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Structure of acid casein gels 1. Formation and model of gel network
Colloids and Surfaces,
50 (1990) 141-159
Elsevier Science Publishers
141
B.V., Amsterdam
Structure of Acid Casein Gels 1. Formation and Model of Gel Network S.P.F.M. ROEFS*, A.E.A. DE GROOT-MOSTERT Department
of Food Science,
Wageningen
and T. VAN VLIET
Agricultural
University,
Wageningen
(The Netherlands)
(Received 2 May 1989; accepted 22 February
1990)
ABSTRACT The formation and the resulting structure of acid casein gels was studied by rheology, permeametry and electron microscopy. Most gels were formed by quiescent heating of casein solutions acidified in the cold at 0-2°C. After acidification of a skim milk powder or a sodium caseinate dispersion to pH 4.6 at low temperature a physically stable suspension of casein particles was obtained. Gelation results from the aggregation of these casein particles at temperatures above about 10” C. These particles have a complex structure due to the association of numerous different casein molecules. Lowering of the temperature after gel formation to 4°C shows that the gel formation is irreversible in this respect. It is shown that the formation of acid casein gels is subject to an activation Gibbs energy, which markedly decreases with increasing temperature and depends on at least two factors. At ageing temperatures above lO”C, the dynamic moduli G’ and G” linearly increase with the logarithm of time over at least a week. Their absolute values depend, primarily, on the heterogeneity of the network. From the strong dependence of the dynamic moduli on the casein concentration, and from permeability measurements and electron microscopy it follows that the gel network is very heterogeneous. It consists of rather big conglomerates and holes each with a diameter of l-10 pm. The big conglomerates are thought to be built of smaller ones, which in turn consist of casein particles aggregated in strands and nodes. This picture implies that acid casein gels, although they are basically built of macromolecules, have a particulate structure. The strands and nodes themselves can be regarded as concentrated ( - 25% ) protein gels with a modulus of about lo5 N m-*.
INTRODUCTION
Proteins constitute an economically and biologically important group of polymers. Because of a few serious drawbacks, such as their complicated molecular structure and reactivity, they have, with few exceptions, scarcely been used in more fundamental (model ) studies on the rheological behaviour of *Present
address: NIZO, P.O. Box 20, Ede, The Netherlands.
0166-6622/90/$03.50
0 1990 -
Elsevier Science Publishers
B.V.
142
polymer systems. A recent review on structural and mechanical properties of biopolymer gels, including protein gels, is by Clark and Ross-Murphy [ 11. In general, several different types of gels formed by macromolecules can be distinguished [ 21: (1) networks of covalent cross-linked flexible polymers, which are completely disordered; (2) networks of flexible polymers with crosslinks formed by physical aggregation, these are predominantly disordered but have regions of local order; (3) particulate disordered gels, e.g., flocculated clays and most partly crystallized fats or gels of aggregated globular proteins. In the so-called rubber theory an equation is derived relating the elastic properties of the type (1) and (2) gels to the number of cross-links in the gel. This theory may be applied as long as the macro molecular chain segments between the cross-links have a length of at least several statistical chain elements. The resistance against deformation of such gels is caused by a decrease in conformational entropy of the chain segments upon deformation [ 31. However, for gels of aggregated proteins (type 3)) including casein gels [4] this theory is not valid. This point will be discussed more extensively further on. In this study casein was chosen as a model protein. It is the main protein in milk and the main component involved in the structure of gels made from milk (e.g., cheese, yogurt and quarg). Four main species of casein may be distinguished; LY,~-,CY,~-,/3-and Ic-casein. Of each the primary structure is known (see, e.g., Ref. [5] ). In milk they are present in a mass ratio of about 38: 11: 36: 13. Their conformation appears to be much like that of denatured globular proteins, which may be partly due to their rather high proline content. All contain many hydrophobic amino acid residues. p-casein has a rather hydrophilic N-terminal part and a hydrophobic C-terminal part. The C-terminal part of K-casein mostly contains a carbohydrate group, comprised of 3 or 4 hexose residues. In milk, virtually all casein is present in fairly large particles of colloidal size (diameter may vary from 20 to 300 nm) , the so-called casein micelles, each containing up to thousands of casein molecules [ 51. Stability is ascribed to electrostatic and steric effects. At pH 6.7 the zeta potential is around - 15 to - 20 mV at 30°C [ 61. This value is too low to stabilize casein micelles in milk solely by electrostatic effects [ 71. The very hydrophilic C-terminal part of Kcasein, which is mainly located at the outside of the casein micelles [ 51, protrudes from the casein micelle surface into the solution, thus stabilizing the casein micelles by steric repulsion [ 81. Flocculation of casein micelles and subsequent gel formation can be induced at pH 6.7 and temperatures above 20’ C by the addition of a proteolytic enzyme (rennet) which specifically splits off the hydrophilic part of Ic-casein. Flocculation can also be induced by lowering the pH. Upon acidification at T> 10’ C all casein will coagulate at pH 4.6, the isoelectric pH of the casein particles. In this study gels were made from a skim milk powder or a sodium caseinate dispersion by acidification with HCl to pH 4.6 at low temperature (O-2’ C 1.
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Then a physically stable suspension of casein particles with an average diameter of 280 nm as measured by photon correlation spectroscopy was obtained [ 91. In a sodium caseinate dispersion of proper ionic strength acidification at low temperature causes the formation of casein particles out of individual casein molecules and smaller casein particles; the size of these sodium caseinate particles was smaller than of those in skim milk at pH 4.6. Gel formation was induced by heating, avoiding stirring or the generation of convection currents. Besides acidification only, some gels were made by a combined effect of acidification to pH 4.6 and rennet action. MATERIALS
AND METHODS
Protein dispersions
Standard reconstituted skim milk was made by dissolving 12 g of a commercial low-heat skim milk powder (casein content 28.3% w/w) in 100 g of demineralized water. The main other components are lactose, serum proteins and salts. To allow establishment of equilibrium, the dispersions were stirred at 30°C overnight (16-20 h) before use. Standard sodium caseinate dispersions were made by dissolving 3 g sodium caseinate powder (caseinate content 92% ) and an appropriate amount of NaCl and/or CaCl, per 100 g dispersion. Sodium caseinate did not dissolve as well as skim milk powder and therefore was stirred for at least 20 h at 30” C before use. The complete composition of the powders has been given before [lo]. To prevent bacterial growth 100 ppm thiomersal ( C,H5HgSCGH,COONa, BDH Chemicals Ltd) was added as a preservative. Protein concentration was normally varied by ultrafiltration of standard skim milk in an Amicon concentrator model CH3, equipped with a hollow fiber cartridge (type Hl PlO). Constituents with molecular mass over 10 000 Daltons were concentrated. Acid whey was prepared from a skim milk gel aged for about 16 h by centrifugation for 30 min at about 2300 g. The whey was filtered just before use. Acidification
and gel formation
The caseinate and skim milk dispersions were acidified at low temperature (0-2°C) to the desired pH with an automatic titration unit consisting of an autoburette (type ABU 13e), coupled to a titrator (type TTT 60a) and a pH meter, all from Radiometer, Copenhagen. The rate of acid addition was slowed down near the pH end point. For skim milk 3 N HCl was used and for sodium caseinate dispersions 0.5 N HCl because otherwise floes were formed during acidification. After transferring the acidified solution to the measuring appa-
144
ratus, gel formation was induced by quiescent heating at a rate of 0.5’ C min- ‘, unless stated otherwise. Gel formation started at temperatures above 10’ C. In time dependent experiments the moment at which the temperature rose to 4’ C was chosen as zero time. A heating rate of 0.5’ C min-’ was chosen, because this was the maximum rate that could be achieved reproducibly in all experimental set-ups. It was checked that using another heating rate did not influence the essential characteristics of the gels. If it was heated following a step function, gels with cracks were often formed. In experiments where the combined effect of pH and rennet action on gelation was studied, 250 ppm rennet was added to the cold acidified skim milk. In this case the moment of mixing was taken as zero time. Rheological measurements Dynamic moduli of the gels were obtained using a rheometer developed and described by Duiser [ 111 and den Otter [ 121. Essentially, the apparatus consists of two coaxial cylinders (length 15 cm, radius inner cylinder 3.75 mm and outer one 4.5 mm) between which the acidified and cooled casein dispersion is brought. After gel formation a sinusoidal rotational oscillation is applied to the inner cylinder by means of a torsion wire and a driving system. The storage moduli G’, the loss moduli G” and tan 6= G”/G’ may be calculated from the amplitude difference and the phase shift between the drive shaft and the inner cylinder; where 6 is the phase difference between the stress and the strain. The angular frequency ok applied was 1 rad s-l. The amplitudes were kept sufficiently low (strain < 0.04) to ensure linear behaviour [lo]. The temperature was controlled within ? 0.1’ C. To prevent evaporation the gels were covered with a little paraffin oil. Permeametry The permeability coefficient B was determined with an apparatus developed and described by Van Dijk [ 13,141. The liquid flux u of whey, through open glass tubes with an inner diameter of 3.7 mm and a length of 25 cm filled with a casein gel, was measured. The flux was caused by a known pressure gradient AP. Gels with a length of about 10 cm were formed in the tubes and these were placed in a gelation vat. AP was mostly about 4.5-6.0*103 Pa m-l. B was calculated by the Darcy equation U= - (B/q) AP
(1)
where q is the viscosity of the whey. The latter was obtained from the density and the kinematic viscosity as determined with an Ubbelohde viscometer. The
145
Reynolds number was low enough to ensure laminar flow [lo]. Variation of dP between 4.0. lo3 and 11. lo3 Pa m-l did not influence the value of B obtained. Electron microscopy Samples were prepared according to the micro-capsule method of Salyev [ 151 as adopted for milk by Henstra and Schmidt [ 16,171.
Agar capsules, made by dipping glass rods with a diameter of - 1 mm in a hot 3% sterilized agar solution, were filled with a cold acidified casein dispersion by withdrawing the glass rods from the formed capsules, which were held in the dispersion at the other end, and then sealing both ends with hot agar. After filling the capsules they were heated in the same acidified dispersion to 30°C. Fixation was achieved by storing for 16 h in a 1% 0~0, solution in a 0.1 Mphosphate buffer of pH 4.6 at O-2’ C. Next, the capsules were dehydrated in a graded alcohol series from 20 to 100% ethanol and subsequently embedded in three steps in 3 parts n-butylmethacrylate and 2 parts styrene. Thin sections (thickness about 60 nm) were studied after post staining with uranylacetate (7 min) and Reynolds lead acetate (7 min) followed by rinsing with 0.01 N NaOH, with a Philips transmission electron microscope (EM 400T). A more extensive description is in Ref. [lo]. RESULTS
AND DISCUSSION
Gel formation and ageing Gel formation and ageing was followed by measuring the dynamic moduli as a function of time at different ageing temperatures (angular frequency o= 1.0 rad s-l ). Measurements were started after visible gel formation had occurred. Results for standard skim milk gels are shown in Figs la (G’ ) and lb (tan S). The curves of G’ and G” (not shown) were similar. After an initial period which included the time needed to heat the system from 4’ C to the measuring (and ageing) temperature, G’ and G” tended to increase linearly with the logarithm of time, except for gels aged at 50’ C. Between 10 and 20’ C a very strong temperature effect on the rate of gelation was found; after ageing at 10°C for 16 h G’ had a value of 13 N me2 in contrast with the value of 250 N m-* after ageing for 16 h at 20” C. Essentially similar ageing curves were obtained for sodium caseinate gels and for skim milk gels heated within 10 s from 4’ C to the ageing temperature (Fig. 2). In all cases even after 7 days (6~10~ s) gelation still proceeded without any sign of reaching a plateau value. Probably the flocculation of the casein aggregates is followed by a rearrangement of the protein molecules that continues for a long time, resulting in the observed increase in G’ and G”.
146
lo-
10'
IO‘
10'
t (sj
103
106 t is1
Fig. 1. Storage modulus G’ (a) and loss tangent tan 6 (b) of acid skim milk gels plotted as a function of ageing time t (s) (logarithmic scale) at different ageing temperatures T. Heating rate 0.5’Cmin-‘;at t=O Twas4”C.Ageingtemperatures (+) 20; (X) 25, (A) 30, (0,m) 40and (0) 50°C.0=1.0rads-
10'
IO"
10'
tlsl
Fig. 2. Storage modulus G’ plotted as a function of ageing time at 30°C. o= 1.0 rad s-r. Curve 1: Skim milk gel at t=O the temperature was raised within 10 s from 4 to 30°C. Curve 2: Caseinate gel heated at a rate of 0.5’ C min-‘; at t = 0 T was 4’ C. Curve 3: Skim milk gel heated as caseinate gel.
As can be seen in Fig. lb tan 6 decreased with ageing time, resulting in approximately the same value (0.23 ) after 5. lo4 s for the gels aged at 20,25 and 30°C. In the beginning of gel formation the strongest decrease of tan 6 was seen. This is to be expected, because tan 6 of a solution is very large. The final value measured for tan 6 for the gels aged at 40 and 50’ C was somewhat lower than 0.23. Apparently the elastic character of these gels increased in the course of time. We will return to this point in a following paper [ 181. The weak maximum, occurring after 4.5. lo3 s in the curve of G’ versus log t of the gel aged at 50°C (Fig. la), can be ascribed to a combined influence of
147
heating and ageing. As can be seen in Fig. 3, G’ decreased with measuring temperature once a gel is formed. Thus during heating from 20 to 50” C the moduli tended to increase due to on going gelation, and to decrease due to the increase in measuring temperature. This resulted in a weak maximum at 4.5. lo3 s, when the temperature was 4O”C, and in a weak minimum at 5.8~10~ s, when the temperature had reached the ageing temperature of 50°C. The strong increase in G’ after lo5 s was not found for G”. This is illustrated in Fig. lb, where at the moment that G’ started to increase more strongly in Fig. la, a dip in the curve of tan S versus ageing time was found. We cannot explain this particular ageing behaviour for the gel at 50°C. Lowering of the temperature after gel formation to 4°C shows that gel formation is irreversible in this respect (Fig. 3). Instead of a dissolution of the gel phase both G’ and G” strongly increased, implying a drastic increase in the number and or the strength of the elastically effective bonds between the protein molecules of different casein particles. Apparently an acidified skim milk dispersion at a temperature of 0-4°C must be regarded as a dispersion which is stable in the colloidal sense, but thermodynamically unstable. Acidification was found to be reversible in that a skim milk dispersion of pH 4.6 after readjustment to pH 6.7 by means of 3 N NaOH exhibited no visible coagulation and appeared stable at 4 and 30’ C. Gelation can be induced at 2 ‘C and pH 4.6 by enzymatically splitting off the hydrophilic, carbohydrate containing part of Ic-casein (Fig. 4). At higher temperature the increase in G’ with ageing time, and likewise that of G” (not shown), was much faster than was the case if K-casein was not split. The nonlinear increase of G’ with the logarithm of ageing time at higher temperature is due to a slow but perceptable proteolytic cleavage of the other caseins by the added enzyme as was determined by a quantitative variant of polyacrylamide G', 5” I Nm-‘1 I
Fig. 3. Storage modulus G’ ( 0 ) and loss modulus G” ( 0 ) of an acid skim milk gel plotted as a function of ageing time t (s) (logarithmic scale). After heating in the standard manner the gel was aged for 18 h at 3O”C, before it was stored 4 days at 4°C. Subsequently it was heated to 30°C. The temperatures are indicated. o= 1.0 rad s-.
148
G'INm-'I
10'
10'
10'
tkl
Fig. 4. The storage modulus G’ as a function of ageing time t for acid skim milk gels (pH 4.6) made with 250 ppm rennet and aged at the indicated temperature. Rennet was added at t= 0. The dashed curve refers to an acid skim milk gel made without rennet and aged at 30’ C. Measurements were made at the ageing temperature. o= 1.0 rad s-l.
gel electrophoresis according to the procedure described in Ref. [ 191. After lo5 s at 25’ C about 25% of the @casein and 40% of the CX~, -casein was degraded [lo]. At lower temperature this was less. The above results show that the formation of acid casein gels is subject to an activation free energy, which decreases with increasing temperature and depends on at least two factors. From other studies (e.g., Ref. [ 51) it is known that at a temperature of around 4°C p-casein, which has a hydrophobic Cterminal part and a rather hydrophilic N-terminal part, tends to dissociate from the casein particles, and it may be assumed that a considerable fraction is at the outside of the particles. The hydrophilic carbohydrate containing part of Ic-casein protrudes from the interface into the solution over the whole temperature range 0-4O”C, while the hydrophilic part of p-casein may do so only at low temperatures. Probably, both the Ic-casein and the /?-casein chains cause a certain steric repulsion, at T=O-4” C and pH 4.6. Probably the steric repulsion due to each factor separately is insufficient, because the particles aggregate at any temperature if the hydrophilic part of the rc-casein is split off, and above 10°C if the K-casein is intact. At higher temperatures the /3-casein presumably migrates to some extent to the interior of the particles because of increased hydrophobic interaction. Both factors can act on unrenneted casein particles below 5 oC and this prevents perceptable aggregation for more than a week. Structural elements and spatial structure of acid casein gels Rheological measurements In order to obtain information on the structural elements (building blocks) of the acid casein gel network, gels were made following three different proce-
149
dures. The results are shown in Fig. 5 where G’ is plotted as a function of casein concentration on a double logarithmic scale. Curve 1 refers to gels made by dissolving skim milk powder in different amounts of demineralized water. Along with the casein, the concentration of the other milk components (e.g., the salts) varied to the same extent. The result was a curved line exhibiting a strong dependence of G’ on the casein concentration. For curve 2 the casein concentration was varied by ultrafiltration at pH 6.7 which allowed the selective separation of casein particles (which include some salts) and other milk proteins from lactose, dissolved salts and water. Then at pH 4.6 the ionic strength I will vary somewhat with the casein concentration, but far less than was the case for curve 1. As can be seen curve 2 is more linear than curve 1. Furthermore the minimum casein concentration at which a gel could be formed was lower for skim milk gels made by dilution with ultrafiltrate ( < 12 g kg-l) than for gels made by dissolving skim milk powder in different amounts of water ( - 15 g kg-’ ). Curve 3 refers to gels made from pure sodium caseinate in a solution of 0.1 M NaCl and 0.007 M CaCl,, so that I was constant over the whole range of casein concentrations. The result for G’ as a function of the casein concentration was a straight line with a slope of 2.6. Similar results were obtained for G” as a function of the casein concentra-
50 C ig
kg-
Fig. 5. Storage modulus G’ as a function of casein concentration c for three different types of acid casein gels. (1) Skim milk powder dissolved in demineralized water. (2) A standard skim milk solution (30 g casein kg-‘) concent,rated or diluted by means of ultrafiltration. (3) Sodium caseinate dissolved in 0.12 M NaCl. Gels were aged at 30°C for 16 h. Q= 1.0 rad SK’.
150
tion. For gels prepared by all three methods tan 6 hardly varied (between 0.21 and 0.24) over the whole casein concentration range. From the similarity of the three curves it may be concluded that in all cases the gel network is primarily built of casein. Serum proteins and lactose are not important. The difference in curvature is related to differences in the changes in I with varying casein concentration. A larger variation of the latter results in greater curvature. Besides, addition of NaCl to a gel made at a low casein concentration by following the procedure referring to curve 1, to an I value obtained as if making a gel according to the procedure referring to curve 2, resulted in the same value for G’ as for a gel of curve 2. These results indicate an important role of I while the type of salt is probably less important. From the strong dependence of G’ on the casein concentration (G’ cc c2.6 for curve 3 ) it can be concluded that the network is very heterogeneous [ 20,211. Straight lines in a modulus-concentration plot may be expected for gels consisting of a collection of aggregates with a fractal nature such as acid sodium caseinate gels probably are [ 221; this in contrast with what may be anticipated from classical theories for polymer gels [ 11. Electron microscopy A few typical examples of electron micrographs obtained are shown in Fig. 6. The picture of the acid skim milk gel (Fig. 6a) is very similar to that of the acid caseinate gel (Fig. 6b), as may be expected from the similarity in the
Fig. 6. Transmission electron micrographs of an acid skim milk gel (a) and an acid sodium caseinate gel (b) at pH 4.6. The sodium caseinate gel was aged for 16 h at 30°C and the skim milk gel for 25 h.
151
rheological properties, and supporting the concept of casein as the main constituent of the network in acid skim milk gels. The electron micrographs are very similar to those reported for acid skim milk gels made by heating cold acidified skim milk to 40’ C [ 231. Both types of casein networks consist of aggregated particles (Fig. 6)) which have only partly fused. The aggregated particles are not homogeneously distributed over the available space. They tend to be grouped in dense areas, which can be considered as large aggregates and conglomerates. On the other hand, the areas without casein represent the relatively large meshes of the gel network. Only a few particulate strands are seen, which is not surprising in view of the thickness of the thin sections (60-100 nm). The diameter of the particles of the acid sodium caseinate gel (d=50-100 nm) seems to be somewhat smaller than in case of the acid skim milk gel (d=80-300 nm). In the acid skim milk gel most particles have a diameter of around 100 nm. On micrographs taken from acid skim milk gels with either half or double the casein concentration, particles had roughly the same size. Comparing the gel situation with that existing prior to aggregation, i.e., comparing the size of the partly fused particles in Fig. 6 with that of the particles before gelation at pH 4.6 and 4’ C [lo] suggests, particularly for sodium caseinate, an increase in diameter of the protein particles during gelation induced by heating. Possibly, these results suggest that small casein particles first coagulate to form larger ones which subsequently take part in the formation of bigger aggregates and strands, ultimately forming the gel. However, more research including other EM techniques, will be necessary to test this hypothesis. Permeability measurements In Fig. 7 the permeability coefficient B of acid skim milk gels is depicted as a function of casein concentration, both on a logarithmic scale. As can be seen the permeability exhibited a very strong dependence on the casein concentration. A straight line with a slope of - 3.3 was found; which implies that B was proportional to [ casein] -3.3 within the range studied. The permeability of the acid easein gels hardly changed with ageing time, in contrast to skim milk gels formed at pH 6.7 by enzyme [rennet] action [ 13,141, indicating that any rearrangements of the gel network after its formation occurred, at most, on a small scale and did not influence the overall structure. Nor did B increase with time due to the pressure gradient imposed (initially between 4.56.0~10~ Pa m-l). In Fig. 8 the permeability coefficient B of acid skim milk gels is depicted as a function of the measuring temperature for gels aged for 16 h at 20,30 and 40 oC, respectively. All experiments were carried out twice, except for the gel aged at 30°C and measured at 40°C. The standard deviation within each experiment varied from 0.05 to 0.25*10W’3 m’, while the difference between duplicate experiments was at most 0.04*10-13 m2.
152
B Im2) 2
2-
\
0
10-'3-
5-
\
2-
8
\
8
10". 10
20
50
IO 1
C(gkg Fig. 7. Permeability
coefficient,
B (m*), as a function of casein concentration,
sion), of acid skim milk gels. The casein concentration gels were aged (16 h) and measured at 30 aC.
c (g kg-’
disper-
was varied by means of ultrafiltration.
The
B (10~'3m2)
is clear B was affected more by ageing temperature than by measuring temperature. The small with measuring temperature may be ascribed a decrease voluminosity of the building with increasing temperature Ref. [ . The influence of ageing temperature on B that the temperature which initial formation takes is of importance for the distribution of the ele-
153
ments. This was confirmed by measuring the permeability of acid skim milk gels heated at different rates to 30’ C, followed by ageing at 30’ C. For heating rates of 30, 12 and 4°C h-l, B was 1.5*10-13, 1.4.10-‘3 and 1.2.10-13 m2, respectively. Coagulation and gel formation, which start above 10” C, need a certain time for completion. Thus, at the lowest heating rate gel formation will occur at a lower temperature. In agreement with the results shown in Fig. 8 a lower temperature during gel formation resulted in a lower permeability. The permeability coefficient of sodium caseinate gels (about 1.05.10W’3 m2) was considerably lower than those of the skim milk gels ( 1.9*10-‘3 m2) at the same casein concentration. The explanation of this difference is uncertain; it may be related to the particles in the sodium caseinate gels being smaller. In general, at the same volume fraction of dispersed particles, a network formed by aggregation of smaller particles is more homogeneous [ 211. DISCUSSION
The exact mechanism of acid casein gel formation is hard to elucidate. Acid casein gels have, although they are primarily built of macromolecules, a particulate structure, as can be seen on electron micrographs. It is clear that gel formation occurs in different stages. Upon heating, the casein particles will aggregate, and small strands and small conglomerates will be formed. Out of these, larger conglomerates with a less dense structure are formed. Subsequently a gel network consisting of strands and of small and large conglomerates of particles will be formed. This network has an inhomogeneous character with dense areas of casein particles alternating with areas without casein. The former represent casein particles coagulated into large, loose aggregates or conglomerates, interconnected by strands, one or a few particle diameters thick. The casein-free areas are relatively large cavities between the strands and conglomerates, filled with liquid. Figure 9 shows a schematic two dimensional picture of such an acid casein network. However for clarity too many particles are drawn, exceeding by far the volume fraction of standard skim milk. Figure 9 may be regarded as a projection of a thin section of the gel network with a thickness of a few particles, not showing the cross sections of all strands in a direction, roughly perpendicular to the plane of projection. That formation of a very open particle network structure is possible has been indicated by, e.g., Sutherland and Goodarz-Nia [ 25-271 and Meakin et al. [ 2% 301, who simulated the floe structure in a system of coagulating particles by means of computer calculations. Meakin et al. used fractal geometry. Random bond breaking [ 291 and the existence of a size dependent activation free energy [ 301 affect to some extent the compactness of the formed floes, and thus presumably the geometry of the eventually formed network, but do not alter the picture in a qualitative sense. In a recent paper [22] it was shown that acid casein gels can be described very well as a collection of fractal clusters and that
Fig. 9. Highly schematic two dimensional picture of the distribution of casein particles in an acid casein gel (pH 4.6). The casein particles have diameters of 80 to 200 nm. The dashed line surrounds a conglomerate of aggregated particles.
in such a way the straight lines observed in the log G-log c plot (Fig. 5 ) and in the log B-log c plot (Fig. 7) may be explained. In the inhomogeneous character of the network different levels may be distinguished. Firstly, the protein particles probably do not have a homogeneous structure with respect to the distribution of the different casein molecules throughout the particles. Secondly, the strands and the small conglomerates are inhomogeneous, partly because of the size distribution of the particles and because of the way of floe formation. Thirdly, the whole network is inhomogeneous, as it consists of large conglomerates and cavities (each up to 10 pm in size ) . The latter inhomogeneity predominantly determines the permeability as illustrated by the following calculation. In principle the permeability of porous media may be calculated for different geometrical models [ 311. The most widely used model is that in which the void structure is represented by a bundle of tortuous, non-interconnecting channels of various cross sections but of a definite length resulting in the so called Kozeny-Carman equation. For a system of spherical particles this equation may be written as [ 13,141: B=
E3es 180(1-E)*
(2)
where E is the porosity and d,, the volume-surface average diameter. E should be smaller than 0.5. In the theory of Iberall [ 311, which may be called a “drag
155
theory” and only holds for dilute systems, the porous medium by a random distribution of circular cylindrical fibres with the In a theory by Brinkman [31], which is also a drag theory, represented by spherical particles of radius R kept in position by The resulting equation for B can written as:
is represented same diameter. solid matrix is external forces.
(3) The volume fraction @of casein particles in the standard gels investigated was about 0.1 [lo] resulting in E= 0.9. The average particle or fiber diameter will be about 150 nm. However by using these data the calculated B values according to the theories mentioned above vary from 5*10-i5 to 4*10-‘4 m2 which is about an order of magnitude smaller than the values found for the acid casein gels (1.0-2.0.10 - l3 m2). Moreover the calculated concentration dependence at @ = 0.1 is much smaller than found experimentally. Since the superficial flow rate through a certain number of pores is proportional to pore diameter squared, flow through the small pores inside the big conglomerates will be negligible as compared to that through the large pores between the big conglomerates. The volume fraction c made up by these large pores is probably about 0.5 and the diameter of the big conglomerates about 10 ,um. This results in values for B of 2.8.10-‘” and 2.5.10-13 m2 as calculated according to Eqns (2 ) and (3 ) , respectively. Then the predicted concentration dependence also fits better with the experimental value. At a value of 0.5 for E the theory of Iberall may be used anymore. As shown above, the permeability and thus the number and size of the large pores in the gel network are at least partly determined by the temperature during the first stage of gel formation. Different factors may be involved in this stage such as the diffusion rate of the aggregating particles, the activation free energy for aggregation and the activation free energy for rearrangement of the gel network (e.g., Refs [ 25-301). As argued above, the activation free energy for aggregation will decrease with increasing temperature, presumably because of migration of part of the p-casein from the surface of the particles to the interior. This may causes the formation of a more heterogeneous gel at the network level [ 301. Mechanical
strength
The mechanical strength of a heterogeneous casein network will be largely determined by the number and the thickness of the strands and their rheological properties which, in turn, depend on the number of protein-protein bonds per cross section and on their strength and relaxation time. If an external force is applied to a gel in the direction X, causing a deformation, this will cause a reaction force - (dfld_r)dx in all chains which pass
156
through a cross section perpendicular to X. df is the change in the interaction force when the elements in a chain between which the bond act are moved over a distance dx, and dx is the distance over which the elements (building blocks) of the network have moved with respect to each other. The force f can generally be expressed as - dF/dx where dF is the change in Gibbs energy. As long as the deformation is linear the change in distance Ax for each strand is directly related to the macroscopically applied shear strain y (or to the elongational strain in tension). If the spatial construction of the network is known y and Ax can in principle be related to each other (as long as all strands have the same dfld.r) via a constant c having the dimension of length. Its value is determined by the geometry of the network. In a real casein gel, as for most protein gels, bonds of various character (i) are involved [ 10,181. The value of (dfld.r)i and with that of ci will depend on the bond type considered. As long as experiments are performed in the linear region their product is independent of it. Summation over bonds of different character is needed, resulting in the next expression for the shear modulus: (4) where Ni is the number of chains per unit area bearing the applied shear stress 0. At present it is a much too complicated task to perform even an order of magnitude calculation of G of a casein network based on Eqn (4). Neither ci, nor Ni, nor (d*F/d_r *) are known. The Ni values will be strongly influenced by the heterogeneity of the network. During the initial stage of gel formation the effective Ni will be related to the number of strands of aggregated protein particles but after some time these start to fuse [10,32] and then Ni will be primarily related to the number of protein chains per unit cross section. Last, but not least, it must noted that F contains both enthalpic and entropic contributions. In casein gels the enthalpic contribution far outweighs the entropic one [ 4,10,18]. Figure la shows G’ considerably increasing with time. Initially, for the greater part, this must be due to an increase in the number of junctions between the casein particles. Subsequently the number of interparticle protein-protein bonds per junction may increase. We have no indications that the nature of the bonds alters much during ageing, except, maybe, during the first hour; this is primarly because tan 6 does not change anymore after one hour. The protein concentration in the strands and nodes will be roughly the same as in the casein particles, viz., 25% [lo]. In fact the strands may be considered as a concentrated protein gel. Assuming a very simplified and naive spatial distribution, it is possible to estimate the order of magnitude of the modulus of this gel. Following the same way of reasoning as in Ref. [ 201 the gel network
157
is thought to be built up of a cubic array of strands, which extend in three perpendicular directions. Each strand reaches from one side of the network to the other. At regular distances, i.e., at the angular points of the cubic array, the strands of particles will intersect each other, forming cross-links. Only a fraction f ’ of the total number of available casein particles will be built into the strands. The remainder of the casein particles is thought to be accumulated at the cross-links, thus forming large aggregates. The segment of a strand between two cross-links may be represented by a cylinder of length L and diameter d. For n segments of strands per m3 the total length of stress carrying segments of strands amounts to nL per m3 of gel. Then the number of segments of strands carrying a tensile stress across 1 m2, which may be set equal to N in Eqn (4)) is as a first approximation, given by:
where @’ = zd 2L/4 the volume fraction of elastically effective segments is equal to f’@, where @ is the volume fraction of casein particles. The elongation force f for a segment of a strand when it is elongated from L to L + dL because of a shearing action can be written as:
where A is the cross-sectional area ( nd2/4) and G, the shear modulus of a strand. G, is considered to have the same value over the whole strand and for all strands. At small deformations the macroscopic shear strain y is equal to 2 dL/L [ 20,33 1, which gives c = L/2. Then the next expression for G, may be obtained using Eqn (4) in the form with dfld.r combined with Eqns (5) and (6): 2G G”=fi
(7)
In this derivation it is implicitely assumed that by using G, the different interaction forces present are accounted for. The factor 2 in this simple relationship is rather arbitrary, because it directly depends on the strongly simplifying assumptions made regarding the geometrical model. Kamphuis and Jongschaap [34] derived a relationship similar to Eqn (7) with a factor 5 instead of 2 using a more sophisticated geometrical model with a random distribution of strands. Consequently Eqn (7 ) seems reasonable for an order of magnitude calculation. First an estimate off’ has to be made. As shown before, acid casein gels are very inhomogeneous; this implies that only a relatively small part of the casein actually contributes to the mechanical properties of the gel. Therefore f ’ = 0.1
158
seems a reasonable order of magnitude. Then for @=O.l [lo] and G= N 500 N m-‘, G, will be approximately lo5 N m-2. This value for G, has to be compared with the scarce data for moduli of about 25 wt% protein gels. Graham [35] found moduli for 10 wt% heat denatured lysozyme and ovalbumin gels of approximately lo4 N m-‘. Van Kleef et al. [ 36,371 found for heat set ovalbumin gels of 10 wt%, storage moduli of 2. 1037. lo3 N rnp2 and for 25 wt% of 105-4. lo5 N rnp2 and for 25 wt% soya protein gels of 1.5*104-lo5 N rnp2. So the value of lo5 N me2 found for G, seems reasonable. ACKNOWLEDGEMENTS
The authors thank Professors A. Prins and P. Walstra for valuable discussions, and the students F.W.J. Duurland, H.H.G. Habets and E. Timmermans for performing part of the experiments. REFERENCES 1 2
A.H. Clark and S.B. Ross-Murphy, Adv. Polym. Sci., 83 (1987) P.J. Flory, Faraday Discuss. Chem. Sot., 57 (1974) 7.
57.
3 4
P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, 1953. T. van Vliet and P. Walstra, Neth. Milk Dairy J., 39 (1985) 115.
5 6 7
P. Walstra and R. Jenness, Dairy Chemistry and Physics, Wiley, New York, 1984. D.G. Dalgleish, J. Dairy Res., 51 (1984) 425. T.A.J. Payens, J. Dairy Res., 46 (1979) 291.
8 9
P. Walstra, J. Dairy Res., 46 (1979) 317. S.P.F.M. Roefs, P. Walstra, D.G. Dalgleish and D.S. Horne, Neth. Milk Dairy J., 39 (1985) 119.
10
S.P.F.M.
11
versity, Wageningen, The Netherlands, 1986. J.A. Duiser, Ph.D. Thesis, State University Leiden, The Netherlands,
Roefs, Structure of acid casein gels, Ph.D. Thesis, Wageningen
Agricultural
Uni-
1965.
12 13
J.L. den Otter, Ph.D. Thesis, State University Leiden, The Netherlands, 1967. H.J.M. van Dijk, Syneresis of Curd, Ph.D. Thesis, Wageningen Agricultural University, eningen, The Netherlands, 1982.
14 15
H.J.M. van Dijk and P. Walstra, Neth. Milk Dairy J., 40 (1986) 3. R.K. Salyev, in D.S. Bocciarella (Ed.), Proc. 4th. Eur. Reg. Conf. Electr. Microsc., Vol. 2, Tipografia Poliglotta Vaticanna, Rome, 1968, p. 151.
16 17
S. Henstra and D.G. Schmidt, Naturwissenschaften, 57 (1970) 247. S. Henstra and D.G. Schmidt, in P. Favard (Ed.), Proc. 7th. Intern. Congr. Electr. Microsc., Grenoble, Sot. Franc. Microsc. Electronique, Paris, 1970, p. 389. S.P.F.M. Roefs and T. van Vliet, Colloids Surfaces, 50 (1990) 161. L. de Jong, Neth. Milk Dairy J., 29 (1975) 162. T. van Vliet, Interactions between adsorbed macromolecules, Ph.D. Thesis, Wageningen Agricultural University, Wageningen, The Netherlands 1977. M. van den Tempel, J. Colloid Interface Sci., 71 (1979) 18. L.G.B. Bremer, T. van Vliet and P. Walstra, J. Chem. Sot. Faraday Trans. 1,85 (1989) 3359. V.R. Harwalker and M. Kalab, Scanning Electron Microscopy, III (1981) 503. D.F. Darling, in Th.F. Tadros (Ed.), The Effect of Polymers on Dispersion Properties, Academic Press, London, 1982, pp. 285-300.
18 19 20 21 22 23 24
Wag-
Rome,
159 D.N. Sutherland, J. Colloid Interface Sci., 22 (1967) 373. D.N. Sutherland and I. Goodarz-Nia, Chem. Eng. Sci., 26 (1971) 2071. I. Goodarz-Nia and D.N. Sutherland, Chem. Eng. Sci., 30 (1975) 407. P. Meakin, J. Colloid Interface Sci., 102 (1984) 491; 505. P. Meakin, J. Chem. Phys., 83 (1985) 3645. F. Family, P. Meakin and T. Vicsek, J. Chem. Phys., 83 (1985) 4144. A.E. Scheidegger, The Physics of Flow Through Porous Media, Oxford University Press, London, 1960, pp. 112-193. 32 P. Walstra and T. van Vliet, Neth. Milk Dairy J., 40 (1986) 241. 33 A.S. Lodge, Elastic Liquids. An Introductory Vector Treatment of Finite Strain Polymer Rheology, Academic Press, London, 1964. 34 H. Kamphuis and R.J.J. Jongschaap, Colloid Polym. Sci., 263 (1985) 1008. 35 D.E. Graham, Ph.D. Thesis, IJnilever Research, Colworth, United Kingdom. 36 F.S.M. van Kleef, J.V. Boskam and M. van den Tempel, Biopolymers, 17 (1978) 225. 37 F.S.M. van Kleef, Biopolymers, 25 (1986) 31.
25 26 27 28 29 30 31
50 (1990) 141-159
Elsevier Science Publishers
141
B.V., Amsterdam
Structure of Acid Casein Gels 1. Formation and Model of Gel Network S.P.F.M. ROEFS*, A.E.A. DE GROOT-MOSTERT Department
of Food Science,
Wageningen
and T. VAN VLIET
Agricultural
University,
Wageningen
(The Netherlands)
(Received 2 May 1989; accepted 22 February
1990)
ABSTRACT The formation and the resulting structure of acid casein gels was studied by rheology, permeametry and electron microscopy. Most gels were formed by quiescent heating of casein solutions acidified in the cold at 0-2°C. After acidification of a skim milk powder or a sodium caseinate dispersion to pH 4.6 at low temperature a physically stable suspension of casein particles was obtained. Gelation results from the aggregation of these casein particles at temperatures above about 10” C. These particles have a complex structure due to the association of numerous different casein molecules. Lowering of the temperature after gel formation to 4°C shows that the gel formation is irreversible in this respect. It is shown that the formation of acid casein gels is subject to an activation Gibbs energy, which markedly decreases with increasing temperature and depends on at least two factors. At ageing temperatures above lO”C, the dynamic moduli G’ and G” linearly increase with the logarithm of time over at least a week. Their absolute values depend, primarily, on the heterogeneity of the network. From the strong dependence of the dynamic moduli on the casein concentration, and from permeability measurements and electron microscopy it follows that the gel network is very heterogeneous. It consists of rather big conglomerates and holes each with a diameter of l-10 pm. The big conglomerates are thought to be built of smaller ones, which in turn consist of casein particles aggregated in strands and nodes. This picture implies that acid casein gels, although they are basically built of macromolecules, have a particulate structure. The strands and nodes themselves can be regarded as concentrated ( - 25% ) protein gels with a modulus of about lo5 N m-*.
INTRODUCTION
Proteins constitute an economically and biologically important group of polymers. Because of a few serious drawbacks, such as their complicated molecular structure and reactivity, they have, with few exceptions, scarcely been used in more fundamental (model ) studies on the rheological behaviour of *Present
address: NIZO, P.O. Box 20, Ede, The Netherlands.
0166-6622/90/$03.50
0 1990 -
Elsevier Science Publishers
B.V.
142
polymer systems. A recent review on structural and mechanical properties of biopolymer gels, including protein gels, is by Clark and Ross-Murphy [ 11. In general, several different types of gels formed by macromolecules can be distinguished [ 21: (1) networks of covalent cross-linked flexible polymers, which are completely disordered; (2) networks of flexible polymers with crosslinks formed by physical aggregation, these are predominantly disordered but have regions of local order; (3) particulate disordered gels, e.g., flocculated clays and most partly crystallized fats or gels of aggregated globular proteins. In the so-called rubber theory an equation is derived relating the elastic properties of the type (1) and (2) gels to the number of cross-links in the gel. This theory may be applied as long as the macro molecular chain segments between the cross-links have a length of at least several statistical chain elements. The resistance against deformation of such gels is caused by a decrease in conformational entropy of the chain segments upon deformation [ 31. However, for gels of aggregated proteins (type 3)) including casein gels [4] this theory is not valid. This point will be discussed more extensively further on. In this study casein was chosen as a model protein. It is the main protein in milk and the main component involved in the structure of gels made from milk (e.g., cheese, yogurt and quarg). Four main species of casein may be distinguished; LY,~-,CY,~-,/3-and Ic-casein. Of each the primary structure is known (see, e.g., Ref. [5] ). In milk they are present in a mass ratio of about 38: 11: 36: 13. Their conformation appears to be much like that of denatured globular proteins, which may be partly due to their rather high proline content. All contain many hydrophobic amino acid residues. p-casein has a rather hydrophilic N-terminal part and a hydrophobic C-terminal part. The C-terminal part of K-casein mostly contains a carbohydrate group, comprised of 3 or 4 hexose residues. In milk, virtually all casein is present in fairly large particles of colloidal size (diameter may vary from 20 to 300 nm) , the so-called casein micelles, each containing up to thousands of casein molecules [ 51. Stability is ascribed to electrostatic and steric effects. At pH 6.7 the zeta potential is around - 15 to - 20 mV at 30°C [ 61. This value is too low to stabilize casein micelles in milk solely by electrostatic effects [ 71. The very hydrophilic C-terminal part of Kcasein, which is mainly located at the outside of the casein micelles [ 51, protrudes from the casein micelle surface into the solution, thus stabilizing the casein micelles by steric repulsion [ 81. Flocculation of casein micelles and subsequent gel formation can be induced at pH 6.7 and temperatures above 20’ C by the addition of a proteolytic enzyme (rennet) which specifically splits off the hydrophilic part of Ic-casein. Flocculation can also be induced by lowering the pH. Upon acidification at T> 10’ C all casein will coagulate at pH 4.6, the isoelectric pH of the casein particles. In this study gels were made from a skim milk powder or a sodium caseinate dispersion by acidification with HCl to pH 4.6 at low temperature (O-2’ C 1.
143
Then a physically stable suspension of casein particles with an average diameter of 280 nm as measured by photon correlation spectroscopy was obtained [ 91. In a sodium caseinate dispersion of proper ionic strength acidification at low temperature causes the formation of casein particles out of individual casein molecules and smaller casein particles; the size of these sodium caseinate particles was smaller than of those in skim milk at pH 4.6. Gel formation was induced by heating, avoiding stirring or the generation of convection currents. Besides acidification only, some gels were made by a combined effect of acidification to pH 4.6 and rennet action. MATERIALS
AND METHODS
Protein dispersions
Standard reconstituted skim milk was made by dissolving 12 g of a commercial low-heat skim milk powder (casein content 28.3% w/w) in 100 g of demineralized water. The main other components are lactose, serum proteins and salts. To allow establishment of equilibrium, the dispersions were stirred at 30°C overnight (16-20 h) before use. Standard sodium caseinate dispersions were made by dissolving 3 g sodium caseinate powder (caseinate content 92% ) and an appropriate amount of NaCl and/or CaCl, per 100 g dispersion. Sodium caseinate did not dissolve as well as skim milk powder and therefore was stirred for at least 20 h at 30” C before use. The complete composition of the powders has been given before [lo]. To prevent bacterial growth 100 ppm thiomersal ( C,H5HgSCGH,COONa, BDH Chemicals Ltd) was added as a preservative. Protein concentration was normally varied by ultrafiltration of standard skim milk in an Amicon concentrator model CH3, equipped with a hollow fiber cartridge (type Hl PlO). Constituents with molecular mass over 10 000 Daltons were concentrated. Acid whey was prepared from a skim milk gel aged for about 16 h by centrifugation for 30 min at about 2300 g. The whey was filtered just before use. Acidification
and gel formation
The caseinate and skim milk dispersions were acidified at low temperature (0-2°C) to the desired pH with an automatic titration unit consisting of an autoburette (type ABU 13e), coupled to a titrator (type TTT 60a) and a pH meter, all from Radiometer, Copenhagen. The rate of acid addition was slowed down near the pH end point. For skim milk 3 N HCl was used and for sodium caseinate dispersions 0.5 N HCl because otherwise floes were formed during acidification. After transferring the acidified solution to the measuring appa-
144
ratus, gel formation was induced by quiescent heating at a rate of 0.5’ C min- ‘, unless stated otherwise. Gel formation started at temperatures above 10’ C. In time dependent experiments the moment at which the temperature rose to 4’ C was chosen as zero time. A heating rate of 0.5’ C min-’ was chosen, because this was the maximum rate that could be achieved reproducibly in all experimental set-ups. It was checked that using another heating rate did not influence the essential characteristics of the gels. If it was heated following a step function, gels with cracks were often formed. In experiments where the combined effect of pH and rennet action on gelation was studied, 250 ppm rennet was added to the cold acidified skim milk. In this case the moment of mixing was taken as zero time. Rheological measurements Dynamic moduli of the gels were obtained using a rheometer developed and described by Duiser [ 111 and den Otter [ 121. Essentially, the apparatus consists of two coaxial cylinders (length 15 cm, radius inner cylinder 3.75 mm and outer one 4.5 mm) between which the acidified and cooled casein dispersion is brought. After gel formation a sinusoidal rotational oscillation is applied to the inner cylinder by means of a torsion wire and a driving system. The storage moduli G’, the loss moduli G” and tan 6= G”/G’ may be calculated from the amplitude difference and the phase shift between the drive shaft and the inner cylinder; where 6 is the phase difference between the stress and the strain. The angular frequency ok applied was 1 rad s-l. The amplitudes were kept sufficiently low (strain < 0.04) to ensure linear behaviour [lo]. The temperature was controlled within ? 0.1’ C. To prevent evaporation the gels were covered with a little paraffin oil. Permeametry The permeability coefficient B was determined with an apparatus developed and described by Van Dijk [ 13,141. The liquid flux u of whey, through open glass tubes with an inner diameter of 3.7 mm and a length of 25 cm filled with a casein gel, was measured. The flux was caused by a known pressure gradient AP. Gels with a length of about 10 cm were formed in the tubes and these were placed in a gelation vat. AP was mostly about 4.5-6.0*103 Pa m-l. B was calculated by the Darcy equation U= - (B/q) AP
(1)
where q is the viscosity of the whey. The latter was obtained from the density and the kinematic viscosity as determined with an Ubbelohde viscometer. The
145
Reynolds number was low enough to ensure laminar flow [lo]. Variation of dP between 4.0. lo3 and 11. lo3 Pa m-l did not influence the value of B obtained. Electron microscopy Samples were prepared according to the micro-capsule method of Salyev [ 151 as adopted for milk by Henstra and Schmidt [ 16,171.
Agar capsules, made by dipping glass rods with a diameter of - 1 mm in a hot 3% sterilized agar solution, were filled with a cold acidified casein dispersion by withdrawing the glass rods from the formed capsules, which were held in the dispersion at the other end, and then sealing both ends with hot agar. After filling the capsules they were heated in the same acidified dispersion to 30°C. Fixation was achieved by storing for 16 h in a 1% 0~0, solution in a 0.1 Mphosphate buffer of pH 4.6 at O-2’ C. Next, the capsules were dehydrated in a graded alcohol series from 20 to 100% ethanol and subsequently embedded in three steps in 3 parts n-butylmethacrylate and 2 parts styrene. Thin sections (thickness about 60 nm) were studied after post staining with uranylacetate (7 min) and Reynolds lead acetate (7 min) followed by rinsing with 0.01 N NaOH, with a Philips transmission electron microscope (EM 400T). A more extensive description is in Ref. [lo]. RESULTS
AND DISCUSSION
Gel formation and ageing Gel formation and ageing was followed by measuring the dynamic moduli as a function of time at different ageing temperatures (angular frequency o= 1.0 rad s-l ). Measurements were started after visible gel formation had occurred. Results for standard skim milk gels are shown in Figs la (G’ ) and lb (tan S). The curves of G’ and G” (not shown) were similar. After an initial period which included the time needed to heat the system from 4’ C to the measuring (and ageing) temperature, G’ and G” tended to increase linearly with the logarithm of time, except for gels aged at 50’ C. Between 10 and 20’ C a very strong temperature effect on the rate of gelation was found; after ageing at 10°C for 16 h G’ had a value of 13 N me2 in contrast with the value of 250 N m-* after ageing for 16 h at 20” C. Essentially similar ageing curves were obtained for sodium caseinate gels and for skim milk gels heated within 10 s from 4’ C to the ageing temperature (Fig. 2). In all cases even after 7 days (6~10~ s) gelation still proceeded without any sign of reaching a plateau value. Probably the flocculation of the casein aggregates is followed by a rearrangement of the protein molecules that continues for a long time, resulting in the observed increase in G’ and G”.
146
lo-
10'
IO‘
10'
t (sj
103
106 t is1
Fig. 1. Storage modulus G’ (a) and loss tangent tan 6 (b) of acid skim milk gels plotted as a function of ageing time t (s) (logarithmic scale) at different ageing temperatures T. Heating rate 0.5’Cmin-‘;at t=O Twas4”C.Ageingtemperatures (+) 20; (X) 25, (A) 30, (0,m) 40and (0) 50°C.0=1.0rads-
10'
IO"
10'
tlsl
Fig. 2. Storage modulus G’ plotted as a function of ageing time at 30°C. o= 1.0 rad s-r. Curve 1: Skim milk gel at t=O the temperature was raised within 10 s from 4 to 30°C. Curve 2: Caseinate gel heated at a rate of 0.5’ C min-‘; at t = 0 T was 4’ C. Curve 3: Skim milk gel heated as caseinate gel.
As can be seen in Fig. lb tan 6 decreased with ageing time, resulting in approximately the same value (0.23 ) after 5. lo4 s for the gels aged at 20,25 and 30°C. In the beginning of gel formation the strongest decrease of tan 6 was seen. This is to be expected, because tan 6 of a solution is very large. The final value measured for tan 6 for the gels aged at 40 and 50’ C was somewhat lower than 0.23. Apparently the elastic character of these gels increased in the course of time. We will return to this point in a following paper [ 181. The weak maximum, occurring after 4.5. lo3 s in the curve of G’ versus log t of the gel aged at 50°C (Fig. la), can be ascribed to a combined influence of
147
heating and ageing. As can be seen in Fig. 3, G’ decreased with measuring temperature once a gel is formed. Thus during heating from 20 to 50” C the moduli tended to increase due to on going gelation, and to decrease due to the increase in measuring temperature. This resulted in a weak maximum at 4.5. lo3 s, when the temperature was 4O”C, and in a weak minimum at 5.8~10~ s, when the temperature had reached the ageing temperature of 50°C. The strong increase in G’ after lo5 s was not found for G”. This is illustrated in Fig. lb, where at the moment that G’ started to increase more strongly in Fig. la, a dip in the curve of tan S versus ageing time was found. We cannot explain this particular ageing behaviour for the gel at 50°C. Lowering of the temperature after gel formation to 4°C shows that gel formation is irreversible in this respect (Fig. 3). Instead of a dissolution of the gel phase both G’ and G” strongly increased, implying a drastic increase in the number and or the strength of the elastically effective bonds between the protein molecules of different casein particles. Apparently an acidified skim milk dispersion at a temperature of 0-4°C must be regarded as a dispersion which is stable in the colloidal sense, but thermodynamically unstable. Acidification was found to be reversible in that a skim milk dispersion of pH 4.6 after readjustment to pH 6.7 by means of 3 N NaOH exhibited no visible coagulation and appeared stable at 4 and 30’ C. Gelation can be induced at 2 ‘C and pH 4.6 by enzymatically splitting off the hydrophilic, carbohydrate containing part of Ic-casein (Fig. 4). At higher temperature the increase in G’ with ageing time, and likewise that of G” (not shown), was much faster than was the case if K-casein was not split. The nonlinear increase of G’ with the logarithm of ageing time at higher temperature is due to a slow but perceptable proteolytic cleavage of the other caseins by the added enzyme as was determined by a quantitative variant of polyacrylamide G', 5” I Nm-‘1 I
Fig. 3. Storage modulus G’ ( 0 ) and loss modulus G” ( 0 ) of an acid skim milk gel plotted as a function of ageing time t (s) (logarithmic scale). After heating in the standard manner the gel was aged for 18 h at 3O”C, before it was stored 4 days at 4°C. Subsequently it was heated to 30°C. The temperatures are indicated. o= 1.0 rad s-.
148
G'INm-'I
10'
10'
10'
tkl
Fig. 4. The storage modulus G’ as a function of ageing time t for acid skim milk gels (pH 4.6) made with 250 ppm rennet and aged at the indicated temperature. Rennet was added at t= 0. The dashed curve refers to an acid skim milk gel made without rennet and aged at 30’ C. Measurements were made at the ageing temperature. o= 1.0 rad s-l.
gel electrophoresis according to the procedure described in Ref. [ 191. After lo5 s at 25’ C about 25% of the @casein and 40% of the CX~, -casein was degraded [lo]. At lower temperature this was less. The above results show that the formation of acid casein gels is subject to an activation free energy, which decreases with increasing temperature and depends on at least two factors. From other studies (e.g., Ref. [ 51) it is known that at a temperature of around 4°C p-casein, which has a hydrophobic Cterminal part and a rather hydrophilic N-terminal part, tends to dissociate from the casein particles, and it may be assumed that a considerable fraction is at the outside of the particles. The hydrophilic carbohydrate containing part of Ic-casein protrudes from the interface into the solution over the whole temperature range 0-4O”C, while the hydrophilic part of p-casein may do so only at low temperatures. Probably, both the Ic-casein and the /?-casein chains cause a certain steric repulsion, at T=O-4” C and pH 4.6. Probably the steric repulsion due to each factor separately is insufficient, because the particles aggregate at any temperature if the hydrophilic part of the rc-casein is split off, and above 10°C if the K-casein is intact. At higher temperatures the /3-casein presumably migrates to some extent to the interior of the particles because of increased hydrophobic interaction. Both factors can act on unrenneted casein particles below 5 oC and this prevents perceptable aggregation for more than a week. Structural elements and spatial structure of acid casein gels Rheological measurements In order to obtain information on the structural elements (building blocks) of the acid casein gel network, gels were made following three different proce-
149
dures. The results are shown in Fig. 5 where G’ is plotted as a function of casein concentration on a double logarithmic scale. Curve 1 refers to gels made by dissolving skim milk powder in different amounts of demineralized water. Along with the casein, the concentration of the other milk components (e.g., the salts) varied to the same extent. The result was a curved line exhibiting a strong dependence of G’ on the casein concentration. For curve 2 the casein concentration was varied by ultrafiltration at pH 6.7 which allowed the selective separation of casein particles (which include some salts) and other milk proteins from lactose, dissolved salts and water. Then at pH 4.6 the ionic strength I will vary somewhat with the casein concentration, but far less than was the case for curve 1. As can be seen curve 2 is more linear than curve 1. Furthermore the minimum casein concentration at which a gel could be formed was lower for skim milk gels made by dilution with ultrafiltrate ( < 12 g kg-l) than for gels made by dissolving skim milk powder in different amounts of water ( - 15 g kg-’ ). Curve 3 refers to gels made from pure sodium caseinate in a solution of 0.1 M NaCl and 0.007 M CaCl,, so that I was constant over the whole range of casein concentrations. The result for G’ as a function of the casein concentration was a straight line with a slope of 2.6. Similar results were obtained for G” as a function of the casein concentra-
50 C ig
kg-
Fig. 5. Storage modulus G’ as a function of casein concentration c for three different types of acid casein gels. (1) Skim milk powder dissolved in demineralized water. (2) A standard skim milk solution (30 g casein kg-‘) concent,rated or diluted by means of ultrafiltration. (3) Sodium caseinate dissolved in 0.12 M NaCl. Gels were aged at 30°C for 16 h. Q= 1.0 rad SK’.
150
tion. For gels prepared by all three methods tan 6 hardly varied (between 0.21 and 0.24) over the whole casein concentration range. From the similarity of the three curves it may be concluded that in all cases the gel network is primarily built of casein. Serum proteins and lactose are not important. The difference in curvature is related to differences in the changes in I with varying casein concentration. A larger variation of the latter results in greater curvature. Besides, addition of NaCl to a gel made at a low casein concentration by following the procedure referring to curve 1, to an I value obtained as if making a gel according to the procedure referring to curve 2, resulted in the same value for G’ as for a gel of curve 2. These results indicate an important role of I while the type of salt is probably less important. From the strong dependence of G’ on the casein concentration (G’ cc c2.6 for curve 3 ) it can be concluded that the network is very heterogeneous [ 20,211. Straight lines in a modulus-concentration plot may be expected for gels consisting of a collection of aggregates with a fractal nature such as acid sodium caseinate gels probably are [ 221; this in contrast with what may be anticipated from classical theories for polymer gels [ 11. Electron microscopy A few typical examples of electron micrographs obtained are shown in Fig. 6. The picture of the acid skim milk gel (Fig. 6a) is very similar to that of the acid caseinate gel (Fig. 6b), as may be expected from the similarity in the
Fig. 6. Transmission electron micrographs of an acid skim milk gel (a) and an acid sodium caseinate gel (b) at pH 4.6. The sodium caseinate gel was aged for 16 h at 30°C and the skim milk gel for 25 h.
151
rheological properties, and supporting the concept of casein as the main constituent of the network in acid skim milk gels. The electron micrographs are very similar to those reported for acid skim milk gels made by heating cold acidified skim milk to 40’ C [ 231. Both types of casein networks consist of aggregated particles (Fig. 6)) which have only partly fused. The aggregated particles are not homogeneously distributed over the available space. They tend to be grouped in dense areas, which can be considered as large aggregates and conglomerates. On the other hand, the areas without casein represent the relatively large meshes of the gel network. Only a few particulate strands are seen, which is not surprising in view of the thickness of the thin sections (60-100 nm). The diameter of the particles of the acid sodium caseinate gel (d=50-100 nm) seems to be somewhat smaller than in case of the acid skim milk gel (d=80-300 nm). In the acid skim milk gel most particles have a diameter of around 100 nm. On micrographs taken from acid skim milk gels with either half or double the casein concentration, particles had roughly the same size. Comparing the gel situation with that existing prior to aggregation, i.e., comparing the size of the partly fused particles in Fig. 6 with that of the particles before gelation at pH 4.6 and 4’ C [lo] suggests, particularly for sodium caseinate, an increase in diameter of the protein particles during gelation induced by heating. Possibly, these results suggest that small casein particles first coagulate to form larger ones which subsequently take part in the formation of bigger aggregates and strands, ultimately forming the gel. However, more research including other EM techniques, will be necessary to test this hypothesis. Permeability measurements In Fig. 7 the permeability coefficient B of acid skim milk gels is depicted as a function of casein concentration, both on a logarithmic scale. As can be seen the permeability exhibited a very strong dependence on the casein concentration. A straight line with a slope of - 3.3 was found; which implies that B was proportional to [ casein] -3.3 within the range studied. The permeability of the acid easein gels hardly changed with ageing time, in contrast to skim milk gels formed at pH 6.7 by enzyme [rennet] action [ 13,141, indicating that any rearrangements of the gel network after its formation occurred, at most, on a small scale and did not influence the overall structure. Nor did B increase with time due to the pressure gradient imposed (initially between 4.56.0~10~ Pa m-l). In Fig. 8 the permeability coefficient B of acid skim milk gels is depicted as a function of the measuring temperature for gels aged for 16 h at 20,30 and 40 oC, respectively. All experiments were carried out twice, except for the gel aged at 30°C and measured at 40°C. The standard deviation within each experiment varied from 0.05 to 0.25*10W’3 m’, while the difference between duplicate experiments was at most 0.04*10-13 m2.
152
B Im2) 2
2-
\
0
10-'3-
5-
\
2-
8
\
8
10". 10
20
50
IO 1
C(gkg Fig. 7. Permeability
coefficient,
B (m*), as a function of casein concentration,
sion), of acid skim milk gels. The casein concentration gels were aged (16 h) and measured at 30 aC.
c (g kg-’
disper-
was varied by means of ultrafiltration.
The
B (10~'3m2)
is clear B was affected more by ageing temperature than by measuring temperature. The small with measuring temperature may be ascribed a decrease voluminosity of the building with increasing temperature Ref. [ . The influence of ageing temperature on B that the temperature which initial formation takes is of importance for the distribution of the ele-
153
ments. This was confirmed by measuring the permeability of acid skim milk gels heated at different rates to 30’ C, followed by ageing at 30’ C. For heating rates of 30, 12 and 4°C h-l, B was 1.5*10-13, 1.4.10-‘3 and 1.2.10-13 m2, respectively. Coagulation and gel formation, which start above 10” C, need a certain time for completion. Thus, at the lowest heating rate gel formation will occur at a lower temperature. In agreement with the results shown in Fig. 8 a lower temperature during gel formation resulted in a lower permeability. The permeability coefficient of sodium caseinate gels (about 1.05.10W’3 m2) was considerably lower than those of the skim milk gels ( 1.9*10-‘3 m2) at the same casein concentration. The explanation of this difference is uncertain; it may be related to the particles in the sodium caseinate gels being smaller. In general, at the same volume fraction of dispersed particles, a network formed by aggregation of smaller particles is more homogeneous [ 211. DISCUSSION
The exact mechanism of acid casein gel formation is hard to elucidate. Acid casein gels have, although they are primarily built of macromolecules, a particulate structure, as can be seen on electron micrographs. It is clear that gel formation occurs in different stages. Upon heating, the casein particles will aggregate, and small strands and small conglomerates will be formed. Out of these, larger conglomerates with a less dense structure are formed. Subsequently a gel network consisting of strands and of small and large conglomerates of particles will be formed. This network has an inhomogeneous character with dense areas of casein particles alternating with areas without casein. The former represent casein particles coagulated into large, loose aggregates or conglomerates, interconnected by strands, one or a few particle diameters thick. The casein-free areas are relatively large cavities between the strands and conglomerates, filled with liquid. Figure 9 shows a schematic two dimensional picture of such an acid casein network. However for clarity too many particles are drawn, exceeding by far the volume fraction of standard skim milk. Figure 9 may be regarded as a projection of a thin section of the gel network with a thickness of a few particles, not showing the cross sections of all strands in a direction, roughly perpendicular to the plane of projection. That formation of a very open particle network structure is possible has been indicated by, e.g., Sutherland and Goodarz-Nia [ 25-271 and Meakin et al. [ 2% 301, who simulated the floe structure in a system of coagulating particles by means of computer calculations. Meakin et al. used fractal geometry. Random bond breaking [ 291 and the existence of a size dependent activation free energy [ 301 affect to some extent the compactness of the formed floes, and thus presumably the geometry of the eventually formed network, but do not alter the picture in a qualitative sense. In a recent paper [22] it was shown that acid casein gels can be described very well as a collection of fractal clusters and that
Fig. 9. Highly schematic two dimensional picture of the distribution of casein particles in an acid casein gel (pH 4.6). The casein particles have diameters of 80 to 200 nm. The dashed line surrounds a conglomerate of aggregated particles.
in such a way the straight lines observed in the log G-log c plot (Fig. 5 ) and in the log B-log c plot (Fig. 7) may be explained. In the inhomogeneous character of the network different levels may be distinguished. Firstly, the protein particles probably do not have a homogeneous structure with respect to the distribution of the different casein molecules throughout the particles. Secondly, the strands and the small conglomerates are inhomogeneous, partly because of the size distribution of the particles and because of the way of floe formation. Thirdly, the whole network is inhomogeneous, as it consists of large conglomerates and cavities (each up to 10 pm in size ) . The latter inhomogeneity predominantly determines the permeability as illustrated by the following calculation. In principle the permeability of porous media may be calculated for different geometrical models [ 311. The most widely used model is that in which the void structure is represented by a bundle of tortuous, non-interconnecting channels of various cross sections but of a definite length resulting in the so called Kozeny-Carman equation. For a system of spherical particles this equation may be written as [ 13,141: B=
E3es 180(1-E)*
(2)
where E is the porosity and d,, the volume-surface average diameter. E should be smaller than 0.5. In the theory of Iberall [ 311, which may be called a “drag
155
theory” and only holds for dilute systems, the porous medium by a random distribution of circular cylindrical fibres with the In a theory by Brinkman [31], which is also a drag theory, represented by spherical particles of radius R kept in position by The resulting equation for B can written as:
is represented same diameter. solid matrix is external forces.
(3) The volume fraction @of casein particles in the standard gels investigated was about 0.1 [lo] resulting in E= 0.9. The average particle or fiber diameter will be about 150 nm. However by using these data the calculated B values according to the theories mentioned above vary from 5*10-i5 to 4*10-‘4 m2 which is about an order of magnitude smaller than the values found for the acid casein gels (1.0-2.0.10 - l3 m2). Moreover the calculated concentration dependence at @ = 0.1 is much smaller than found experimentally. Since the superficial flow rate through a certain number of pores is proportional to pore diameter squared, flow through the small pores inside the big conglomerates will be negligible as compared to that through the large pores between the big conglomerates. The volume fraction c made up by these large pores is probably about 0.5 and the diameter of the big conglomerates about 10 ,um. This results in values for B of 2.8.10-‘” and 2.5.10-13 m2 as calculated according to Eqns (2 ) and (3 ) , respectively. Then the predicted concentration dependence also fits better with the experimental value. At a value of 0.5 for E the theory of Iberall may be used anymore. As shown above, the permeability and thus the number and size of the large pores in the gel network are at least partly determined by the temperature during the first stage of gel formation. Different factors may be involved in this stage such as the diffusion rate of the aggregating particles, the activation free energy for aggregation and the activation free energy for rearrangement of the gel network (e.g., Refs [ 25-301). As argued above, the activation free energy for aggregation will decrease with increasing temperature, presumably because of migration of part of the p-casein from the surface of the particles to the interior. This may causes the formation of a more heterogeneous gel at the network level [ 301. Mechanical
strength
The mechanical strength of a heterogeneous casein network will be largely determined by the number and the thickness of the strands and their rheological properties which, in turn, depend on the number of protein-protein bonds per cross section and on their strength and relaxation time. If an external force is applied to a gel in the direction X, causing a deformation, this will cause a reaction force - (dfld_r)dx in all chains which pass
156
through a cross section perpendicular to X. df is the change in the interaction force when the elements in a chain between which the bond act are moved over a distance dx, and dx is the distance over which the elements (building blocks) of the network have moved with respect to each other. The force f can generally be expressed as - dF/dx where dF is the change in Gibbs energy. As long as the deformation is linear the change in distance Ax for each strand is directly related to the macroscopically applied shear strain y (or to the elongational strain in tension). If the spatial construction of the network is known y and Ax can in principle be related to each other (as long as all strands have the same dfld.r) via a constant c having the dimension of length. Its value is determined by the geometry of the network. In a real casein gel, as for most protein gels, bonds of various character (i) are involved [ 10,181. The value of (dfld.r)i and with that of ci will depend on the bond type considered. As long as experiments are performed in the linear region their product is independent of it. Summation over bonds of different character is needed, resulting in the next expression for the shear modulus: (4) where Ni is the number of chains per unit area bearing the applied shear stress 0. At present it is a much too complicated task to perform even an order of magnitude calculation of G of a casein network based on Eqn (4). Neither ci, nor Ni, nor (d*F/d_r *) are known. The Ni values will be strongly influenced by the heterogeneity of the network. During the initial stage of gel formation the effective Ni will be related to the number of strands of aggregated protein particles but after some time these start to fuse [10,32] and then Ni will be primarily related to the number of protein chains per unit cross section. Last, but not least, it must noted that F contains both enthalpic and entropic contributions. In casein gels the enthalpic contribution far outweighs the entropic one [ 4,10,18]. Figure la shows G’ considerably increasing with time. Initially, for the greater part, this must be due to an increase in the number of junctions between the casein particles. Subsequently the number of interparticle protein-protein bonds per junction may increase. We have no indications that the nature of the bonds alters much during ageing, except, maybe, during the first hour; this is primarly because tan 6 does not change anymore after one hour. The protein concentration in the strands and nodes will be roughly the same as in the casein particles, viz., 25% [lo]. In fact the strands may be considered as a concentrated protein gel. Assuming a very simplified and naive spatial distribution, it is possible to estimate the order of magnitude of the modulus of this gel. Following the same way of reasoning as in Ref. [ 201 the gel network
157
is thought to be built up of a cubic array of strands, which extend in three perpendicular directions. Each strand reaches from one side of the network to the other. At regular distances, i.e., at the angular points of the cubic array, the strands of particles will intersect each other, forming cross-links. Only a fraction f ’ of the total number of available casein particles will be built into the strands. The remainder of the casein particles is thought to be accumulated at the cross-links, thus forming large aggregates. The segment of a strand between two cross-links may be represented by a cylinder of length L and diameter d. For n segments of strands per m3 the total length of stress carrying segments of strands amounts to nL per m3 of gel. Then the number of segments of strands carrying a tensile stress across 1 m2, which may be set equal to N in Eqn (4)) is as a first approximation, given by:
where @’ = zd 2L/4 the volume fraction of elastically effective segments is equal to f’@, where @ is the volume fraction of casein particles. The elongation force f for a segment of a strand when it is elongated from L to L + dL because of a shearing action can be written as:
where A is the cross-sectional area ( nd2/4) and G, the shear modulus of a strand. G, is considered to have the same value over the whole strand and for all strands. At small deformations the macroscopic shear strain y is equal to 2 dL/L [ 20,33 1, which gives c = L/2. Then the next expression for G, may be obtained using Eqn (4) in the form with dfld.r combined with Eqns (5) and (6): 2G G”=fi
(7)
In this derivation it is implicitely assumed that by using G, the different interaction forces present are accounted for. The factor 2 in this simple relationship is rather arbitrary, because it directly depends on the strongly simplifying assumptions made regarding the geometrical model. Kamphuis and Jongschaap [34] derived a relationship similar to Eqn (7) with a factor 5 instead of 2 using a more sophisticated geometrical model with a random distribution of strands. Consequently Eqn (7 ) seems reasonable for an order of magnitude calculation. First an estimate off’ has to be made. As shown before, acid casein gels are very inhomogeneous; this implies that only a relatively small part of the casein actually contributes to the mechanical properties of the gel. Therefore f ’ = 0.1
158
seems a reasonable order of magnitude. Then for @=O.l [lo] and G= N 500 N m-‘, G, will be approximately lo5 N m-2. This value for G, has to be compared with the scarce data for moduli of about 25 wt% protein gels. Graham [35] found moduli for 10 wt% heat denatured lysozyme and ovalbumin gels of approximately lo4 N m-‘. Van Kleef et al. [ 36,371 found for heat set ovalbumin gels of 10 wt%, storage moduli of 2. 1037. lo3 N rnp2 and for 25 wt% of 105-4. lo5 N rnp2 and for 25 wt% soya protein gels of 1.5*104-lo5 N rnp2. So the value of lo5 N me2 found for G, seems reasonable. ACKNOWLEDGEMENTS
The authors thank Professors A. Prins and P. Walstra for valuable discussions, and the students F.W.J. Duurland, H.H.G. Habets and E. Timmermans for performing part of the experiments. REFERENCES 1 2
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