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Original Articles

Viscoelastic Properties of Part Skim Mozzarella Cheese: Effect of Calcium, Storage, and Test Temperature

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Pages 239-252 | Received 10 Nov 2002, Accepted 22 May 2003, Published online: 06 Feb 2007

Abstract

Part skim Mozzarella cheeses with four levels of calcium (0.65% in control, 0.48% in T 1, 0.42% in T 2, and 0.35% in T 3) were manufactured on four separate occasions. Effect of varying calcium levels on viscoelastic properties of these cheeses was studied. Elastic (G′) and viscous (G′′) modulus were determined on day 1, 7, 15, and 30. Effect of increasing cheese temperature from 25 to 45°C during the test was also determined. Low calcium cheeses (0.35% in T 3 vs. 0.65% in control) had lower value of elastic (0.83 MPa vs. 1.89 MPa) and viscous modulus (0.57 MPa vs. 1.43 MPa). During storage, a decline in viscoelastic properties of the cheese was also noticed. After 30 days of storage, the elastic modulus of control and lowest calcium cheese (T 3) declined from 1.89 MPa to 1.69 MPa and from 0.83 to 0.55 MPa, respectively. Similar reduction in viscous modulus of control and lowest calcium cheeses (T 3) was also noticed after 30 days, i.e., values of G′′ declined from 1.43 to 1.25 MPa in control and from 0.57 to 0.27 MPa in T 3. A decline in elastic as well as viscous modulus with increase in cheese temperature during the test was observed. Values of elastic modulus were always higher than viscous modulus, indicating dominance of elastic nature of Mozzarella cheese. This information would help the manufacturers to produce cheeses with specific functional properties.

#Published with the approval of Director of the South Dakota Agricultural Experiment Station as Publication Number 4321 of the Journal Series.

Introduction

Mozzarella cheese production has increased dramatically in last two decades, and its production now rivals to that of Cheddar cheese. This is mainly due to increased use of Mozzarella cheese in food service, specifically Pizza industries. The viscoelastic nature of Mozzarella cheese is unique among the other cheese varieties, which might be one of the reasons for its increased demand. The protein network structure is responsible for the viscoelastic behavior of Mozzarella cheese.Citation1 The knowledge of viscoelasticity is helpful to correlate structural and functional characteristics and thereby handling and processing of Mozzarella cheese at different temperatures.

Dynamic testing is a fundamental method for determining rheological properties of visco-elastic materials.Citation2 These tests employ small amplitude oscillatory shear so that minimum physical and chemical changes occur in the samples. Mechanical properties such as Young's modulus be determined at various frequencies and temperatures within a short time and extremely small stain (<1%) can be imposed on the sample, which assures linear stress–stain behavior and applicability of mathematical models. This is a rapid and simple technique, which is an additional advantage especially for quality assurance in an industry. Measurement of elastic and viscous modulus gives indication of the interaction between flow units (protein aggregates or fat globules) in cheese.Citation3

A sample disk is placed between two parallel plates and subjected to sinusoidal oscillation. The lower plate is rotated at a specific frequency and transient responses are recorded. The ratio of elastic to viscous properties depends on time scale of deformation. During short time scale the cheese behaves elastically, i.e., a sample regains its original shape after the applied stress is removed, whereas, at long time scale it is mainly viscous, i.e., most of the deformation remains after stress is removed.Citation4 Elastic modulus, also known as storage modulus (G′), is a measure of energy stored and subsequently released per cycle of deformation of cheese sample. Viscous modulus or loss modulus (G′′) is a measure of energy dissipated per cycle of deformation of cheese sample. These measurements yield true engineering values for elasticity and viscosity in contrast to the approximations obtained from other methods.

Viscoelastic properties of Mozzarella cheese have been thoroughly studied using dynamic rheological tests and many studies on dynamic rheological aspect of Mozzarella cheese have been undertaken. Measurement of dynamic rheological properties provided objective basis to distinguish between natural and imitation low moisture part skim Mozzarella cheese.Citation1 Hsieh et al.,Citation5 while studying rheological properties of filled Mozzarella cheese found that inclusion of different proteins, viz. whey proteins, caseinates, egg, soy, and gelatin showed considerable water retention and altered viscoelasticity of the cheese. However, the textural properties of Mozzarella cheese made from milk added with 1 to 2% calcium caseinates or nonfat dried milk was unaffected.Citation6 Dynamic rheological tests differentiated the cheese characteristics in better manner as compared to other tests, viz. melt profile test and stress relaxation test when used to evaluate functionality of cheese.Citation7 Many studies involving measurement of dynamic rheological parameters in correlating effects of various aspects of Mozzarella cheese, viz. storage,Citation7 Citation8 Citation9 Citation10 Citation11 Citation12 physical form (frozen and thawed) of Mozzarella cheese,Citation8 and microstructureCitation13 have been undertaken. Recently, Dave et al.Citation14 studied effects of starter culture and coagulating enzymes on viscoelastic behavior of Mozzarella cheese. It was observed that viscoelastic properties of Mozzarella cheese reduced during storage and the decrease in G′ and G′′ was higher in the cheese made using mixed culture as compared to the cheese made single culture and the differences were higher in cheeses made with 6 X enzyme concentration as compared to 1 X enzyme. All the above studies indicated that viscoelasticity of Mozzarella cheese is a function of composition, manufacture, and storage conditions and proteolysis during storage.

Calcium content of Mozzarella cheese is important in deciding functional properties, especially melting.Citation15 It is generally accepted that reduced calcium cheese has higher meltability. It was recently reported that low calcium Mozzarella cheese possessed lower elastic shear modulus.Citation16 The authors correlated values of elastic modulus and phase angle with flow of the cheese. Metzger et al.Citation17 observed that Mozzarella cheese with reduced calcium had lower firmness. Joshi et al.Citation18 demonstrated that in comparison to soluble calcium colloidal calcium played an important role in deciding functionality i.e., softening, melting, and flow of salted and unsalted part skim Mozzarella cheese. In another studyCitation19 it was also revealed that reduction of approximately 35% calcium almost doubled the melt area of the cheese and also caused reduction in time-temperature required for softening and melting of part skim Mozzarella cheese on d1.

However, little is known as to how various levels of calcium affect the elastic and viscous modulus and what correlation exists between calcium content and viscoelasticity of Mozzarella cheese during storage. The objective of present research was to study the effects of different calcium levels on viscoelastic properties (elastic (G′) and viscous (G′′) modulus) of Mozzarella cheese, so that the cheese manufacturers have information on the critical level of calcium required to bring desirable viscoelastic properties in cheese. Additionally, we also studied the effect of test temperature and storage on viscoelasticity of these cheeses.

Materials and Methods

Cheese Manufacture

Calcium content was altered by preacidifying pasteurized and standardized (1.8% fat) milk at 4°C with citric acid and dilute acetic acid (10% v/v) to different pH viz. 6.2 (T 1), 5.9 (T 2), and 5.6 (T 3). The untreated milk served as control. Part skim Mozzarella cheese was made by direct acidification method.Citation19 Glucono-δ-lactone was used to lower pH of curd to 5.1 before whey draining. Cooking time-temperature and final draining of whey from all cheese curd were adjusted in such a way that uniform moisture obtained in all the cheeses. Cheese curd was then salted (2% w/w), hand stretched in 5% salt brine at 77°C, filled in small wooden molds and immersed in ice water bath for 1 h. The cold cheese blocks were cut into four pieces, individually vacuum packaged using a Spiro Mac vacuum packaging machine in a barrier bag and stored at 4°C until analysis on day 1, 7, 15, and 30.

Chemical Analyses

Moisture of cheese was determined gravimetrically using a Mojonnier methodCitation20 and fat by modified Babcock method.Citation21 Protein content was determined by measuring total nitrogen content of the cheese by Kjeldahl methodCitation22 and multiplying it by a factor of 6.38. Ash content was determined by using a muffle furnaceCitation22 and salt by Volhard method.Citation22 For calcium determination, cheese samples were dried, ashed, and residues were dissolved and diluted in acidified aqueous solution. The portion was diluted for AAS (Atomic Adsorption Spectroscopy) determination at 422.7 nm.Citation22 Proteolysis in cheeses was monitored on day 1, 7, 15, and 30 by determining the soluble protein content by the Kjeldahl method of extract of grated cheese using Sharpe's solution.Citation23

Dynamic Rheology Measurement

Dynamic oscillatory testing of cheese was performed using a Haake® viscometer (HB Instruments Inc., Paramus, NJ). A sensor system RV20 to control the shear rate and a sensor system CV20 to control amplitude and frequency were used during the test. Heating of sample during test was accomplished by connecting the sensor system to Haake® circulator. An external heating system (Model 742 G, Allied Precision Ind., Elburn, IL) was used to enhance the heating rate. The data were collected and analyzed using a personal computer with software (Haake® Software, Rotovisco RV20, Oscillation, Version 2.23).

Mozzarella cheese samples were prepared by cutting a thin slice (3.6 mm) using a food slicer (Model MS 1043-W, The Rival Co. Kansas, MO) in a direction parallel to the flow of fibers. Cylindrical specimens of 20.4 mm diameter were cut using a cork borer. The samples were placed in a petri plate and transferred to refrigerator (4–6°C) until testing. A copper-constantan precision fine wire thermocouple (0.005 Ga diameter) was inserted at the center and then the specimen was heated without running actual test to calibrate changes in temperature during the test.

Peripheral surface of the sample was oiled to avoid moisture loss during the test. The cylindrical specimen was then placed between parallel plates (˜20 mm diameter) of CV20 sensor system before performing the actual test. A constant frequency of 1 Hz and constant stain of 0.5% were used through out the study. A time sweep mode was used to calculate the rheological properties. Temperature of sample was adjusted to 25°C at the onset of testing, which was then increased to 45°C at a rate of 1°C/min. The parameters measured included the elastic modulus (G′) and the tangent angle (tan δ). Viscous modulus (G′′) was computed using the equation: G′′ = G′× tan δ. All the measurements were done in triplicates.

Statistical Analysis

Four vats of cheese (control, T 1, T 2, and T 3) were made on the same day to study effects of calcium. Cheese making was replicated four times. Cheese samples were analyzed on day 1, 7, 15, and 30 and each analysis was done in triplicate thus, 4 replications × 4 treatments × 4 storage periods × 3 samples = 192 specimens were tested. Data were statistically analyzed using PROC GLM of SAS® softwareCitation24 to find significant differences.

Results and Discussion

Composition

Table shows composition of part skim Mozzarella cheese. As mentioned earlier, we aimed to achieve same moisture level while manufacturing the control as well as experimental cheeses. Moisture, fat, protein, and salt contents of all the cheeses were similar (P > 0.05). However, the control cheese had maximum (P < 0.05) calcium and ash contents (0.65 and 3.03 kg per 100 kg cheese) followed by T 1 (0.48 and 2.90 kg per 100 kg cheese), T 2 (0.42 and 2.65 kg per 100 kg cheese), and T 3 (0.35 and 2.44 kg per 100 kg cheese) respectively. Preacidification resulted in solubilization of minerals in milk including calcium and thus low calcium and ash contents in the experimental cheeses (P < 0.05).

Table 1 Average (N  =  4) composition (kg/100 kg cheese) of part skim Mozzarella cheese

Effect of Calcium on Viscoelasticity

With reduction in calcium content of cheeses from 0.65 kg per 100 kg cheese (control) to 0.48 kg per 100 kg cheese (T 1), 0.42 kg per 100 kg cheese (T 2), and 0.35 kg per 100 kg cheese (T 3) there was a concomitant reduction in elastic modulus, from 1.89 MPa to 1.29, 1.12, and 0.83 MPa respectively (Table ) on day 1. Similar trend was also observed in viscous modulus (Table ), i.e., the values of viscous modulus of fresh cheeses (day 1) declined from 1.43 MPa (control) to 0.79 MPa (T 1), 0.67 MPa (T 2), and 0.57 MPa (T 3). The values of elastic modulus were always higher than the respective values of viscous modulus showing the dominance of elastic nature of Mozzarella cheese. However, reduction in values of elastic modulus with reduction in calcium content indicated that elasticity of Mozzarella cheese slowly diminished upon reduction of calcium. While studying the effect of pH and calcium concentration on some textural and functional properties of Mozzarella cheese Guinee et al.Citation16 observed that the fresh cheese with low calcium content possessed lowest value of elastic shear modulus (G′). No apparent reason for lower value of elastic shear modulus in the cheese containing low calcium concentration was put forwarded by the authors. Joshi et al.Citation25 observed greater degree of protein swelling with greater degree of casein hydration in reduced calcium Mozzarella cheeses on d 1. Hydration of protein and rearrangement of fat particles in the structure of cheese upon reduction of calcium concentration is thought to be responsible for weakening of the cheese matrix, which might have caused lowering of viscoelastic properties of our cheeses. Other reportCitation26 also indicated that solubilization of micellar calcium can promote hydration of paracasein in cheese. Solubilization of calcium may affect the binding sites on the casein molecules and influence the structure of casein matrix.Citation3 Thus calcium is thought to be important for controlling interactions of proteins in the cheese matrix and affecting the viscoelastic properties of Mozzarella cheese.

Table 2 Effects of calcium, storage, and cheese temperature on elastic (G′) and viscous (G′′) modulus (MPa) of part skim Mozzarella cheese

Increase in viscous modulus with decrease in elastic modulus was expected upon reduction of calcium, however, the effect was not so noticeable. The difference between values of elastic and viscous modulus became narrow as the calcium content of cheeses reduced. This indicated that though there was no increase in value of viscous component upon reduction of calcium level, its decline was less as compared to the decline in elastic component of the cheeses. The low calcium cheeses had less free serum and more hydrated protein (data not shown), which might have contributed to relatively less decline in their viscous modulus compare to elastic modulus. However, effect of hydration of protein and subsequent increase in viscous modulus might not be so significant to indicate direct increase in the value of viscous modulus.

Effect of Storage on Viscoelasticity

Storage of Mozzarella cheese for up to 30 days caused reduction in values of both elastic and viscous modulus (Figs. a–d and a–d). The elastic modulus of control, T 1, T 2, and T 3 cheeses declined from 1.89, 1.29, 1.12, and 0.83 on d 1 to 1.69, 0.89, 0.75, and 0.55 MPa respectively on d 30. Similarly, values of viscous modulus in control, T 1, T 2, and T 3 cheeses reduced from 1.43, 0.79, 0.67, and 0.57 to 1.25, 0.60, 0.57, and 0.27 MPa, respectively (Table ). The viscoelastic nature of Mozzarella cheese is due to cross-linking of proteins and also due to bonds like salt linkages and hydrogen bonds in casein network.Citation27 Higher values of elastic and viscous modulus in fresh cheese are believed to be due to these cross linkages and strong protein–protein interactions. Effect of storage on proteolysis of part skim Mozzarella cheese containing different concentration of calcium is shown (Fig. ). The control cheese had less soluble nitrogen on d 1 and throughout the storage as compared to experimental cheeses containing reduced amount of calcium. Break down products of protein (due to proteolysis) during storage are hydrophobic in nature, which allow absorption of moisture from fat channels into protein matrix. Subsequently, the protein network become more hydrated and weakened resulting into decrease in visco-elastic characteristics. This might be one of the reasons for lower values of both modulus of our cheeses during storage. The degradation products of protein contribute less to the modulus as compared to the intact casein.Citation28 Tunick et al.Citation6 observed significant decrease in values of G′ (from 55.2 to 42.2 kPa) and G′′ (from 19.9 to 14.6 kPa) in Mozzarella cheese upon refrigerated storage of 6 weeks. Small peptides formed during proteolysis of cheese move easily upon application when shear force is applied and this might have resulted into lowering the values of viscoelastic parameters.Citation6 Ak and GunasekaranCitation10 observed decrease in values of G′ and G′′ upon refrigerated storage. They further reported that the effect was more noticeable at 20°C and during first 2 weeks of storage. Diefes et al.,Citation8 Yun et al.,Citation9 Subramaniyan and Gunasekaran,Citation11 and Sharma,Citation12 also observed such decrease in elastic and viscous modulus upon storage of Mozzarella cheese. Cheese becomes more elastic liquid as the storage proceeds.Citation8 Softening of internal structure during storage may be attributed for lowering of elasticity of cheeses. Tunick et al.Citation29 observed decrease in strength of cheese matrix upon storage, which allowed the fat globules to coalesce and caused decline in elastic and viscous modulus. They also correlated these changes with proteolysis of α s 1 casein upon storage indicating that proteolytic break down of α s 1 casein in Mozzarella cheese that leads to reorganization and weakening of matrix, resulting in a softer and less elastic cheese. Increase in viscous modulus with decrease in elastic modulus was expected, however, that behavior was not observed in the present study. Ak and GunasekaranCitation10 indicated that binding of water by ionic groups generated during proteolysis might also contribute to reduction in viscous modulus upon storage.

Figure 1. (a) Effects of calcium level and cheese temperature on elastic modulus of part skim Mozzarella cheese at day 1; (b) Effects of calcium level and cheese temperature on elastic modulus of part skim Mozzarella cheese at day 7; (c) Effects of calcium level and cheese temperature on elastic modulus of part skim Mozzarella cheese at day 15; (d) Effects of calcium level and cheese temperature on elastic modulus of part skim Mozzarella cheese at day 30. (♦) = Control (0.65 kg calcium/100 kg cheese), (□) = T 1 (0.48 kg calcium/100 kg cheese), (▴) = T 2 (0.42 kg calcium/100 kg cheese), and (X) = T 3 (0.35 kg calcium/100 kg cheese).

Figure 1. (a) Effects of calcium level and cheese temperature on elastic modulus of part skim Mozzarella cheese at day 1; (b) Effects of calcium level and cheese temperature on elastic modulus of part skim Mozzarella cheese at day 7; (c) Effects of calcium level and cheese temperature on elastic modulus of part skim Mozzarella cheese at day 15; (d) Effects of calcium level and cheese temperature on elastic modulus of part skim Mozzarella cheese at day 30. (♦) = Control (0.65 kg calcium/100 kg cheese), (□) = T 1 (0.48 kg calcium/100 kg cheese), (▴) = T 2 (0.42 kg calcium/100 kg cheese), and (X) = T 3 (0.35 kg calcium/100 kg cheese).

Figure 2. (a) Effects of calcium level and cheese temperature on viscous modulus of part skim Mozzarella cheese at day 1; (b) Effects of calcium level and cheese temperature on viscous modulus of part skim Mozzarella cheese at day 7; (c) Effects of calcium level and cheese temperature on viscous modulus of part skim Mozzarella cheese at day 15; (d) Effects of calcium level and cheese temperature on viscous modulus of part skim Mozzarella cheese at day 30. (♦) = Control (0.65 kg calcium/100 kg cheese), (□) = T 1 (0.48 kg calcium/100 kg cheese), (▴) = T 2 (0.42 kg calcium/100 kg cheese), and (X) = T 3 (0.35 kg calcium/100 kg cheese).

Figure 2. (a) Effects of calcium level and cheese temperature on viscous modulus of part skim Mozzarella cheese at day 1; (b) Effects of calcium level and cheese temperature on viscous modulus of part skim Mozzarella cheese at day 7; (c) Effects of calcium level and cheese temperature on viscous modulus of part skim Mozzarella cheese at day 15; (d) Effects of calcium level and cheese temperature on viscous modulus of part skim Mozzarella cheese at day 30. (♦) = Control (0.65 kg calcium/100 kg cheese), (□) = T 1 (0.48 kg calcium/100 kg cheese), (▴) = T 2 (0.42 kg calcium/100 kg cheese), and (X) = T 3 (0.35 kg calcium/100 kg cheese).

Figure 3. Soluble nitrogen (%) of part skim Mozzarella cheese. Control = 0.65 kg calcium/100 kg cheese, T 1 = 0.48 kg calcium/100 kg cheese, T 2 = 0.42 kg calcium/100 kg cheese, and T 3 = 0.35 kg calcium/100 kg cheese. [a,b,c,dBars within same day not sharing common superscript are different (P < 0.05). A,B,C,DBars not sharing common superscript are different (P < 0.05) for storage period.]

Figure 3. Soluble nitrogen (%) of part skim Mozzarella cheese. Control = 0.65 kg calcium/100 kg cheese, T 1 = 0.48 kg calcium/100 kg cheese, T 2 = 0.42 kg calcium/100 kg cheese, and T 3 = 0.35 kg calcium/100 kg cheese. [a,b,c,dBars within same day not sharing common superscript are different (P < 0.05). A,B,C,DBars not sharing common superscript are different (P < 0.05) for storage period.]

Effect of Cheese Temperature on Viscoelasticity

At refrigerated temperature of cheese the fat is in crystalline state, and transition of its status begin as the cheese temperature rises. However, no major change takes place until the temperature reaches near its melting point (i.e., 37°C). Our aim was to study the effect of change in the status of fat, i.e., from solid to liquid by increasing the cheese temperature on the viscoelastic properties of cheese. Mozzarella cheese has temperature of around 70°C when it is melted on pizza. Looking to this, we intended to increase the cheese temperature from 25 to 70°C and measure the viscoelastic properties. However, during preliminary trials the experimental cheeses (i.e., T 1, T 2, and T 3) became too soft to handle causing slippage and distorted results beyond 45°C. Hence, it was decided to study the effect of increase in temperature from 25 to 45°C. Decline in values of both elastic and viscous modulus was observed as the cheese temperature increased from 25 to 45°C (Figs. a–d and a–d). The elastic modulus of control T 1, T 2, and T 3 cheeses declined from 1.89 to 0.37 MPa, 1.29 to 0.18 MPa, 1.12 to 0.14 MPa, and from 0.83 to 0.13 MPa respectively when the cheese temperature increased from 25 to 45°C. Similarly, with increase in temperature, the values of viscous modulus declined from 1.43 to 0.08 MPa, 0.79 to 0.09 MPa, 0.67 to 0.04 MPa, and from 0.57 to 0.01 MPa respectively in control, T 1, T 2, and T 3 cheeses at day 1 (Table ). It was also observed that at 25°C, when the fats in cheese were in crystalline form, the values of G′ and G′′ were significantly (P < 0.05) different in all the cheeses on d 1 and on d 30. However, when the cheese temperature was increased to 45°C, the fats were in molten stage and values of G′ in low calcium cheeses were same on d 1 as well as on d 30. This suggested that there was no any additional effects of lowering the calcium on G′ of Mozzarella cheese. On the contrary, at 45°C the T 1 and T 2 had similar (P > 0.05), but T 3 had lower (P < 0.05) value of G′′, on d 1, however on d 30 all the low calcium cheeses had similar (P > 0.05) values of G′′.

Thus, upon heating the cheese lost its elastic solid characteristics and turned into a viscous fluid. Easy flow of molten fat through smoothened protein strands due to heating might have caused cheese matrix to soften and thus reduction in viscoelastic properties. Hsieh et al.Citation5 and Venugopal and MuthukumarappanCitation7 observed reduction in elastic and viscous modulus of Mozzarella cheese upon heating from 25°C to 60°C. Guinee et al.Citation16 observed a steep reduction from 20 to 45°C and then gradual reduction up to 80°C in elastic shear modulus of Mozzarella cheeses. The faster reduction in elastic modulus was attributed to liquefaction of the fat phase at 40°C. These changes were also attributed to alteration in the structure of the cheese upon heating.

Conclusions

Study of dynamic rheology is an important tool to understand the viscoelastic behavior of cheese. Calcium played key role in functional and rheological properties of Mozzarella cheese. Reducing level of calcium in part skim Mozzarella cheese caused decline in its viscoelastic properties. Reduction of calcium concentration from 0.65 kg per 100 kg cheese in control to 0.35 kg per 100 kg cheese in T 3 caused 44 and 40% respectively reduction in the value of elastic and viscous modulus at 25°C. However, when viscoelasticity was measured at higher temperature (45°C when fats were in molten stage), lowering of calcium from 0.65 kg per 100 kg cheese to 0.48 kg per 100 kg cheese was critical and no significant effect of calcium lowering was observed beyond that level. Decline in values of elastic and viscous modulus was also observed during 30 days refrigerated (4°C) storage of these cheeses. The effect of reducing calcium on viscoelasticity of Mozzarella cheese was more prominent on the cheese compared to effect of storage up to 30 days. Increasing the cheese temperature during the test caused further decline in its viscoelastic properties. Elastic nature of Mozzarella cheese diminished with reduction in its calcium content, increase in age and increase in cheese temperature. However, the values of elastic modulus were always higher than those of viscous modulus indicating the dominance of elastic nature of even low calcium Mozzarella cheese.

Acknowledgments

This work is based upon work supported by the NRICGP (Award No: 2001-35503-10813, NRI Competitive Grants Program/USDA). College of Agriculture and Biological Sciences at South Dakota State University provided part of the funding through funds from the Agricultural Experimental Station.

Notes

#Published with the approval of Director of the South Dakota Agricultural Experiment Station as Publication Number 4321 of the Journal Series.

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