The photostability of different chlorophyll forms in dark grown leaves of wheat

Formulae were developed for calculation of the relative amount of different pigment forms of dark grown leaves of wheat, present before and after photoreduction of the protochlorophyllide. Three pigment forms were calculated from in vivo absorption spectra: the photoreducible protochlorophyllide with absorption maximum at 650 nm and the two chlorophyll(ide) forms with absorption maximum at 684 nm and 673 nm, respectively. The formulae were used to study the changes of the pigment forms at repeated photoreduction of the protochlorophyllide, and at a repeated treatment involving photoreduction of the protochlorophyllide followed by partial photo-decomposition of the chlorophyllide formed. Five consecutive photoreductions and reaccumulations of protochlorophyllide were carried out by high intensity irradiations of one second (red light, 700 W m^-2) given at intervals of 3 h. The results show that the pool size of reaccumulated protochlorophyllide decreased sharply with the number of photoreductions performed. The absorption spectrum of the chlorophyllide formed at each photoreduction proceeded through the Shibata shift (transformation of the 684-form to the 673-form) and the late red-shift (transformation of the 673-form to other pigment form(s) in the dark). High intensity irradiation for ten minutes (red light, 700 W m^-2) immediately after each phototransformation caused a photodecomposition of about three quarters of the newly formed chlorophyllide (which was in the 684-form) while the earlier formed chlorophyll(ide) (in the 673-form) appeared not to be decomposed. This partial photodecomposition of the chlorophyllide had no effect on further accumulation of protochlorophyllide in the dark, and the absorption spectrum of the remaining chlorophyllide proceeded through the Shibata shift. The partial photodecomposition caused an inhibition of the late red-shift, and the accumulated chlorophyll(ide) remained in the 673-form.     

The Photostability of Different Chlorophyll Forms in Dark Grown Leaves of Wheat

The stability against high intensity irradiation (red light, 700 W m^?2) was investigated for the chlorophyll(ide) pigments formed after the primary photoreduction of the protochlorophyll(ide) in dark grown leaves of wheat. After photoreduction, most of the chlorophyll(ide) exists in a form with an absorption maximum at 684 nm. This form is gradually transformed into a form with an absorption maximum at 673 nm (the Shibata shift). It was possible to ascribe a specific photostability to each of the pigment forms. This photostability was higher for the 673-form than for the 684-form. A red-shift in the absorption maximum following upon the Shibata shift, reflects the successive transformation of the 673-form into other pigment forms, which were quite photostable at the intensity used.     

The Photostability of Different Chlorophyll Forms in Dark Grown Leaves of Wheat

The effect of denaturing treatments on the stability against high intensity irradiation (red light, 700 W m^?2) was investigated in vivo for various chlorophyll forms in wheat. Three pigment forms were investigated: the 650-form (protochlorophyllide) present in dark grown leaves; the 684-form (chlorophyllide) formed within 5 s after photoreduction of the 650-form; and the 673-form (chlorophyll), into which the 684-form has been transformed 25 min after photoreduction of the 650-form. (The pigment forms are denoted by their absorption maxima in the red region before denaturation.) Two denaturing treatments were used: heat treatment (water of 55°C for 2 min) and freezing and thawing (freezing in liquid nitrogen followed by thawing in water of 25°C). Heat treatment as well as freezing and thawing caused a shift in the absorption peak of the two nonesterified pigment forms. The peak of of the chlorophyllide 684-form shifted to 673 nm and that of the protochlorophyllide 650-form to 636 nm. The absorption maximum of the chlorophyll 673-form was not affected by the above treatments. Heat treatment as well as freezing and thawing had profound effects on the structural organization of the plastid pigments, as shown by a decrease in the photostability. For the 684-form, heat treatment reduced the photostability by a factor of about 14 (half-life in strong light changed from 170 s to 12 s). Freezing and thawing also reduced the photostability, although the effect was less pronounced (c. 3–4 times decrease in half-life). Upon transformation of the chlorophyllide 684-form into the chlorophyll 673-form (the Shibata-shift) the pigments became less sensitive to light, and were no longer “aggregated” by heat treatment. The “aggregating” effect of freezing and thawing was still present after the Shibata shift. The results thus verify a clear difference in structural organization of the 684-form and the 673-form, since the two pigment forms were differently affected by heat treatment. The 650-form behaved similarly to the 684-form, although it appeared to be slightly less aggregated by heat treatment. — The decrease in photostability, caused by heat treatment of the 684-form, changed the kinetics for the photodecomposition from a first towards a second order reaction.     

Breakdown of photosynthetic pigments and lipids in spinach leaves with ozone fumigation: Role of active oxygens

Dark-grown wheat leaves ( Triticum L. cv. Starke II Weibull) were illuminated repeatedly with light flashes giving partial phototransformation of protochlorophyllide to chlorophyllide. After short flashes (e.g. 15 ms red light, 250 W m⁻²), transforming only a minor part of the protochlorophyllide present, the first more stable chlorophyll(ide) measured ca 15 s after the phototransformation had its absorption maximum in the red around 672 nm. It stayed there during the following 30 min in darkness. After longer flashes (e.g. 125 ms), transforming a larger portion of the protochlorophyllide, the chlorophyll(ide) formed had its maximum absorption more towards 684 nm and shifted to 672 nm during a subsequent period in darkness. Thus, in this case a Shibata shift took place.
The conditions which produce the "stable" 672 nm form, without a Shibata shift, are discussed. The presence of large amounts of non-transformed protochlorophyllide remaining after the phototransformation seems to be important. Under such conditions it is possible that the Shibata shift is completed within a very short time.
Also the possible existence of two kinds of phototransformable protochlorophyllide is discussed. According to this idea one of the two protochlorophyllide forms produces a chlorophyllide absorbing at 672 nm shortly after phototransformation without having passed a Shibata shift. The other protochlorophyllide form photo-transforms to a chlorophyllide which proceeds through the Shibata shift.     

Oak seedlings grown in different light qualities

Oak seedlings (Quercus robur L.) were germinated in darkness for 3 weeks and then given continuous long wavelength far-red light (LFR; wavelengths longer than 700 nm). A control group of seedlings was kept in darkness. After 2 additional weeks the chlorophyll formation ability in red light was examined in the different seedlings. The stability of the protochlorophyll(ide) and chlorophyll(ide) forms to high intensity red irradiation was also measured. Oak seedlings grown in darkness accumulated protochlorophyll(ide) (6 μg per g fresh matter). Absorption spectra and fluorescence spectra indicated the presence of more protochlorophyll(ide)_628–632 than protochlorophyllide_650–657. The level of protochlorophyll(ide) was higher in leaves of plants cultivated in LFR light (13 μg per g fresh matter) than in leaves of dark grown plants. 12% of the protochlorophyll(ide) was esterified in both cases. The level of protochlorophyll(ide)_628–632 in LFR grown oaks varied with the age of the leaves, being higher in the older (basal) leaves, but also in the very youngest (top-most) leaves. The ability of the leaves to form photostable chlorophyll in red light showed a similar age dependence, being low in rather young and in older leaves. A low ability to form photostable chlorophyll thus appears to be correlated with a high content of protochlorophyll(ide)_628–632. Upon irradiation only the protochlorophyllide_650–657 was transformed to chlorophyllide. After this phototransformation the chlorophyllide peak at 684 nm shifted to 671 nm within about 30 min in darkness. This shift took place without any accompanying change in photostability of the chlorophyll(ide). Upon irradiation with strong red light a similar shift took place within one minute. This indicates that the chlorophyllide after phototransformation was rather loosely bound to the photoreducing enzyme. The development towards photostable chlorophyll forms consists of three phases and is discussed.     

The Pool Size of Protochlorophyllide during Different Stages of Greening of Dark Grown Wheat Leaves

The pool size of protochlorophyllide in wheat leaves irradiated for 5 minutes to 6 hours was studied. Protochlorophyllide then accumulated in the dark, but the pool size of regenerated protochlorophyllide was considerably smaller in leaves irradiated for six hours than in leaves irradiated for 5 minutes. The decrease in pool size of regenerated protochlorophyllide was found to take place at the time when the chlorophyll formation had accelerated and reached the linear phase. The protochlorophyllide accumulated is the form with absorption maximum at 650 nm, which is phototransformed to chlorophyllide with maximum absorption at 684 nm. This species goes through the Shibata shift when formed even after 6 hours of irradiation. If leaves, irradiated for 1 or 6 hours, were fed with δ-amino-levulinic acid the protochlorophyllide synthesis was only 1.2 times faster in the leaves irradiated for 6 hours than in those irradiated for 1 hour. In the case of leaves fed with δ-amino-levulinic acid the absorption maximum of protochlorophyllide is at 636 nm and the absorption maximum of the chlorophyllide formed is at 672 nm.     

The Shibata Shift and the Transformation of Etioplasts to Chloroplasts in Wheat with Clomazone (FMC 57020) and Amiprophos-Methyl (Tokunol M)

The Shibata shift is a change in the absorption maximum of chlorophyllide from 684 to 672 nanometers that occurs within approximately 0.5 hour of phototransformation of protochlorophyllide to chlorophyllide. Two compounds, clomazone and amiprophos-methyl, which previously have been shown to inhibit the Shibata shift in vivo, were used to look for correlations between the Shibata shift and other processes that occur during etioplast to chloroplast transformation. Leaf sections from 6-day-old etiolated wheat seedlings (Triticum aestivum L. cv Walde) were treated with 0.5 millimolar clomazone or 0.1 millimolar amiprophos-methyl in darkness. In addition to the Shibata shift, the esterification of chlorophyllide to chlorophyll and the relocation of protochlorophyllide reductase from the prolamellar bodies to the developing thylakoids were inhibited by these treatments. Prolamellar body transformation did not appear to be affected by amiprophos-methyl and was only slightly affected by clomazone. The results indicate that: (a) there is a strong correlation between the occurrence of the Shibata shift and esterification activity; (b) transformation of the prolamellar bodies does not depend on the Shibata shift; and (c) the occurrence of the Shibata shift may be a prerequisite to the relocation of protochlorophyllide reductase from prolamellar bodies to thylakoids.     

Characterization and Properties of a Protochlorophyllide Ester in Leaves of Dark Grown Barley with Geranylgeraniol as Esterifying Alcohol

The protochlorophyllide ester isolated from dark grown barley leaves was shown to contain geranylgeraniol as esterifying alcohol. No phytylester was found. The qualitative analyses were performed with combined gas chromatography-mass spec-trometry. Chromatographic separation and spectrofluorometric determination of the protochlorophyll and chlorophyll pigments before and after irradiation of the dark grown leaves with light flashes at 2°C showed that part of the protochlorophyllide ester was photoconverted to chlorophyll a.     

On the nature of the two pathways in chlorophyll formation from protochlorophyllide

The kinetics of formation of esterified chlorophyll in etiolated barley (Hordeum vulgare L.) leaves after illumination with a single flash was studied. It was found that after partial (14–24%) and after full photoreduction of protochlorophyllide, the same quantity of esterified products appear during the first 5 s after the flash. The rest of formed chlorophyllide was esterified in a slow process during at least 30 min at 15 °C. The product of fast esterification can be correlated with ‘short-wavelength’ chlorophyll, characterized by a fluorescence emission peak at 673–675 nm. This is the only chlorophyll form detectable within 20 s after partial (14%) photoconversion, and it appears at the same time as the shoulder of the chlorophyll(ide) fluorescence after full photoconversion. The main product after full photoconversion shows a fluorescence at 689 nm shifting in darkness within 15 s to 693 nm and then within 30 min to 682 nm (Shibata shift). The slow esterification proceeds with similar kinetics as the Shibata shift. We propose that the fast esterification of only part of total chlorophyllide after full photoconversion of protochlorophyllide in etiolated leaves reflects the restricted capacity of the esterifying system. The slow esterification of the residual chlorophyllide may be time-limited by its release from protochlorophyllide oxidoreductase, by disaggregation of prolamellar bodies and by diffusion of tetraprenyl diphosphates towards chlorophyll synthase. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Effect of Phytohormones on Chlorophyll(ide), Protochlorophyll(ide) and Carotenoid Formation in Greening Dark Grown Wheat Leaves

The influence of phytohormones on chlorophyll and carotenoid formation during the greening of irradiated dark grown wheat leaves (Triticum aestivum L. cv. Starke II Weibull) was studied. Leaves were floated on solutions of abscisic acid, gibberellic acid and kinetin for 24 h. The chlorophyll and carotenoid contents were determined during a subsequent period of 48 h of continuous irradiation. Leaves treated with abscisic acid showed a longer lag phase and a lower rate of accumulation of chlorophyll as compared to the control than did leaves treated with gibberellic acid and kinetin. The carotenoid content was low both in leaves treated with abscisic acid and in those treated with gibberellic acid. Treatment with abscisic acid lowered the protochlorophyllide regeneration after a saturating light flash while gibberellic acid as well as kinetin had no effect. The influence of ABA was partly dependent on an increase of the wounded part of the cut leaf segments. The accumulation of protochlorophyllide in leaves treated with δ-aminolevulinic acid was not affected by the different hormonal treatments. These results suggest that the main effect of abscisic acid is probably outside the chloroplast, i.e. on the formation or transport of δ-aminolevulinic acid.     

High salt stress in wheat leaves causes retardation of chlorophyll accumulation due to a limited rate of protochlorophyllide formation

When exposed to salt stress, leaves from dark-grown wheat seedlings ( Triticum aestivum , cv. Giza 168) showed reduced accumulation of chlorophyll during irradiation. To elucidate the mechanism behind salt-influenced reduction of chlorophyll biosynthesis, we have investigated the effect of salt stress on the spectral forms of Pchlide, the phototransformation of Pchlide to Chlide, the Shibata shift, the regeneration of Pchlide and the accumulation of Pchlide from 5-aminolevulinic acid (ALA). We found that the phototransformation of Pchlide to Chlide was not affected by salt stress. The blue shift (Shibata shift) of newly formed Chlide was delayed both after flash irradiation and in continuous light. The reformation of Pchlide in darkness after a flash irradiation or after a period of 3-h irradiation was retarded in the salt-treated leaves. However, after a 20-h dark period, Pchlide was reformed even in salt-treated leaves but the formation of short-wavelength Pchlide was suppressed. Compared to controls, salt treatment also reduced the amount of Pchlide accumulated in leaves floated on ALA. The increase in the low temperature fluorescence emission spectrum at 735 nm, which occurred gradually during several hours of irradiation with continuous light in control leaves, was completely suppressed in salt-treated leaves. It is concluded that salt stress inhibits chlorophyll accumulation partly by reducing the rate of porphyrin formation but, as discussed, also by a possible reduction in the formation of chlorophyll-binding proteins.     

The Light Induced Protochlorophyll–Chlorophyll a-Transformation and the Succeeding Interconversions of the Different Forms of Chlorophyll

Curve resolution into Gaussian components of the absorption spectra during the varying stages of the Shibata shift in dark grown, irradiated leaves of barley indicates that the chlorophyll a forms formed after irradiation consist of the same main components which have been reported to be present in all hitherto investigated plant materials (peak values in the red region 662, 670, 677 and 683 nm, respectively) but in varying proportions. The spectra during the Shibata shift proper can be satisfied by a mixture of two single components gradually changing their proportions, although a four component system gives a still better fit to the measured absorption curves. It is also shown that curves taken before and after the shift and added together in the appropriate proportions will match the absorption spectrum measured with peak at the isosbestic point (after ca. 15 min at room temperature).     

The Influence of 8-Hydroxyquinoline on the Accumulation of Porphyrins in Dark-Grown Wheat Leaves Treated with δ-Aminolevulinic Acid

Dark-grown wheat leaves treated with δ-aminolevulinic acid and 8-hydroxyquinoline accumulated porphyrins, most of which were protochlorophyllide and magnesiumprotoporphyrin monomethylester. The ratio between these two components was dependent on the concentration of 8-hydroxyquinoline. Small amounts of other porphyrins could also be detected. The treatment with 8-hydroxyquinoline and the presence of large amounts of porphyrins other than protochlorophyllide did not influence the photoreduction of protochlorophyllide or the Shibata shift. 8-Hydroxyquinoline caused an inhibition of protochlorophyllide biosynthesis, which could be reversed by rinsing the leaves several times with phosphate buffer. Magnesiumprotoporphyrin monomethylester was then converted to protochlorophyllide. The reversal induced by washing was increased if the buffer contained iron. The possible function of iron in the chlorophyll metabolism and its role in the inhibition reactions with 8-hydroxyquinoline are discussed.     

Protochlorophyll(ide) accumulation and degradation in the dark and photoconversion to chlorophyll in the light in pigment mutant C-2A' of Scenedesmus obliquus

Pigment mutant C-2A' of Scenedesmus obliquus accumulates only traces of chlorophyll, when grown heterotrophically in the dark. Immediately upon transfer of cells into fresh medium protochlorophyllide and protochlorophyll are formed, which accumulate to their maximum concentrations within 8 to 12 h. Subsequently, this protochlorophyll(ide) is degraded in the dark, but not transformed into chlorophyll. After 6–8 days of dark growth no protochlorophyll(ide) can be detected any more. The protochlorophyll(ide) pool of cultures, which contain reduced concentrations, can be reestablished either by addition of glucose or illumination with blue light; both increase the rate of respiration.
By low temperature spectroscopy in vivo and by absorption and fluorescence emission spectroscopy of pigment extracts it is shown that the protochlorophyllide accumulated in freshly inoculated cultures can be converted to chlorophyll in light.
From the action spectrum for chlorophyll formation after addition of glucose it can be seen that protochlorophyllide 636 and 649 are present and are photoconvertible in this mutant.     

The influence of glycerol and chloroplast lipids on the spectral shifts of pigments associated with NADPH:protochlorophyllide oxidoreductase from Avena sativa L.

Dark-grown angiosperm seedlings lack chlorophylls, but accumulate protochlorophyllide a complexed with the light-dependent enzyme NADPH:protochlorophyllide oxidoreductase. Previous investigators correlated spectral heterogeneity of in vivo protochlorophyllide forms and a shift of chlorophyllide forms from 680 to 672 nm (Shibata shift) occurring after irradiation, with intact membrane structures which are destroyed by solubilization. We demonstrate here that the various protochlorophyllide forms and the Shibata shift which disappear upon solubilization are restored if the reconstituted complex is treated with plastid lipids and 80% (w/v) glycerol. We hypothesize that the lipids can form a cubic phase and that this is the precondition in vitro and in vivo for the observed spectral properties before and after irradiation.     

Control of chlorophyll synthesis by phytochrome

Summary The rate of chlorophyllide esterification in mustard cotyledons can be increased by a pretreatment with 5 min red light applied 24 h prior to the protochlorophyll(ide)chlorophyll(ide) photoconversion at 60 h after sowing. Simultaneously the red light pulse pretreatment leads to a decrease of the total amount of chlorophyll(ide) a in darkness. It has been proven that phytochrome (P_fr) is the photoeffector for both. Since the amounts of esterified chlorophyllide are determined by the ratio [chlorophyll a]/[chlorophyllide a+chlorophyll a] it is assumed that P_fr increases the rate of esterification indirectly via stimulating the decrease of chlorophyll(ide) a. The regulation of chlorophyll synthesis by P_fr does not seem to involve a control of esterification. The duration of the chlorophyllide esterification differs from the duration of the Shibata shift although both are greatly shortened by the red light pulse pretreatment. The effect of 5 min red light on the duration of the esterification is fully reversible by 5 min far-red light while the reversibility with respect to the Shibata shift is lost within 2 min [Jabben, M. and H. Mohr, Photochem. Photobiol. 22, 55–58 (1975)]. We conclude that the control of the chlorophyllide esterification and the control of the Shibata shift cannot be traced back to the same initial action of P_fr.Abbreviations Chl chlorophyll - Chlide chlorophyllide - Chl(ide) sum of Chl and Chlide - PChl protochlorophyll - PChlide protochlorophyllide - PChl(ide) sum of PChl and PChlide - P_fr far-red absorbing form of the phytochrome system     

Far-red induced changes of the protochlorophyllide components in wheat leaves

Biosynthesis of chlorophyll is partly controlled by the phytochrome system. In order to study the effects of an activated phytochrome system on the protochlorophyllide (PChlide) biosynthesis without accompanying phototransformation to chlorophyll, wheat seedlings (Triticum aestivum L. cv. Starke II Weibull) were irradiated with long wavelength far-red light of low intensity. Absorption spectra were measured in vivo after different times in the far-red light or in darkness. The relationship between the different PChlide forms, the absorbance ratio _{650nm636 nm} changed with age in darkness, and the change was more pronounced when the leaves were grown in far-red light. Absorption spectra of dark-grown leaves always showed a maximum in the red region at 650 nm. For leaves grown in far-red light the absorption at 636 nm was high, with a maximum at the 5 day stage where it exceeded the absorption at 650 nm. At the same time there was a maximum in the total amount of PChlide accumulated in the leaves, about 30% more than in leaves grown in darkness. But the amount of the directly phototransformable PChlide, mainly PChlide_650–657, was not increased. The amount of PChlide_628–632, or more probably the amount of (PChlide_628–632, + PChlide _636–657) was thus higher in young wheat leaves grown in far-red light than in those grown in darkness. After the 5 day stage the absorption at 636 nm relative to 650 nm decreased with age, and at the 8 day stage the spectra were almost the same in both types of leaves. Low temperature fluorescence spectra of the leaves also showed a change in the ratio between the different PChlide forms. The height of the fluorescence peak at 632 nm relative to the peak at 657 nm was higher in leaves grown in far-red light than in dark-grown leaves. – After exposure of the leaves to a light flash, the half time for the Shibata shift was measured. It increased with age both for leaves grown in darkness and in far-red light; but in older leaves grown in far-red light (7–8 days) the half time was slightly longer than in dark-grown leaves. – The chlorophyll accumulation in white light as well as the leaf unrolling were faster for leaves pre-irradiated with far-red light. The total length of the seedlings was equal or somewhat shorter in far-red light, but the length of the coleoptile was markedly reduced from 8.1 ± 0.1 cm for dark-grown seedlings to 5.2 ± 0.1 cm for seedlings grown in far-red light.     

Changing ratios of phototransformable protochlorophyll and protochlorophyllide of bean seedlings developing in the dark

Protochlorophyll (Pchl) and protochlorophyllide (Pchlide) are at comparable levels in 2-day-old (young) etiolated bean leaves (Phaseolus vulgaris L. var. Red Kidney). During subsequent development in the dark, both pigments increase, but the rate of Pchlide increase is greater than that of Pchl, leading to the commonly observed predominance of Pchlide beyond 7 days (old leaves). Both protopigments are phototransformable to their respective chlorophyll(ide) photoproducts throughout dark development. The rate of protopigment regeneration in young leaves after illumination is rapid and displays no lag, whereas this process in old leaves begins slowly and achieves only about one-fifth the rate of younger leaves. The rate of chlorophyllide esterification is also faster in the younger tissue. Since the proplastid-related properties of young bean leaves are quite similar to those of Euglena, young leaves and Euglena may represent an evolutionarily primitive case compared with older bean leaves which contain etioplasts. Since Euglena and young beans green perfectly well when exposed to light, the extensive modifications associated with prolonged dark growth do not seem to be obligatory for plastid development. The properties of older beans are viewed as being the consequence of prolonged etiolation which may provide a faster rate of plastid development and appearance of photosynthesis as the plant nears the limits of its stored reserves.     

The influence of glycerol and chloroplast lipids on the spectral shifts of pigments associated with NADPH: protochlorophyllide oxidoreductase from Avena sativa L

Dark-grown angiosperm seedlings lack chlorophylls, but accumulate protochlorophyllide a complexed with the light-dependent enzyme NADPH:protochlorophyllide oxidoreductase. Previous investigators correlated spectral heterogeneity of in vivo protochlorophyllide forms and a shift of chlorophyllide forms from 680 to 672 nm (Shibata shift) occurring after irradiation, with intact membrane structures which are destroyed by solubilization. We demonstrate here that the various protochlorophyllide forms and the Shibata shift which disappear upon solubilization are restored if the reconstituted complex is treated with plastid lipids and 80% (w/v) glycerol. We hypothesize that the lipids can form a cubic phase and that this is the precondition in vitro and in vivo for the observed spectral properties before and after irradiation.     

Quantum yield and energy dependence for photooxidation of chlorophyllide in greening wheat

Dark grown leaves of wheat were irradiated with red light of different intensities, at a temperature close to 0°C. The rate of photoreduction of the protochlorophyllide 650-form into chlorophyllide 684-form was measured. On continued irradiation the chlorophyllide 684-form was photodecomposed. By comparing the rates of the two processes the quantum yield for photooxidation of the chlorophyllide 684-form was calculated. The quantum yield was 2°10^-5 at an intensity of 2200 W m^-2, and increased with decreasing light intensity to 3.2°10^-5 at an intensity of 170 W m^-2.