Interactions of Food Proteins - American Chemical Society

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Chapter 15

Rheology A Tool for Understanding Thermally Induced Protein Gelation D. D. Hamann

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Food Science Department, North Carolina State University, Raleigh, NC 27695-7624

General concepts of rheology are discussed as applied to the protein gelation process and the texture of the final gel. Small strain oscillatory experiments are presented as a means of studying the gelation process. Large strain (fracture) rheology is presented as a means of studying the fundamental mechanical properties of the final gel. Examples of oscillatory testing show rheological changes during heating and cooling thermal scans and isothermal heating. Fracture testing examples show effects offillersand enzymatic hydrolysis. Many foods are formed by the gelation of proteins. This gelation transforms the material physically from a viscous sol or liquid into a solid which is quite elastic in its response to a physical force application. Rheology has been defined as "the science of deformation of matter" (1) and is therefore an appropriate tool for observing physical characteristic changes influenced by variables such as time, temperature and pH or various combinations. Rheology as used by polymer chemists and others in the study of non-food materials has usually been limited to materials that flow (do not exhibit catastrophic fracture) or small strain studies of viscoelastic solids (strains are smaller than those producing catastrophic fracture). Whorlow (2) discusses the narrowing of the meaning of the term rheology. When fracture is of interest, it is usually studied in a separate area calledfracturemechanics. Emphasis is on the study of crack extension as a function of applied forces (3). Linear fracture mechanics is a term used when large plastically yielded regions surrounding cracks or flaws are not present. The separation of the study of food deformation into rheology and fracture mechanics does not seem practical because a primary concern is how food flows or moves during mastication which, in the case of a solid, is a function of how it fractures and breaks down. There are relatively few food rheologists and most of these must, of necessity, work with the full range of foods, liquid to solid. The food rheologist must base studies on the physics of flow, small strain deformation, and fracture mechanics and it is desirable they be familiar with the psychorheology of sensory food evaluations (4). 0097-6156/91/0454-O212$06.00/0 © 1991 American Chemical Society In Interactions of Food Proteins; Parris, N., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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Typical food protein gels include frankfurters and other comminuted meat products, egg products, shellfish analogs from surimi, dairy protein gels, and plant protein gels. Some of these will be used as examples in this chapter. The objective of the chapter is to demonstrate how food rheology can be used to better understand gelation transitions involved in product manufacture and how material properties, quantified in fundamental units, relate to sensory quality.

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Sol-Gel Transition Rheology Background. Modern rheometers distinguish between viscous and elastic resistance to forces as well as quantify the magnitudes of resistance, deformation, and rate of deformation. Figure 1 represents a deformed element of material originally a rectangular parallelepiped of length (L) and height (h). The top has been pushed to the right by a tangential force (F) so that the side view is now a parallelogram rather than a rectangle. This type of deformation changes shape but does not change the volume of the material element. It is called shear and is the only type of deformation that will be discussed in this chapter. If the motion of the top surface is continuous we have the situation common to fluids tested in viscometers. The shearing surfaces may be curved in various ways but the shearing action is always present. Shear strain (γ) is defined as Y«tany=AL/h

(1)

The rate at which this angle changes is the shear strain rate (shear rate) and is commonly the controlled variable in viscometry. Shear stress is the applied force divided by the area of the surface to which it is applied tangentially. In Figure 1 the force would be applied to the top surface area and the bottom surface provide an equal magnitude but opposite direction force with the result being the deformation shown. In the case of fluids behaving in a viscous manner, the viscosity (η) is T| = [shear stress] / [shear rate]

(2)

For solids, shear strain is assumed small and a shear modulus (G) is defined as G = [shear stress] / [shear strain]

(3)

G is sometimes referred to as the modulus of rigidity. Common Test Modes. Consider the rheometer in Figure 2. It will operate in several modes including: (1) Viscometry mode - shear strain rate is increased in increments and the output at each is viscosity, shear stress, and strain rate. The material is assumed to be viscous in this test. (2) Flow relaxation - after a specified shear history, the instrument stops its motion (strain rate = zero) and the decay in shear stress is monitored. (3) Relaxation - with the material at rest, a specified small strain is imposed and maintained constant. The decay in shear stress is monitored. (4) Stress growth - a specified shear strain rate is applied and the shear

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γ

Figure 1. An element of material deformed in shear

Figure 2. A modern rheometer (courtesy ofBohlin Rheologi)

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stress monitored. A typical response is that the stress vs strain rate line is fairly linear to a maximum stress (yield stress) after which the stress drops to a lower stable value. (5) Strain sweep - sinusoidal oscillatory shear strain is imposed and the resulting shear stress monitored. Frequency is held constant and strain amplitude increased incrementallyfroma minimum to a maximum or other sequence as desired. (6) Frequency sweep - this is similar to (5) but the strain amplitude is held constant andfrequencyvaried incrementally. Superimposed on any of the above tests is a programed temperature history that can imitate a cooking process or other event. Physical Meaning of Rheological Information. Proper interpretation of results is critical. A brief mathematical description with explanation of physical meaning will be presented for the case of imposed sinusoidal shear strain. Sinusoidal shear strain can be written as γ = γ sin(û)t) ο

(4)

where Y is the strain amplitude, ω is the angularfrequencyin radians/s and t is the q

time. The shear rate will be the derivative of Equation 4 with respect to time shear rate = γ^ω cos(cot)

(5)

The shear stress (T) will, in general, be out of phase from the strain by an angle δ and can be written as T = T sin(cût + 5) 0

(6)

;

where X is the stress amplitude. The ratio of shear stress divided by shear strain can be q

written as the sum of two components, one in phase with the strain and the other 90° out of phase (5). A complex number coordinate system is often used for mathematical clarity and easy manipulation. The y axis is the imaginary axis and the real part of the number is represented on the χ axis. The real term is the in-phase part and the imaginary term is the out of phase part G

*= (VYo) t

c o s

δ + i sin δ] = G ' + i G " 1/2

(7)

where i is the imaginary number (-1) , G ' is the storage modulus, G " is the loss modulus and G * is the complex modulus. The ratio (XQ/YQ) is the absolute modulus, IG*I. The absolute modulus is a measure of the total unit material shear resistance to deformation (elastic + viscous). For a perfectly elastic material the stress and strain are

In Interactions of Food Proteins; Parris, N., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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in phase (δ = 0) and the imaginary term is zero. In the case of a perfectly viscous material δ = 90°=π/2 radians and the real part is zero. The ratio G7G' is called the loss tangent and is equal to the tangent of the phase angle

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tan δ = G / G '

(8)

This is proportional to the (energy dissipated) / (energy stored) per cycle. Specifically, the energy dissipated due to viscous behavior per cycle divided by the maximum elastic energy stored is 2π tan δ (6). A perfectly elastic material would exhibit δ = 0 whereas for a perfectly viscous material δ = 90°. In this later case G' = zero and all work of deformation is converted to heat raising the temperature of the material. Protein gels are normally quite elastic so values of δ are near 10°. A muscle sol prior to cooking exhibits some elasticity but is viscous so a typical δ would be 45°. The transition from a sol to a gel is very evidentfromchanges in δ. Most food gelation studies have been done at a constant ω (often < 1 Hz) with temperature and/or time varying (7-11). Egelandsdal et al., (12) found significant effects on G' and δ of myosin gels when strain amplitude was varied from 0.003 to 0.1. It is necessary to know and record instrument controlled variables including oscillationfrequencyand strain amplitude. An Example - Conalbumin. A relatively straightforward rheological study of gelation can be done using an oscillatory test mode holding frequency and strain amplitude constant while varying temperature through a gel forming history. Best results are usually obtained at low frequencies because it is at low strain rates that molecular properties are elucidated (13.14). Figure 3 shows heating and cooling response curves for conalbumin protein. Below about 62°C the conalbumin solution behaved primarily as a low viscosity liquid and the torque sensing element used was not able to detect fluid resistance to shear above instrument noise. At about 62°C it could be seen that the phase angle was low, about 5°, and tending to decrease. This indicated elastic response was dominant suggesting an elastic structure was forming, but it was not very rigid since G' was very low. At about 63°C, G started to increase rapidly indicating the elastic structure was being stiffened, probably by additional bonds being formed. This continued to near 75 °C at which temperature the rate of increase in G started to decrease and the phase angle started to increase with the slope increasing as temperature increased. The increase in phase angle indicates more of the strain energy was going into viscous energy loss. This suggests an increase in volume fraction of the protein caused by additional unfolding of the molecules. From 80°C to 95°C, G' was stable but the phase angle continued to increase. Evidently, protein unfolding continued to 95°C. This is different than what has been observed for muscle proteins where the phase angle decreases to a low value where it remains as temperature is increased (e.g., 15). Upon reaching 95°C, the conalbumin was cooled at 1°C / min to 25°C. Except for a flat regionfrom95°C to 88°C, G increased linearly as temperature decreased. This was probably due to increased hydrogen bonding. The phase angle decreased at a steep slope to about 55°C temperature after which it was stable at an angle near 4°. Phase angles for foods do not normally drop much below 4°. The G flat region, 85°-95°C, is probably controlled by hydrophobic or covalent associations. !

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HAMANN

Figure 3. Heating and cooling thermal scans of 10% conalbumin in 0.85 NaCl solution; scanning rate 1 °C per min

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Limitation of the Thermal Scanning Technique. A limitation of the thermal scanning method is that a favorable protein gelation temperature range may not be maintained for an adequate time to fully develop a gel characteristic of that range, particularly if the protein concentration is low (Wu, J.Q. et al. J. Agric. Food Chem.. in review). It has been reported that slow aggregation produces a "more ordered" gel network characterized by higher elasticity (16). Wu et al. (Wu, J.Q. et al. J. Agric. Food Chem.. in review) have shown that isothermal conditions producing myosin gels of high shear modulus and elasticity require a long time for full development (Figure 4) with gel development being delayed by low myosin concentration. This paper also discusses myosin unfolding as the most likely critical factor with lower temperatures being favorable to aggregation and gelation. It is well known that some fish muscle sols gel irreversibly overnight at 0°C (17). Wu et al. (Wu, J.Q. et al. J. Agric. Food Chem.. in review) show that chicken myosin heated very rapidly to temperatures of 74°C or above produced no gel whereas good gels were formed rapidly at lower temperatures, 48°C being near optimum. With the limitations discussed in mind, thermal scanning rheology is a useful tool for the study of food protein gelation. Changes in the gelation curves can be studied as affected by protein source, protein concentration, specific cooking histories, pH adjustment, additives and many other factors. The phase angle, δ, and storage modulus, G', (or other parameters obtainablefromthese) are key indicators of gelation occurring as already discussed with respect to Figure 3. Fundamental Properties of Food Gels Related to Texture Definitions. Transition rheology helps understand protein gelation chemistry which produces final gel properties. However, it is difficult to consistently predict sensory texture from thermal rheology scans or other physical testing of the gels at strains insufficient to cause gelfracture(rupture). Depending on the literature on the class of materials tested, properties at rupture may be called, ultimate, failure, rupture, fracture or by some other descriptive term. To be consistent, in this chapter we will use the adjective 'fracture' to describe these properties. Axial Compression. Equations for calculating stresses, strains or moduli from instrumental tests are based on assumptions that may not be valid for the very deformed conditions causing fracture. This is particularly true if an assumption was small deformation. Axial compression of a cylindrical specimen between parallel plates, for example, causes the specimens height to decrease and its diameter to increase. Using the undeformed height and diameter in equations based on the assumption of small deformation is inappropriate if the ratio of decrease in height divided by initial height is larger than about 0.1. Many protein food gels are very deformable and this ratio can approach unity so, if fundamental units independent of a specific test are to be used to specifyfractureconditions, equations based on larger strain conditions should be used. A number of approaches to this are in the literature (see 18). One approach to developing an appropriate axial strain equation for compression of

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cylinders at large axial strain is to assume the basic material properties are independent of the deformation and to consider the appropriate strain to be the sum of an infinité number of small axial strain changes. Integrating these small strains ( each one based on the previous specimen height), the result is Hencky's strain and given by Hencky's strain = - In [1- (Ah/h)]

(9)

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If a gel is fairlyfreeof voids (gas space) it will be nearly incompressible (in terms of no volume change). Equation 9, the assumption of incompressibility, and the relationship between axial strain and shear strain (19) can be used to develop the following equation forfractureshear strain: Y =1.5{-ln[l-(Ah/h)]}

(10)

f

where

is thefractureshear strain. Inserting Ah/h values into this equation reveals that

a Ah equal to 50% of h produces a

of about 1.0. Thus, a distorted specimen is

required to produce a y of 1.0. With the incompressibility assumption the volumes of the undeformed cylinder and the deformed cylinder will be equal and the equation for shear stress can be written f

2

T = 0.5 F /frR /(l-Ah/h)] f

(11)

c

where T^. is the fracture shear stress, F is the uniaxial compression force at fracture, c

and R is the initial cylinder radius. Many food gels including frankfurters, surimi based seafood analogs, and unwhipped egg white can be considered incompressible so the above equations are suitable. Peleg (20) discusses aspects of the Hencky strain approach applied to food force /deformation curves. One reason shear stress and strain are calculated is that, experimentally, shear fracture is almost always exhibited by the specimens subjected to axial compression. The maximum shear stresses and strains can be shown to be at an angle of 45° from the cylinder axis which for a perfectly homogeneous specimen would produce conical fracture surfaces. Actual gels tend tofragmentsomewhat but the 45° angles (based on the deformed cylinder height) are usually very evident. Compression failure is resisted by gel incompressibility. Rarely,fracturemay occur as a vertical crack in the surface of the cylinder. Culioli and Sherman, (21) show this is common for cheese. This is a tensionfractureand can be thought of as the type of failure prevented in a barrel by hoops. Other assumptions are made in developing Equations 10 and 11 which one needs to be aware of. It is assumed that the deformed shape is still that of a cylinder, not a barrel shape or a hourglass shape. It is also assumed that the friction between the plates and the specimen as R increases can be neglected. Actually, these are not independent. If friction is high, a barrelling will occur and if friction is very low a hourglass shape will develop. The plates may have to be lubricated so the deformed specimen cross-section

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is of approximately constant area throughout its length. Experimentally, the length to diameter ratio can have an effect on results, particularly if the ratio is less than about 0.7 (20.22,2i). In the references cited in this chapter, the length to diameter ratio ranged from 0.7 to near 2.0. It would seem from all the considerations discussed above that a uniaxial compression test may not be the best test for obtaining data onfracturestress and strain conditions in terms of fundamental units. Although this is probably the case, it is an easy test to perform and collect data. If care is taken it seems that valid basic information can be obtained up to shear strains somewhat over 1.0. Montejano et al. (24) evaluated fracture of fish surimi gels at room temperature using axial compression and compared results with data from a torsion method finding results from the two methods in general agreement. Shear strains below 1.1 were not significantly different (p>0.05). For shear strains much above 1.0, however, a better method is needed. An approach similar to that above can be used for axial tension (18). Because of sample attachment difficulties, tension has not been used as frequently as axial compression. This may change as some ingenious attachment methods have been described recently (e.g.. 25). Torsion Testing. Many of the uncertainties in calculating fundamental fracture parameters can be eliminated by going to a torsion (twisting) test. Consider the following advantages: (1) This test produces what is called pure shear, a stress condition that does not change the specimen volume even if the material is compressible.. (2) The specimen shape is maintained during the test minimizing geometric considerations. (3) Because of (1) and (2), the calculated shear stresses and strains are true values up to large twist angles (45°, equivalent to shear strains near 1.0 ). (4) There is no restriction on the criterion for fracture. The material can fail in shear, tension, compression, or a combination mode. (5) Principle (maximum) shear, tension, and compression stresses all have the same magnitude but act in different directions so it is easy to determine if the material failed due to shear, tension, or compression. (6) Friction between the specimen and test fixture does not have to be considered. Several assumptions are made in developing the equations for torsion of specimens with circular cross sections (see any strength of materials book; e.g., 2Q which have been shown to be valid at small strains. Based on the work of several authors (27-30). Diehl et al. (22) presented a method for torsion testing of solid homogeneous foods extending the applicable strain range much higher. It was later shown that protein gels tested in this manner produced results that correlated with sensory texture profiling (31). Fracture shear stress correlated best with sensory hardness and fracture shear strain with sensory cohesiveness. This was confirmed for surimi gels (22). From experimental results it seems that the shear strain limit for the torsion test is when the specimen shape at the critical cross section noticeably changes. For surimi gels this can be at a shear strain as high as 3.0 (32. 33). A specimen ready for twisting in a Brookfield viscometer, model 5xHBTD (Brookfield Engineering Laboratories, Inc., Stoughton, MA) is shown in Figure 5. In

In Interactions of Food Proteins; Parris, N., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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o Experimental data — Calculated values

221

T=44° C

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Critical time tc •oaeaee»

Ge=14.8 Pa tc=16.0 min n

I

•

20

ι

·

60

40 Time (min) m

Figure 4. Shear modulus development of chicken myosin at 44 C; protein concentration mg/mL (ReprintedfromWu, J. Q. et al J. Agric. Food Chem., in press. Copyright 1991 American Chemical Society).

Figure 5. Placing the torsion specimen in the test instrument

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the example that will be used here specimens are preparedfromcylindrical specimens (length = 2.87 cm, diameter approximately 1.9 cm) by gluing a disposable notched styrene disk on each end (cyanoacrylate glue), placing in a machining instrument, and machining an annular groove around the cylinder. The disks also serve to hold the specimen in the test viscometer and transmit the twisting rotation to the specimen. The annular groove insures that fracture occurs at the base of the groove not affected by the glued ends or sharp angles between specimen surfaces. Geometric factors can be included in equation constants producing fairly simple algebraic equations for calculatingfractureshear stress and strain. Gels are known for elastic behavior and this is generally true for protein gels. Torque vs angle of twist graphs are normally quite linear. With the assumption of a linear torque vs angle of twist, a rotational rate of 2.5 rpm, a groove width of 1.27 cm and a 1.0 cm cross-section diameter at the center of the groove, typical equations for fracture shear stress and uncorrected shear strain (Y) are T Pa = 1580 χ the torque in instrument units r

(12)

1

Y, dimensionless = 0.150, s' χtimeto fracture, s -0.008848 χ the torque in instrument units

(13)

The last term in Equation 13 is due to spring windup in the 5xHBTD viscometer. For an instrument with a very stiff sensing element this term would not be present. If shear strain is above about 1.0, γ should be corrected using an equation given by Nadai (29). Returning to the notation that γ^ is the true shear strain of interest 2

2

1/2

Y = ln[l + γ / 2 + γ(1 + Y /4) ] f

(14)

A fractured surimi gel specimen is shown in Figure 6. In contrast to axial compression testing, a diagonal crack in torsion indicates failure in tension (24)· If the break was perpendicular to the cylindrical axis of the specimen it would be a shear fracture. Saliba et al. (35) used axial compression and torsion to evaluate frankfurter fracture. At torsion shear strains of 1.45 axial compression results were about 13% higher for both stress and strain (note that Ah/h was 0.62 so the original cylinder was grossly deformed). A possible factor in this study was that the torsion test involves the interior of the original specimen whereas the axial compression of unmachined cylindrical specimens involved material closer to the cooking tube surface. If radial nonhomogeneity is present, material at the largest test cross-section radii will have the greatest influence. Unpublished results for frankfurters from the authors laboratory suggest that, if similar cross section locations are used in both axial compression and torsion testing, shear stresses agree quite closely if torsional Yf is below about 1.4 but axial compression γ^ values are somewhat lower than 1.4. For larger strain conditions,

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typical of chicken frankfurters and surimi based gels, the axial compression T is larger f

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than the torsion value and the axial compression γ^· is smaller than the torsion value. From comparisons made to date it seems that protein gel fracture shear stress and strain datafromaxial compression tests (usually with the ends lubricated) and torsion agree quite well up to shear strains of about 1.0 and do not become greatly different up to shear strains of about 1.4. More work needs to be done on this. Example application of shear stress and shear strain data. An example of how fracture stress and strain values can be used effectively will be based on Figure 7. Each data point in Figure 7 is the mean of 2 replications tested in torsion at room temperature using the methodology compatible with Equations 12-14. Twenty three different commercial labels were tested with 10 specimens tested per replication (unpublished data). The geometric shapes are drawn to show the grouping of the data. Notice that there is a general linear relation between stress and strain with all data considered. It can then be seen that pork/beef combinations (all were 30% fat) were at the low stress/ strain end and chicken frankfurters (about 20% fat) were at the high end. Beef franks were at about the same strain level as pork/beef combinations but tended to be higher in stress. Turkey (20% fat)frankshad about the same stress level as beef franks but were higher in strain. In general, the commercial poultry franks exhibited higher strain values than the commercial red meat products. All of the observations above were highly significant statistically. Sensory texture profile development for each of the products was consistent with the instrumental results. Specifically, the chicken and turkey products were the most cohesive (deformable) and the red meat products the least cohesive. Figure 7 is a tentative base for adjusting textural attributes. If one desires to make a chicken frank with the texture of a pork/beef frank it is obvious that the fracture shear strain must be decreased and also the shear stress. Protein concentration, thermal process, and a number of other modifications can be used to adjust shear stress but shear strain is harder to change (36. 37). The base gel seems to be the primary factor affectingfracturestrain and this gel must be interfered with or enhanced as the case may be (33). Recent unpublished work in the authors laboratory used Figure 7 as base information for evaluating the suitability of a proposed fat substitute in frankfurters. Both red meat and poultry applications were tested and it was possible to keep red meat at a strain of about 1.3 and move chickenfranksto near the red meat data and at the same time reduce both the fat content and calorie level. Sensory profile evaluation again confirmed the instrumental results. A Second Example. This example is taken from Hamann et al. (33) and demonstrates the effects of a change in the base gel and/or a filler ingredient. Figure 8 shows how two variables, protease inhibition and/or starch addition, influenced thefractureof gels madefroma specific lot of menhaden (Brevoortia tvrannus) surimi. Surimi made from this species (and many others) contains a heat stable alkaline protease which causes gel degradation at temperatures near 60°C (38). Hamann et al. (33) give evidence that beef plasma or egg white will inhibit the enzymatic breakdown of the protein. Figure 8 shows fracture results for 9 % protein, 2% NaCl surimi gels formed by thermally processing at 60°C for 30 min followed by 15 min at 90°C. The inhibitors increased the

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Figure 6. Surimi gel specimen showing the fracture 40

Shear

Strain

Figure 7. Fracture shear stress - shear strain means for 23 commercialfrankfurters (23 different labels)

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Menhaden control

Menhaden w/ plasma

Menhaden w/ egg white

Figure 8. The effects ofprotease inhibitors (plasma or egg white) and 5% unmodified potato starch on fracture shear stress and strain of menhaden surimi gels cooked at 60 °Cfor 30 min followed by 90 °Cfor 15 min (Reproduced with permission from ref. $±. Copyright 1990 Institute of Food Technologists.)

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fracture shear strain by about 60-70% and tripled thefractureshear stress. The second variable, adding 5% potato starch, doubled the shear stress but did not affect the shear strain significantly. These results are consistent with results from earlier work (37. 39) showing that proteolytic activity affects the base gel while starch acts as a filler influencing primarily gel hardness. Hamann and Lanier (32) show that protein dilution by adding water to a surimi gel lowers stress but has a very limited effect on fracture strain. Some general observations are that: (1) Changes in the base gel result in changes in both fracture stress and strain (in the above example the protease degraded the base gel). (2) Non reactivefillers,protein dilution, or other changes that do not change the base gel affect primarily fracture stress (the starch increased the fracture stress but not the fracture strain; added water decreases stress). Concluding Remarks This brief chapter with examples gives some insight into the use of rheology to better understand gel formation and gel quality. Articles on the subject are becoming much more numerous and rheology combined with companion tools such as scanning electron microscopy and differential scanning calorimetry will enable us to probe the intricacies of protein gels. Literature Cited 1. Muller, H.G. An Introduction to Food Rheology; Crane, Russak & Co.: New York, 1973; p 1. 2. Whorlow, R.W. RheologicalTechniques;Ellis Horwood: Chichester, UK, 1980; p 17. 3. Kobyayashi, A.S. Experimental Techniques in Fracture Mechanics; Monograph No. 1, Soc. for Exp. Stress Anal.: Westport, CN, 1973; p 4. 4. Frijters, J.E.R. In Sensory Analysis of Foods; Piggott, J.R., Ed.; 2nd ed.; Elsevier: Barking, Essex, England, 1988; p 131. 5. Dealy, J.M. Rheometers for Molten Plastics; Van Nostrand Reinhold: New York, 1982; p 51. 6. Whorlow, R.W. RheologicalTechniques;Ellis Horwood: Chichester, UK, 1980; p 250. 7. Beveridge, T.; Jones, L.; Tung, M.A. J. Agric. Food Chem. 1984, 32, 307. 8. Bohlin, L.; Hebb, P.; Ljusberg-Wahren, H. J. Dairy Sci. 1984, 67, 729. 9. Beveridge,T.; Timbers, G.E. J. Texture Stud. 1985, 16, 333. 10. Samejima, K.; Egelandsdal, B.; Fretheim, K. J. Food Sci. 1985, 50, 1540. 11. Noguchi, S.F. Bull. Jap. Soc. Sci. Fish. 1986, 52, 1261. 12. Egelandsdal, B.; Fretheim, K.; Harbitz, O. J. Sci. Food Agric. 1986, 37, 944. 13. Bohlin, L; Egelandsdal, B.; Martens, M. In Gums and Stabilizers for the Food Industry3;Phillips, G.O.; Wedlock, D.J.; Williams, P.A., Eds.; Elsevier: Barking, Essex, England, 1986;p111. 14. Hamann, D.D.; Purkayastha, S.; Lanier, T.C. In Thermal Analysis of Foods; Harwalker, V.R.; Ma, C.Y., Eds.; Elsevier: Barking, Essex, England, 1990; p 330. In Interactions of Food Proteins; Parris, N., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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15. Sano, T.; Noguchi, S.F.; Matsumoto, J.J.; Tsuchiya, T. J. Food Sci. 1990, 55, 51. 16.Gossett, P.W.; Rizvi, S.S.H.; Baker, R.C. Food Technol. 1984,38(5) 67. 17. Ikeuchi, T.; Simidu, W. Bull. Jap. Soc. Sci. Fish. 1963, 29, 151. 18. Peleg, M. J. Texture Stud. 1985, 16, 119. 19. Polakowski, N.H.; Ripling, E.J. Srength and Structure of Engineering Materials; Prentice-Hall: Englewood Cliffs, NJ, 1966; pp. 57-60. 20. Peleg, M. J. Texture Stud. 1977, 8, 282. 21. Culioli, J.; Sherman, P. J. Texture Stud. 1976,7,353. 22. Diehl, K.C.; Hamann, D.D.; Whitfield, J.K. J. Texture Stud. 1979, 10, 371. 23. Chu, C.F.; Peleg, M. J. Texture Stud. 1985, 16, 451. 24. Montejano, J.G.; Hamann, D.D.; Lanier, T.C. J. Rheology. 1983, 27, 557. 25. Langley, K.R.; Millard, D.; Evans, E.W. J. Dairy Res. 1986, 53, 285. 26. Polakowski, N.H.; Ripling, E.J. Srength and Structure of Engineering Materials; Prentice-Hall: Englewood Cliffs, NJ, 1966;p377. 27. Davis, E.A. J. Appl. Physics. 1937, 8, 231. 28. Morrison,J.L.M. Proc. Inst. Mech. Engrs. 1948, 159, 81. 29. Nadai, A. J. Appl. Physics. 1937, 8, 205. 30. Neuber, H. AEC Translation Series. AEC-tr-44547, 1958 31. Montejano, J.G.; Hamann, D.D.; Lanier, T.C. J. Texture Stud. 1985, 16, 403. 32. Hamann, D.D.; Lanier, T.C. In Seafood Quality Determination; Kramer, D.E.; Liston, J., Eds.; Elsevier: Barking, Essex, England, 1987; p 123. 33. Hamann, D.D.; Amato, P.M.; Foegeding, E.A. J. Food Sci. 1990, 55, 665. 34. Hamann, D.D. In Physical Properties of Foods; Peleg, M.; Bagley, E.B., Eds.; AVI: Westport, CN, 1983; Chapter 13. 35. Saliba, D.A.; Foegeding, E.A.; Hamann, D.D. J. Texture Stud. 1987, 18, 241. 36. Wu, M.C.; Hamann, D.D. J. Texture Stud. 1985, 16, 53. 37. Hamann, D.D. Food Technol. 1988, 42 (6), 66. 38. Boye, S.W.; Lanier, T.C. J. Food Sci. 1988, 53, 1340. 39. Kim, B.Y.; Hamann, D.D.; Lanier, T.C.; Wu,M . C .J. Food Sci. 1986, 51, 951. R E C E I V E D August 14, 1990

In Interactions of Food Proteins; Parris, N., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.