Does the photosynthetic light-acclimation need change in leaf anatomy?

Authors


Correspondence: Riichi Oguchi, Department of Plant Ecology, Biological Institute, Graduate School of Life Sciences, Tohoku University, Aoba, Sendai 980–8578, Japan. Fax: + 81 (0)22 217 6699; e-mail: riichi@biology.tohoku.ac.jp

ABSTRACT

There is a strong correlation between leaf thickness and the light-saturated rate of photosynthesis per unit leaf area (Pmax). However, when leaves are exposed to higher light intensities after maturation, Pmax often increases without increasing leaf thickness. To elucidate the mechanism with which mature leaves increase Pmax, the change in anatomical and physiological characteristics of mature leaves of Chenopodium album, which was transferred from low to high light condition, were examined. When compared with leaves subjected to low light continuously (LL leaves), the leaves transferred from low to high light (LH leaves) significantly increased Pmax. The transfer also increased the area of chloroplasts facing the intercellular space (Sc) and maintained a strong correlation between Pmax and Sc. The mesophyll cells of LL leaves had open spaces along cell walls where chloroplasts were absent, which enabled the leaves to increase Pmax when they were exposed to high light (LH). However, the LH leaves were not thick enough to allow further increase in Pmax to the level in HH leaves. Thus leaf thickness determines an upper limit of Pmax of leaves subjected to a change from low to high light conditions. Shade leaves would only increase Pmax when they have open space to accommodate chloroplasts which elongate after light conditions improve.

INTRODUCTION

Light is an indispensable resource for plant growth. In nature, the light availability for plants varies spatially and temporary by over two orders of magnitude. In response to changes in light availability, plants differentiate sun and shade leaves, where sun leaves have higher photosynthetic capacity (light-saturated rate of photosynthesis on a leaf area basis), greater leaf thickness and greater nitrogen content than shade leaves (Björkman 1981; Murchie & Horton 1997). However, maintaining high photosynthetic capacity is costly, and advantageous only under high light conditions (Mooney & Gulmon 1979).

The high photosynthetic capacity in sun leaves is supported by constructions of thick leaves (Terashima, Miyazawa & Hanba 2001) with a large investment of nitrogen in photosynthetic enzymes (Boardman 1977; Björkman 1981; von Caemmerer & Farquhar 1981). Since all photosynthetic enzymes are involved in chloroplasts, sun leaves need to have a large number of chloroplasts in the mesophyll cells. CO2 diffusion in the liquid phase is very slow and chloroplasts distribute near the cell surface. If a leaf increased the number of chloroplasts without thickening the mesophyll layer, some chloroplasts would become separated from the cell surface and any increase in such chloroplasts contributes little to increasing photosynthetic capacity because they do not receive sufficient CO2 to fix. Therefore, sun leaves are thick in order to arrange all chloroplasts along the mesophyll cell surface. Hence there are strong correlations between photosynthetic capacity and leaf thickness (McClendon 1962; Jurik 1986), between photosynthetic capacity and mesophyll cell surface area (Nobel, Zaragoza & Smith 1975), and between the internal conductance of CO2 and chloroplast surface area facing the intercellular space (von Caemmerer & Evans 1991; Evans et al. 1994).

However, high photosynthetic capacity is not always accompanied by thick leaves. Leaf thickness is determined by the irradiance at leaf development, and changes little after they have matured (Milthorpe & Newton 1963; Wilson 1966; Verbelen & De Greef 1979; Sims & Pearcy 1992). Nevertheless, when leaves are subjected to higher irradiance after maturation, their photosynthetic capacity often increases (Jurik, Chabot & Chabot 1979; Turnbull, Doley & Yates 1993; Pearcy & Sims 1994; Yamashita et al. 2000) even though it may not achieve the level of leaves developed at high irradiance (Frak et al. 2001). Does this imply that leaves do not have to become thick to increase their photosynthetic capacity?

Although several studies have reported alteration in chloroplast ultrastructure when leaves are transferred from low to high irradiance (Prioul, Brangeon & Reyss 1980; Sebaa, Prioul & Brangeon 1987), its relation to the ability of photosynthetic capacity is unclear. The aim of the present study was to elucidate the mechanism that increased the photosynthetic capacity when mature leaves were subjected to a higher light condition. Given that the photosynthetic capacity is determined by the amount of Rubisco in chloroplasts (Björkman 1968, 1981), we hypothesized that the increase in the photosynthetic capacity in a high light condition was due to: (1) increased activity of Rubisco; (2) increased concentration of Rubisco in chloroplasts; (3) increased number of chloroplasts; (4) increased volume of chloroplasts; or (5) a combination of some of them. With this hypothesis, we examined changes in anatomical and physiological characteristics in leaves of Chenopodium album L. when transferred from low to high light condition. Photosynthetic capacity, Rubisco concentration, chloroplast thickness, chloroplast surface area and chloroplast number were determined for leaves grown in different light conditions.

MATERIALS AND METHODS

Chenopodium album, an annual herb, was grown in a growth cabinet where leaf temperature and air humidity were controlled at 25 °C and 80%, respectively, and the light : dark period was 14 h : 10 h. Light was provided by metalhalide lamps (MLBOC400C-U; Toshiba, Tokyo, Japan). Plants were grown in 1.5 L pots filled with washed river sand. Each day 150 mL of nutrient solution containing 4 mm KNO3, 4 mm Ca(NO3)2, 1.33 mm NaH2PO4 and microelements was applied per plant. Photosynthetic photon flux density (PPFD) was 700 µmol m−2 s−1 in high light and 70 µmol m−2 s−1 in low light. Neutral shade cloth was used to produce the low light condition in the growth cabinet. Plants that were grown continuously at low or high light were designated LL and HH, respectively. Part of the plants grown in the low light environment was transferred when they had 8–10 fully developed leaves (LH plants). We prepared seven, eight and four plants for LL, LH and HH leaves, respectively. Only leaves that ceased expansion before transfer were used for measurements.

Photosynthetic rates were determined with an infrared gas analyser–leaf chamber system (LI-6400; Li-Cor Inc., Lincoln, NE, USA). Light was provided by LED (model 6400–02B; Li-Cor Inc.). The photosynthetic rate was measured at 2000 µmol m−2 s−1 and then the light intensity was decreased in a stepwise manner to obtain the light–response curve. Leaf temperature was adjusted to 25 °C.

After the photosynthesis measurements, four discs, 1 cm in diameter, were punched out and leaf pieces for measurement of anatomy were cut off from the leaf. One disc was used to determine the chlorophyll (Chl) content spectrophotometrically after extraction with dimethylformamide (Porra, Thompson & Kriedemann 1989). The other three leaf discs were dried at 80 °C in an oven for more than 3 d. After dry mass determination, nitrogen (N) content was determined with an NC analyser (NC-80; Shimadzu, Kyoto, Japan). The remaining lamina tissues were stored at −80 °C for determination of Rubisco (Hikosaka & Terashima 1996).

The leaf pieces were infiltrated and fixed in 2.5% glutaraldehyde in 100 mm phosphate buffer (pH 7.0) for a minimum of overnight at 0 °C. They were post-fixed in 2% osmium tetroxide for 2 h before being dehydrated in an ethanol series and propylene oxide, and were embedded in Spurr's resin. Sections, 0.8 µm thick, were cut by an ultra-microtome (Leica VIM-535; Reichert-Nissei Ultracuts, Vienna, Austria) and stained with methylene blue for light microscopy. Microscopic photographs were taken from these sections at a magnification of 200×.

The area of the mesophyll cell surface was calculated from photographs. To convert length in cross-section to surface area, a curvature factor (F) was determined assuming that the shape of the palisade tissue cells was a cylinder with flat ends and that of the sponge cells was a spheroid (Thain 1983). The value of F was 1.33–1.42 in the palisade and 1.34–1.56 in the spongy cells. The surface area of the mesophyll cells facing the intercellular space per unit leaf area, Smes[the same as Ames/A of Nobel et al. (1975)] was determined by

image(1)

where w is the width of the section being measured, and Lmes is the total length of mesophyll cells facing the intercellular space in the section. The area of chloroplast surfaces facing the intercellular space per unit leaf area, Sc, was determined by

image(2)

where Lc is the total length of chloroplasts facing the intercellular space in the section. The total chloroplast volume per unit leaf area, Vchr, was calculated from the integration of the cross-sectional area of the chloroplasts. The number of chloroplasts per unit leaf area, nchr, was determined by

image(3)

where z is the chloroplast number in the section.

Statistical analyses were performed with the StatView statistical software (version 5.0, SAS Institute Inc., Cary, NC, USA). Comparisons of means for all parameters between growth conditions were made using the Tukey–Kramer test.

Model

Light-saturated rate of photosynthesis per unit leaf area (Pmax) was analysed as the product of five factors:

image(4)

where [Rubisco] is the Rubisco content per unit leaf area. Pmax/[Rubisco] indicates the specific Rubisco activity in vivo, which may decrease when CO2 concentration in the chloroplast decreases, or when the activation state decreases. [Rubisco]/Vchr indicates Rubisco concentration in the chloroplasts; Vchr/Sc, chloroplast thickness; and Sc/nchr, the area of a chloroplast surface facing the intercellular space.

RESULTS

Light-saturated rates of photosynthesis on a leaf area basis (Pmax) of LL and HH leaves were 10.7 and 27.1 µmol m−2  s−1, respectively (Table 1). The value of Pmax of the LH leaves increased until 4 d after transfer, and then decreased gradually (Fig. 1). In the following analyses LH leaves harvested 4 d after transfer were used. The Pmax of LH leaves was 16.7 µmol m−2 s−1, which was significantly higher than that of LL leaves, but far less than the Pmax of HH leaves (Table 1). The respiration rate of LL, LH and HH leaves was 0.75, 1.69 and 2.15 µmol m−2 s−1, respectively, which were significantly different from each other.

Table 1.  Physiological and anatomical parameters for mature leaves grown continuously in low light (LL), high light (HH), and leaves transferred from low to high light (LH)
 LLLHH
  1. We used leaves harvested at 4 d after transfer in the following analyses of LH leaves. All data are presented as mean ± S.D. Different letters indicate significant difference at P < 0.05 in Tukey–Kramer test.

Pmax (µmol m−2 s−1) 10.7 ± 1.9a 16.7 ± 1.4b 27.1 ± 1.8c
Respiration rate (µmol m−2 s−1)−0.75 ± 0.27a−1.69 ± 0.11b−2.15 ± 0.33c
Chlorophyll content (mmol m−2)0.442 ± 0.033a0.396 ± 0.023a0.675 ± 0.063b
Chlorophyll a/b ratio 3.47 ± 0.16a 3.92 ± 0.08b 4.12 ± 0.08c
Rubisco content (µmol m−2) 2.38 ± 0.26a 3.33 ± 0.54b 7.22 ± 0.99c
Leaf nitrogen (mmol m−2) 79.1 ± 10.6a 94.7 ± 5.3b169.7 ± 4.0c
Chl/N (µmol mmol−2) 5.65 ± 0.67a 4.19 ± 0.29b 3.97 ± 0.35b
Leaf mass per area (g m−2) 18.4 ± 2.0a 29.5 ± 2.1b 64.7 ± 10.6c
Leaf mesophyll thickness (µm)0.135 ± 0.011a0.154 ± 0.010b0.216 ± 0.022c
Leaf thickness (µm)0.176 ± 0.011a0.195 ± 0.010b0.250 ± 0.023c
Smes(m2 m−2) 10.1 ± 0.6a 10.5 ± 0.5a 23.2 ± 3.1b
Sc(m2 m−2)  7.9 ± 0.9a 10.0 ± 0.5b 22.0 ± 3.3c
Sc/Smes0.779 ± 0.076a0.956 ± 0.016b0.948 ± 0.030b
Figure 1.

Time-course of the light-saturated photosynthetic rate (Pmax) in mature leaves following transfer from a low to a high light condition (open triangles) or leaves grown continuously in low light (closed circles). Bars indicate ± SD of the mean.

Nitrogen content, Rubisco content and leaf mass per area (LMA) were significantly greater in HH than LL leaves (Table 1). They were also significantly greater in LH than in LL leaves, but the values in LH were about one-half of those in HH. Chlorophyll content of LH was significantly lower than that of LL leaves, whereas the Chl a/b ratio of LH was significantly higher than that of LL leaves. Both Chl content and Chl a/b ratio were highest in HH leaves.

Light-microscopic photographs of cross-sections of leaves (Fig. 2) showed that LL and LH leaves had one layer of palisade whereas HH leaves had two layers. Although no difference was found in the arrangement of cells between LL and LH leaves, there was a difference in the distribution of chloroplasts in the cell. In LL leaves, there were large open spaces along the mesophyll cell walls facing the intercellular space, especially in the sponge cells (Fig. 2a). In LH leaves, chloroplasts covered nearly all the cell walls facing the intercellular space with little open space left (Fig. 2b).

Figure 2.

Leaf cross-sections of mature leaves grown continuously in low light (LL) (a), high light (HH) (c) or transferred from low to high light condition (LH) (b). Light micrograph magnification is 400×. The depth of cross-sections was 0.8 µm. Arrowheads show the open space for chloroplasts. Starch grains were observed in some (LH) and almost all (HH) chloroplasts.

The LH leaves were significantly thicker than LL leaves (Table 1), but the difference was small (13.8% in leaf thickness and 11.1% in mesophyll thickness). There was no difference in the surface area of mesophyll cells facing the intercellular space (Smes) between LH and LL leaves. However, the area of chloroplast surfaces facing the intercellular space, Sc, was significantly higher in LH than in LL leaves (22.7%). This resulted in a significant increase in the fraction of mesophyll cell surface covered by chloroplasts (Sc/Smes) after transfer from low to high light (78% in LL and 96% in LH). The HH leaves had significantly greater leaf and mesophyll thickness than LL and LH leaves. The values of Sc and Smes were also largest in HH leaves, whereas the Sc/Smes in HH leaves was similar to that in LH leaves.

To examine which physiological and anatomical parameters influenced the photosynthetic capacity most, we analysed it into five components (Eqn 4, Table 2). Between LL and LH leaves, there was no significant difference in Pmax per Rubisco, Rubisco concentration in chloroplast, chloroplast thickness and chloroplast number per leaf area. Only the area of a chloroplast facing the intercellular space significantly increased (34.7%) after transfer from low to high light. On the other hand, between LH and HH leaves, there were significant differences in those components except Rubisco concentration and chloroplast thickness.

Table 2.  Factors that determine Pmax(see Eqn 4) in mature leaves grown continuously in low light (LL), high light (HH) and transferred from low to high light condition (LH), and their percentage change after transfer from low to high light (LH/LL)
 Rubisco activityRubisco concentration
in chloroplasts
Chloroplast
thickness
Area of chloroplast
exposed to cell surface
Chloroplast number
inline imageinline imageinline imageinline imagenchr
(mol mol−1 s−1)(mm)(µm)(µm2)(chloroplast µm−2)
  1. We used leaves harvested at 4 d after transfer in the following analyses of LH leaves. All data are presented as mean ± SD. Different letters indicate significant difference at P < 0.05 in Tukey–Kramer test.

LL4.53 ± 0.70ab0.101 ± 0.020a3.03 ± 0.37a6.55 ± 0.68a1.21 ± 0.07a
LH5.09 ± 0.72a0.103 ± 0.015a3.22 ± 0.23ab8.63 ± 0.70b1.17 ± 0.08a
HH3.79 ± 0.32b0.093 ± 0.028a3.64 ± 0.33b4.16 ± 0.45c5.36 ± 1.14b
% change (LH/LL)12.51.86.131.9−3.5

Figure 3 shows the relationships between Pmax and Sc, and between Rubisco content and Sc. Both Pmax and Rubisco content increased with increasing Sc across different light conditions. The transfer of leaves from low to high light increased Sc, which was accompanied by higher Pmax and Rubisco content.

Figure 3.

Relationships between light-saturated photosynthetic rate (Pmax) and the area of chloroplast surface facing the intercellular space per unit leaf area (Sc) (a), and between Rubisco content and Sc (b). Data for the leaves grown continuously in low light (LL) (closed circles), high light (HH) (open squares) or transferred from low to high light condition (LH) (open triangles) are plotted. Regressions: (a), Y= 5.0 + 0.99X, R= 0.89; (b), Y= 0.17 + 0.30X, R= 0.90.

Daily photosynthetic rates were calculated from the light–response curve of photosynthesis. Daytime photosynthesis is the product of the photosynthetic rate at 70 or 700 µmol m−2 s−1 and day length (14 h) and night respiration is the product of the dark respiration rate and the period (10 h). The photosynthetic rates of LL leaves in a high light condition and of LH and HH leaves at a low light condition were also calculated (Fig. 4). In low light, the LL leaves had the highest daily photosynthetic rates, whereas the HH leaves had the lowest. In high light, the HH leaves had the highest daily photosynthesis and LL leaves the lowest.

Figure 4.

Relationship between leaf nitrogen content and the daily photosynthetic rate. Circles, leaves grown continuously in low light (LL); squares, leaves grown continuously in high light (HH); triangles, leaves transferred from low to high light (LH). Determined in high (open) and low (closed) irradiance.

DISCUSSION

Physiological and anatomical mechanisms of the increase in the photosynthetic capacity after transfer from low to high light

The difference in leaf thickness between LH leaves and LL leaves was 10%, whereas the difference in the Pmax was 50% (Table 1). Thus Pmax can increase to a larger extent than the leaf thickness with increase in light intensity. However, the increase in Pmax was limited and the Pmax of the LH leaves did not reach the level of HH leaves (Table 1).

We factorized Pmax into five components (Eqn 4, Table 2). When comparisons were made between LL and LH leaves, only the area of the chloroplasts facing the intercellular space was significantly higher in LH leaves. Pmax was linearly related to Sc across different light conditions (Fig. 3). These results suggest that an enlarged volume of chloroplasts was a primary factor for the increase in Pmax. An increase in the area of a chloroplast facing the intercellular space is possible only when open space is available along the mesophyll cell surface (Fig. 2). The value of Sc/Smes increased from 78% in LL leaves to 96% in LH leaves. As little open space is available to further increase Sc in LH leaves, any further increase in Pmax would not be possible. However, Pmax can increase within the availability of the open mesophyll cell surface.

The open space at the cell surface where chloroplasts are absent has been observed in several studies (Honda & Wildman 1971; Evans et al. 1994; Syvertsen et al. 1995). Honda & Wildman (1971) reported different values of Sc/Smes among species; for example, 73% in Spinacia oleracea L and 25% in Nicotiana gultinosa L. Honda & Wildman (1971) argued that each species had its own Sc/Smes that determined the chloroplast number per cell. However, the present study shows that the Sc/Smes can change with chloroplasts expansion even though the chloroplast number does not change after leaf development.

The thickness of the chloroplast and its Rubisco concentration were not increased by transfer to high light. Since diffusion of CO2 in the liquid phase is very slow (Nobel 1991), CO2 conductance from the intercellular space to chloroplasts depends on the chloroplast surface area (Evans et al. 1994). If the Rubisco content per chloroplast surface area increased, the CO2 consumption rate would increase without increase in CO2 transfer conductance. This would reduce CO2 concentration in chloroplasts, leading to a reduction in Pmax per Rubisco (Farquhar, von Caemmerer & Berry 1980; Terashima et al. 2001). On the other hand, if the chloroplast surface area increased, both CO2 consumption rates and transfer conductance would increase without reduction in the CO2 concentration at chloroplasts. This was the case in the present experiment where Pmax/Rubisco did not decrease after transfer to high light (Table 2).

The number of chloroplasts did not increase after transfer to high light (Table 2). Chloroplasts stop division at the beginning of leaf development (Mullet 1988; Pyke 1999). However, mature leaves have high plasticity in chloroplast volume and partitioning of proteins in chloroplasts, which enables leaves to increase Pmax after chloroplasts division stopped.

Although the mesophyll thickness significantly increased after transfer from low to high light, the surface area of mesophyll cells (Smes) did not increase (Table 1). As the Smes is the space in which the chloroplasts can physically exist, the increase in leaf thickness alone did not seem to contribute to increasing Pmax in LH leaves.

In LH leaves, Chl a/b ratio increased (Table 1). This means that the physiology of chloroplasts as well as the size of chloroplasts changed. It is widely known that the organization of the photosynthetic apparatus changes with change in irradiance, which is represented by the change in Chl a/b and Rubisco/Chl ratios. In high light, the amount of Rubisco and the reaction centre of photosystem (PS) II increase at the expense of the light-harvesting complex of PSII (LHCII) (Evans 1989a, b; Hikosaka & Terashima 1995). These changes increase the Rubisco/Chl and PSII/Chl ratios. As the core complex of PSII mainly has Chl a and the LHCII has both Chl a and b, the Chl a/b ratio also increases. Although transfer to high light had an effect similar to that of the change in irradiance, changes in Chl content were different: LH leaves had a lower Chl content than LL leaves, whereas HH leaves had the highest (Table 1). The lowest Chl content of LH leaves may have resulted from lower Chl/N ratios in high than low light combined with limited availability of N in LH than in HH leaves.

Ecological significance

The relationship between the daily photosynthetic rate and N content per leaf area often shows a convex curve having a maximum (Hirose & Werger 1987; Hikosaka & Terashima 1995). The optimal N content that maximizes the daily photosynthesis depends on growing irradiances: the higher the growth irradiance, the higher the optimal N content. The present study showed that LL leaves had the highest daily photosynthesis in low light whereas HH leaves had the highest daily photosynthesis in high light (Fig. 4). These results suggest that both LL and HH leaves used N efficiently at the respective light availabilities. Although the daily photosynthetic rate of LH leaves was lower than that of HH leaves, the LH leaves increased daily photosynthetic rates by increasing N content per leaf area (Fig. 4 in high light), which was accompanied by elongation of the chloroplasts that filled the open space prepared by the cell grown in low light. Thus, the change in anatomy and physiology worked effectively in growth after transfer from low to high light.

High plasticity in photosynthetic light acclimation of mature leaves would be advantageous when growth irradiance suddenly increased (Turnbull et al. 1993; Kursar & Coley 1999; Yamashita et al. 2000). Yamashita et al. (2000) performed a transplant experiment from low to high light with four native tree species of the subtropical forest of the Bonin Islands and one invaded tree species (Bischofia javanica Blume). The photosynthetic capacity increased more in B. javanica (100%) than in the native species (0–50%). When gap formation increased the irradiance at an understorey, such plants that increase their photosynthetic capacity can grow faster. Because typhoons frequently disturb canopy layers and create gaps in the Bonin Islands, the high plasticity in photosynthetic light acclimation would help B. javanica invade and expand its distribution (Yamashita et al. 2000). Thus, the photosynthetic light-acclimation capacity of matured leaves may have important effects on forest composition and regeneration.

It has been indicated that leaf age or ontogenic status can also strongly influence the capacity of photosynthetic acclimation (Jurik et al. 1979; Bauer & Thoni 1988; Sims & Pearcy 1992; Frak et al. 2001). When immature leaves are transferred from low to high light, leaf thickness increases and enables a large increase in photosynthetic capacity (Sims & Pearcy 1992). However, mature leaves little change their thickness (Milthorpe & Newton 1963; Wilson 1966; Verbelen & De Greef 1979; Sims & Pearcy 1992), which limits capacity of photosynthetic acclimation although a small change is allowed by the open space to be filled with enlarged chloroplasts. These results imply that in a disturbed regime the ecological success of some species is not only due to leaf photosynthetic plasticity but is also linked with leaf production and turnover.

Maintaining plasticity in photosynthetic light acclimation of mature leaves, however, may not always be advantageous. Leaves need to be thicker to have greater open space along the mesophyll surface. However, thick leaves imply a large investment of biomass, which may be costly for leaves living in the shade. Furthermore, if the light environment was not improved, this investment would not pay back. There may be two alternative strategies. One is that optimistic species which have leaves with the open space to have high light acclimation capacity in the shade expecting an improvement of irradiance, and the other is pessimistic species that do not expect an improvement in irradiance and have leaves with no open space to reduce the cost of thicker leaves.

CONCLUSION

Mature leaves of C. album grown in low light increased Pmax following transfer to high light. This increase was due to the open space along the cell walls, which enabled chloroplasts to increase their surface area facing the intercellular space. However, the Pmax of leaves subjected to high light did not reach the level of leaves developed in high light, due to limited thickness in the former. Leaf thickness determines the availability of space to accommodate chloroplasts and thus an upper limit of Pmax of leaves subjected from low to high light conditions.

ACKNOWLEDGMENTS

We thank Ken-ichi Sato and Masaharu Kato for the experimental set-up. We are also grateful to Satoki Sakai and Hiroshi Ishii for helpful advice in the collection of data; Yuko Hanba and Tomoyuki Kawasaki for advice in mircroscopy and anatomical measurements; Toshihiko Kinugasa, Teruya Fujitaka and Yusuke Onoda for support and advice. This work was financially supported in part by Grants-in-aid of the Japan Ministry of Education, Science and Culture.

Received 29 May 2002; received in revised form 30 August 2002; accepted for publication 20 September 2002

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