The photoactivation energy of the visual pigment in two spectrally different populations of <Emphasis Type="Italic">Mysis relicta</Emphasis> (Crustacea,Mysida)

We report the first study of the relation between the wavelength of maximum absorbance (λ_max) and the photoactivation energy (E _a) in invertebrate visual pigments. Two populations of the opossum shrimp Mysis relicta were compared. The two have been separated for 9,000 years and have adapted to different spectral environments (“Sea” and “Lake”) with porphyropsins peaking at λ_max=529 nm and 554 nm, respectively. The estimation of E _a was based on measurement of temperature effects on the spectral sensitivity of the eye. In accordance with theory (Stiles in Transactions of the optical convention of the worshipful company of spectacle makers. Spectacle Makers’ Co., London, 1948), relative sensitivity to long wavelengths increased with rising temperature. The estimates calculated from this effect are E _a,529=47.8±1.8 kcal/mol and E _a,554=41.5±0.7 kcal/mol (different at P<0.01). Thus the red-shift of λ_max in the “Lake” population, correlating with the long-wavelength dominated light environment, is achieved by changes in the opsin that decrease the energy gap between the ground state and the first excited state of the chromophore. We propose that this will carry a cost in terms of increased thermal noise, and that evolutionary adaptation of the visual pigment to the light environment is directed towards maximizing the signal-to-noise ratio rather than the quantum catch.     

Visual pigments of marine carnivores: pinnipeds, polar bear, and sea otter

Rod and cone visual pigments of 11 marine carnivores were evaluated. Rod, middle/long-wavelength sensitive (M/L) cone, and short-wavelength sensitive (S) cone opsin (if present) sequences were obtained from retinal mRNA. Spectral sensitivity was inferred through evaluation of known spectral tuning residues. The rod pigments of all but one of the pinnipeds were similar to those of the sea otter, polar bear, and most other terrestrial carnivores with spectral peak sensitivities (λ_max) of 499 or 501 nm. Similarly, the M/L cone pigments of the pinnipeds, polar bear, and otter had inferred λ_max of 545 to 560 nm. Only the rod opsin sequence of the elephant seal had sensitivity characteristic of adaptation for vision in the marine environment, with an inferred λ_max of 487 nm. No evidence of S cones was found for any of the pinnipeds. The polar bear and otter had S cones with inferred λ_max of ∼440 nm. Flicker-photometric ERG was additionally used to examine the in situ sensitivities of three species of pinniped. Despite the use of conditions previously shown to evoke cone responses in other mammals, no cone responses could be elicited from any of these pinnipeds. Rod photoreceptor responses for all three species were as predicted by the genetic data.Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Chemical Characterization,Crossfeeding and Uptake Studies on Hydroxamate Siderophore of <Emphasis Type="Italic">Alcaligenes faecalis</Emphasis>

We report the production of two types of siderophores namely catecholate and hydroxamate in modified succinic acid medium (SM) from Alcaligenes faecalis. Two fractions of siderophores were purified on amberlite XAD, major fraction was hydroxamate type having a λ_max at 224 nm and minor fraction appeared as catecholate with a λ_max of 264 nm. The recovery yield obtained from major and minor fractions was 297 and 50 mg ml⁻¹ respectively. The IEF pattern of XAD-4 purified siderophore suggested the pI value of 6.5. Cross feeding studies revealed that A. faecalis accepts heterologous as well as self (hydroxamate) siderophore in both free and iron complexed forms however; the rate of siderophore uptake was more in case of siderophores complexed to iron. Siderophore iron uptake studies indicated the differences between hydroxamate siderophore of A. faecalis and Alc E, a siderophore of Alcaligenes eutrophus.     

Structural and biochemical properties of glycosylated and deglycosylated glucose oxidase from Penicillium amagasakiense

Glucose oxidase from Penicillium amagasakiense was purified to homogeneity by ion-exchange chromatography and deglycosylated with endoglycosidase H. On the basis of gas chromatography and sodium dodecyl sulphate/polyacrylamide gel electrophoretic (SDS-PAGE) analyses, the protein-bound high-mannose-type carbohydrate moiety corresponded to 13% of the molecular mass of glycosylated glucose oxidase. A total of six N-glycosylation sites per dimer were determined from the N-acetylglucosamine content. The enzymatically deglycosylated enzyme contained less than 5% of the original carbohydrate moiety. A molecular mass of 130 kDa (gel filtration) and 133 kDa (native PAGE) was determined for the dimer and 67 kDa (SDS-PAGE) for the monomer of the deglycosylated enzyme. The N-terminal sequence, which has not been published for glucose oxidase from P. amagasakiense to date and which showed less than 50% homology to the N terminus of glucose oxidase from Aspergillus niger, and the amino acid composition were not altered by the deglycosylation. Deglycosylation also did not affect the kinetics of glucose oxidation or the pH and temperature optima. It also did not increase the susceptibility of the enzyme to proteolytic degradation. However, deglycosylated glucose oxidase exhibited decreased pH and thermal stability. The thermal stability of both enzymes was shown to be dependent on the buffer concentration and was enhanced by certain additives, particularly 1 M (NH₄)₂SO₄, which stabilised glucose oxidase 100- to 300-fold at 50 °C and pH 7–8, and 2 M KF, which stabilised the enzyme up to 36-fold at 60 °C and pH 6. In sodium acetate buffer, changes in pH (4–6) affected the affinity for glucose but had no effect on the V _max of the reaction. In contrast, in TRIS buffer, pH 8, a 10-fold decrease in V _max and a 2-fold decrease in K _m were observed. Received: 8 October 1996 / Received revision: 14 January 1997 / Accepted: 17 January 1997     

Evidence for glucose-mediated covalent cross-linking of collagen after glycosylation in vitro.

Rabbit forelimb tendons incubated for 15 or 21 days at 35 degrees C in the presence of 8 or 24 mg of glucose/ml were shown to change their chemical, biochemical and mechanical characteristics. The tendons treated with glucose contained up to three times as much hexosyl-lysine and hexosylhydroxylysine as did control tendons as judged by assay of NaB3H4-reduced samples. Measurement of the force generated on thermal contraction showed significant increases in glycosylated tendons compared with controls, indicating the formation of new covalent stabilizing bonds. This conclusion was supported by the decreased solubility of intact tendons and re-formed fibres glycosylated in vitro, and by the evidence from peptide maps of CNBr-digested glucose-incubated tendons. The latter, when compared with peptide maps of control tendons, revealed the presence of additional high-Mr peptide material. These peptides appear to be cross-linked by a new type of covalent bond stable to mild thermal and chemical treatment. This system in vitro provides a readily controlled model for the study of the chemistry of changes brought about in collagen by non-enzymic glycosylation in diabetes.     

Relationship between the wavelength maximum of a protein and the temperature dependence of its intrinsic tryptophan fluorescence intensity

Proper determination of the temperature dependence of intrinsic tryptophan fluorescence intensity in native and denatured states is an essential prerequisite for extracting the free energy of protein unfolding from the thermal denaturation profile. The most common method employed in determining the temperature dependence of these conformations is through the determination of slopes of pre- and post-transition baselines. However, simulations of protein unfolding profiles suggest that this method does not work for marginally stable proteins. We show herein that the temperature dependence of the fluorescence intensity of N-acetyl tryptophanamide (NATA) in organic solvents and water may be used to represent the temperature dependence of the fluorescence intensity of tryptophan in native and denatured conformations of a protein, respectively. The wavelength of the emission maximum, λ _max, of N-acetyl tryptophanamide (NATA) in a particular solvent or tryptophan in proteins is related to the temperature dependence (m) of its fluorescence intensity by the equation: m (K⁻¹) = (−0.000299 ± 2.2 × 10⁻⁵ K⁻¹ nm⁻¹) × λ _max (nm) + (0.0919 ± 0.0025 K⁻¹).     

The Molecular Evolution of Visual Pigments of Freshwater Crayfishes (Decapoda: Cambaridae)

This study examines the diverse maximum wavelength absorption (λ_max) found in crayfishes (Decapoda: Cambaridae and Parastacidae) and the associated genetic variation in their opsin locus. We measured the wavelength absorption in the photoreceptors of six species that inhabit environments of different light intensities (i.e., burrows, streams, standing waters, and subterranean waters). Our results indicate that there is relatively little variation in λ_max (522–530 nm) among species from different genera and families. The existing variation did not correlate with the habitat differences of the crayfishes studied. We simultaneously sequenced the rhodopsin gene to identify the amino acid replacements that affect shifts in maximum wavelength absorption. We then related these to changes that correlated with shifts in λ_max by reconstructing ancestral character states using a maximum-likelihood approach. Using amino acid sequences obtained from five species (all were 301 amino acids in length), we identified a number of candidates for producing shifts of 4 to 8 nm in λ_max. These amino acid replacements occurred in similar regions to those involved in spectral shifts in vertebrates. Received: 12 March 1997 / Accepted: 3 June 1997     

The nonenzymatic glycosylation of collagen

Calf skin acid-soluble collagen, containing about 34 residues of lysine plus hydroxylysine per 100,000 dalton polypeptide chain, was treated with [¹⁴C]glucose in the presence or absence of NaCNBH₃. In 144 h, under the conditions employed, the presence of NaCNBH₃ increased the extent of glycosylation from 8 to 15% of the total residues of lysine plus hydroxylysine. The extent of glycosylation was estimated, using acid hydrolysates of the protein, by isolation and determination of reduced adducts (1-lysinohexitols) employing a system of paper chromatography followed by chromatography on an amino acid analyzer. By those means the difficulties of using specific color reactions such as that with thiobarbituric acid were obviated. Identification of the reduced adducts as forms of 1-lysinohexitol was made by comparison of that substance prepared by treatment of polylysine with [¹⁴C]glucose in the presence of NaCNBH₃. Of interest is the fact that treatment of the polymer with glucose for 144 h under conditions similar to those used for the collagen, resulted in an increase of extent of glycosylation from 3 to about 50% of the total lysine residues when NaCNBH₃ was present in the incubation medium. The greater degree of glycosylation of lysine residues in polylysine as compared with collagen (15 versus about 50%) may be ascribed to the different orders of macromolecular structure in the protein that could sequester certain of the residues from reaction with glucose. 1-Lysinohexitol was also identified in hydrolysates of neutral salt-soluble guinea pig skin collagen that had been reacted with glucose and then treated with NaB³H₄. The glycosylated collagens were fragmented by treatment with CNBr, and modified lysine residues were found to occur along the entire length of the collagen chains. The use of NaCNBH₃ in the manner described above permits measurement of both aldimine and ketoamine forms of the adducts made with glucose. The possible physiological significance of the reversibility of the ketoamine form of adduct is discussed briefly.     

Improved Bioavailability of Poorly Water-Soluble Drug Curcumin in Cellulose Acetate Solid Dispersion

Curcumin (Cur), one of the most widely used natural active constituents with a great variety of beneficial biological and pharmacological activities, is a practically water-insoluble substance with a short biologic half-life. The aim of this study was to develop a sustained-release solid dispersion by employing water-insoluble carrier cellulose acetate for solubility enhancement, release control, and oral bioavailability improvement of Cur. Solid dispersions were characterized by solubility, in vitro drug release, Fourier transform infrared spectroscopy, X-ray diffractometry, and differential scanning calorimetry studies. The in vivo performance was assessed by a pharmacokinetic study. Solid-state characterization techniques revealed the amorphous nature of Cur in solid dispersions. Solubility/dissolution of Cur was enhanced in the formulations in comparison with pure drug. Sustained-release profiles of Cur from the solid dispersions were ideally controlled in vitro up to 12 h. The optimized formulation provided an improved pharmacokinetic parameter (C _max = 187.03 ng/ml, t _max = 1.95 h) in rats as compared with pure drug (C _max = 87.06 ng/ml, t _max = 0.66 h). The information from this study suggests that the developed solid dispersions successfully enhanced the solubility and sustained release of poorly water-soluble drug Cur, thus improving its oral bioavailability effectively.     

Assessing the use of genomic DNA as a predictor of the maximum absorbance wavelength of avian SWS1 opsin visual pigments

Recently, in vitro mutation studies have made it possible to predict the wavelengths of maximum absorbance (λ_max) of avian UV/violet sensitive visual pigments (SWS1) from the identity of a few key amino acid residues in the opsin gene. Given that the absorbance spectrum of a cone’s visual pigment and of its pigmented oil droplet can be predicted from just the λ_max, it may become possible to predict the entire spectral sensitivity of a bird using genetic samples from live birds or museum specimens. However, whilst this concept is attractive, it must be validated to assess the reliability of the predictions of λ_max from opsin amino acid sequences. In this paper, we have obtained partial sequences covering three of the known spectral tuning sites in the SWS1 opsin and predicted λ_max of all bird species for which the spectral absorbance has been measured using microspectrophotometry. Our results validate the use of molecular data from genomic DNA to predict the gross differences in λ_max between the violet- and ultraviolet-sensitive subtypes of SWS1 opsin. Additionally, we demonstrate that a bird, the bobolink Dolichonyx oryzivorus L., can have more than one SWS1 visual pigment in its retina.     

Aromatic amino acid oxidation products as antioxidants

The accumulation of UV photolysis products of amino acids tyrosine and tryptophan, which possess antioxidant activity, has been studied by the method of luminol-dependent chemiluminescence. The amount of antioxidant products was judged by the value of the total antioxidant potential of a UV-irradiated solution, the measure of which was the distance between the peaks of the chemiluminescence curve in the system 2,2′-azo-bis(2-amidinopropane) hydrochloride + luminol with a UV-irradiated and an unirradiated sample (induction period, τ _i ). Simultaneously, the absorption and fluorescence spectra of unirradiared and UV-irradiated amino acid solutions were recorded. It was shown that exposure of a tryptophan solution to radiation led to accumulation of a fluorescent product N-formyl kynurenine (λ_em = 325 nm, λ_max = 440 nm), and the curve of its accumulation was similar to the growth of antioxidant potential. When a tyrosine solution was irradiated, the main fluorescent product was dityrosine (λ_em = 310 nm, λ_max = 415 nm). Nevertheless, the dose dependences of the formation of dityrosine and the total antioxidant potential were completely different. It was found that another product of tyrosine UV photolysis, dihydroxyphenylalanine, possessed pronounced antioxidant activity. It was concluded that the main antioxidant produced under UV irradiation of tryptophan is formyl kynurenine, and under irradiation of tyrosine it is dihydroxyphenylalanine.     

Inhibition of collagen glycation and crosslinking in vitro by methanolic extracts of Finger millet (Eleusine coracana) and Kodo millet (Paspalum scrobiculatum)

The present investigation was carried out to study the effects of methanolic extracts of Finger millet (Eleusine coracana) and Kodo millet (Paspalum scrobiculatum) on glycation and crosslinking of collagen. Tail tendons obtained from rats weighing 200-225 g were incubated with glucose (50 mM) and 3 mg of extracts of the above millets in methanol under physiological conditions of temperature and pH for 10 days. Early glycation was estimated by phenol-sulfuric acid method and the crosslinking was assessed by pepsin digestion, cyanogen bromide peptide map and viscosity measurements. Tendon collagen incubated with glucose (50 mM) showed 65% solubility on pepsin treatment; poor resolution of bands in the cyanogen bromide peptide map, and intrinsic viscosity of 0.84 dl/g. The collagen incubated with Finger millet and Kodo millet extracts inhibited glycation; 89% and 92% solubility in pepsin; good resolution of bands in the cyanogen bromide peptide map and intrinsic viscosity of 0.46 and 0.58 dl/g respectively. The study implicates the potential usefulness of the above millets in protection against glycation and crosslinking of collagen.     

Physiological characterization of the compound eye in monarch butterflies with focus on the dorsal rim area

The spectral, angular and polarization sensitivities of photoreceptors in the compound eye of the monarch butterfly (Danaus plexippus) are examined using electrophysiological methods. Intracellular recordings reveal a spectrally homogenous population of UV receptors with optical axes directed upwards and ≥10° to the contralateral side. Based on optical considerations and on the opsin expression pattern (Sauman et al. 2005), we conclude that these UV receptors belong to the anatomically specialized dorsal rim area (DRA) of the eye. Photoreceptors in the main retina with optical axes <10° contralateral or ipsilateral have maximal sensitivities in the UV (λ_max≤340 nm), the blue (λ_max=435 nm) or in the long-wave range (green, λ_max=540 nm). The polarization sensitivity (PS) of the UV receptors in the DRA is much higher (PS=9.4) than in the UV cells (PS=2.9) or green cells (PS=2.8) of the main retina. The physiological properties of the photoreceptors in the DRA and in the main retina fit closely with the anatomy and the opsin expression patterns described in these eye regions. The data are discussed in the light of present knowledge about polarized skylight navigation in Lepidopterans.     

Apolipoprotein H Is Not Affected by In Vitro Glycosylation

Increased nonenzymatic glycosylation of all major classes of apolipoproteins has been demonstrated in diabetes. In this work we deal with the in vitro nonenzymatic glycosylation of apolipoprotein H, whose role in lipid metabolism is still poorly understood and whose levels increase in diabetes. Apolipoprotein H was isolated from human plasma and purified through a combination of affinity chromatography and continuous elution electrophoresis. The in vitro glycosylation was performed by incubating purified apolipoprotein H with high concentration of glucose. Our results indicate that the in vitro nonenzymatic glycosylation has no effect on the physical properties of apolipoprotein H, despite the fact that this apolipoprotein contains a high number of lysine residues. Since the in vitro concentration of glucose was far higher than the levels normally found in diabetic subjects, it is unlikely for apolipoprotein H to become glycosylated in diabetes.     

Visual pigments, oil droplets, ocular media and cone photoreceptor distribution in two species of passerine bird: the blue tit (Parus caeruleus L.) and the blackbird (Turdus merula L.)

The spectral absorption characteristics of the retinal photoreceptors of the blue tit (Parus caeruleus) and blackbird (Turdus merula) were investigated using microspectrophotometry. The retinae of both species contained rods, double cones and four spectrally distinct types of single cone. Whilst the visual pigments and cone oil droplets in the other receptor types are very similar in both species, the wavelength of maximum sensitivity (λ_max) of long-wavelength-sensitive single and double cone visual pigment occurs at a shorter wavelength (557 nm) in the blackbird than in the blue tit (563 nm). Oil droplets located in the long-wavelength-sensitivesingle cones of both species cut off wavelengths below 570–573 nm, theoretically shifting cone peak spectral sensitivity some 40 nm towards the long-wavelength end of the spectrum. This raises the possibility that the precise λ_max of the long-wavelength-sensitive visual pigment is optimised for the visual function of the double cones. The distribution of cone photoreceptors across the retina, determined using conventional light and fluorescence microscopy, also varies between the two species and may reflect differences in their visual ecology. Accepted: 8 January 2000     

Purification and initial characterization of phycobiliproteins from the endophytic cyanobacterium of Azolla

The endophytic cyanobacterium, Anabaena azollae, isolated from laboratory cultures of Azolla caroliniana Willd., contains three spectroscopically distinct biliproteins. About 70% of the biliprotein is c-phycocyanin (_max 610 nm) and 13% is allophycocyanin (_max 647 nm, shoulder 620 nm). A third pigment corresponds to phycoerythrocyanin (_max 570 nm, shoulder 590 nm). In very dilute solutions of allophycocyanin, at constant pH and buffer strength, the 647 nm maximum disappears and a single _max occurs at 615–620 nm. The 647 nm absorption maximum reappears upon concentrating the dilute solution. Very dilute solutions of phycoerythrocyanin exhibit a broad peak between 570 and 590 nm. Absorption spectra of c-phycocyanin are not significantly altered upon dilution. Fluorescence emission maxima of phycoerythrocyanin, c-phycocyanin, and allophycocyanin occur at 630 nm, 643 nm and 660 nm respectively, using 540 nm excitation. Two subunits, of molecular weight 16,500 () and 20,600 (), are seen in c-phycocyanin upon dissociation with SDS. Dissociation of allophycocyanin and phycoerythrocyanin with SDS yields one sizeclass of subunits, with a molecular weight of about 17,500 for allophycocyanin and 18,000 for phycoerythrocyanin.Contribution No. 684 Offprint requests to: G. A. Peters     

Fe2+-catalyzed non-enzymatic glycosylation alters collagen conformation during AGE-collagen formation in vitro

Advanced glycation end-products (AGEs) are one of the major factors of hyperglycemia related complications for diabetic patients. We studied the formation of AGEs in type I collagen after Fe²⁺-catalyzed non-enzymatic glycosylation in vitro. Type I collagen isolated from rat tail tendon was incubated with glucose and increasing concentrations of iron ions Fe²⁺. After 4 weeks incubation, cytotoxity of AGEs was indicated by the cytotoxity assay of primary human umbilical vein endothelial cells and primary human monocytes cultured with glycosylated collagen AGEs. Fourier transform infrared spectroscopy analysis revealed that structural changes of functional groups in glycosylated collagen are accelerated by the catalyst Fe²⁺. Using two-dimensional Fourier-transform infrared correlation spectroscopy analyses, for the first time, we demonstrated that the order of structural changes of these functional groups is -CH- > Amide I > Amide II > Amide III > ν(CO) the carboxylic group of Asn, Gln or polyproline amino acid residue in the course of AGE-collagen formation. Knowing the positions of these functional groups in collagen, this order of changes indicates that during glycation of collagen, the structure of the main chain residues in collagen changed first, and then the side chain changed gradually, which may lead to more carboxylic groups exposed to glucose for further formation of AGE-collagen irreversibly. The findings presented may support the design of new therapeutic strategies to prevent or slow down the Fe²⁺-catalyzed glycosylation of collagen and other matrix proteins.     

Effect of Sugars on Rabbit Serum Albumin Stability and Induction of Secondary Structure

The effect of sugars (sucrose, maltose, and glucose) on the thermal and chemical denaturation of rabbit serum albumin (RSA) has been examined by viscosity and far UV circular dichroism measurements. The viscosity measurements indicate a change in the reduced viscosity from 4.18 to 16.23 ml/g in the temperature range from 20 to 90°C. The T _m value for RSA obtained by viscosity measurements in the absence of sugar was found to be 63.2°C, but this value increased to 68.4, 70.3, and 73.2°C in the presence of 0.5 M sucrose, 0.5 M glucose, and 0.5 M maltose, respectively. Further, the stability of RSA in the presence of 0.5 M sugars was also investigated by measuring the mean residue ellipticity at 222 nm (MRE₂₂₂) using chemical (0-6 M guanidine hydrochloride) and thermal (20-90°C) transition processes. At the midpoint of the chemical denaturation, the increase in the MRE values at 222 nm in the presence of 0.5 M sugars were of the same order as the increase in the T _m values, i.e., maltose > glucose > sucrose. Interestingly, a mixture of 0.25 M glucose and 0.25 M fructose showed a cumulative effect on the thermal as well as chemical stability as compared to 0.5 M sucrose alone. In the case of both thermal and chemical denaturation, there was an increase in the MRE₂₂₂ values upon addition of various sugars, this indicating induction of secondary structure in the protein.     

Inhibition of hexose transport by glucose in a glucose-6-phosphate isomerase mutant ofSaccharomyces cerevisiae

The rate of hexose transport was approximately 60% lower for both the high- and the low-affinity components of hexose uptake when a glucose-6-phosphate isomerase mutant ofSaccharomyces cerevisiae was preincubated with glucose, as compared with preincubation with water. Similarly theJ _max value of the high-affinity system of the mutant was 25–35 % of the correspondingJ _max value for normal cells incubated with glucose. Accumulation of glucose 6-phosphate or of some other metabolite, such as fructose 6-phosphate or trehalose, may be responsible for this striking inhibition.     

A proposal for universal formulas for estimating leaf water status of herbaceous and woody plants based on spectral reflectance properties

The present study deals with the relationships between water status parameters of plant leaves and reflectances (R_λ) at characteristic wavelengths, between 522 and 2450 nm, as well as reflectance ratios, R_λ/R₁₄₃₀, R_λ/R₁₆₅₀, R_λ/R₁₈₅₀, R_λ/R₁₉₂₀, and R_λ/R₁₉₅₀, based on the air-drying experimental results of soybean (Glycine max Merr.), maize (Zea mays L.), tuliptree (Liriodendron tulipifera L.) and viburnum (Viburnum awabuki K. Koch.) plants. The water status parameters include leaf water content per unit leaf area (LWC), specific leaf water content (SWC), leaf moisture percentage of fresh weight (LMP), relative leaf water content (RWC) and relative leaf moisture percentage on fresh weight basis (RMP). Effective spectral reflectances and reflectance ratios for estimating the LWC, SWC, LMP, RWC and RMP were identified. With these spectral indices, approaches to estimating LWC, RWC and RMP were discussed. Eventually, an attempt on universal formulas was made for estimating the leaf moisture conditions of both herbaceous and woody plants as mentioned above. Moreover, applicability of these formulas was checked with the field experimental results of soybean and maize grown under water and nutrient stresses. This revised version was published online in June 2006 with corrections to the Cover Date.