Biochimica et Biophysica Acta, 400 (1975) 293-301

© Elsevier Scientific Publishing Company, Amsterdam- Printed in The Netherlands BBA 37108 CASEIN M I C E L L E SIZE F R O M ELASTIC A N D QUASI-ELASTIC L I G H T SCATTERING MEASUREMENTS*

CARL HOLT Hannah Research Institute, Ayr, KA6 5HL ( U.K.)

(Received December 5th, 1974) (Revised manuscript received April 10th, 1975)

SUMMARY The average molecular weight, particle radius and size distribution of particles in skim milk from eight cows in mid-lactation have been measured by means of elastic and quasi-elastic light scattering techniques. The properties of sub-micellar casein particles in the milk of each cow were also studied. Particular attention has been given to the effects of particle size heterogeneity in the interpretation of results. The weight average molecular weight of the particles from different cows varied from 2.6-l0 s to 15. l0 s and the corresponding average particle radius varied between 90 and 130 nm. An unusual feature of these particles is their high water content, which was found to vary from 2.4 to 6.4 ml/g with a positive correlation between average particle density and average particle mass. Variations in particle water content can be most readily understood in terms of a gel-like casein micelle.

INTRODUCTION The macromolecular constituents in skim milk can be considered as two fractions, designated soluble and colloidal (or micellar). The latter is the dominant component on a weight fraction and molecular weight basis and hence elastic light scattering and quasi-elastic light scattering measurements on skim milk can be interpreted largely in terms of the properties of the colloid fraction. The size of the particles in skim milk has been investigated by both electron microscopy and quasi-elastic light scattering. With one exception [1] the average particle sizes determined by electron microscopy [2-4] are smaller than those found by quasi-elastic light scattering [5, 6]. Carrol et al. [1] considered the discrepancy to be due to shrinkage of micelles on the electron microscope grid, but no measurements have been made by the two techniques on the same sample and some natural variation in micelle size would be expected. Molecular weight estimations for casein micelles have been made by Nitschmann [2] using electron microscopy, by Dewan and Bloomfield [7] from a combination of diffusion and viscosity measurements, by Morr et al. [8] and Dewan et al. [6] from sedimentation and diffusion measurements and by Schmidt et al. [10] using conventional elastic light scattering. The estimations for similarly sized particles * H. R. I. Reprint No. 871

294 differ by about a factor of 4, but the effects of both natural variations in micelle density and different experimental techniques cannot be separated. Dewan et al. [6] found that the sedimentation coefficient of micelles fractionated according to size was proportional to the two thirds power of the molecular weight, indicating that they behave as spheres of constant density. The less extensive results of Morr et al. [8] are not consistent with this conclusion. Using their results for the sedimentation and diffusion coefficients of two micelle fractions to calculate the voluminosity gives 4.8 ml/g for particles of radius 76 nm, molecular weight 2.3.108 and 14.8 ml/g for particles of radius 220 nm, molecular weight 1.8.109. This investigation was designed to provide information on some of the natural variations to be found in the sizes of casein micelles. In order to achieve this, molecular weights and particle radii were calculated from a combination of elastic and quasi-elastic light scattering measurements on diluted skim milk solutions. The results are interpreted as the properties of casein micelles, neglecting the small amount of light scattered by other types of particles. EXPERIMENTAL DETAILS

Milk and diffusate Weekly milk samples were obtained over a 3-week period from each of eight Ayrshire cows in mid-lactation on an all-grass summer diet. Skimmed milk was obtained by centrifuging the samples at 1200 × g for 30 min at 20 °C. A hole was made in the cream layer and the underlying milk sucked out, taking care not to disturb the cream or sedimented layers. This milk was diluted with diffusate from milk of the same cow in order to disturb the environment of the micelles as little as possible. The diffusate was prepared by dialysing 15 ml of 5 ~ lactose solution against 1.5 1 of milk containing 0 . 0 2 ~ NaN3 for approx. 17 h at room temperature, then used immediately. Dialysis for longer times and using a smaller ratio of lactose solution to milk did not have any effect on the results obtained. The concentration of non-diffusible material in the milk was found from the difference in the weights of known volumes (20 ml) of freeze dried milk and diffusate. On several occasions, these values were checked by evaporating milk and diffusate to dryness at 100 °C for 12 h. The differences in dry weights agreed to better than 2 ~o.

Light scattering The experimental techniques and definitions of symbols have been given in the previous paper [9]. Solutions used for light scattering measurements were clarified by filtration. To check the efficiency of this procedure, the light scattered by solutions was measured after adding enough 10 ~ EDTA to completely dissociate the particles. The intensity of scattered light measured using the autocorrelation apparatus was usually only 3 - 5 ~ of the intensity before dissociation. This is consistent with negligible background scatter due to dust, non-dissociating particles and reflections. Dissociated particles gave no autocorrelation curve when measured under the same conditions as were used for observing micelles. Occasionally, a larger than usual turbidity remained after dissociating the micelles, amounting to 10-15~ at 550 nm of the turbidity measured beforehand.




0.515 1.03 1.52 2.00

0.124 0.252 0.373 0.486

0.096 0.094 0.094 0.095

Autocorrelation analysis under optimum conditions showed that the particles mainly responsible for the residual turbidity had radii of the order of 500 nm. It was concluded that these were fat globules which had not been removed by skimming. In order to correct turbidities for these non-micellar particles, the residual turbidities were subtracted from those measured before dissociation, at each of the wavelengths used. This procedure resulted in decreases in fl of 0.2-0.3. The corrected fl values were in good agreement with measurements on different samples of skim milk from the same cows which had lower residual turbidities. RESULTS The turbidity of skim milk diluted with diffusate initially decreases by 1-2 over a period of 10 min and then remains virtually constant. As a result, all measurements were made 10 min after dilution. The effect of diluting skim milk to different extents was investigated and it was found that c/~ was independent of the protein concentration (Table I). This demonstrates that micelle solutions are thermodynamically ideal at the concentrations used. The results of the quasi-elastic light scattering measurements are presented in Table II. The range of values of the distribution width parameter z for milk from the same cow over the 3-week period was always broad. The variations in z over the 3-week period were only slightly greater than the variations in z observed with TABLE II AVERAGE PARTICLE RADII BY ELASTIC AND QUASI-ELASTIC LIGHT SCATTERING m

Cow 1 2 3 4 5 6 7 8

d log ~ d log ~ 2.94 2.85 2.90 3.10 3.10 3.19 2.94 2.92

(R2)~* (nm)

Ray* (nm)


150 180 150 110 115 105 150 150

105 130 105 90 90 90 105 105

2.7 3.3 2.7 7.1 5.1 9.8 2.7 2.7

* The estimated error in the radii is 4-5 nm.



Cow NO.

Turbidity (20 550 nm)

Dilution factor

(. 10 -8)

(~Qw)m (. 10 -8)

1 2 3 4 5 6 7 8

0.262 0.284 0.301 0.139 0.168 0.172 0.264 0.290

61 61 51 61 71 61 61 71

9.1 15.0 7.8 4.1 3.1 2.6 9. I 9.3

10.7 16.5 9.6 4.6 3.6 2.9 11.4 11.0

duplicate measurements on the same sample of milk. A value of z was chosen which was consistent with the particle size measurements by both elastic and quasi-elastic light scattering. In all cases, this value of z was within the range of values of z calculated from the moment analysis of the autocorrelation curves [9]. The particle dissipation factor Q, was calculated using the best fitting value of z and the directly observed value for ft. The weight average molecular weight of the micelles Mw was then calculated using a value of 0.181 ml/g for the specific refractive index increment [10]. It is sometimes convenient to subdivide the non-diffusible components of skim milk into soluble and micellar fractions. In this work, a micellar fraction was defined as that fraction of the non-diffusible components which sedimented to form a pellet when centrifuged at 100 000 × g for 30 min at 20 °C. The molecular weight of the micellar component (Mw)m may be estimated from the observed weight average molecular weight Mw using the relationship: m






wm(Mw)m+ w~(Mw)~


where Ws and Wm are the weight fractions of soluble and micellar material, respectively. Since w~(/~w)~ < Wm(/~w)m,then

(mw)m ~ /~wlli'm


The calculated molecular weights of the non-diffusible components in the milk of the eight cows are presented in Table Ill. The voluminosity may be calculated as described by Dewan and Bloomfield [7], using the molecular weight and particle radius, but it is necessary to use corresponding averages. The average radius R,v corresponding to ~-/w is not Rw as might be expected but:

[ ~o w(R)R3dR



R.v = fo w(R) dR


Voluminosity Water (ml/g) content (ml/g)

Water contentprotein solvation (ml/g)


3.2 3.7 3.7 4.6 6.0 7.1 3.2 3.1

2.1 2.6 2.6 3.5 4.9 6.0 2.1 2.0

2 3 4 5 6 7 8

2.5 3.0 3.0 3.9 5.3 6.4 2.5 2.4

which for a distribution of the form

w(R) oc R'e -yR



[ F(z q- 4) 1)']'/3/y

Ray = LF(z ~-


where F denotes the gamma function. Ray is usually somewhat less than the average (R-1)-1 evaluated from the diffusion coefficient. Calculated values of the voluminosity of casein micelles from the milk of the eight cows are given in Table IV together with the calculated water contents assuming a partial specific volume of 0.7 for casein [7]. DISCUSSION Particle radii and molecular weights have been calculated here using a model in which skim milk is considered as a suspension of homogeneous spheres of molecular weight proportional to the cube of the particle radius. The model does not assume that the constant of proportionality is the same for different milks. It is insensitive to the nature of low molecular weight components in the milk, so the measurements apply to the particles normally called casein micelles. Casein micelles may have a sub-unit structure, but this does not seriously affect the validity of the homogeneous sphere assumption since the proposed sub-unit radii are only about 0.05 of a typical micelle radius [11-13]. The uncertainty in the width parameter z characterising the micelle size distribution is large in all of the measurements reported here. For this reason, models of casein micelles more complicated than the homogeneous sphere model are not justified. Dewan et al. [6] have presented evidence that casein micelles are in fact homogeneous spheres o f constant density. They fractionated pooled milk micelles by rate zone ultracentrifugation in a gradient formed from sucrose and synthetic milk

298 8-

E :>,

o E >o


Mw x lO-e--~

Fig. 1. The relationship between micelle voluminosity and molecular weight, y axis, voluminosity (ml/g); x axis, Jffw"10-s. serum. The sucrose was dialysed out from each fraction and the diffusion and sedimentation coefficients were then determined. It was found that the sedimentation coefficient was proportional to the two thirds power of the molecular weight, a result which is consistent with homogeneous spheres of constant density. It can be seen from Fig. 1 and Table IV that different milks contain micelles of different voluminosity, with particles of higher molecular weight more compact than particles of lower molecular weight. There is therefore an apparent discrepancy between these results and those of Dewan et al. [6]. Evidence has been obtained that the voluminosity of micelles is mainly determined by the concentration of free Ca z+ in milk serum (Holt, C., unpublished). The pooling of milks and the procedures involved in fractionation allow micelles of different voluminosities to reach a common value, in equilibrium with the newly established free Ca z÷ concentration and hence, pooled milk micelles have the properties of particles of constant density. This demonstrates the need, when studying the properties of native casein micelles, to make the smallest possible changes in their environment. However, the fact that there are differences in the voluminosities of micelles from different cows does not imply that there is any such heterogeneity in the milk from an individual cow. The micellar water contents quoted in Table IV correspond to protein volume fractions of 10-23 ~o and micelles can therefore be regarded as dispersions of protein in solvent. These values for the water content are in general agreement with the findings of Dewan and co-workers [6-8] and on average higher than those found by pelleting experiments [16, 17]. In order to explain this discrepancy Bloomfield and Morr [18] suggested that water can be squeezed out of micelles during pelleting. It is desirable to know how much of the water in micelles is water of solvation and how much is merely present within the hydrodynamic unit but not interacting strongly with any solute component. In an attempt to solve part of this problem, the solvation of the protein component was calculated from its amino acid composition using a method devised by Kuntz and Kauzmann [14] and Kuntz [15]. The solvations of the three main caseins, calculated by this method, are given in Table V. Two very different estimations of the solvation of phosphoserine residues have been used. A value of 8HzO/mol was taken to represent a charged phosphoserine and a value of 2H20 was taken to represent a residue neutralised by a Ca z+. The differences between the last two columns of Table V correspond to the estimated differences in solvation on


Solvation (g water/g protein)

fl K

cq:fl:x =




0.39 0.25 0.40 0.35

0.46 0.27 0.41 0.39

binding a number of Ca 2+ equal to the number of phosphoserine residues. No matter what reasonable estimate is made of the bound Ca 2÷ concentration in milk, the water of hydration of the protein will be about 0.35 g water/g protein, which is only about 10 ~ of the total water content. The question arises as to what role, if any, the rest of the water has in determining micelle structure. A sub-unit structure for casein micelles is now widely accepted [11-13], mainly on the basis of electron micrographs of freeze-etched and negatively stained preparations. These show an apparent sub-structure consisting of regions with dimensions of 6--15 nm. It has also been observed [19] that micelles can be dissociated by removing Ca 2+ and at low protein concentration, a unit complex has been identified with a diameter of 10 nm and a molecular weight of 270 000. In order to see how the sub-unit model accounts for the high water content of micelles, it is assumed that sub-units of radius a are arranged in a simple cubic array of unit cell dimension 2a + h. If all of the tightly bound water is associated with the sub-units, they will have a voluminosity of about 1.05 ml/g. The volume fraction of sub-units ~ is given by: 4~

~o = ~ - - ( - 2





and the close packing condition (h = 0) corresponds to ~-----zt/6 and a micelle voluminosity of 2.0 ml/g. Taking a typical value for the voluminosity of micelles of 3.7 ml/g gives ~ = 0.28 and h/a = 0.46. If the radii of sub-units are about 6 nm [13] then h = 2.8 nm. Thus, either the sub-units are separated by large distances or the sub-units themselves have a high voluminosity. However, the unit complexes formed by dissociation of casein micelles [19] have a voluminosity of only 1.16 ml/g. Furthermore, the evidence that the hydration of casein precipitates decreases with increasing Ca 2+ concentration [20] suggests that the voluminosity of the unit complexes will be greater than that of micelle sub-units. It follows therefore that the sub-units are relatively far apart, which is consistent with electron micrographs of casein micelles, e.g. Buchheim and Welsch [12] found spacings of 5-10 nm between the proposed sub-units. Although electron micrographs have provided the main evidence for a sub-unit structure, the dissociation of micelles has also been interpreted as providing evidence

300 for this model [12, 19]. However, properties of the particles formed by dissociation of casein micelles, such as molecular weight, radius and composition, are unlikely to be the same as the properties of the proposed sub-units because of the changes in C a 2+ and protein concentrations required to induce dissociation. There are also the following complications: (1) Casein micelles have variable proportions of a~-,/~- and K-caseins which would require sub-units also to have a variable composition. (2) When micelles are dissociated by removing Ca 2+ [21], there is an initial loss of K- and fl-caseins in preference to a~-casein. Thus, either sub-units rich in K- and /J-caseins preferentially dissociate or the dissociation process does not involve whole sub-units. (3) When micelles are dissociated by removing Ca 2+, there is an initial decrease of molecular weight but no corresponding decrease in hydrodynamic radius [21] or radius of gyration (Holt, C., unpublished). This suggests that micelles have a framework structure [21] the material of which does not pass into solution until the final stages of dissociation. It appears, therefore, that a sub-unit structure is not necessary for an understanding of the dissociation of casein micelles. The question then arises as to whether sub-units exist as separate entities within micelles. In order to reconcile the evidence concerning micelle structure from electron microscopy, dissociation experiments and water content measurements, it is suggested that micelles be regarded as coarse proteinaceous gels. In this model, there are no discrete sub-units, merely regions containing more or less hydrophobic material. The different regions of the gel will stain to a variable extent and be etched to different extents, giving rise to the appearance of a sub-unit structure in electron micrographs. Since there are no discrete sub-units, dissociation procedes by the loss of material from the more hydrophilic regions which would be expected to contain predominantly /3- and K-caseins rather than the more strongly associating as-caseins. Thus the dissociation process is explained in terms of the relative solubilities of the casein components, modified by the strength with which they are bound to the irregular gel network. The concept of a gel structure is helpful in explaining the very high water content of micelles. The protein and calcium phosphate components may together occupy less than 1 0 ~ of the total micelle volume. However, the whole particle is made rigid by cross-links between the hydrophobic regions so that there are no discrete sub-units. The variability of the water content can be understood in terms of the variable protein content in the more hydrophilic regions of the gel. In addition, the degree of swelling of the gel will depend on the extent of cross-linking and the strength of the solute-solvent interactions. Waugh et al. [20] have described how the water content of a~- and fl-casein precipitates depends on the number of bound Ca z+ ~. In both cases, the water content was found to decrease from about 3.6 ml/g protein to about 1.6 ml/g protein as ~ increased. The regions around 5 ~ 5 for/#casein and ~ = 8 for try-casein were found to be regions of both high and very variable water content. It can readily be shown, using binding isotherm data on these caseins [20, 22] together with the free Ca/+ and M f + concentrations in milk, that for/#casein ~ ~ 4 and for ~ts-casein ~ ~ 7. Therefore the casein in milk is in a state in which both high and very variable water contents would be expected provided casein micelles behave in a similar way to casein precipitates. Since this is exactly what is observed experimentally, it supports the idea of a gel-like particle rather than one composed of discrete sub-units.

301 ACKNOWLEDGMENT I would like to express m y appreciation of the technical assistance of L. Fergus d u r i n g this work. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

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Casein micelle size from elastic and quasi-elastic light scattering measurements.

The average molecular weight, particle radius and size distribution of particles in skim milk from eight cows in mid-lactation have been measured by m...
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