Can. lnst. Food Sci. Technol. J. Vol. 19, No. 1, pp. 17-22, 1986

Effects of Chemical Modifications on the Physicochemical and Cake-Baking Properties of Egg White

C.Y. Ma, L.M. Poste
Food Research Institute
Agriculture Canada
Ottawa, Ontario K1A 0C6
and
J. Holme
The Griffith Laboratories, Ltd.
Scarborough. Ontario MIL 3J8

Contribution No. 646 Food Research Institute, Agriculture Canada
Copyright © 1986 Canadian Institute of Food Science and Technology

Abstract

Egg white solids (EWE) were modified with succinic anhydride and a water-soluble carbodiimide. Both succinylation and carboxyl modification caused a shift in net charge but no marked changes in surface hydrophobicity or SH content. The surface and interfacial tensions were increased by succinylation. The denaturation temperatures (Td) of the proteins from both unmodified and carboxyl-modified EWS were increased by the addition of 50% sucrose, whereas the Td's of the highly succinylated egg white proteins were not changed. Succinylation improved the emulsification properties and lowered the foaming performance of EWS. The heat coagulability of egg white proteins at pH 7.2 was decreased by both modifications, while at pH 5.8, the highly succinylated (91.6%) EWS was relatively heat stable. The layer cake baking performance was improved by succinylation at both low (24.5%) and high (91.6%) levels of modification. Highly succinylated EWS, however, showed poor performance in an angel food cake system; this could be attributed to poor foaming properties and low heat coagulability. Carboxyl modification did not cause marked changes in functional and baking properties of EWS.

Résumé

Des extraits secs de blanc d'oeuf (EWS) furent modifiés à l'anhydride succinique et avec un carbodiimide hydrosoluble. L'un et l'autre, la succinylation et la modification des carboxyles, ont changé la charge nette, mais sans influencer pour la peine l'hydrophobicité de surface ou la teneur en SH. La succinylation a eu l'effet d'augmenter les tensions de surface et d'interface. Les températures de dénaturation (Td) des protéines des EWS témoins et des EWS aux carboxyles modifiés furent augmentées par l'addition de 50% de sucrose, tandis que les Td des protéines de blanc d'oeuf très succinylées ne furent pas affectées. La succinylation a amélioré les propriétés émulsifiantes et affaibli l'aptitude à mousser des EWS. La coagulabilité thermique des protéines de blanc d'oeuf au pH 7.2 fut diminuée par l'une et l'autre des modifications, tandis qu'au pH 5.8, les WES très succimylées (91.6%) furent relativement thermostables. La performance à la cuisson du gâteau sandwich fut améliorée par la succinylation aux niveaux de modification faibles (24.5%) ou élevés (91.6°,6). Toutefois, dans un système de gâteau aux anges, les EWS très succinylées n'ont pas donné de bons résultais, probablement à cause des mauvaises propriétés moussantes et d'une coagulabilité thermique faible. La modification des carboxyles ne produisit aucun changement important dans les propriétés fonctionnelles et de cuisson des EWS.

Introduction

Egg white is a major ingredient in cake formulations, and the ability of the egg white proteins to foam and gel at elevated temperature is critical in the, baking of cakes. However, the inter-relationship between physicochemical and functional properties of egg white proteins and their baking performance in different cake systems is not completely understood.

One approach to study such a relationship is to change the physicochemical characteristics of egg white proteins by chemical modifications. Ghandi et al. (1968) modified egg white with a dicarboxylic anhydride, 3,3-dimethylglutaric anhydride, and observed improved heat stability and emulsifying capacity. The angel cake performance was improved at low levels of modification (5-50% modification) but decreased at high levels of treatment (60-90% modification). Egg white proteins were also acylated by succinic and acetic anhydrides (Sato and Nakamura, 1977; Ball and Winn, 1982). Sato and Nakamura (1977) observed improved foaming ability and heat stability in both acetylated and succinylated egg white (70-90% acylated). Ball and Winn (1982) showed that acetylation (24-48% modification) diminished heat stability and angel cake performance, while succinylated (24-48% modification) egg white exhibited improved heat stability and foamability, but the angel cake performance was not affected. The above studies were limited to acylation and to the angel cake system, and lacked detailed assessment of the physicochemical properties of the modified proteins. The exact role of egg white proteins in the high ratio layer cake system is not clearly understood although reduction or omission of egg albumen caused a deterioration in layer cake performance (Paton et al., 1981).

In a previous work (Ma and Holme, 1982), egg albumen was modified by succinylation and carboxyl modification and the data suggested that thermal coagulation of egg albumen involves hydrophobic and ionic interactions. In the present study, commercial egg white solids (EWS) were similarly modified. The changes in some physicochemical and functional properties were determined and related to the performance in both layer cake and angel cake systems.

Materials and Methods

Commercial spray-dried egg white solids (EWS) were a product of Export Packers Company, Ltd., Winnipeg, Manitoba. Succinic anhydride was purchased from Eastman Organic Company, Rochester, N.Y.; 1-ethyl-3 (3-dimethylaminopropyl) carbodiimide (EDC) and glycine methyl ester were products of Sigma Chemical Company, St. Louis, MO. All the chemicals used were of reagent grade.

Succinylation

EWS were succinylated according to the procedure described by Groninger (1973). Succinic anhydride was added at two levels--10:1 and 50:1 (g protein:g anhydride). The extent of succinylation was determined from the free amino contents by the method of Concon (1975) using dinitrobenzene sulfonate (DNBS).

Carboxyl modification

The carboxyl groups in EWS were modified by the carbodiimide-promoted amide formation (Hoare and Koshland, 1967), using 10 mM of a water soluble carbodiimide, EDC, and glycine methyl ester (as a nucleophile) at two different concentrations (20 and 50 mM respectively). The extent of modification was determined from amino acid analysis by measuring the increase in glycine content of the protein after modification (Hoare and Koshland, 1967).

Physicochemical properties

The net charge of the unmodified and modified EWS was determined from titration curves as described previously (Ma and Holme, 1982). Surface or effective hydrophobicity was determined by the fluorescence probe method of Kato and Nakai (1980). The surface and interfacial tension of 1070 (w/v) reconstituted egg white solutions were measured using a Fisher Surface Tensiomat (Model 21). The sulfhydryl contents of the EWS samples were determined by the method of Beveridge et al (1974).

The thermal characteristics of the unmodified and modified EWS were studied by differential scanning calorimetry (DSC), using a Dupont 1090 thermal analyser equipped with a 910 DSC cell base and a high pressure DSC cell. The EWS were dissolved in either distilled water or 50% sucrose at a protein concentration of 10%, and a 10 ì L aliquot was pipetted into the sample pan. An empty pan was used as a reference. A linear heating rate of 10°C/min was used. Both the denaturation temperature (Td) and heat of transition (H) were computed from the thermograms by the 1090 analyser.

Functional properties

Emulsifying capacity (EC) of the EWS samples was determined by the oil titration method of Swift et al. (1961). The emulsifying activity index (EAI) and emulsion stability index (ESI) were determined by the method of Pearce and Kinsella (1978) which measures the turbidity of an oil/water emulsion diluted with 0.1% SDS. The foaming capacity and stability were determined by the procedure of Yasumatsu et al. (1972).

Heat coagulability

EWS were reconstituted in distilled water at 10% (w/v), and the pH was adjusted to 5.8 or 7.2 by the addition of 1N HCl or NaOH. Aliquots of the solution were heated in glass centrifuge tubes in a boiling water bath for 5 min and immediately cooled. The heated samples were then centrifuged at 5,000 X g and the protein contents in the supernatant were estimated by the method of Lowry et al. (1951). Heat coagulability was reported as the amount of protein aggregated and removed by centrifugation.

Cake baking performance

High ratio white layer cakes were prepared according to the method described by Paton et al. (1981). The cake formula was: cake flour, 95 g; white granulated sugar, 120 g; EWS, 7g; salt, 2.5 g; double-acting baking powder, 15 g; water, 163 g; vanilla, 2.5 g; and an oil mixture, 2.5 g. The oil mixture (liquid shortening) contained 83% oil, 14% propylene-glycol monostearate (PGMS), and 3% stearic acid. The batter density and cake volume index were determined according to AACC (1976), method 10-90.

Angel food cakes were prepared and evaluated for specific gravity, cake volume and shrinkage index according to the AACC (1976), method 10-15; the amount of all ingredients was halved due to limited quantities of modified EWS. A household Sunbeam mixer with a small mixing bowl was used, and the whipping time was between 7 and 9.5 min. Firmness measurements were made according to the procedure described by Johnson and Zabik (1981). Cakes were stored at -20°C until testing, and were sliced while still frozen to prevent collapse of the fragile structure. One inch cubes were cut from the inner area of the frozen cake, and the firmness of the thawed cubes (five per cake) was measured with the Ottawa Texture Measuring System (OTMS), using a flat plate compression cell and a crosshead speed of 10 cm/min. Samples were compressed to a height of 0.8 cm. The physicochemical properties and cake baking data were evaluated by analysis of variance (ANOVA) and Duncan's multiple range test at the 5% level.

Table 1. Some physicochemical properties of unmodified and modified EWS.1

EWS Extent of Modification(%) Charge4 (m mole H+/g) Surface Hydrophobicity SH content(ìM/g) Surface Tension (dynes/cm2) Interfacial Tension (dynes/cm2)
Unmodified 0 1.30 ± 0.10a 22 ± 2a 41.2 ± 1.0a 50.5 ± 1.5a 11.8 ± 0.2a
Succinylated (50:1)2 24.5 1.38 ± 0.12b 25 ± 1b 40.0 ± 0.ßa 51.5 ± 1.5a 13.5 ± 0.2a
Succinylated (10:1) 91.6 1.53 ± 0.12b 27 ± 2b 38.3 ± 0.7ab 55.4 ± 1.4b 18.2 ± 0.3b
Carboxyl-modified (20mM GME)3 25.2 1.14 ± 0.08c 26 ± 1b 37.0 ± 0.86 48.4 ± 1.4a 12.0 ± 0.3a
Carboxyl-modified (50mM GME) 68.5 1.04 ± 0.06c 34 ± 2c 38.9 ± 1.lab 48.8 ± 1.3a 11.8 ± 0.2a

1 Average of two or three determinations ± standard error. Means in a column bearing the same letter are not significantly different (p > 0.05) as determined by Duncan's multiple range test.

2 Protein: succinic anhydride (sew)

3 GIycine methyl ester.

4 Determined from titration curves.

Results

Physicochemical properties of modified E WS

The extent of lysine and carboxyl modifications is shown in Table 1. By using two levels of reagents, modified EWS with a low (25%) and high (over 60%) degree of derivatization were produced.

Some physicochemical properties of the unmodified and modified EWS are presented in Table 1. Succinylation at 91.6% resulted in a significant increase in the total bound H+, indicating an increase in net negative charge. The amount of bound H+ was decreased by carboxyl modification, showing that the net negative charge was lowered. Both succinylation and carboxyl modification led to a relatively small but significant increase in surface hydrophobicity, while the sulfhydryl content was not substantially changed by tine two reactions. The surface and interfacial tensions were significantly increased by succinylation at 91.6% but were not markedly changed by carboxyl modification.

Graph

Fig. 1. DSC thermograms of EWS. a,d: unmodified; b,e: 68.5% carboxyl-modified; c,f: 91.6% succinylated; a,b,c,: no sucrose; d,e,f: in the presence of 50% sucrose.

Figure 1 shows the DSC thermograms of the unmodified and modified EWS; the enthalpies of denaturation (H) are shown in Table 2. The control sample (curve a) showed two endothermic peaks with Td at 65 and 85°C, corresponding to the major egg white proteins--conalbumin and ovalbumin respectively (Donovan et al., 1975). The 68.5% carboxyl-modified (b) and 91.6% succinylated (c) EWS exhibited thermograms similar to the control, but with considerable broadening of the peaks. OH values (Table 2) were significantly decreased only by succinylation at 91.6%. In the presence of 50% sucrose, the Td's of proteins from the unmodified EWS (d) were markedly shifted to a range between 75 and 110°C, with the major peak (ovalbumin) near 95°C. The endothermic peaks of the carboxyl-modified EWS (e) were further broadened in the presence of sucrose, and the Td's were also shifted upward, but to a temperature range lower than that of the control. The high sucrose content did not cause any significant change in the thermogram of the highly succinylated EWS (f), although [H was significantly decreased (Table 2). The Td's of the 24.5% succinylated and the 25.2% carboxyl-modified EWS (data not shown) were raised by the addition of sucrose to a. temperature range slightly lower than that of the control, while the enthalpies were not significantly changed (Table 2).

Table 2. Enthalpy of denaturation of unmodified and mollified

EWS1 (J/g)

No sucrose + 50% sucrose
Unmodified 15.33 ± 1.05a 14.99 ± 0.84a
Succinylated (24.5%)2 14.53 ± 1.13a 14.28 ± 0.97a
Succinylated (91.6%) 12.68 ± 0.92b 12.47 ± 0.92b
Carboxyl-modified (25.2%) 14.91 ± 0.76a 14.70 ± 0,84a
Carboxyl-modified (68.5%) 13.90 ± 0.63ab 13.78 ± 1.09ab

1 Average of duplicate determinations ± standard error. Means in a column bearing the same letter are not significantly different (p > 0.05) as determined by Duncan's multiple range test.

2 % modification

Table 3. Emulsifying and foaming properties of unmodified and modified EWS1


EC (mL oil/g) EAI4 (m2/g) ES15 (min.) Foamability (%) Foam Stability(%)6
Unmodified 770 ± 25a 37.2 ± 2.2a 2.7 ± 0.2a 200 ± 10a 33 ± 2a
Succinylated (24.5%)2 742 ± 31a 41.4 ± 1.9ab 5.0 ± 0.3b 145 ± 5b 23 ± 2b
Succinylated (91.6%) 849 ± 28b 50.0 ± 2.1c 19.5 ± 0.4c 140 ± 5b 20 ± 1b
Carboxyl-Modified (25.2%) 712 ± 22c 45.0 ± 2.2bc 7.5 ± 0.3b 210 ± 10a 35 ± 2a
Carboxyl-Modified (68.5%) 691 ± 20c 46.0 ± 1.8bc 16.8 ± 0.3c 225 ± 15a 37 ± 1a

1 Averages of triplicate determinations ± standard error. Means in a column bearing the same letter are not significantly different (p > 0.05) as determined by Duncan's multiple range test.

2 % modification.

3 Emulsifying capacity.

4 Emulsifying activity index.

5 Emulsion stability index.

6 % foam remaining after 60 min.

Functional properties

The emulsification and foaming properties of the unmodified and modified EWS are presented in Table 3. A significant increase in emulsifying capacity (EC) was observed in the highly succinylated EWS, while carboxyl modification led to a decrease in EC. The emulsifying activity index (EAI) and emulsion stability index (ESI) were significantly increased by both modifications, but the increases in ESI were much more pronounced. The highly succinylated EWS showed the highest EC, EAI and ESI values among all samples. The foamability and foam stability were significantly decreased by succinylation, and were slightly improved by carboxyl modification.

Heat coagulability

Table 4 shows the thermal aggregating behaviour of the unmodified and modified EWS at pH 5.8 and 7.2. The results show that at pH 5.8, all the EWS samples, except the highly succinylated EWS, formed an opaque, solid gel upon heating, and over 90070 of the protein was coagulated. The 91.6% succinylated EWS formed a transparent, loose gel and only about 50% of the protein was aggregated at 100°C. At pH 7.2, the unmodified EWS formed an opaque gel but with a weaker structure, and about 95% of the protein was heat coagulated. Both the succinylated and carboxyl-modified EWS did not gel when heated, bust showed the formation of some precipitate or an increase in viscosity. When the heated solutions were centrifuged, most of the protein (70-80%) remained in the supernatants.

Cake baking performance

Table 5 shows the performance of unmodified and modified EWS in the high ratio layer cake system. There was no significant change in the batter density by either modification, but the cake volume index was significantly increased by succinylation.

The performance of the various EWS products in angel food cakes is presented in Table 6. Succinylation caused a significant increase in meringue specific gravity, indicating a decrease in whippability. Cake volume was markedly decreased by succinylation at the high level, but not significantly changed by carboxyl modification. The shrinkage index was not affected by either modification. Cakes prepared from the native EWS had a tender texture as indicated by a low firmness reading. Succinylation and carboxyl modification caused a significant increase in firmness; the highly succinylated EWS produced tough, flat cakes with highest firmness values.

Discussion

The present data show that succinylation and carboxyl modification of EWS led to changes in some physicochemical and functional properties. Succinylation increased the net negative charge in the protein by replacing the amino groups of lysine with free carboxyl groups, while carboxyl modification decreased the net negative charge by binding neutral glycine to free carboxyl groups. The relatively small increase in surface hydrophobicity and decrease in H suggest that succinylation and carboxyl modification did not cause extensive unfolding or denaturation of the egg white proteins. These observations are consistent with previous data on purified egg albumen (Ma and Holme, 1982). Other workers (Habeeb, 1968; Carraway and Triplett, 1970) also reported that the sulf-hydryl content in egg albumen was not changed by the two reactions, although free SH groups and tyrosine OH groups are known to be reactive to succinic anhydride.

Table 4. Heat coagulability of unmodified and modified EWS1


Visual changes % Coagulated protein3

pH 5.8 pH 7.2 pH 5.8 pH 7.2
Unmodified opaque opaque 94 ± 1.2a 94.6 ± 1.5a
solid gel loose gel
Succinylated (24.5%)2 opaque clear solution 93.1 ± 1.7a 30.4 ± 1.0b
solid gel with ppt.
Succinylated (91.6%) transparent clear viscous 49.0 ± 0.8b 19.6 ± 0.7c
loose gel solution
Carboxyl-Modified (25.2%) opaque milky solution 94.7 ± 1.5a 19.2 ± 0.5c
solid gel with ppt.
Carboxyl-Modified (68.5%) opaque clear solution 94.4 ± 1.4a 18.5 ± 0.4c
solid gel with ppt.

1 Protein solutions (10070, w/v) were heated at 100°C for 5 min.

2 % modification

3 Averages of duplicate determinations t standard error. Means in a column bearing the same letter are not significantly different (p > 0.05) as determined by Duncan's multiple range test.

Table 5. Performance of unmodified and modified EWS in layer cakes1

EWS Batter Density Volume Index
Unmodified 0.74a3 8.57a
Succinylated (24.5%)2 0.73a 10.90b
Succinylated (91.6%) 0.69a 11.09b
Carboxyl-Modified (25.2%) 0.69a 8.12a
Carboxyl-modified (68.5%) 0.70a 7.70a

1 Average of four determinations.

2 °% modification.

3 Means in a column bearing the same letter are not significantly different (p > 0.05) as determined by Duncan's multiple range test.

The change in some functional properties in the modified EWS may be related to alterations in physicochemical characteristics. Protein is a key ingredient in many food emulsions and foams, and one of the roles played by protein is to act as a surfactant to lower the surface (air/water) and interfacial (oil/water) tensions at interfaces. Decreases in foaming capacity and stability produced by succinylation (Table 3) can therefore be related to higher surface tension (Table 1), particularly at higher level of acylation. However, significant increases in emulsion performance by succinylation and carboxyl modification did not seem to correlate with the changes in interfacial tension. A lack of correlation between emulsification and interfacial behavior has been reported in whey proteins (Tornberg, 1979). Changes in other physicochemical properties such as charge, hydrophobicity and conformation can account for the enhancement of emulsification properties in the modified EWS.

Glutaration and succinylation of various egg white products have been shown to enhance the heat stability of the albumen proteins (Gandhi et al., 1968; Sato and Nakamura, 1977; Ball and Winn, 1982; Ma and Holme, 1982), whereas a decrease in thermal stability was reported for acetylated egg white (Ball and Winn, 1982). In these studies, heating experiments were carried out at relatively low temperature (60-80°C) and at pH above neutrality (7-8.5). In the present work, the pH (5.8 and 7.2) and temperature (100°C) chosen for the heating tests were close to the conditions of the angel cake and layer cake batter during baking. The data show that at the pH of the angel cake system (pH 5.8), only the highly succinylated EWS failed to gel, while at the pH of the layer cake system (pH 7.2), both modifications caused a significant increase in heat stability. As suggested by other workers (Nakamura et al, 1978; Shimada and Matsushita, 1980), ionic repulsion can prevent thermocoagulation, and the increase in net charge in the modified egg proteins may promote such electrostatic repulsion to hinder the formation of coagulum.

Table 6. Performance of unmodified and modified EWS in angel food cakes.1


Meringue specific gravity Cake Volume Shrinkage Index Firmness (N/mm)
Unmodified 0.144c3 1202a 1.37a 3.34c
Succinylated (24.5 %)2 0.156b 1163a 1.48a 9.77b
Succinylated (91.6%) 0.173a 795b 1.49a 21.96a
Carboxyl-modified (25.2%) 0.144c 1223a 1.20a 8.39b
Carboxyl-modified (68.5 %) 0.147c 1243a 1.72a 8.79b

1 Average of four determinations.

2 % modification.

3 Means in a column bearing the same letter are not significantly different (p > 0.05) as determined by Duncan's multiple range test.

The roles of major ingredients in cake formulations have been considered by many workers (Howard, 1972; Donovan, 1977; Paton et al., 1981). Major functions which have been identified include the incorporation of air into the batter system, the stabilization of the expanding foam structure during baking and the "setting" of the solid structure through gelatinization of starch and coagulation of protein. Starch, protein and surface-active lipids have been recognized as ingredients of major importance in properly balancing such functions. The objective of the present: study was to determine the effect of chemical modification of the major foamable and heat coagulable protein system, egg white, on baking properties. The interpretation of results presented here is complicated by the fact that the two cake systems chosen, layer cake and angel food cake, did not respond to modifications of egg albumen in the same way, suggesting that in details the changes caused by baking are different for each product.

In the layer cake system, the modifications did not affect the air incorporation into the batters nor did they result in significant decreases in cake volume. This indicates that the changes in physicochemical properties of modified egg white proteins did not detrimentally affect initial foam formation, high temperature foam stability during baking, nor the thermal setting process of converting the batter into a cake. The most surprising aspect of this might be that the thermal setting process appeared to proceed normally even though the heat coagulability of the modified egg white in an isolated, model system had been markedly affected at the pH of the system. This suggests that heat coagulability is not an essential property of egg white in the layer cake, and that starch can serve as the principal if not the sole contributor to the critical thermal setting process. However, egg white proteins still played an important role in the initial foam formation and stabilization of foam structure; reduction or omission of egg albumen in the formulation has been shown to cause deterioration in layer cake performance (Paton et al., 1981).

In the angel food cake system, the baking performance was more closely related to the foaming properties and heat coagulability of the egg white proteins. The foaming ability and the high temperature foam stability are recognized as important properties of egg white in controlling air incorporation into the batter and the stabilization of the expanding foam structure during baking, while thermal setting in angel food cake depends on the heat coagulation of the egg white proteins. The reduction in volume of cakes containing highly succinylated egg albumen was therefore directly related to the marked decreases in foamability, foam stability, and heat coagulability at pH 5.8, close to that of the angel cake system. The relative importance of foaming properties and heat coagulability in the angel food cake cannot be determined from this work. Other modifications which could yield identifiable differentiation between these two properties may be required.

The present data show that succinylation at 24.5% did not cause marked changes in angel cake volume. Glutaration (Gandhi et al., 1968) and succinylation (Ball and Winn, 1982) of egg white at levels below 50°70 were also found to have no deteriorative effect on the angel cake system. However, the angel cake performance was affected by glutaration at higher levels (60-90%) of modification, and was again attributed to improved heat stability (Gandhi et al., 1968).

Sucrose has been suggested to have an influence on angel cake texture. Donovan (1977) showed that sucrose increased the denaturation temperature of both egg white proteins and starch to near 95°C, at approximately the maximum temperature attained by the cake when it reached maximum volume in the oven. Since coagulation of egg albumen is preceded by denaturation (Ma and Holme 1982), an increase in Td would delay albumen coagulation and a more tender cake structure should be obtained. In the present study, angel cakes containing mildly succinylated and carboxyl-modified EWS had firmness values higher than that of the control, although cake volume was not significantly decreases. These modified proteins had Td values (in the presence of sycrose) slightly lower than that of the unmodified egg white, and the firmer texture could be due to denaturation (and gelation) of the modified egg albumen before the batter reached maximum volume. The Td of the highly succinylated egg albumen was not increased by sucrose. However, the poor angel cake texture was more likely attributable to the extremely low cake volume rather than premature coagulation of the modified proteins in the batter.

Acknowledgement

The technical assistance of G. Khanzada and C. Patterson is acknowledged. The authors also thank Dr. S. Nakai of University of British Columbia for surface and interfacial tension measurements, and M. Kloeck of Engineering and Statistical Research Institute, Agriculture Canada, for rheological assessment of angel cakes.

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Submitted May 9, 1985
Revised July 31, 1985
Accepted August 6, 1985