimuth

Azimuth Azimuth

x 10-4 x10-5

C 2.1251 ,- 12.5398r

Azimuth Azimuth

Fig. 10. The same treatment as in Fig. 9 except that the photoreceptor is assumed to be located at the tonoplast. After Steinhardt et al. [12].

column presents the results for a subcritical value n=L280<n,, where a positive angle of photogravitropic equilibrium ( + 20”) has been observed. The right-hand column shows the profile for a supercritical value IZ = 1.320 >n,, where a negative photogravitropic equilibrium angle of -20” has been found. There are no differences between the subcritical and super-critical profiles, i.e. the photoreceptor does not see changes in the stimulus which reverse the bending.

In contrast, a photoreceptor molecule located on the plasma membrane senses these changes, as can be seen from Fig. 12.

4.3. The “natural compensation” results not from attenuation but from the action of a separate UK- photoreceptor

As presented in Section 2.1, the negative tropism in the far UV range appears because practically no light reaches the distal part owing to strong absorption by the gallic acid which is produced in the cytoplasm and accumulated at a high concentration in the vacuole (attenuation hypothesis [2]). The natural compensation at A = 305 nm marks the point where the lens-effect dependent action of the photoreceptor located on the plasma membrane (“focusing advantage”) is exactly counterbalanced by this screening contribution (“attenuation disadvantage”). In therms of the spatial analysis (Section 4.1), this means a symmetry break of the excitation profile as a function of the optical parameters at A =305 nm and a change from positive (A > 305 nm) to negative (A <305 nm) asymmetry.

As the calculations show, however, this is not the case here. The shape of the light profile at 305 nm is between those shown in Figs. 6(a) and 13(a) (see Fig. 3 in ref. 13) with strong focal bands. Also, at shorter wavelengths where negative bending occurs, the shapes of the excitation profiles have positive asymmetry; the light profile in Fig. 13(a) and the representative excitation profile for transversely tangential dipole orientation in Fig. 13(b) are calculated for A=280 mn. Even when the absorption coefficient of the vacuole exceeds by 100 fold that which has been actually measured and that for an artificially increased vacuole diameter, the profile retains positive asymmetry (Fig. 5 in ref. 13). Actually, the reason for this becomes obvious after a glance at Fig. 5(A): most of the light forming the focal bands bypasses the vacuole.

Thus the attenuation hypothesis is challenged. Moreover, according to the discussion in Section 4.1, another light-mediated input should exist which promotes negative tropism and counterbalances

A 1.15752r

175

Azimuth Azimuth Azimuth


5 2

0

,‘ d

6.4452

t s 0

B z

lz 0.0000


Fig. 11. The receptor is assumed to be located at the tonoplast. Comparison of excitation profiles in a sporangiophore in fluorocarbon medium with subcritical refractive index ni = 1.280 <n, (left), critical refractive index ni =nc = 1.306 (middle) and supercritical refractive index ni=1.320>n, (right). Panels (A), (B), (C) re p resent the same dipole orientation as in Fig. 9. Calculation carried out for A=495 nm. After Steinhardt et al. [12].

the positive action at the compensation point. The idea of this factor being a separate W photoreceptor was corroborated by the shorter latency and faster kinetics of negative tropism (which in the framework of the new hypothesis could not have been explained on the basis of the attenuation as presented in Section 2.1). Another point was the adaptation which in the far UV seems to have completely different kinetics or even disappear (see ref. 13 and Section 5). The following predictions have been made. (1) Since the absorption spectra of the proposed UV receptor and the “regular” blue-light receptor overlap (which is to be expected from the flavin absorption spectrum),

natural compensation points at other wavelengths in the far UV may be found; they will appear for each wavelength at a specific intensity value. (2) Given that a compensation point can be found, an increase in intensity should cause negative bending and a decrease in intensity should cause positive bending, since the receptor providing negative bending has smaller adaptation (if any) than the receptor providing positive bending. (3) Since symmetrical irradiation with far UV promotes growth, the negative tropism (i.e. faster growth of the proximal side) mediated by the proposed W receptor should be not due to the lens effect but due to attenuation; the photoreceptor should be

176 L. Fukshansky I Phototropism in Phycomyces

x 104

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Fig. 12. As Fig. 11 except that the receptor is assumed to be located at the plasma membrane.

located in an area with a small lens effect, e.g. on the tonoplast or in the cytoplasm.

Two initial predictions have been directly confirmed by experiment. Positive tropism at lower intensities in the far UV has been found at four different wavelengths [13]. The compensation spectrum - a curve separating the area of positive (below) and negative (above) tropism on the “wavelength-intensity” plane - connects the compensation points which have intensity coordinates between lo-’ and 10e5 W rne2. (The compensation spectrum in Fig. 6 of ref. 13 is erroneously about 1.5 decades too high and will be redetermined

P%)

The novel UV-induced positive tropism as demonstrated by immersion experiments is promoted by the lens effect. This is an experimental refutation of the attenuation hypothesis since the immersion abolishes the lens effect alone without changing the relation between the total amount of light on the distal and proximal sides (i.e. the focal bands should have been present before immersion).

A comparison of Figs. 13 and 14 brings out unmistakably the discrepancy between the sym- metries of stimulus and response as discussed above. Figure 13 presents light and excitation (for a transversely tangential oriented dipole) profiles in air at 281 nm for the compensating intensity (vertical growth). Figure 14 shows those profiles

L. Fukshansky / Phototropkm in Phycomyces 177

I 2.0427

a

Azimuth (cp) 135 I80

Azimuth(p)

Fig. 13. Light (a) and excitation (b) profiles for a sporangiophore irradiated at A=281 nm (in air) with the intensity providing natural compensation (vertical growth). After Popescu et al. [13].

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3.4446 ’

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0 0.0000 0 45 90 I35 I60 0 45 90 135 I60

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Fig. 14. Light (a) and excitation (b) profiles for a sporangiophore irradiated at A = 281 nm (in fluorocarbon) with the same intensity as in Fig. 13. With this symmetrical profile negative bending occurs. After Popescu et al. [13].

in fluorocarbon (lens effect abolished, negative bending). Not only does a totally asymmetrical stimulus (Fig. 13) cause a symmetrical response, but a strong increase in symmetry of the stimulus (Fig. 14) breaks the symmetry of response. This implies that an additional spatially asymmetrical factor counterbalances the asymmetrical profile in Fig. 13(b). Furthermore, this factor, unlike the lens effect, is not removed by immersion; it causes the asymmetry of response under these conditions.

An obvious suggestion is now to look for W- specific mad mutants having unaffected blue-light responses. The first such mutants have already been found. The characterization of these mutants requires a major effort since they seem to require cultivation as a heterocaryon because the mutation itself is perhaps lethal (Cerdi-Olmedo et al. [60]).

5. Limitations, future aims

5.1. Limitations imposed on spatial analysis It is necessary to recognize the restrictions of

the conclusions and arguments of spatial analysis; these appear for several reasons. First, the light pattern underlying further analysis has until now only been calculated for normal incidence of a planar wavefront on the sporangiophore. There- fore, neither treatments with oblique light incidence nor irradiation in the time course of bending can be analyzed quantitatively by these methods.

There are, however, many important problems which require analysis of the balanced responses or of the earlier stages of the phototropic reaction before the bending starts.

A fundamental problem arises in connection with the possible multicomponent structure of the photoreceptor. It appears that there are problems for which the spatial analysis is applicable independently of the structure of the photoreceptor (single vs. multicomponent) and the conclusions are valid for any structure. There are problems for which the area of applicability of the spatial methods may be more restricted and the conclusions should be modified for a multicomponent receptor. There are also problems which cannot be discussed for multicomponent receptors. Usually the structure of the photoreceptor is unknown. Therefore, the general question of whether the unknown structure of the photoreceptor may be a source of erroneous conclusions should be included in the treatment of each problem. This question is formulated as follows: can a multicomponent receptor in a situation which contradicts our conclusion mimic the behavior of a single receptor in a situation which corresponds to our conclusion?

We consider now whether the conclusions which have been drawn for a single photoreceptor in Sections 4.2 and 4.3 must be dismissed or modified under the assumption of a multicomponent receptor. The conclusion in Section 4.2 is that a photoreceptor located on the tonoplast is blind with respect to the lens-effect mediated change in stimulus which causes the reversal of bending. Obviously any part of a multicomponent receptor will be blind on the tonoplast independently of the nature of its interactions. Thus, this conclusion is generally valid.

Our conclusion from Section 4.3 is that the negative bending is not due to attenuation but to a novel W receptor which is not located on the plasma membrane. The existence of focal bands and the positive tropism in the UV range, both

178 L. Fukshansky I Phototropkm in Phycomyces

removable by means of immersion, do not depend on the complexity of the photoreceptor. However, the question is whether the jump from positive to negative bending, due to a change in the intensity of the unilaterally applied light, can be caused by a photoreceptor constellation different from that in our conclusion. For example, could two counteracting receptors with different absorption spectra both located on the plasma membrane cause this jump? The answer given by a comparison of Figs. 13 and 14 is negative. No interaction of components whatsoever can transform the highly asymmetrical light profile (Fig. 13) into a symmetrical signal and simultaneously transform the rather symmetrical profile of the same intensity (Fig. 14) into an asymmetrical signal.

Thus both results in Section 4 remain unques- tioned by any possible multiplicity of the photoreceptors. However, the situation may be more complicated when the spatial analysis involves model constructions and more complex interactions between patterns (see Section 5.3).

5.2. Limitations on other considerations imposed by the spatial factors

Many aspects of the phototropic studies are affected by the spatial factors. Here the question concerning possible errors in our conclusions reads: can a spatially heterogeneous transduction chain in a situation which contradicts our conclusion mimic the behavior of a homogeneous chain in a situation corresponding to our conclusion? The subsequent discussion covers only one group of considerations which all result in the claim of multiplicity of the photoreceptors but are based on different observations and provide different kinds of evidence.

The possible long lifetime (up to minutes) of the metastable excited states of flavins and their rich redox behavior favor (as has been pointed out by Hertel [5]) the involvement of a flavin- photoreceptor in the photochemical processes and reaction cycles which can display complex kinetics and have adaptive properties.

However, the arguments in favor of a multicomponent receptor and the suggested properties of its components should be advanced very cau- tiously and be confronted with the counter-arguments, in particular those based on the spatial non-uniformity of the involved states and processes. Unfortunately, in the last few years this has not always been the case. Therefore, the following considerations are presented in the provocative manner of a devil’s advocat, to facilitate the discussion and make up for lost time. All the ar-

guments are discussed successively below in the order listed in Section 2.6.

(a) The pulse experiments prove only that in one or several steps after the photoreaction (in the time range within 1 min) a red-absorbing component of the transduction chain is formed. The second blue pulse can be mediated by the same photoreceptor as the first pulse; its inhibiting action may appear on the basis of a pulsating movement of some diffusible intermediate caused by the pulse stimulus, as well as on the basis of delayed adaptation oscillations (resonance effects).

(b) The Bunsen-Roscoe law of reciprocity can in principle be violated even when a single photoreceptor and a single primary photoreaction mediate the response. This can happen as a result of the kinetics in the transduction chain (for detailed treatment see ref. 61). As a consequence of the reciprocity failure, a different kind of dependence of response on the pulse duration at different total fixed fluence levels can occur. This is by no means evidence for different photoreceptor systems acting at these different fluence levels. The rather short pulses producing this effect may indicate that steps very close to the photoreceptor or even the kinetics of an excited state are involved.

(c) If a case should be found where a single oriented receptor provides fluence rate-response curves of bending with the same slopes at different wavelengths, this should be considered a miracle. First of all, the transition dipoles have different orientations at different wavelengths, providing different excitation profiles and, therefore, different spatiotemporal kinetics in the transduction chain (see Section 3.3). Furthermore, the angles between the E-vector of light and the transition dipoles vary at different wavelengths during bending in a completely different way. Even the total absorbed energy will have different kinetics at different wavelengths. This energy absorbed per second and its pattern affects the bending rate at every moment and vice versa. The action spectrum of photogravitropic equilibrium resulting from these kinetics cannot be identical with the action spectrum of the phototropic balance because of the completely different geometry of the vectorial interaction between light and photoreceptor.

(d) Let us consider one example which is instructive for all statements involving the action spectra of an oriented photoreceptor. We perform the direct profile adjustment as defined in Section 4.1 in order to simulate the action spectrum of the phototropic balance. To do this we take an absorption spectrum of a flavoprotein (d-amino acid oxidase as measured by Massey et al. [S],


see continuous curve in Figs. 15(A) and 15(B)), postulate the dipole orientation at different wavelengths every 10 nm within a chosen spectral interval, lix the reference wavelength (A, = 450 nm) and reference intensity (Ir = 1) and try to achieve at each wavelength the highest distal-proximal symmetry of the bilateral excitation profile (i.e. the best coincidence of the central parts of the distal and proximal sides of a profile as presented in Fig. 6(a)) by varying the testing intensity It. Those values It which produce the highest symmetry are used to construct the action spectrum.

In the first simulation performed for a range from 400 to 500 nm, a random orientation of the photoreceptor, i.e. of the dipoles at each wavelength, was postulated. The action spectrum obtained under this assumption is shown as a dashed line in Fig. 15(A). The difference between the initial absorption spectrum and the resulting action spectrum is due to the optics, which are auto- matically accounted for in the calculation of the light profile. As expected, small differences in the light attenuation at different wavelengths within the almost transparent sporangiophore result in a rather non-significant distortion of the action spectrum.

I .28433 A

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In the second simulation, performed for the range from 375 to 445 nm, it is postulated that all dipoles have transverse orientation. The dipole at 450 nm is transversely radial. For other dipoles a shift along the spectrum towards shorter wavelengths results in an azimuthal shift in the orientation of 5.3” counter-clockwise per 10 nm. The action spectrum obtained under this assumption is shown as a dashed line in Fig. 15(B). The dramatic distortions of this spectrum are due to both optical artifacts and receptor orientation. Since according to Fig. 15(A) the optics only introduce minor distortion, the strong effect of the receptor orientation becomes evident.

Obviously, another choice of reference wavelength can cause strong changes in the shape of the action spectrum. Therefore, the dependence of this shape on the reference wavelength cannot be used as an argument in favor of the multiplicity of the photoreceptor. It is also clear now why the shapes of the action spectra of the phototropic balance and of the photogravitropic equilibrium may differ.

There are also many reasons for the dependence of the balance action spectrum on the intensity range. One of these might be the increase in

a

,I\ OI 300 350 400 450 500 550 300 350 400 450 500 550

325 375 425 475 525 325 375 425 475 525

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Fig. 15. Deviations of the action spectrum of phototropic balance (---) from the absorption spectrum of assumed photoreceptor (-, d-ammo acid oxidase as measured by Massey et al. [S]). Action spectra obtained by direct profile adjustment. (A) Deviations due to optical artifacts; randomly oriented photoreceptor. (B) Deviations due to both optical artifacts and different orientations of dipoles at different wavelengths. After Fukshansky and Steinhardt [19].


absolute value of the scattered light with increasing incident intensity. At high intensity the scattered light in the shade azimuthal region can exceed the threshold level and thus strongly affect the contrast ratio. This can happen at lower intensities for the wavelengths of the maxima of the action spectrum. The result will be a flattening of the action spectrum at high intensities which has been observed.

(e) This is the weakest argument in this series. Here all the criticisms from both point (c) and point (d) are relevant.

(f) In general the adaptation kinetics should be wavelength dependent in the case of a single photoreceptor as discussed in Section 4.3. The effect of the intermediate low-intensity light which accelerates the adaptation is very interesting. It shows that some light-dependent reactions affect the adaptation mechanism. This, however, does not involve the phototropic photoreceptor, since the spectral range mediating the accelerating mechanism is inactive in promoting the phototropic reaction.

(g) Discrepancies in the photogravitropic spectra of the wild-type and mad mutants have per se no connection to the problem of whether the photoreceptor is multicomponent or not.

5.3. Outlook Many current problems can now be studied by

spatial analysis in combination with other methods. The most obvious consequence of the results reported above is the branched character of the transduction chain (at least when considering the blue-light vs. UV stimulus). A genetic dissection of the branched chain can be approached by the comparative characterization of the classic mad mutants and the novel UV mutants (threshold in blue light vs. in the UV range, natural compensation). In parallel, a functional dissection can be attempted in two directions. First, factors should be looked for which affect blue-light and UV mediated tropism in a different way. Second, one can try to allocate some specific components of the transduction chain to the different branches. Such a treatment can be performed for phototropic adaptation as discussed below.

One can ask whether the individual components of the adaptation mechanism are confined to different branches. (In the extreme case they all can be concentrated on a single branch.) This can be investigated in a comparative study of the adaptation kinetics in specially designed experiments with exchangeable stimuli for both promoting and testing the adaptation states. One compares blue-

light vs. UV preadapted objects and tests their adaptation states with the blue-light vs. UV testing stimuli. Initial results of such experiments are presented in Fig. 16 (Roessler [62]). The experimental procedure can be described using Fig. 3(B), where a variable dark interval k is inserted between the symmetrical irradiation (with I,) and the unilateral testing irradiation (with It <I,). Within this interval the current adaptation state will change (dark adaptation) toward the dark- adapted stationary state, passing through the

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aptation levels corresponding to different intensities (see Sections 2.3 and 2.4). If for some At value, At =A@*), the adaptation state should at the end of the dark interval exactly reach the level It, then the phototropic latency 7 after onset of the unilateral stimulus It will have the shortest possible duration. It will be equal to the intrinsic latency r. occurring in the experiment shown in Fig. 3(A), where the testing intensity exactly corresponds to the adaptation level, &=I,. For either At < At(&) or At > At(1J, larger values r > r. should be observed because the specimen needs additional time for dark or light adaptation. Repeating the latency tests with variable At and fixed I,;one can estimate the time interval required for the current adaptation state to reach the level It. This will be exactly the At value providing the minimal phototropic latency At(&). The curve connecting the closed circles in Fig. 16(A) presents a sequence of such tests. The ordinate shows the phototropic latency 7 obtained with the preadaptation level 1, = 10-l W m-* and testing intensity It = 10m5 W m -’ after different dark intervals At (abscissa). The minimal latency (and therefore the current adaptation level of 10e5 W m-‘) was reached after 55 min. For identical experiments with different It values, times of passage through different adaptation levels have been estimated. These kinetics are presented in Fig. 16(B).

This method, already applied by Galland and coworkers [50, 511, is a sort of zero-point analysis. It is rather cumbersome (only one point of a kinetic curve is gained from a series of experiments) but has two advantages compared with the standard phototropic latency method described in Section 2.4. First, the intrinsic kinetics are measured directly and not approximated by the values of phototropic latency. Second, the adaptation kinetics under symmetrical and asymmetrical irradiation are not mixed together; they can be clearly separated and also compared if necessary (see Section 2.4).

Our purpose in applying this experiment is, however, to compare (see Fig. 16(A)) blue-light (closed circles) and W (closed triangles) testing stimuli. The curve for UV tests does not show minimum latency, indicating a basic difference in the kinetics of the adaptation state. Any conclusion will, however, be premature until analogous tests with UV-promoted preadaptation and also with light adaptation kinetics have been carried out. Also, special tests with experimental set-up identical with that shown in Fig. 3(A) should be performed to ensure that the minimal latency is indeed equal to the intrinsic latency 7m

The basic line of spatial analysis is, however, to contribute to our understanding of the shape, origin and kinetics of the different spatial patterns and their interactions in the course of signal processing. It is equally, along with other approaches, an indispensable component of a comprehensive study of a spatially non-uniform transduction chain. At the moment the following very preliminary set of spatial factors to be evaluated can be suggested: (a) receptor(s) localization, (b) receptor(s) orientation, (c) pattern of phototropic sensitivity, (d) non-local signal processing, (e) pattern of adaptation.

Often these factors can only be studied in com- mon. For example any treatment of factor (c) involves information (known or postulated) concerning factors (a), (b) and (d), while information about factor (e) for some (especially short-time) treatments can be omitted from consideration.

The following general research program can be envisaged. Model descriptions of the phototropic signal processing involving the spatial factors should be confronted with the appropriate experiments in order to verify or reject our hypotheses concerning these factors.

This program can be carried out only if there exist a sufficient number of feasible approaches and tools providing the experimental tests and also if a suitable quantitative description of the corresponding spatial factors is feasible at this stage. To what extent are these two necessary conditions fulfilled?

The following experimental approaches targeting spatial factors are feasible.

(1) Immersion in media with variable refractive index to manipulate the degree of symmetry of the light pattern.

(2) Bilateral irradiation with different intensities of counteracting fluxes to control the relation between the total fluxes on the distal and proximal sides.

(3) Application of light with variable polarization state to affect the shape of the excitation profile and the total absorbed energy.

(4) Rotation of the specimen with variable velocity to achieve temporal averaging of the stimulus over different time intervals. (The notion of time averaging is specified in the example given below, see Fig. 17.)

(5) Turns of the specimen of 90” and 180” around the cylinder axis after short preadaptation (within the time span of latency) with simultaneous changes in the wavelength, intensity and/or polarization of the unilaterally applied light. These experiments conducted by Hertel [5] and Wulff [63] are very well suited for spatial analysis.

182 L. F&handy / Phototropism in Phycomyces

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(6) Probing with a vibrating microelectrode of the three-dimensional pattern of ion fluxes around the growing zone of a sporangiophore immersed in a weak electrolyte. This is the only direct study of a pattern considered to be connected with light- induced growth regulation. These experiments, planned and conducted under the guidance of Professor Weisenseel are in the initial stage; the existence of external ion fluxes has now been demonstrated.

This list is by no means complete. Different combinations of the tools presented ensure flex- ibility of the experimental tests.

As for quantitative descriptions of the spatial factors, they cannot exceed the stage of our knowledge. At the current stage no approach can be built up on the basis of a detailed description of states and processes in terms, say, of partial differential equations. Therefore, the first steps should be taken by estimating the global results

of interactions, setting the intervals of influence, indicating directions and limits of changes and, of course, analyzing symmetry and symmetry breaks. For example, the non-local signal processing can be presented at the fnst stage as an interaction between azimuthal neighbors with a few simple characteristics. It is also reasonable to treat numerous partial problems corresponding to the experimental set-up. In the course of these studies information may be accumulated for a more general and rigorous description.

It is reasonable to exemplify the above general discussion by concrete problems. Let us return to the experiment described in Section 2.4 providing evidence in favor of the merry-go-around hypothesis which had been advanced to explain non- adapting phototropism. The counter-rotation (10” min-‘) of a sporangiophore irradiated bilaterally with unequal intensities (ratio 1:0.61) abolished the bending which otherwise would occur. The

L. Fukshansky / Phototropirm in Phycomyces 183

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18. Excitation profiles under unilateral irradiation with polarized light at 450 nm. Not only the shape of the profile but also the total absorbed energy is affected by the state of polarization (note the different scales). (A) E-vector of light parallel to the Z-axis (the axis of the sporangiophore); the transition dipole is at 80” to the Z-axis and radial. (B) E-vector of light at 45” to the Z-axis; the transition dipole is transversely tangential. (C) E-vector as in (B); the transition dipole is transversely radial.

subsequent discussion was concentrated on the question of whether this evidence proves or not the suggested rotation of the population of photoreceptor molecules (together with the plasma membrane where they are located) as a cause of non-adapting phototropism.

Surprisingly, both disputing parties did not re- alize that the abolishing of bending due to counter- rotation could be evidence against the merry-go- around hypothesis, as is shown here using a concrete profile. The bilateral excitation profile in Fig. 17(A) simulates bilateral irradiation without the counter-rotation for a transversely tangential oriented photoreceptor having a flavin absorption coefficient at 510 nm. (Of course, another absorption coefficient or orientation would not affect the subsequent argument.) We use here an “un- folded” profile along the full azimuthal range without mapping the distal side into the proximal

azimuthal range, as this is more convenient in this case. In an experiment this profile causes regular bending which would not adapt, as has been demonstrated on Dennison’s tropostat for unilateral irradiation (Section 2.4). According to the merry- go-around hypothesis, the adaptation does not take place because the excitation profile shown in Fig. 17(A) rotates with respect to the photoreceptor owing to “spiral growth”; therefore, single azimuthal loci are exposed to a changing local intensity to which they have no time to adapt. The counter- rotation of the entire sporangiophore nullifies the rotation; thus the profile in Fig. 17(A) stops with respect to the receptor and hence it can be adapted at each azimuthal locus so no bending occurs. This argument has one weak point. Before the adaptation is manifested, a much faster bending should occur, as is generally the case under asymmetrical (unilateral) irradiation. Therefore, observing no

184 L. Fukshansb / Phototropism in Phycomyces

bending under conditions of counter-rotation is evidence against the merry-go-around hypothesis or at least not in favor of it.

Another more likely reason why the bending under counter-rotation ceases is shown in Figs. 17(B) and 17(C). This reason is the temporal averaging of the stimulus. Only because of temporal averaging are we able to simulate symmetrical irradiation by unilateral irradiation of a fast rotating sporangiophore. It is expected that the phototropic mechanism averages the light flux over l-2 min. The curves in Figs. 17(B) and 17(C) show the excitation perceived by the phototropic mechanism during the counter-rotation (10” min-l) when the stimulus is averaged over 1 or 2 min respectively. These two profiles have strongly decreased asymmetry compared with the profile without counter-rotation (note the changed ordinate scale) and may well be perceived as symmetrical. The reader may compare the temporal averaging with the spatial averaging demonstrated in Fig. 8. These are related phenomena. However, the spatial averaging changes the information about the shape of a profile perceived by our measuring device, while the temporal averaging, discussed here, changes the shape of a profile as it is perceived by the specimen itself. The crucial experiment proposed by Thomas Richter is very simple: if reversal of the counter-rotation gives the same results, then the temporal averaging hypothesis is supported and the merry-go-around hypothesis is refuted. Temporal averaging studies in combination with bilateral profiles having different degrees of asymmetry and different polarization of light can give valuable information about receptor orientation, the profile of phototropic sensitivity and the kinetics of the interaction of the neighboring azimuthal areas.

The most important information about photoreceptor orientation is expected from bilateral irradiation with the same wavelength but different polarization states. By arriving at phototropic balance with different polarization states, one can at least exclude some dipole orientations of the photoreceptor at the studied wavelength. To give the reader an impression of how variable and even bizarre a profile may be used when there is no averaging over the direction of the E-vector of light (e.g. polarized light is applied), we show in conclusion three profiles under polarized light (Richter [64]) in Fig. 18 (note, please, the ordinate scale!).

In conclusion, it should be emphasized that spatial analysis can only be really successful in investigating signal processing if it is applied within

a general concept including other methods and approaches which have not been discussed here.

Acknowledgments

Creative discussions and collaboration with many colleagues, first of all Enrique Cerda-Ohnedo (Se- ville), Rainer Hertel (Freiburg) and Martin Wei- senseel (Karlsruhe) have been fruitful. Important contributions of my former and current students Dr. Alfred Steinhardt, Dr. Teodor Popescu, An- dreas Roessler, Thomas Richter, Micha Reinhardt and Susanne Kiewisch, are included in this report. I am very thankful to all of them. I am indebted to Dr. R. Cassada for critically reading the man- uscript. Supported by the Deutsche Forschungs- gemeinschaft (SFB 206, D5) and in part by the Alexander-von-Humboldt Foundation (11 SPA 5869).

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Documents

New trends in photobiology: Intracellular processing of a spatially non-uniform stimulus: Case study of phototropism in Phycomyces