the determination of the maximal bending angle inphycomyces sporangiophores

EXPERIMENTAL MYCOLOGY 15, 336-345 (191)

The Determination of the Maximal Bending Angle in Phycomyces Sporangiophores

TAMOTSU OOTAKI,*,~ NIKO ISHIKAWA,* ATSUSHI MIYAZAKI,” AND TOSHISUKE TSURU?

*Institute of Genetic Ecology, Tohoku University, Katahira, Sendai 980, Japan; and TFaculty of Education, Yamagata University, Yamagata 990, Japan

Accepted for publication September 9, 1991

OOTAKI, T., ISHIKAWA, N., MIYAZAKI, A., AND TSURU, T. 1991. The determination of the maximal bending angle in Phycomyces sporangiophores. Experimental Mycology 15,336-345. The maximal phototropic bending angle of the Phycomyces sporangiophore (spph) was always smaller than 90” from the vertical, Experimental results, using a clinostat apparatus and both a gravitropic mutant and the wild-type spphs placed vertically or horizontally and illuminated from different directions, revealed that this angle resulted from a balance between a negative gravitropism and a phototropism whose direction (positive or negative) and magnitude depended on the bending angle of the spph, because of the involvement of the optical properties of the spph, probably the ratio of the maximal light-fluence rate between the proximal side (Zr,-) and the distal side (In,,,) of the spph. Shadowing of the extension zone by the sporangium was estimated to be complete only when the bending angle was larger than 86.4” from the vertical. Q 1991 Academic PKSS, IX.

INDEX DESCRIPTORS: bending angle; gravitropism; lens effect; phototropism; photogravitropic equilibrium; Phycomyces sporangiophore.

In Phycomyces, phototropism and gravitropism are remarkable behavioral phenomena and have long been studied (re- viewed by Galland and Lipson, 1987; Shropshire and Lafay 1987), although their physiological mechanisms are still poorly understood. The wild-type sporangiophores (spphs)2 at stage IVb (the develop- mental stage after sporangium formation) elongating in the extension zone beneath the sporangium show a negative gravitropism when placed horizontally and a positive phototropism when unilaterally illuminated with parallel white (= blue) light. The maximal phototropic bending angle is, however, around 70-75” from the vertical in response to a horizontal beam of white light over a wide range of fluence rates (lop9 to 1 W/m*) (Varju et al., 1961; Bergman et al., 1973; Ootaki et al., 1974; Lipson, 1983).

r To whom correspondence should be addressed. * Abbreviations used: spph, sporangiophore; SE,

standard error.

This was believed to result from a photogravitropic equilibrium, which is a vectoral balance between a positive phototropism and a negative gravitropism.

We previously found that a negative phototropism to unilateral white light occurred in the spphs of the piloboloid mutant (genotype pil), whose extension zone expands ra- dially at stage IVb to exceed 210 pm in diameter after a gradual cessation of elongation (Koga et al., 1984), and also in the spphs of the p-carotene-overproducing mutant (genotype, cars) growing on vitamin A-supplemented medium, which accumu- lated a large amount of p-carotene in the cytoplasm (Ootaki et al., 1988). This led us to suggest that the optical properties of the nearly transparent extension zone of the spphs are involved in the determination of phototropic direction, positive or negative. Parallel, unilateral light incident upon one side of the extension zone (proximal side) converges on the opposite side (distal side) through the spph cytoplasm which func-

336 0147-5975191 $3.00 Copyright 0 1991 by Academic Press, Inc. All rights of reproduction in any form resewed.

TROPIC ANGLE DETERMINATION IN Phycomyces 337

tions as a cyrindrical converging lens (Blaauw, 1914). Thus, the distal side receives more intense light than the proximal side, resulting in greater stimulation for elongation at the former than the latter (the “focusing advantage” at the distal side; Shropshire, 1962). We proposed that the orientation of phototropism is determined by the ratio of the maximal light-fluence rates between the proximal side (Zp,m,,) and the distal side(Zi,m,), which is greatly influenced by the magnitude of the intracellular light attenuation (Tsuru et al., 1988; Ootaki et al., 1988). If Z,,,, is smaller than I D,max, the phototropism is positive (wild type), but if the former is larger than the latter, the phototropism is negative, as in the pi1 and cars mutants. In these mutants, the intracellular light attenuation may be large enough to eliminate the focusing advantage at the distal side, because of an increase in the intracellular light path length (through the large diameter; pil mutant) or an increase in the light attenuation coefficient (through light absorption by excess @-carotene; cm-S mutant).

When we applied this hypothesis to a spph bending toward a light source, with a 1.38 refractive index of cytoplasm (Castle, 1933), we found that the ZP,max/Zn,max ratio reversed when the spph reached about 72” from the vertical (Ootaki et al., 1991). If our hypothesis is valid and if the gravitropic effect is not considered, the spph should stop bending at this point. Beyond this critical angle, the spph is “negatively” phototro- pit. Thus, the spph varies its phototropic direction, positive or negative, as well as its magnitude, depending on the bending an- gIe. This critical angle is a function of the intracellular light attenuation, which is greatly influenced by the light path length (spph diameter) and the light attenuation coefficient (amount of cell contents). In ac- cordance with our hypothesis, we confirmed that the wild-type spphs with a longer light path length (diameter) or a larger light attenuation coefficient (amount

of p-carotene) have a smaller critical (= the maximal bending angle) than with a shorter light path length or a srna~~e~ light attenuation coefficient (Ootaki et al., 1991).

In these calculations of the critical angle we did not consider the effect of a ~~gat~v~ gravitropism. However, the gravitro~i~ response is likely to influence the determi tion of the maximal phototropic bendi gle (Pilet, 1956; Dennison, 1958, 195 nison and Shropshire, 1984). In the work, we investigate the interaction among a gravitropic response, a phototr~~ic response, and a shadowing effect of the s rangium, in determining the otropic bending angle of Phycomyces

MATERIALS AND METHO

Strains

The fungus Phycomyces Bgff. was used throughout. the standard wild type (mating typ tained from the Northern Regi search Laboratory (Peoria, IL). C5 [genotype, carBl0, geo-lO( - )], an albino gravitropic mutant, accumulates a 1 amount of phytoene (Meissner and brtick, 1968; Heisenber Olmedo, 1968) and respond to gravitational stimulation and Lipson, 1987). The C5 strain was obtained by one-step mutagenesis NRRL1555 with nitrosoguanidine ( ner and Delbriick, I968).

Culture Conditions

One or a few spores of the wil the C5 mutant were aseptically after heat activation at 48°C for 18 min into separate glass-shell vials (1 cm in diameters 3 cm high) containing glucose-asparagine- agar (SIV medium; Sutter, 1975) mented with yeast extract (Difco, MI; 1 g/liter) and Bactocasitone (

338 OOTAKI ET AL.

g/liter) (SIVYC medium). Several vials placed in a 5-cm-diameter petri dish bottom within a 9-cm-diameter petri dish bottom were covered with an inverted 200-ml bea- ker to allow adequate clearance for aerial spphs .

The cultures were grown at 20°C under overhead continuous white light (fluores- cent light, cool white, FL40SD/38, Toshiba Electric Co., Tokyo) at 0.1 W/m2 at myce- lial level.

Measurement of Tropic Bending Angle

Only one or two straight spphs at stage I (before sporangium formation and elongation at the apex) (Castle, 1958) or at early stage IVb, about 3 cm in length, were left in each vial after the removal of excess spphs. The vials, whose bottoms were fixed in holes of a Lucite holder (12 x 12 x 2 cm), were transferred and fixed on the bottom or back wall of a black test box, 13 x 21 x 13 cm, with a window on the front to admit collimated white light of 0.1 W/m2 from a 30-W incandescent lamp (LSD, Olympus, Tokyo) after passing through a convex collimating lens and a heat absorption filter. The side of the black box facing the ob- server was made of red Plexiglas (No. 2444, Rohm and Haas, Philadelphia, PA), so that the tropic behavior of the spphs was easily observable through the side window without disturbing their behavior. The black box was placed facing upward, downward, or horizontally and illuminated through the front window. Thus, the spphs receive the stimulation of Earth’s gravity and illumination from different directions, corresponding to the combination of orientation of the light source and the black box carrying horizontal or vertical spphs.

After 8-9 h, the spphs were placed on a glass plate (20 x 25 cm), photocopied, and measured for their bending angles with a protractor on the photocopied images. The bending angle (a) was designated as the an-

gle between two spph axes before and after stimulation (Fig. 2).

Sequences of spph angles during bending were measured on the enlarged images of serial photographs, which were taken at 15 min intervals with a motor-driven camera with magnifying rings connected to a time- lapse autotimer (Nikon CFMA, Nikon, To- kyo). The growth of spph was also recorded with a 16-mm movie camera (H16RX-5, Bolex, Switzerland) with a time-lapse autotimer and magnifying rings. Serial photographs of spphs, taken at 1-min intervals, were analyzed with a film analyzer (Filmo- tion, F-105, Kawabe Denki Kogyo Co., To- kyo) .

Variation of phototropic bending angles was given as the standard error (SE), and analysis of variance was used for statistical comparisons.

Clinostat Experiment

A vial with a straight spph at early stage IVb was tightly fixed at the horizontal po- sition on the center of a turntable (Fig. 1). The vial was covered with a black box, 10 x 10 x 15 cm, with a window on one side to admit horizontal, collimated white light of about 0.1 W/m2 from an incandescent lamp (LSD, Olympus) after passing through a system of a convex collimating lens, a dia- phragm, and refractive mirrors. The turnta-

turntable mirror mirror

FIG. 1. Schematic diagram of the use of a clinostat for elucidating the relationship between phototropic and gravitropic responses in Phycomyces spph. A stage IVb spph was fixed on the center of turntable and covered with a black box. The whole apparatus was rotated at 1 rpm, so that the spph was unilaterally illuminated from a fixed side through the window of the black box with collimated parallel light.

ble carrying the whole apparatus was connected to a motor (Oriental Motor Q59, To- kyo) and a homemade variable transformer and was rotated in a dark room at 1 rpm, which was slow enough not to influence the spph growth. The spph, therefore, receives a stimulus identical to the Earth’s gravity all around the spph axis but light stimulation only from a fixed side during rotation. After 8 and 12 h, the bending angle of the spph was measured on the photocopied im- age, as described above.

69. l”, was smaller than that of the wi spphs, probably because of the e a larger negative gravitropic re$~~~~~~ The difference in the angles betw two strains was significant at the level.

The maximal bending angles o wild-type and mutant spphs were tively, 80.1” and 80.2” on average and these were significantly larger than those e stage IVb spphs (Table 1,B).

RESULTS

Tropism ofHorizontal Spphs to Lig from Above

Gravitropism of Spphs

When placed horizontally and kept for 8-9 h in the dark (Fig. 2A), the wild-type spphs bent upward at an angle of 63.8” on average because of a negative gravitropism (Table 1,A). The spphs were capable of reaching an angle of 90” at about 19 h after the onset of the stimulus (Fig. 3). The bending rate decreased with an increase in the bending angle, agreeing with Denni- son (1958) that the bending rate was dependent on the spph’s deviation from the vertical.

When horizontally placed spp luminated from above, the direction of t two vectors of positive phototropism a negative gravitropism of the spphs is identical (Fig. 2C). The bending angle of the wild-type spphs was about 76.7” on average at 8-9 h after the onset of the experiment (Table 1,C) and never reached 90” e ter 12 h (Fig. 4).

The mutant (C-5) spphs started bending upward with a short lag period (less than 30 min) and reached an angle of 90” at about 7 h (Fig. 3; Table l,A). Therefore, the bending rate of the mutant was much larger than that of the wild type, as described by CerdCOlmedo and Lipson (1987).

In the mutant spphs, on the other the bending angle reached the maxim about 4 h after the onset of illumi After reaching the maximal angle, a slight fluctuation of angle from 90” was it remained within about 5” (Fig.

Tropism of Horizontal Spphs to Light from Beiow

Tropism of Vertical Spphs to Unilateral Light

When vertical wild-type spphs at stage IVb were unilaterally illuminated (Fig. 2B), the spphs started bending with a lag period of about 30 min and reached an angle of around 71.5” at about 6 h from the onset of illumination. This angle was maintained even after 8-9 h (Table l,B).

When horizontally placed luminated from below, the dir vectors of phototropism and of spphs are opposed (Fig. light-fluence rate used here, pit response is larger than t response; hence the spphs ben to the light source. Witk an phototropic bending angle, magnitude of the phototropi creases and, conversely, that of the gravitropic response increases.

The resulting bending angles, due to sue In the mutant spphs the bending angle, . y nhotorrravitronic eauilibrium. were 7 I L ,


340 OOTAKI ET AL.

Bending Angle (I%)

FIG. 2. Experiments studying the phototropic and gravitropic responses of Phycomyces spphs placed vertically or horizontally with (B-E) or without (A) illumination by parallel white light. The spphs show a negative gravitropism (GT.; black arrow) and a positive phototropism (PT; white arrow) in different directions, depending on the direction of light stimulus. (Y is the bending angle. For each experiment the maximal bending angle was predicted for the wild type (black arrowhead) and the gravitropic mutant (white arrowhead), assuming that the bending angle is determined as a result of photogravitropic equilibrium and that the phototropic direction and magnitude are governed by the optical properties of spph. If a positive phototropism occurs only when the maximal light-fluence rate of the distal side of the unilaterally illuminated spph (Zr,max ) is larger than that of the proximal side (ZPJnax 1 ) further bending stops at the critical point (black dot), where these light-tluence rate values become equivalent (about 72”; Ootaki et al., 1991), because the spph is negatively phototropic beyond the critical point. Magnitudes of phototropic (solid line) and gravitropic (broken lines) stimuli which drive the spph to positive (+) or negative (-) tropism and which change as a function of the bending angle are illustrated for the wild type (W) and the mutant (M). The shading on the diagram indicates where the whole extension zone of the proximal side of the spph is shaded by sporangium (see Fig. 7).

average for the wild type and 67.8” for the the spphs that were horizontally placed and mutant (Table 1 ,D). The difference was sig- illuminated from above (Fig. 2C; Table Scant at the P = 0.05 level. These angles 1 ,C), implying that a negative gravitropism were also significantly smaller than those of affects the maximal bending angle.

TROPIC ANGLE DETERMINATION IN ~~~c~~yces 341

TABLE 1 Bending Angles of Phycomyces Spphs under Various

Combinations of Phototropic and Gravitropic Stimulation

Experiments NRRL1555 (wild type)

c5 (gravitropic mutant)

A 63.8 f 1.4 (34) 87.6 5 0.3 (59) B

Stage I 80.1 f 0.4 (156) 80.2 t 0.3 (117) Stage 1% 71.5 2 0.5 (156) 69.1 " 0.8 (30)

c 76.7 f 0.7 (85) 83.5 r 0.4 (73) D 70.9 rt 0.9 (32) 67.8 2 0.3 (57) E 25.9 c 1.3 (33) 40.2 zk 2.1 (35)

Note. Capital letters correspond to those in Fii. 2. Bending angles were measured after 8-9 h stimuiation. The number of spphs measured is in parentheses. Values are means with SE. The difference in the means for each experiment between the wild type and the mutant is significant at P = 0.05, except for stage I spphs. The differences between B and C, and C and D were also significant for both the wild type and the mutant.

When horizontally placed spphs were illuminated from the front (Fig. 2E), the extension zone, 0.1-3 mm beneath the sporangium (Castle, 1958), was initially shaded by the sporangium. After 8-9 h, the spphs bent upward to about 25.9” on average for the wild type and 40.2” for the mutant, with a significant difference (Table 1 ,E) . In these spphs, the initial bending was introduced by a negative gravitropism and continued until reaching the angle of photogravitropic e~uilib~um.

0 2 a 6 8 10 12 14 15 18 20 FIG. 5. ~hototrop~c response of the ~il~-ty~~ and itME (h) the gravitropic mutant spphs of Phycomyce~~ which

FIG. 3. Gravitropic response of the wild-type (solid were placed vertically (al) or inclined obliquely (01~) aF circles) and the gravitropic mutant (solid squares) about 75” from the horizontal, as a function of time. spphs of Phycomyces in the dark (as in Fig. 2A) as a The spphs were illuminated with parallel white tight function of time. Each point shows a mean of about 10 from above. Each point shows a mean of about 6-8 sppbs with SE. spphs with SE.

F! 20~JL i

m 0x-1, I , / I / LL&w

0 1 2 3 4 5 6 7 8 3 10 1: 12

TIME (h)

FIG. 4. Phototropic response ofehe wild-type (opea circles) and the gravitropic mutant (open squares) spphs, which were ho~~on~y placed and ~ll~~~at~~ from above (Fig. 2C), as a function of time. Each poi41’ shows a mean of 9-12 spphs with SE.

Light from Above

Figures 5 and 5 show the photo the spphs inclined obliquely at from the horizont~ and iUu above. The vertically placed w mutant spphs (90”; control straight upward (toward the 1 as we have observed hitherto. spphs of the wild type, however, many- tained the initial angie and did not bend toward the light source, ~tho~~ th mutant continued beading to 98”. suits are consisted with the results of experiment C (Fig. 2C), in w were placed horizontally and i~~~rn~~~te~

2 3 4 5 TIME (h)

342 OOTAKI ET AL.

FIG. 6. Photographic records of the phototropic response of wild-type Phycomyces spphs which were placed vertically (VR) or inclined obliquely (OB) at about 75” from the horizontal and illuminated from above. The vertical spph elongated straight upward, toward the light source, but the spph inclined elongated maintaining the initial angle without bending toward the light source. Photograph B was taken 1.5 h after A. Photographs were enlarged from a 16-mm mo- tion-picture film. Bar = 0.5 mm.

from above; the wild-type spphs curved to about 75” and then bent no further, but the mutant spphs bent fully toward the light source (Fig. 4).

When the spphs were inclined at an angle of about 82” from the horizontal, the spphs bent slightly downward to about 75” and then maintained this angle during elongation (Table 2).

Tropism of Unilaterally Illuminated Spphs on a Clinostat

Table 3 shows the bending angles of the wild-type and the gravitropic mutant spphs, which were horizontally placed on a rotating clinostat and unilaterally illuminated from a fixed side. Without illumination, the spphs elongated almost horizontally. When no rotation was attempted, the spphs nor- mally bend upward, depending on a negative gravitropism. The mutant spphs reached 90” from horizontal after 8 h.

When unilaterally illuminated on the ro-

TABLE 2 Phototropic Bending Angle of Phycomyces Spphs Obliquely Inclined under Overhead Illumination

Time (h) Bending angles (0~)

0 82.4 2 0.9 1 80.2 + 0.9 2 79.1 + 1.0 3 76.8 + 0.8 4 75.8 + 0.6 5 76.0 + 1.0

Note. The wild-type spphs at stage IVb of Phyco- myces were inclined at 82.4” on average from- the horizontal under overhead illumination (0 h) and their bending angles were successively measured. The number of spphs measured is 12-13. Values are means with SE.

tating clinostat, the spphs showed a positive phototropism, but the maximal bending angle obtained was 72”-73” for both strains, implying that a limiting factor, probably optical, acts at these bending angles.

Shadowing Effect of Sporangium

The stage IVb spph carries a sporangium of about 500 pm in diameter just above the cylindrical extension zone (Fig. 7). With an increase in the bending angle, therefore, shading by the sporangium occurs initially on the uppermost region of the extension zone and enlarges downward along the spph axis. Calculation revealed that the whole proximal side of the extension zone (0.1-3 mm) was shaded at a bending angle of about 86.4” when the spph was 100 pm in diameter and carried a 500~pm-diameter sporangium (Fig. 7). This angle slightly shifted within a range of 0.2” in the spphs with diameters of 80 or 110 Frn. Variation in sporangium diameter also caused a slight shift of the bending angle; a 20% increment or decrement of sporangium diameter resulted in a shift of about 1” of the bending angle. In the wild-type spph bending at an angle of 71.5”, which was vertically placed and unilaterally illuminated (Fig. 2B; Table 1 ,B), only one-eighth of the extension zone was shaded (Fig. 7), implying that the shad-


TABLE 3 ~~ototro~ic Bending Angle of P~yc~~y~e~ Spphs Rotating on a Clinostat

Experimental conditions

Rotation and illumination

portion in dark

x\Bo rotation in dark

Strain

Wild type Mutant Wild type Mutant Wild type Mutant

Bending angles (cc)

8h 12 h

75.5 + 2.x 74.4 + 3.0 - 73.0 rt 0.6

2.2 t 1.9 - 1.5 2 1.0 -

44.5 f 4.9 - 90.1 iz 2.1 -

Nate. A stage IVb spph, selected from a wild type (NRRL1555) and a gravitropic mutant (CS), was horizoon- tally pfaced on the center of a clinostat turntable rotating at 1 rpm. The spph was illuminated from a fixed side with parallel white light thro~hout the experiment. For control ex~~meRts, the bending angles of spphs, placed on the turntable with or without rotation in the dark. were also measured. The slumber of sppbs measured is 5-24. Values are means with SE.

owing effect of the sporangium was un- likely to be sololey responsible for the determination of this angle.

DISCUSSION

We previously suggested that the phototropic direction, positive or negative, is determined by the ~~,~~/~~,~~ ratio (Tsuru et al., 1988; Ootaki et aE, 1988) and that this ratio reverses when the bending angle reaches about 72” if the gravitropic effect is ignored (Ootaki ef af., 1991). At an angle smaller than this, 1, rnax is larger than ir,,, and the spph is positively phototropic, but at a larger angle, the former is smaller than the latter and the spph is negatively phototropic. Supporting this hypothesis, the present results imply an inhibition of positive phototropism beyond a certain bending angle, probably resulting from the optical properties of spph. If no such optical inhibition exists, then the bending angle of the spph placed horizontally and illuminated from above must reach 90“ from horizontal (Fig. 2C; Table 1 ,C), because the directions of the vectors of both photo- and gravitro- pisms are identical. The spphs illuminated unilaterally on a rotating clinostat, where we may rule out the effect of a negative

ravitropism, also must reach 90”. The re- s~ltant angles were, however, smaller than

_________-__ -___-- ___-_____ “I

~ { i

0 65 70 75 80 85 90 BENDING ANGLE a (degree)

FIG. 7. The relationship between the bending arrgle and the length of the shaded region of the ~rox~~~a~ side (Lf of a ~~y~~~y~@s spph, which was ve~ica~~ placed and unilaterally illuminated. ~a~c~~atio~ was carried out for spphs of 60, 100, or 140 ym in diameter (D) carrying a 500~pm-diameter sporangium QR) also for 100-m spphs carrying a 400”, &lO-, or pm-diameter s~r~gium. The extension zome (EZ) of the spph occurs from 0.1 to 3 mm ~e~eat~ the sporan&m.

-- ________________ --_._--__- -____ --_ .- 2R=50Opm /

1

344 OOTAKI ET AL.

90” in both cases (Fig. 4; Table 3). Thus, the direction of phototropism is dependent on the bending angle, although the gravitropism is always negative, regardless of the bending angle. A decrease in the bending angle to 75” in the spphs inclined at about 82” under overhead illumination (Table 2) strongly implies the existence of negative phototropism beyond the critical angle.

If the optically controlled maximal bending angle exists, the wild-type spph inclined at the maximal bending angle under overhead illumination should elongate obliquely along the spph axis maintaining the initial angle without bending toward the light source. The gravitropic mutant spph under the same conditions, on the other hand, may bend fully toward the light source, because of its stronger response to gravity than to light at this angle. Our present work confirmed these phenomena (Figs, 5 and 6). Vatjti et al. (1961) reported that for small angles of incidence to the axis of the spph near photogravitropic equilibria, the phototropic stimulus was relatively ineffective. Although they concluded that this phenom- enon occurred in part because of shading of the extension zone by the sporangium, it is more likely to be due to the optical properties of spph. This is because the whole extension zone is shaded only when the bending angle exceeds about 86.4”, and because the spph whose extension zone was completely shaded will grow directly upward as a result of negative gravitropism. The extension zone of the vertically elongating spph under overhead illumination is in the shade of the sporangium, and the spph no longer acts as a lens.

Gravitropism influences the maximal bending angle, because the bending angles of the spphs in experiments C and D dif- fered, because the spph in experiment E bent upward (Fig. 2; Table l), and because the gravitropic mutant did not reach 90” on the rotating clinostat (Table 3) but did in experiment C (Fig. 2; Table 1). The gravitropic bending rate depends on the spph’s extent of deviation from the vertical. The

greater the differential gravitational stimulus across the extension zone, the faster the initial bending rate (Dennison, 1958). Thus, the spph perceives a different magnitude of the gravitropic stimulus corresponding to the bending angle reached. This is also true for the magnitude of the phototropic stimulus. The maximal bending angle of the spph is determined by a balance between a negative gravitropism and a positive or negative phototropism, which varies depending on the bending angle, and by a balance of these two tropic magnitudes. As a result, the maximal bending angle shifts to an angle that is larger or smaller than the critical angle (Fig. 2).

On the basis of such reasoning, we may estimate the range of the maximal bending angles of spphs perceiving phototropic and gravitropic stimuli with different directions and magnitudes (Fig. 2). In the phototropism of a vertical spph to unilateral light (Fig. 2B), for example, the magnitude of phototropic stimulus which a spph perceives decreases with an increase in the bending angle and reaches zero at 72”, which is the optically critical angle where I P,max is identical to In,,,. Beyond the critical angle, the spph will receive a phototro- pically negative stimulus, until the extension zone is completely shaded. The gravitropic stimulus which the spph perceives, on the other hand, increases with an increase in the bending angle. Because of a balance between these photo- and gravitropic stimuli, the maximal bending angle of this spph will be smaller than the critical angle, 72”. In the gravitropic mutant, the gravitropic stimulus induces a larger response and the equilibrium angle becomes much smaller than that of the wild type. For the same reason, the bending angle of the wild-type spph, placed horizontally and illuminated from above (Fig. 2C), will be larger than the critical angle, and the angle of the mutant will be much larger, probably above 86.4” where the whole extension zone is shaded.

In this study, we ignored the effect of a

TROPIC ANGLE DETERMINATION IN Phycomyces

partial shadowing of the extension zone by the sporangium on the maximal bending angle. The maximal bending angles of stage I spphs of both strains were larger than those of stage IVb spphs (Table 1). At present, however, we do not know whether this is due to the elimination of the shadowing effect of extension zone, a conical shape of the apical extension zone with a short light path length (Ootaki et a/., 1991), or physiological characteristics of stage I spphs. further analysis is required.

ACKNOWLEDGMENTS

This work was carried out under the Joint Research Program of the Institute of Genetic Ecology, Tohoku elniversity, Japan (882004). We also thank Dr. H. Kataoka of our Institute, who constructed the clinostat used in the present work. Ms. Reiko Kohata is also acknowledged for her helpful assistance.

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