- Email: [email protected]
Composite blends from heat-denatured and undenatured whey protein: Emulsifying properties
Int. Dairy Journal 4 (1994) 25-36
Composite Blends from Heat-Denatured and Undenatured Whey Protein: Emulsifying Properties
M. Britten, H. J. Giroux, Y. Jean & N. Rodrigue Food Research and Development Centre, Agriculture Canada, 3600 Casavant Blvd West, St-Hyacinthe, Quebec, Canada J2S 8E3 (Received 29 September 1992; revised version accepted 7 December 1992)
ABSTRACT A solution of commercial whey proteh~ &olate was heat-denatured (D WPI) and combined in various ratios with undenatured whey protein isolate (WPI). Emulsions with an oil volume fraction varying from 0.05 to 0.26 were prepared from these mixtures using a lab scale valve homogenizer. The protein content of the aqueous phase was standardized to 3%. The emulsifying activity index of the protein mixtures was determined and the emulsions were analysed for resistance to stirring-induced coalescence, separation stability, viscosity and age thickening. Higher levels of D WPI in the protein blend and higher oil volume fractions of the emulsion increased emulsifying activity, emulsion viscosity and stability. However, these emulsions showed evidence of age thickening. Resistance to stirring-induced coalescence was improved by increasing the proportion of D WPI in the blend and by reducing the oil content of the emulsion. The roles of heat-denatured and undenatured whey proteins in emulsified systems appeared complementary.
INTRODUCTION The growing consumer demand for prepared foods with high nutritional value and long shelf life without artificial additives emphasizes the requirement for highly functional natural ingredients. The protein fraction 25 Int. Dairy Journal 0958-6946/93/$06.00 © 1993 Elsevier Science Publishers Ltd, England. Printed in Ireland
26
M. Britten, H. J. Giroux, Y. Jean, N. Rodrigue
from cheese whey has excellent nutritional value and could be used to affect the structural properties and the stability of formulated foods. The tensio-active properties of whey proteins allow them to concentrate and form membranes at the surface of fat droplets (Shimizu et al., 1981; Leman and Kinsella, 1989). They could be used to stabilize the oil in emulsified food products. The properties of the protein film surrounding a fat droplet are likely to affect the stability and rheological properties of the emulsion. The emulsifying behaviour of proteins depends on their structure (Nakai, 1983; Kinsella and Whitehead, 1989; Patel and Kilara, 1990); several approaches have been used in order to alter whey protein structure and improve their functional properties (Kester and Richardson, 1984). Among these approaches, heat treatments received considerable attention (Modler and Emmons, 1976; Harwalkar and Modler, 1981; Kato et al., 1983; deWit and Klarenbeek, 1984; Morr, 1985; Multilangi and Kilara, 1985a). Heat treatments induce denaturation, aggregation and precipitation of whey proteins which in turn influence functional properties. Although a number of studies showed negative effects of heat-denaturation on functional properties (Multilangi and Kilara, 1985b), some authors showed beneficial effects (deWit and Hontelez-Backx, 1981; Harwalkar and Modler, 1981). Conflicting conclusions arise from differences in denaturation conditions. Factors such as mineral environment, pH, protein concentration, heating temperature and time determine the nature and the properties of heated whey proteins (deRham and Chanton, 1984; Harwalkar and Kalab, 1985a, b, c; Harwalkar, 1986; Mulhvihill and Donovan, 1987). Structural modifications associated with heat treatment of whey proteins are likely to result in new functional attributes while impairing some original functional attributes. It was hypothesized that mixtures of denatured and undenatured whey proteins may have complementary roles with respect to emulsifying properties. Depending on the protein mixture ratio and the oil volume fraction of the emulsion, a composite protein blend could improve emulsion properties. It was the objective of this study to verify possible synergistic effects from recombination of denatured and undenatured whey protein isolates in model emulsion systems.
MATERIALS AND METHODS
Preparation of protein blends A commercial whey protein isolate (Le Sueur Isolates, Le Sueur, MN, USA) with a protein content of 89-3% was used throughout the study.
Blends from heat-denatured and undenatured protein
27
Protein was dispersed in 0.067 M phosphate buffer (pH 7.0) at a protein concentration of 3-0%. Sodium azide (0.2%) was added to inhibit microbial growth. The protein solution was partitioned into two fractions. The first fraction did not received any treatment while the second fraction was heated to 80°C, held at that temperature for 15 min, and then cooled to room temperature. The solubilities of the denatured whey protein isolate (DWPI) and the undenatured whey protein isolate (WPI) were obtained from the protein contents of the supernatants after centrifugation at 20 000g for 15 min. Protein concentration was determined by a modified biuret reaction (BCA protein assay Reagent, Pierce, Rockford, IL, USA). Percentage of denaturation was calculated as the difference in the solubilities measured at pH 4.5. DWPI and WPI fractions were mixed in the following ratios: 0/3, 1/2, 2/1 and 3/0. The final concentration of protein blends remained unchanged at 3.0%.
Emulsion formation DWPI/WPI blend solutions were used to prepare emulsions containing 5, 12, 19 or 26% (v/v) commercial soya oil (Crisco Ltd, Toronto, Canada). Emulsions were produced at 40°C with a single stage mini-lab homogenizer (Type 8.30 H, Rannie, Albertslund, Denmark) operating at a pressure of 40 MPa for the first pass and 3 MPa for the second. The effluents were cooled immediately to room temperature.
Emulsifying activity index The emulsifying activity index (EAI) was determined according to Pearce and Kinsella (1978). Emulsions were diluted in 0-01 M, pH7.0 sodium phosphate buffer containing 0.5% sodium dodecyl sulfate (SDS), to a final oil volume fraction of 6 × 10-5. The optical density of diluted emulsions was measured at 500nm with a Beckman DU-7 spectrophotometer (Beckman Instruments, Palo Alto, CA, USA). The EAI was calculated according to Cameron et al. (1991).
Emulsion coalescence stability The coalescence index of the emulsions was determined according to the method of Britten and Giroux (1991). Emulsion samples (125ml) were placed in an orbital stirring cabinet (Lab-Line Instruments Inc., Melrose Park, IL, USA) and agitated at 250 rev/min for 6 h. Aliquots (0.1 ml) were taken hourly and diluted in 0-01 M, pH7.0 sodium phosphate buffer containing 0.5% sodium dodecyl sulfate (SDS), to a final oil volume
28
M. Britten, H. J. Giroux, Y. Jean, N. Rodrigue
fraction of 6 × 10-5. The optical density of the diluted emulsions was measured at 500 nm with a Beckman DU-7 spectrophotometer (Beckman Instruments, Palo Alto, CA, USA). The coalescence index (CI) was related to the decrease of turbidity with time during agitation and was expressed as follows:
ci_d(To/z) dt
(1)
where To is the initial turbidity and -c the turbidity at time t. A high coalescence index indicates poor resistance to stirring-induced coalescence.
Emulsion separation stability Emulsion stability upon storage was evaluated from the change in densitometric profile of the emulsion. According to the method of Britten et al. (1991), emulsion samples were placed in 10 × 0.6cm glass tubes, sealed at both ends and stored in a vertical position at room temperature. Emulsion samples were scanned after 4 weeks storage in a modified densitometer (Beckman model CDS-200, Beckman Instruments, Palo Alto, CA, USA), and the densitometric profiles were automatically recorded. A separation index was calculated from the profile. For that purpose, a vertical line corresponding to the mid-height of the sample was drawn on the profile and the surface under the curve was measured on both sides of the vertical line. The stability index was obtained from the ratio of the surface area corresponding to the bottom half of the sample and the surface area corresponding to the top half. The index varied from 0 (unstable) to 1 (stable).
Emulsion apparent viscosity The emulsion apparent viscosity was measured with a Brookfield viscometer (model LVTDV-II, Stoughton, MA, USA) at 23 + I°C. The viscosity was measured immediately after emulsion formation and after 4 weeks of storage.
Statistical analyses The emulsions were prepared in triplicate according to a 4 2 completely randomized design. The factors were the oil volume fraction of the emulsion (0.05, 0.12, 0.19 or 0.26) and the DWPI/WPI ratio in the protein blend (0/3, 1/2, 2/1 or 3/0). Analysis of variance was used to determine if the factors and their interaction had a significant effect on the measured
Blends from heat-denatured and undenatured protein
29
properties (SAS Institute, 1989). Statistical analyses were performed at 0~= 0.05; thus, effects associated with factors or interaction with a p value lower than 0-05 were statistically significant. A logarithmic transformation was applied to the emulsifying activity index, coalescence index and viscosity results to stabilize the variance. For these variables, results are presented on a logarithmic scale to avoid the bias constituted by returning to the original scale after logarithmic transformation (Ung and V6giard, 1988). Unless otherwise stated, significant effects or interactions were partitioned into linear, quadratic and cubic components using orthogonal polynomials in order to develop empirical models (Little and Hills, 1978). The models were tested for lack of fit (Khuri and Cornell, 1987).
RESULTS AND DISCUSSION
Characteristics of blend components Whey protein isolate was highly soluble (Table 1) and produced clear protein dispersions. Heating induced some aggregation as evidenced by the milky appearance of the dispersion after treatment. However, the aggregates formed were virtually non-sedimentable with a decrease in solubility of only 10% (Table 1). The low ionic strength and protein concentration during heat treatment at pH 7 prevented the formation of large aggregates (Harwalkar and Kalab, 1985a). Under these conditions, no mechanical treatment was required to maintain dispersibility. Despite high solubility, heat-treated whey protein showed a high denaturation level which confirms that important structural changes occurred during the treatment (Table 1). The preparation of highly soluble denatured-whey protein concentrates has been proposed first by deWit (1981).
The emulsifying activity index The EAI is related to the surface area stabilized by a unit mass of protein under standard emulsification conditions. An empirical model which relates the EAI to the emulsion oil volume fraction and the DWPI/WPI TABLE 1 Characteristics of Protein Blend Components
Solubility (pH 7.0) (%) Denaturation (%)
WPI
DWPI
98.5 6.8
88.7 85~8
30
M. Britten, H. J. Giroux, Y. Jean, N. Rodrigue
1.75 1.50
19
~--"-~0/3
Oil Volume Fraction "12
.05
Fig, 1. Emulsifying activity index of DWPI/WPI protein blends (standard errors of predicted values were lower than 0-021 log units. R 2 of the fitted model: 0-990.
ratio in the protein blend has been developed from experimental results. The lack of fit test of the model was not significant (p --- 0.1598). The response surface corresponding to the model is presented in Fig. 1. The oil volume fraction of the emulsion was the main factor influencing the EAI (p -- 0.0001). Predictably, the surface area of the dispersed phase stabilized by the protein increased with the amount of oil to be homogenized. Increasing DWPI in the protein blend also had an effect on the EAI (p = 0-0001) and the effect varied depending on the oil volume fraction of the emulsion (p = 0-0001). For low oil volume fraction emulsions (0.05), EAI was constant and did not depend on the protein blend ratio as shown by multiple comparisons of least squares means. With the homogenization conditions used in the present investigation, the protein quality was not a limiting factor for the creation of new interfaces. It is likely that the energy input was not sufficient to further reduce droplet size (Haque and Kinsella, 1989). However, at higher oil volume fractions, the composition of the protein blend had an effect and the EAI improved with an increasing proportion of DWPI. This result was attributed to the aggregated nature of DWPI which contributed to the formation of thicker membranes around fat droplets. These membranes prevented recoalescence, which had been identified as an important factor limiting droplet size reduction in a valve homogenizer (Pearce and Kinsella, 1978). The improvement of the EAI with increasing DWPI in the protein blend showed a maximum for emulsions containing more than 19% oil; further increase in DWPI resulted in decreased EAI. Optimal emulsifying activity then required a minimal amount of WPI and this amount appeared to increase with the oil content of the emulsion. This suggests that the emulsifying activities of WPI and
Blends from heat-denatured and undenatured protein
31
DWPI are due to different reasons. WPI has the ability to create large interfaces through rapid adsorption onto fat droplets while DWPI seems to prevent recoalescence within the valve homogenizer. The emulsion coalescence index
The susceptibility of an emulsion to stirring-induced coalescence is an indication of the mechanical resistance of the membranes surrounding fat droplets. From coalescence index measurements, an empirical model was developed to express the effect of the protein blend ratio and the oil volume fraction of the emulsion on the coalescence index. The lack of fit test of the model was not significant (p --- 0.7044). The response surface corresponding to the model is presented in Fig. 2. The DWPI/WPI ratio of the protein blend had a significant effect on the coalescence index of the emulsion (p = 0.0001). Increasing DWPI in the blend reduced the coalescence index of the emulsion, probably as a result of increased mechanical resistance of the membranes. This observation parallels the inhibition of recoalescence explaining the improved emulsifying activity of DWPI/WPI protein blends (Fig. 1). The oil volume fraction of the emulsion also had a significant effect on the emulsion coalescence index (p ~-0-0003). Increasing oil volume fraction increased the collision rate (Reddy and Fogler, 1981) and promoted the formation of larger droplets during homogenization (Walstra, 1975), both factors leading to higher coalescence index. However, the effect of oil volume fraction was dependent upon the DWPI/WPI ratio in the protein blend (p = 0-0001). The coalescence index of emulsions
0
-0.6
°m (D
0
-1.2
- 0/3
-1 .e
"J
1/2 -2. D W P I / W P I Ratio Oil V o l u m e F r a c t i o n .19
.26
- 3/0
Fig. 2. Resistance to stirring-induced coalescence of oil-in-water emulsions stabilized by DWPI/WPI protein blends (standard errors of predicted values were lower than 0.097 log units. R 2 of the fitted model: 0.943).
32
M. Britten, H. J. Giroux, Y. Jean, N. Rodrigue
produced from pure WPI (0/3 ratio) increased with the oil volume fraction while emulsions produced from pure DWPI (3/0 ratio) were stable against coalescence whatever the oil volume fraction was. These results emphasize the role of the DWPI soluble aggregates in the formation of thick membranes which prevent mechanical deformations and resist coalescence.
The emulsion viscosity and age thickening Viscosity is an important property which influences the stability of emulsified products. The apparent viscosity of the emulsions was measured immediately after formation. A response surface was generated through spline interpolation, and results are presented as contour plots. Contour levels are expressed on a logarithmic scale (Fig. 3(a)). The emulsion apparent viscosity was affected by both factors, the oil volume fraction (p = 0.0001) and the DWPI/WPI ratio in the protein blend (p = 0.0001). As a general trend, increasing DWPI in the protein blend increased the emulsion viscosity. However, this effect was related to the oil volume fraction of the emulsion (p = 0.0001). For low-fat emulsions, the viscosity increase was very slight while high-fat emulsions became very viscous with increasing DWPI. It should be noted that maximum viscosity was reached for DWPI/WPI ratios around 2/1; a further increase in DWPI reduced the viscosity of high-fat emulsions. The lower viscosity of .26
~
.o
~ .19
LL
E ~.12
05/~ 0/3
1/2 I
2/1
1/2 3/0 0/3 DWPI/WPI Ratio
2/1
3/0
Log viscosity(mPa.s) 1.0 1.5 2.0 2.5 3.0 3.5 I I I I
Fig. 3. Apparent viscosity of oil-in-water emulsions produced from DWPI/WPI protein blends. (a) Initial viscosity; (b) viscosity after 4 weeks storage. The dashed line in (b) links the conditions where minimal age thickening occurred.
Blends from heat-denatured and undenatured protein
33
emulsions produced from high DWPI protein blends correlates with the reduced emulsifying activity of DWPI-rich blends (Fig. 1). It has been shown that the viscosity of an emulsion is related to the size of fat droplets (Dickinson and Stainsby, 1982). Larger fat droplets produced by high DWPI protein blends could then explain the emulsion viscosity decrease. The change in viscosity upon storage is an indication of age thickening. Emulsion apparent viscosity was measured after 4 weeks of storage and results are presented in Fig. 3(b). High DWPI/WPI ratio in the protein blend led to severe age thickening as evidenced by the difference between viscosity contour plots obtained immediately after emulsion formation (Fig. 3(a)) and after 4 weeks storage (Fig. 3(b)). The high concentration of soluble aggregates seems to promote the formation of a protein network during storage. High oil volume fraction is another factor promoting age thickening. This result is in agreement with the literature and emphasizes the involvement of fat droplets in the network formation (Harwalkar, 1982; Pouliot et al., 1990). The dashed line in Fig. 3(b) links the conditions of minimal age thickening, indicating a complex balance between the oil volume fraction and the proportion of DWPI in the protein blend.
The emulsion separation stability After 4 week storage, the opacity profile of the emulsions was monitored and the stability index was calculated. The results were used to establish an empirical model relating the stability index to the oil volume fraction of the emulsion and the DWPI/WPI ratio. The lack of fit test was non-significant (p = 0.1028). The response surface corresponding to the model is presented in Fig. 4. The oil volume fraction (p = 0.0001) and the DWPI/WPI ratio in the blend (p = 0-0001) had significant effects on emulsion stability. The emulsion stability could be related to the emulsion viscosity (Fig. 3), recognized as an important factor controlling the emulsion stability (Hailing, 1981). However, emulsions produced from pure WPI showed greater stability when the oil volume fraction increased despite a very slight change in viscosity. Crowding of the dispersed phase in high-fat emulsions might be responsible for this phenomenon (Dickinson, 1988). It was also noticed that emulsions with a 0.05 oil volume fraction showed increased stability with increasing DWPI in the protein blend despite a very slight change in viscosity. The reason for this stabilizing role is not known. DWPI could induce the formation of a soft network and/or it could form thicker membranes which increase the density of the dispersed phase, both factors improving the separation stability of the emulsion.
34
M. Britten, H. J. Giroux, Y. Jean, N. Rodrigue
o.
310
//7"~ 2/1 0 ' 5 5 . 2 6 ~ .19 Oil VolumeFraction12
4~/" 1/a 0/3 DWPI/WPI Ratio .05
Fig. 4. Separation stability of oil-in-water emulsions stabilized by DWPI/WPI protein
blends (standard errors of predicted values were lower than 0-038. R2 of the fitted model: 0,862). CONCLUSION Heat-denaturation of a whey protein isolate in solutions at pH 7.0 induced the formation of non-sedimentable aggregates of colloidal size. Mixtures of denatured and undenatured whey protein isolate solutions have been used to produce oil-in-water emulsions varying stabilities. The mixtures showed synergistic effects with respect to emulsifying activity. Emulsion stability against coalescence and separation was improved by the presence of DWPI in the blend. The viscosity of the emulsion was controlled by the DWPI/ WPI ratio in the protein blend. Proper balance between protein ingredients and the oil volume fraction of the emulsion reduced age thickening. Mixtures of denatured/undenatured whey protein fractions could be used to enlarge the utilization spectrum of whey proteins in food applications.
REFERENCES Britten, M. & Giroux, H. J. (1991). Coalescence index of protein-stabilized emulsions. J. Food Sci., 56, 792-5. Britten, M., Giroux, H. J. & Lavoie, L. (1991). Phase separation in dairy products monitored by optical densitometry. Milchwissenschaft, 46, 300-3. Cameron, D. R., Weber, M. E., Idziak, E. S., Neufeld, R. J. & Cooper, D. G. (1991). Determination of interracial areas in emulsions using turbidimetric and droplet size data: Correction of the formula for emulsifying activity index. J. Agric. Food Chem., 39, 655-9. deRham, O. & Chanton, S. (1984). Role of ionic environment in insolubilization of whey protein during heat treatment of whey products. J. Dairy Sci., 67, 939-49.
Blendsfrom heat-denatured and undenatured protein
35
deWit, J. N. (1981). Soluble denatured whey protein. UK Patent Application no. 2 063 273A. deWit, J. N. & Hontelez-Backx, E. (1981). Les propri&6s fonctionelles des prot6ines du lactos6rum; cons6quences des traitements thermiques. Technique Laiti~re, 952, 19-22. deWit, J. N. & Klarenbeek, G. (1984). Effects of various heat treatments on structure and solubility of whey proteins. J. Dairy Sci., 67, 2701-10. Dickinson, E. (1988). Emulsion stability. In Advances in Food Emulsions and Foams, eds E. Dickinson and G. Stainsby, Elsevier Applied Science, London, ch. 1, pp. 1-44. Dickinson, E. & Stainsby, G. (1982). Colloids in Foods, Applied Science Publishers, London, pp. 331-407. Halling, P. J. (1981). Protein-stabilized foams and emulsions. CRC Crit. Rev. Food Sci. Nutr., 15, 155-203. Haque, Z. & Kinsella, J. E. (1989). Emulsifying properties of food proteins: development of a standardized emulsification method. J. Food Sci., 54, 39-44. Harwalkar, V. R. (1982). Age gelation of sterilized milks. In Developments in Dairy Chemistry-1. Proteins, ed. P. F. Fox, Applied Science Publishers, London, pp. 229-69. Harwalkar, V. R. (1986). Kinetic study of thermal denaturation of proteins in whey. Milchwissenschaft, 41, 206-9. Harwalkar, V. R. & Kalab, M. (1985a). Thermal denaturation and aggregation of /%lactoglobulin at pH 2.5. Effect of ionic strength and protein concentration. Milchwissenschaft, 40, 31-4. Harwalkar, V. R. & Kalab, M. (1985b). Thermal denaturation and aggregation of fl-lactoglobulin in solution. Electron microscopic study. Milchwissenschaft, 40, 65-8. Harwalkar, V. R. & Kalab, M. (1985c). Microstructure of isoelectric precipitates from/~-lactoglobulin solutions heated at various pH values. Milchwissenschaft, 40, 665-8. Harwalkar, V. R. & Modler, H. W. (1981). Whey protein concentrate by heating under acidic conditions. 2. Physico-chemical evaluation of proteins. Milchwissenschaft, 36, 594-7. Kato, A., Osaka, O., Matsudomi, N. & Kobayashi, K. (1983). Changes in the emulsifying and foaming properties of proteins during heat denaturation. Agric. Biol. Chem., 47, 33-7. Kester, J. J. & Richardson, T. (1984). Modification of whey proteins to improve functionality. J. Dairy Sci., 67, 2757-74. Khuri, Andr6 I. & Cornell, John A. (1987). Response Surfaces Designs and Analyses, Marcel Dekker, New York, 405 pp. Kinsella, J. E. & Whitehead, D. M. (1989). Proteins in whey: chemical, physical and functional properties. Adv. Food Nutr. Res., 33, 343-438. Leman, J. & Kinsella, J. E. (1989). Surface activity, film formation, and emulsifying properties of milk proteins. CRC Crit. Rev. Food Sci. Nutr., 28, 115-37. Little, T. N. & Hills, F. J. (1978). Agricultural Experimentation Design and Analysis, John Wiley, New York, 350 pp. Modler, H. W. & Emmons, D. B. (1976). Properties of whey protein concentrates prepared by heating under acidic conditions. J. Dairy Sci., 60, 177-84.
36
M. Britten, H. J. Giroux, Y. Jean, N. Rodrigue
Morr, C. V. (1985). Functionality of heated milk proteins in dairy and related foods. J. Dairy Sci., 68, 2773-81. Multilangi, W. A. M. & Kilara, A. (1985a). Functional properties of heatdenatured whey proteins. 1. Solubility. Milehwissensehaft, 40, 338-41. Multilangi, W. A. M. & Kilara, A. (1985b). Functional properties of heatdenatured whey proteins. 2. Emulsification and foaming properties. Milchwissenschaft, 40, 391-3. Mulvihili, D. M. & Donovan, M. (1987). Whey proteins and their thermal denaturation - - a review. Irish J. Food Sci. Teehnol., 11, 43-75. Nakai, S. (1983). Structure-function relationships of food proteins with emphasis on the importance of protein hydrophobicity. J. Agric. Food Chem., 31, 676-83. Patel, M. T. & Kilara, A. (1990). Studies on whey protein concentrates. 2. Foaming and emulsifying properties and their relationships with physicochemical properties. J. Dairy Sci., 73, 2731-40. Pearce, K. N. & Kinsella, J. E. (1978). Emulsifying properties of proteins: Evaluation of a turbidimetric technique. J. Agric. Food Chem., 26, 71 6-23. Pouliot, Y., Britten, M. & Latreille, B. (1990). Effect of high-pressure homogenization on a sterilized infant formula: Microstructure and age gelation. Food Microstruct., 9, 1-8. Reddy, S. R. & Fogler, H. S. (1981). Emulsion stability: Determination from turbidity. J. Coll. lnterf. Sci., 79, 101-4. SAS Institute Inc. (1989). S A S / S T A T User's guide, Vol. 2, Version 6, 4 edn, SAS Institute Inc., Cary, NC, 846 pp. Shimizu, M., Kamiya, T. & Yamauchi, K. (1981). The adsorption of whey proteins on the surface of emulsified fat. Agric. Biol. Chem., 45, 2491~5. Ung, C. H. & V6giard, S. (1988). Probl6mes d'inf6rence statistique reli6s ~ la transformation logarithmique. Can. J. Forest Res., 18, 733-8. Walstra, P. (1975). Effect of homogenization on the fat globule size distribution in milk. Neth. Milk Dairy J., 29, 279-94.
Composite Blends from Heat-Denatured and Undenatured Whey Protein: Emulsifying Properties
M. Britten, H. J. Giroux, Y. Jean & N. Rodrigue Food Research and Development Centre, Agriculture Canada, 3600 Casavant Blvd West, St-Hyacinthe, Quebec, Canada J2S 8E3 (Received 29 September 1992; revised version accepted 7 December 1992)
ABSTRACT A solution of commercial whey proteh~ &olate was heat-denatured (D WPI) and combined in various ratios with undenatured whey protein isolate (WPI). Emulsions with an oil volume fraction varying from 0.05 to 0.26 were prepared from these mixtures using a lab scale valve homogenizer. The protein content of the aqueous phase was standardized to 3%. The emulsifying activity index of the protein mixtures was determined and the emulsions were analysed for resistance to stirring-induced coalescence, separation stability, viscosity and age thickening. Higher levels of D WPI in the protein blend and higher oil volume fractions of the emulsion increased emulsifying activity, emulsion viscosity and stability. However, these emulsions showed evidence of age thickening. Resistance to stirring-induced coalescence was improved by increasing the proportion of D WPI in the blend and by reducing the oil content of the emulsion. The roles of heat-denatured and undenatured whey proteins in emulsified systems appeared complementary.
INTRODUCTION The growing consumer demand for prepared foods with high nutritional value and long shelf life without artificial additives emphasizes the requirement for highly functional natural ingredients. The protein fraction 25 Int. Dairy Journal 0958-6946/93/$06.00 © 1993 Elsevier Science Publishers Ltd, England. Printed in Ireland
26
M. Britten, H. J. Giroux, Y. Jean, N. Rodrigue
from cheese whey has excellent nutritional value and could be used to affect the structural properties and the stability of formulated foods. The tensio-active properties of whey proteins allow them to concentrate and form membranes at the surface of fat droplets (Shimizu et al., 1981; Leman and Kinsella, 1989). They could be used to stabilize the oil in emulsified food products. The properties of the protein film surrounding a fat droplet are likely to affect the stability and rheological properties of the emulsion. The emulsifying behaviour of proteins depends on their structure (Nakai, 1983; Kinsella and Whitehead, 1989; Patel and Kilara, 1990); several approaches have been used in order to alter whey protein structure and improve their functional properties (Kester and Richardson, 1984). Among these approaches, heat treatments received considerable attention (Modler and Emmons, 1976; Harwalkar and Modler, 1981; Kato et al., 1983; deWit and Klarenbeek, 1984; Morr, 1985; Multilangi and Kilara, 1985a). Heat treatments induce denaturation, aggregation and precipitation of whey proteins which in turn influence functional properties. Although a number of studies showed negative effects of heat-denaturation on functional properties (Multilangi and Kilara, 1985b), some authors showed beneficial effects (deWit and Hontelez-Backx, 1981; Harwalkar and Modler, 1981). Conflicting conclusions arise from differences in denaturation conditions. Factors such as mineral environment, pH, protein concentration, heating temperature and time determine the nature and the properties of heated whey proteins (deRham and Chanton, 1984; Harwalkar and Kalab, 1985a, b, c; Harwalkar, 1986; Mulhvihill and Donovan, 1987). Structural modifications associated with heat treatment of whey proteins are likely to result in new functional attributes while impairing some original functional attributes. It was hypothesized that mixtures of denatured and undenatured whey proteins may have complementary roles with respect to emulsifying properties. Depending on the protein mixture ratio and the oil volume fraction of the emulsion, a composite protein blend could improve emulsion properties. It was the objective of this study to verify possible synergistic effects from recombination of denatured and undenatured whey protein isolates in model emulsion systems.
MATERIALS AND METHODS
Preparation of protein blends A commercial whey protein isolate (Le Sueur Isolates, Le Sueur, MN, USA) with a protein content of 89-3% was used throughout the study.
Blends from heat-denatured and undenatured protein
27
Protein was dispersed in 0.067 M phosphate buffer (pH 7.0) at a protein concentration of 3-0%. Sodium azide (0.2%) was added to inhibit microbial growth. The protein solution was partitioned into two fractions. The first fraction did not received any treatment while the second fraction was heated to 80°C, held at that temperature for 15 min, and then cooled to room temperature. The solubilities of the denatured whey protein isolate (DWPI) and the undenatured whey protein isolate (WPI) were obtained from the protein contents of the supernatants after centrifugation at 20 000g for 15 min. Protein concentration was determined by a modified biuret reaction (BCA protein assay Reagent, Pierce, Rockford, IL, USA). Percentage of denaturation was calculated as the difference in the solubilities measured at pH 4.5. DWPI and WPI fractions were mixed in the following ratios: 0/3, 1/2, 2/1 and 3/0. The final concentration of protein blends remained unchanged at 3.0%.
Emulsion formation DWPI/WPI blend solutions were used to prepare emulsions containing 5, 12, 19 or 26% (v/v) commercial soya oil (Crisco Ltd, Toronto, Canada). Emulsions were produced at 40°C with a single stage mini-lab homogenizer (Type 8.30 H, Rannie, Albertslund, Denmark) operating at a pressure of 40 MPa for the first pass and 3 MPa for the second. The effluents were cooled immediately to room temperature.
Emulsifying activity index The emulsifying activity index (EAI) was determined according to Pearce and Kinsella (1978). Emulsions were diluted in 0-01 M, pH7.0 sodium phosphate buffer containing 0.5% sodium dodecyl sulfate (SDS), to a final oil volume fraction of 6 × 10-5. The optical density of diluted emulsions was measured at 500nm with a Beckman DU-7 spectrophotometer (Beckman Instruments, Palo Alto, CA, USA). The EAI was calculated according to Cameron et al. (1991).
Emulsion coalescence stability The coalescence index of the emulsions was determined according to the method of Britten and Giroux (1991). Emulsion samples (125ml) were placed in an orbital stirring cabinet (Lab-Line Instruments Inc., Melrose Park, IL, USA) and agitated at 250 rev/min for 6 h. Aliquots (0.1 ml) were taken hourly and diluted in 0-01 M, pH7.0 sodium phosphate buffer containing 0.5% sodium dodecyl sulfate (SDS), to a final oil volume
28
M. Britten, H. J. Giroux, Y. Jean, N. Rodrigue
fraction of 6 × 10-5. The optical density of the diluted emulsions was measured at 500 nm with a Beckman DU-7 spectrophotometer (Beckman Instruments, Palo Alto, CA, USA). The coalescence index (CI) was related to the decrease of turbidity with time during agitation and was expressed as follows:
ci_d(To/z) dt
(1)
where To is the initial turbidity and -c the turbidity at time t. A high coalescence index indicates poor resistance to stirring-induced coalescence.
Emulsion separation stability Emulsion stability upon storage was evaluated from the change in densitometric profile of the emulsion. According to the method of Britten et al. (1991), emulsion samples were placed in 10 × 0.6cm glass tubes, sealed at both ends and stored in a vertical position at room temperature. Emulsion samples were scanned after 4 weeks storage in a modified densitometer (Beckman model CDS-200, Beckman Instruments, Palo Alto, CA, USA), and the densitometric profiles were automatically recorded. A separation index was calculated from the profile. For that purpose, a vertical line corresponding to the mid-height of the sample was drawn on the profile and the surface under the curve was measured on both sides of the vertical line. The stability index was obtained from the ratio of the surface area corresponding to the bottom half of the sample and the surface area corresponding to the top half. The index varied from 0 (unstable) to 1 (stable).
Emulsion apparent viscosity The emulsion apparent viscosity was measured with a Brookfield viscometer (model LVTDV-II, Stoughton, MA, USA) at 23 + I°C. The viscosity was measured immediately after emulsion formation and after 4 weeks of storage.
Statistical analyses The emulsions were prepared in triplicate according to a 4 2 completely randomized design. The factors were the oil volume fraction of the emulsion (0.05, 0.12, 0.19 or 0.26) and the DWPI/WPI ratio in the protein blend (0/3, 1/2, 2/1 or 3/0). Analysis of variance was used to determine if the factors and their interaction had a significant effect on the measured
Blends from heat-denatured and undenatured protein
29
properties (SAS Institute, 1989). Statistical analyses were performed at 0~= 0.05; thus, effects associated with factors or interaction with a p value lower than 0-05 were statistically significant. A logarithmic transformation was applied to the emulsifying activity index, coalescence index and viscosity results to stabilize the variance. For these variables, results are presented on a logarithmic scale to avoid the bias constituted by returning to the original scale after logarithmic transformation (Ung and V6giard, 1988). Unless otherwise stated, significant effects or interactions were partitioned into linear, quadratic and cubic components using orthogonal polynomials in order to develop empirical models (Little and Hills, 1978). The models were tested for lack of fit (Khuri and Cornell, 1987).
RESULTS AND DISCUSSION
Characteristics of blend components Whey protein isolate was highly soluble (Table 1) and produced clear protein dispersions. Heating induced some aggregation as evidenced by the milky appearance of the dispersion after treatment. However, the aggregates formed were virtually non-sedimentable with a decrease in solubility of only 10% (Table 1). The low ionic strength and protein concentration during heat treatment at pH 7 prevented the formation of large aggregates (Harwalkar and Kalab, 1985a). Under these conditions, no mechanical treatment was required to maintain dispersibility. Despite high solubility, heat-treated whey protein showed a high denaturation level which confirms that important structural changes occurred during the treatment (Table 1). The preparation of highly soluble denatured-whey protein concentrates has been proposed first by deWit (1981).
The emulsifying activity index The EAI is related to the surface area stabilized by a unit mass of protein under standard emulsification conditions. An empirical model which relates the EAI to the emulsion oil volume fraction and the DWPI/WPI TABLE 1 Characteristics of Protein Blend Components
Solubility (pH 7.0) (%) Denaturation (%)
WPI
DWPI
98.5 6.8
88.7 85~8
30
M. Britten, H. J. Giroux, Y. Jean, N. Rodrigue
1.75 1.50
19
~--"-~0/3
Oil Volume Fraction "12
.05
Fig, 1. Emulsifying activity index of DWPI/WPI protein blends (standard errors of predicted values were lower than 0-021 log units. R 2 of the fitted model: 0-990.
ratio in the protein blend has been developed from experimental results. The lack of fit test of the model was not significant (p --- 0.1598). The response surface corresponding to the model is presented in Fig. 1. The oil volume fraction of the emulsion was the main factor influencing the EAI (p -- 0.0001). Predictably, the surface area of the dispersed phase stabilized by the protein increased with the amount of oil to be homogenized. Increasing DWPI in the protein blend also had an effect on the EAI (p = 0-0001) and the effect varied depending on the oil volume fraction of the emulsion (p = 0-0001). For low oil volume fraction emulsions (0.05), EAI was constant and did not depend on the protein blend ratio as shown by multiple comparisons of least squares means. With the homogenization conditions used in the present investigation, the protein quality was not a limiting factor for the creation of new interfaces. It is likely that the energy input was not sufficient to further reduce droplet size (Haque and Kinsella, 1989). However, at higher oil volume fractions, the composition of the protein blend had an effect and the EAI improved with an increasing proportion of DWPI. This result was attributed to the aggregated nature of DWPI which contributed to the formation of thicker membranes around fat droplets. These membranes prevented recoalescence, which had been identified as an important factor limiting droplet size reduction in a valve homogenizer (Pearce and Kinsella, 1978). The improvement of the EAI with increasing DWPI in the protein blend showed a maximum for emulsions containing more than 19% oil; further increase in DWPI resulted in decreased EAI. Optimal emulsifying activity then required a minimal amount of WPI and this amount appeared to increase with the oil content of the emulsion. This suggests that the emulsifying activities of WPI and
Blends from heat-denatured and undenatured protein
31
DWPI are due to different reasons. WPI has the ability to create large interfaces through rapid adsorption onto fat droplets while DWPI seems to prevent recoalescence within the valve homogenizer. The emulsion coalescence index
The susceptibility of an emulsion to stirring-induced coalescence is an indication of the mechanical resistance of the membranes surrounding fat droplets. From coalescence index measurements, an empirical model was developed to express the effect of the protein blend ratio and the oil volume fraction of the emulsion on the coalescence index. The lack of fit test of the model was not significant (p --- 0.7044). The response surface corresponding to the model is presented in Fig. 2. The DWPI/WPI ratio of the protein blend had a significant effect on the coalescence index of the emulsion (p = 0.0001). Increasing DWPI in the blend reduced the coalescence index of the emulsion, probably as a result of increased mechanical resistance of the membranes. This observation parallels the inhibition of recoalescence explaining the improved emulsifying activity of DWPI/WPI protein blends (Fig. 1). The oil volume fraction of the emulsion also had a significant effect on the emulsion coalescence index (p ~-0-0003). Increasing oil volume fraction increased the collision rate (Reddy and Fogler, 1981) and promoted the formation of larger droplets during homogenization (Walstra, 1975), both factors leading to higher coalescence index. However, the effect of oil volume fraction was dependent upon the DWPI/WPI ratio in the protein blend (p = 0-0001). The coalescence index of emulsions
0
-0.6
°m (D
0
-1.2
- 0/3
-1 .e
"J
1/2 -2. D W P I / W P I Ratio Oil V o l u m e F r a c t i o n .19
.26
- 3/0
Fig. 2. Resistance to stirring-induced coalescence of oil-in-water emulsions stabilized by DWPI/WPI protein blends (standard errors of predicted values were lower than 0.097 log units. R 2 of the fitted model: 0.943).
32
M. Britten, H. J. Giroux, Y. Jean, N. Rodrigue
produced from pure WPI (0/3 ratio) increased with the oil volume fraction while emulsions produced from pure DWPI (3/0 ratio) were stable against coalescence whatever the oil volume fraction was. These results emphasize the role of the DWPI soluble aggregates in the formation of thick membranes which prevent mechanical deformations and resist coalescence.
The emulsion viscosity and age thickening Viscosity is an important property which influences the stability of emulsified products. The apparent viscosity of the emulsions was measured immediately after formation. A response surface was generated through spline interpolation, and results are presented as contour plots. Contour levels are expressed on a logarithmic scale (Fig. 3(a)). The emulsion apparent viscosity was affected by both factors, the oil volume fraction (p = 0.0001) and the DWPI/WPI ratio in the protein blend (p = 0.0001). As a general trend, increasing DWPI in the protein blend increased the emulsion viscosity. However, this effect was related to the oil volume fraction of the emulsion (p = 0.0001). For low-fat emulsions, the viscosity increase was very slight while high-fat emulsions became very viscous with increasing DWPI. It should be noted that maximum viscosity was reached for DWPI/WPI ratios around 2/1; a further increase in DWPI reduced the viscosity of high-fat emulsions. The lower viscosity of .26
~
.o
~ .19
LL
E ~.12
05/~ 0/3
1/2 I
2/1
1/2 3/0 0/3 DWPI/WPI Ratio
2/1
3/0
Log viscosity(mPa.s) 1.0 1.5 2.0 2.5 3.0 3.5 I I I I
Fig. 3. Apparent viscosity of oil-in-water emulsions produced from DWPI/WPI protein blends. (a) Initial viscosity; (b) viscosity after 4 weeks storage. The dashed line in (b) links the conditions where minimal age thickening occurred.
Blends from heat-denatured and undenatured protein
33
emulsions produced from high DWPI protein blends correlates with the reduced emulsifying activity of DWPI-rich blends (Fig. 1). It has been shown that the viscosity of an emulsion is related to the size of fat droplets (Dickinson and Stainsby, 1982). Larger fat droplets produced by high DWPI protein blends could then explain the emulsion viscosity decrease. The change in viscosity upon storage is an indication of age thickening. Emulsion apparent viscosity was measured after 4 weeks of storage and results are presented in Fig. 3(b). High DWPI/WPI ratio in the protein blend led to severe age thickening as evidenced by the difference between viscosity contour plots obtained immediately after emulsion formation (Fig. 3(a)) and after 4 weeks storage (Fig. 3(b)). The high concentration of soluble aggregates seems to promote the formation of a protein network during storage. High oil volume fraction is another factor promoting age thickening. This result is in agreement with the literature and emphasizes the involvement of fat droplets in the network formation (Harwalkar, 1982; Pouliot et al., 1990). The dashed line in Fig. 3(b) links the conditions of minimal age thickening, indicating a complex balance between the oil volume fraction and the proportion of DWPI in the protein blend.
The emulsion separation stability After 4 week storage, the opacity profile of the emulsions was monitored and the stability index was calculated. The results were used to establish an empirical model relating the stability index to the oil volume fraction of the emulsion and the DWPI/WPI ratio. The lack of fit test was non-significant (p = 0.1028). The response surface corresponding to the model is presented in Fig. 4. The oil volume fraction (p = 0.0001) and the DWPI/WPI ratio in the blend (p = 0-0001) had significant effects on emulsion stability. The emulsion stability could be related to the emulsion viscosity (Fig. 3), recognized as an important factor controlling the emulsion stability (Hailing, 1981). However, emulsions produced from pure WPI showed greater stability when the oil volume fraction increased despite a very slight change in viscosity. Crowding of the dispersed phase in high-fat emulsions might be responsible for this phenomenon (Dickinson, 1988). It was also noticed that emulsions with a 0.05 oil volume fraction showed increased stability with increasing DWPI in the protein blend despite a very slight change in viscosity. The reason for this stabilizing role is not known. DWPI could induce the formation of a soft network and/or it could form thicker membranes which increase the density of the dispersed phase, both factors improving the separation stability of the emulsion.
34
M. Britten, H. J. Giroux, Y. Jean, N. Rodrigue
o.
310
//7"~ 2/1 0 ' 5 5 . 2 6 ~ .19 Oil VolumeFraction12
4~/" 1/a 0/3 DWPI/WPI Ratio .05
Fig. 4. Separation stability of oil-in-water emulsions stabilized by DWPI/WPI protein
blends (standard errors of predicted values were lower than 0-038. R2 of the fitted model: 0,862). CONCLUSION Heat-denaturation of a whey protein isolate in solutions at pH 7.0 induced the formation of non-sedimentable aggregates of colloidal size. Mixtures of denatured and undenatured whey protein isolate solutions have been used to produce oil-in-water emulsions varying stabilities. The mixtures showed synergistic effects with respect to emulsifying activity. Emulsion stability against coalescence and separation was improved by the presence of DWPI in the blend. The viscosity of the emulsion was controlled by the DWPI/ WPI ratio in the protein blend. Proper balance between protein ingredients and the oil volume fraction of the emulsion reduced age thickening. Mixtures of denatured/undenatured whey protein fractions could be used to enlarge the utilization spectrum of whey proteins in food applications.
REFERENCES Britten, M. & Giroux, H. J. (1991). Coalescence index of protein-stabilized emulsions. J. Food Sci., 56, 792-5. Britten, M., Giroux, H. J. & Lavoie, L. (1991). Phase separation in dairy products monitored by optical densitometry. Milchwissenschaft, 46, 300-3. Cameron, D. R., Weber, M. E., Idziak, E. S., Neufeld, R. J. & Cooper, D. G. (1991). Determination of interracial areas in emulsions using turbidimetric and droplet size data: Correction of the formula for emulsifying activity index. J. Agric. Food Chem., 39, 655-9. deRham, O. & Chanton, S. (1984). Role of ionic environment in insolubilization of whey protein during heat treatment of whey products. J. Dairy Sci., 67, 939-49.
Blendsfrom heat-denatured and undenatured protein
35
deWit, J. N. (1981). Soluble denatured whey protein. UK Patent Application no. 2 063 273A. deWit, J. N. & Hontelez-Backx, E. (1981). Les propri&6s fonctionelles des prot6ines du lactos6rum; cons6quences des traitements thermiques. Technique Laiti~re, 952, 19-22. deWit, J. N. & Klarenbeek, G. (1984). Effects of various heat treatments on structure and solubility of whey proteins. J. Dairy Sci., 67, 2701-10. Dickinson, E. (1988). Emulsion stability. In Advances in Food Emulsions and Foams, eds E. Dickinson and G. Stainsby, Elsevier Applied Science, London, ch. 1, pp. 1-44. Dickinson, E. & Stainsby, G. (1982). Colloids in Foods, Applied Science Publishers, London, pp. 331-407. Halling, P. J. (1981). Protein-stabilized foams and emulsions. CRC Crit. Rev. Food Sci. Nutr., 15, 155-203. Haque, Z. & Kinsella, J. E. (1989). Emulsifying properties of food proteins: development of a standardized emulsification method. J. Food Sci., 54, 39-44. Harwalkar, V. R. (1982). Age gelation of sterilized milks. In Developments in Dairy Chemistry-1. Proteins, ed. P. F. Fox, Applied Science Publishers, London, pp. 229-69. Harwalkar, V. R. (1986). Kinetic study of thermal denaturation of proteins in whey. Milchwissenschaft, 41, 206-9. Harwalkar, V. R. & Kalab, M. (1985a). Thermal denaturation and aggregation of /%lactoglobulin at pH 2.5. Effect of ionic strength and protein concentration. Milchwissenschaft, 40, 31-4. Harwalkar, V. R. & Kalab, M. (1985b). Thermal denaturation and aggregation of fl-lactoglobulin in solution. Electron microscopic study. Milchwissenschaft, 40, 65-8. Harwalkar, V. R. & Kalab, M. (1985c). Microstructure of isoelectric precipitates from/~-lactoglobulin solutions heated at various pH values. Milchwissenschaft, 40, 665-8. Harwalkar, V. R. & Modler, H. W. (1981). Whey protein concentrate by heating under acidic conditions. 2. Physico-chemical evaluation of proteins. Milchwissenschaft, 36, 594-7. Kato, A., Osaka, O., Matsudomi, N. & Kobayashi, K. (1983). Changes in the emulsifying and foaming properties of proteins during heat denaturation. Agric. Biol. Chem., 47, 33-7. Kester, J. J. & Richardson, T. (1984). Modification of whey proteins to improve functionality. J. Dairy Sci., 67, 2757-74. Khuri, Andr6 I. & Cornell, John A. (1987). Response Surfaces Designs and Analyses, Marcel Dekker, New York, 405 pp. Kinsella, J. E. & Whitehead, D. M. (1989). Proteins in whey: chemical, physical and functional properties. Adv. Food Nutr. Res., 33, 343-438. Leman, J. & Kinsella, J. E. (1989). Surface activity, film formation, and emulsifying properties of milk proteins. CRC Crit. Rev. Food Sci. Nutr., 28, 115-37. Little, T. N. & Hills, F. J. (1978). Agricultural Experimentation Design and Analysis, John Wiley, New York, 350 pp. Modler, H. W. & Emmons, D. B. (1976). Properties of whey protein concentrates prepared by heating under acidic conditions. J. Dairy Sci., 60, 177-84.
36
M. Britten, H. J. Giroux, Y. Jean, N. Rodrigue
Morr, C. V. (1985). Functionality of heated milk proteins in dairy and related foods. J. Dairy Sci., 68, 2773-81. Multilangi, W. A. M. & Kilara, A. (1985a). Functional properties of heatdenatured whey proteins. 1. Solubility. Milehwissensehaft, 40, 338-41. Multilangi, W. A. M. & Kilara, A. (1985b). Functional properties of heatdenatured whey proteins. 2. Emulsification and foaming properties. Milchwissenschaft, 40, 391-3. Mulvihili, D. M. & Donovan, M. (1987). Whey proteins and their thermal denaturation - - a review. Irish J. Food Sci. Teehnol., 11, 43-75. Nakai, S. (1983). Structure-function relationships of food proteins with emphasis on the importance of protein hydrophobicity. J. Agric. Food Chem., 31, 676-83. Patel, M. T. & Kilara, A. (1990). Studies on whey protein concentrates. 2. Foaming and emulsifying properties and their relationships with physicochemical properties. J. Dairy Sci., 73, 2731-40. Pearce, K. N. & Kinsella, J. E. (1978). Emulsifying properties of proteins: Evaluation of a turbidimetric technique. J. Agric. Food Chem., 26, 71 6-23. Pouliot, Y., Britten, M. & Latreille, B. (1990). Effect of high-pressure homogenization on a sterilized infant formula: Microstructure and age gelation. Food Microstruct., 9, 1-8. Reddy, S. R. & Fogler, H. S. (1981). Emulsion stability: Determination from turbidity. J. Coll. lnterf. Sci., 79, 101-4. SAS Institute Inc. (1989). S A S / S T A T User's guide, Vol. 2, Version 6, 4 edn, SAS Institute Inc., Cary, NC, 846 pp. Shimizu, M., Kamiya, T. & Yamauchi, K. (1981). The adsorption of whey proteins on the surface of emulsified fat. Agric. Biol. Chem., 45, 2491~5. Ung, C. H. & V6giard, S. (1988). Probl6mes d'inf6rence statistique reli6s ~ la transformation logarithmique. Can. J. Forest Res., 18, 733-8. Walstra, P. (1975). Effect of homogenization on the fat globule size distribution in milk. Neth. Milk Dairy J., 29, 279-94.