Structural studies of casein micelles using photon correlation spectroscopy

Structural Studies of Casein Micelles Using Photon Correlation Spectroscopy M A R Y C. AMBROSE G R I F F I N AFRC Institute of Food Research, Reading Laboratory, Shinfield, Reading RG2 9AT, United Kingdom

Received March 15, 1985; accepted May 27, 1986 The intensity-weighted average diffusion coefficient of casein micelles from bovine skim milk was measured as a function of scattering angle. These values were compared with values calculated using Mie theory or Rayleigh-Gans-Debye theory, and the micelle size distribution was determined experimentally. The differencesfound could be reconciled if the refractiveindex of the micellesincreaseswith increasing micellesize. The effectof treatment of the casein micelleswith chymosin at 4°C was to reduce the hydrodynamic diameter, calculated from the intensity-weighted averagediffusion coefficient, over a range of scattering angles. © i987AcademicPress,Inc. INTRODUCTION The caseins constitute more than 80% of the protein in bovine milk (1). There are four different types of casein polypeptide: ~sl, ~s2, /3, and K; they form approximately spherical aggregates of variable stoichiometry (2, 3), which are known as casein "micelles" and are responsible for the "milkiness," i.e., turbidity, of skim milk. Casein micelles also contain inorganic calcium phosphate and citrate. The molecular organization of the micellar constituents is not known at present although electron microscopy (2) supported by neutron scattering studies (4) suggests that the micelles are assemblies of smaller aggregates of casein known as submicelles [diameter approximately 17 n m (4)]. Casein micelles range from 20 to 680 n m in diameter (5). The size distribution of the micelles has been determined by electron microscopy (6, 7) and by photon correlation spectroscopy (PCS) after fractionation according to size, either by centrifugation (8) or by exclusion chromatography (9). Consistently, sizes obtained by light scattering methods are larger than those obtained using electron microscopy. PCS is a useful technique for determining diffusion coefficients of colloidal particles (10).

Because casein micelles have dimensions of the same order as the wavelength of light, the intensity-weighted average diffusion coefficient measured by PCS is not the z average (which is obtained for point scatterers). The weighting is a function of scattering angle and so the average diffusion coefficient varies with angle. It has been suggested (11, 12) that for polydisperse samples, a " Z i m m plot" could be constructed in which the z-average diffusion coefficient was obtained as the intercept at zero scattering angle and zero concentration. However, as shown in this work, for samples of casein micelles the standard deviation in the measurements increases as the scattering angle is reduced. H o m e (13) recently obtained the best fit, using R a y l e i g h - G a n s - D e b y e (RGD) theory, of a Schulz-Zimm distribution to PCS data from casein micelles. However, this gave rise to significant deviation from the experimental results at scattering angles below 75 ° . An experimentally determined distribution was used here to obtain a theoretical curve to compare with the experimentally determined angular dependence of the diffusion coefficient. During digestion of milk by the young suckling, the r-casein polypeptide, which is situated at the surface of the casein micelle

499 0021-9797/87 $3.00 Journal of Colloid and Interface Science, Vol. 115, No. 2, February 1987

Copyright © 1987 by Academic Press, Inc. All fights of reproduction in any form reserved.

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MARY C. AMBROSE GRIFFIN

(14), is cleaved by chymosin (EC 3.4.23.4) and exactly, except that, to obtain a size distribupepsin (EC 3.4.23.1). This destabilizes the tion, protein concentrations were determined suspension of casein micelles, which aggregate using the micro-Kjeldahl method (20). and form a gel. (The same reaction is exploited Samples were prepared for light scattering in cheese making.) Studies of this process by by diluting the skim milk approximately PCS at a single scattering vector of (a) the 1:500 into simulated milk ultrafiltrate (SMUF) whole size distribution of casein micelles in (21), pH 6.6, filtered through a 0.2-t~m milk (15) and (b) a fraction of micelles of nar- Schleicher and Schiill filter. rower size range (16) suggested that there was A Malvern spectrometer equipped with a an initial decrease of about 10 nm in the hy- Spectra-Physics He-Ne 15-mW laser, in condrodynamic diameter of casein micelles after junction with a 64-channel Malvern multibit treatment with chymosin, followed by an in- correlator type K7025, was used for photon crease at the onset of aggregation. These results correlation spectroscopy. Water at 20 or 4°C were related to a model for the casein micelles was circulated through the cell holder to conin which "hairs" of r-casein, which protrude trol the temperature of the samples. Each corinto the aqueous medium and are cleavable relation function recorded had more than 106 by chymosin or pepsin, provide steric stabili- counts per channel before normalization. Auzation for the micelles. The present work de- tocorrelation data were analyzed in two difscribes a more detailed study of the first stage ferent ways. of the process over a range of scattering angles, (1) The normalized correlation functions made possible by working at 4°C, at which g(2~(r) were fitted, using the cumulants method temperature the aggregation is very much in- (11) and the linear least-squares method, to hibited (17, 18). the polynomial 1

MATERIALS AND METHODS

Raw Friesian milk from a bulk storage tank was centrifuged for 20 min at 1000g at 5°C, after which the cream was removed; this procedure was repeated. The skim milk obtained was then filtered through a 0.8-#m Schleicher and Schtill filter. This filtered milk was used for all the experiments described here. Fixation of the casein micelles was carried out by treating the skim milk, cooled in an ice/water mixture, with glutaraldehyde (0.5%) for 15 min before dilution. Treatment with glutaraldehyde has been shown not to cause artifactual changes in the size distribution of casein micelles (19). The size distribution of the casein micelles was determined in the following way. Size exclusion chromatography was carried out on a controlled-pore glass column as described previously (9), and hydrodynamic diameters of each fraction were obtained using the light scattering equipment described below, at a scattering angle of 90 °. The method described in Ref. 9 was followed Journal of Colloid and Interface Science, Vol. 115, No. 2, February 1987

ln(g(2)(r) - 1)1/2 Ao - F r + ~.. #2r z _~

1 - 3~/z3r3

+ l [ .u 4 -

3#~]r 4 . . . .

[11

weighting the data as (g(2)(r) - 1)2. From the value of P, the average diffusion coefficient was calculated as D = r / K 2, where K is the length of the Scattering vector K [K = 4~rn/ X0" sin 0/2, where n is the refractive index of the medium, X0 is the wavelength of light (632.5 nm), and 0 is the scattering angle]. Six measurements of D were made at a series of four fixed channel times, at each of which a mean diffusion coefficient, i5, was calculated. A linear extrapolation gave a value for the diffusion coefficient at zero channel time, 15o [this is similar to the method described by Brown et al. (11) for obtaining the diffusion coefficient of a polydisperse sample]. For the experiment at 4°C, values of D were multiplied by )14/)12o × 293/277, where )17-is the viscosity at temperature T°C, to correct for the change in temperature and the corresponding change in

STRUCTURAL

viscosity. Errors given are those calculated from linear regression. (2) The normalized correlation functions were fitted by a nonlinear fitting routine to the sum of two exponential decays, as described by Chu (22). From the best fit to the equation, [g(2)('r) -- 1] 1/2 =

Blexp(-Flz) + B2exp(-P2~-),

[2] P, and hence/), was calculated from __ ( B I P I -F B2I~2)

diffusion coefficient, D(K), as a function of the scattering vector K. A similar calculation was carried out by Pusey and van Megen (23) for both a Schulz-Zimm distribution and a twocomponent mixture of monodisperse particles. For a suspension of monodisperse macromolecules, the normalized electric field correlation function g(°(r) = exp(-F~'), where F = D K 2. The normalized intensity autocorrelation function g(2)(r), which is determined experimentally, is related to g(O(r) by

[3] /3{g(1)(r)}2 = g(2)('r) --

BI +B2

Comparison of the values for the diffusion coefficients obtained by the two methods showed very little difference. The diffusion coefficient shown under Results is that obtained from the cumulants method, fitting to a third-order polynomial, which gave good agreement with the double exponential method. The hydrodynamic diameter, dh, was calculated from the Stokes relationship D = kT/3~rndh. Treatment of casein micelles with chymosin was carried out at 4°C. Samples were diluted into SMUF, as described earlier in this section. Chymosin, dissolved in SMUF, was added to a concentration of approximately 0.05 mg/ml. A decrease was observed in the hydrodynamic diameter measured by PCS, and after 30-60 min it had reached a new steady value. At this point the study of the angular dependence o f the diffusion coefficient was commenced, the initial and final sets of correlation data being obtained at 0 = 90 ° for comparison to check that no further changes had occurred in the measured hydrodynamic diameter. Finally, the sample was allowed to warm up to room temperature and the aggregation of the chymosin-cleaved micelles was observed. THEORY

501

STUDIES OF CASEIN MICELLES

AND CALCULATIONS

This section describes the calculation, from a given frequency curve of particle sizes that can be approximated as a mixture of n different sets ofmonodisperse particles, of the value expected for the intensity-weighted average

1,

[41

where/3 is a spatial coherence factor [described in Ref. (22)], obtained from Eq. [1] (the cumulants method) as In/3 = 2A0 and from Eq. [2] as/3 = (B1 + B2)2. g(°('r) is therefore calculated from the experimental values ofg(2)(r). We now consider a suspension of n different sets of particles, where each set i consists of N/ particles of identical composition and uniform size. The subscript i is used throughout to denote those properties associated with the ith set of particles; thus the /th set of particles contains N,- particles of diffusion coefficient Di. For the suspension n

gO)(r) = ~ Gi(K)exp(-Ffr),

[5]

i=1

where N~I~(K) Gi(K)= n

EN~Ii(K) i=l

the fraction of the total intensity of scattered light that is scattered by the ith set of particles in the direction of K, where the effect of any internal modes has been neglected. For a continuous distribution, where G(P, K ) d r is the fraction of the total intensity of scattered light that is scattered in the direction of K by particles with decay constants in the range P to F+dF, g(1)('r) =

G(F,K)exp(-rr)dr.

[61

Brown et aL (11) showed that if the correlation function g(l)(r) was analyzed in terms of CUJournal of Colloid and Interface Science, Vol. 115, No. 2, February 1987

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M A R Y C. A M B R O S E G R I F F I N

mulants, as outlined under Materials and Methods, then the first cumulant gave the intensity-weighted average value of/). For partides of the size studied here (KR >~ 1),/5 is a function of the scattering vector, K. Thus for a fixed K and for n different sets of particles,

Brown et al. (1 l) showed that the intensityweighted average value of the diffusion coefficient,

/5(K) = F(K)/K 2 n

Nili(K)Oi(K)

n

K2/5(K) = r(K) = ~ FiGi(K).

.

[7]

[11]

E Nili

i=l

i=l

For interpreting the light scattering data from casein micelles the theory described here is that appropriate for homogeneous spheres, since the only structural features detected [by electron microscopy (2) and neutron scattering (4)] are on a size scale (<20 nm) that would be very difficult to detect by light scattering over the range of wavevectors used in this work. For homogeneous spherical particles, if Im I I ~ 1 and aim - 11 41, where m is the ratio of the refractive index of the particles to that of the medium, and a = ~rdn/ko, where d is the diameter, then, according to RGD theory (24), Ii(K) oc d6p(K),

Using the Stokes relationship, D = kT/3r~dh, we then obtain n

--

Z Nile(K)/dh,

[~-~h]=i=ln

[12]

~, Nili(K) i=l

Thus, from a known frequency curve of particle sizes, and assuming a homogeneous sphere model for each particle, we may calculate the angular variation of the intensityweighted mean value of[1/dh]-I and hence of the diffusion coefficient, /9(K) (= (kT/3rro) × [1/dh]).

where RESULTS

P(K) =

(sin u - u cos u)

and

Figure 1 shows the variation of the intensityweighted average diffusion coefficient with u = ½Kd. [81 scattering angle for casein micelles fixed with Thus glutaraldehyde. Other unfixed raw skim milk samples gave results similar to those in Fig. 1. Ii(K) oc -~6 [sin ½Kd- ½Kd cos 1Kd] 2. [9] The advantage of the fixation was that data could be recorded from the same sample for For arbitrary values of a and m, Mie theory a longer time without fear of micelle disaggreapplies exactly, and for vertically polarized in- gation. Figure 2 shows the cumulative size cident light (as obtains here experimentally) distribution of the casein micelles in the skim milk. The solid lines in Figure 1 show the angular {.=~1 i = 2 l ' [ 1 Ii(K) = ~ [ a i ( l ) T r i ( l , cos 0) variation of the average diffusion coefficient calculated from the original chromatographic + bi(l)ri(l, cos 0)] , [10] data of protein (casein micelle) concentration and average hydrodynamic diameter for each where ai(l), bi(l), ~ri(l, cos 0) and ri(l, cos 0) fraction, from which Fig. 2 is derived, as decorrespond to the values of an, bn, ~rn, and rn, scribed in the previous section. Mie theory for as defined by van de Hulst (25), for the ith set a homogeneous sphere model was used. Furof particles. ther details are given later in this section. Journal of Colloid andlnterface Science,

Vol. 115, No. 2, February 1987

503

S T R U C T U R A L STUDIES OF CASEIN MICELLES 0.30

0.25

\ I~ 0.20

// //

0.15 K2/1014m-2 FIG. 1. Angular variation of the measured intensityweighted average diffusion coefficient of casein micelles that had been treated with glutaraldehyde. Sample temperature was 20°C. Solid and dotted lines derive from theoretical calculations described in the text.

The effect of chymosin treatment on the hydrodynamic size of the casein micelles was studied at 4°C, to prevent aggregation of the 1.0 °°o o

0

0

enzymatically cleaved casein micelles (17, 18). Figure 3 shows the angular dependence of the intensity-weighted average diffusion coefficient of unfixed casein micelles before and after treatment with chymosin. The measurements of/% of the unfixed casein micelles at 4°C and at all values ofK 2 are in good agreement with those of glutaraldehyde-fixed casein miceUes at 20°C. The mean value for the diffusion coefficient at each angle increased on treatment with chymosin, the differences between the two sets of values being statistically significant. To estimate the change in hydrodynamic diameter represented by these data, exponential curves were fitted to the relationships between hydrodynamic diameter and K 2 (this being the simplest type of curve that gave a reasonable fit to the data). The parameters of the curves were estimated by weighted least squares, the weights being inversely proportional to the variance within each mean value of hydrodynamic diameter. Analysis of variance revealed that the curves for the two sets of data were displaced vertically (P < 0.001), but there was no evidence that they differed

0

0.30

0 oo

0.8

0 0 0

~1 0.25

0

,=_o0.6;

~ ' ' ' ' ~

%

0

&

0

g

ID

0

0.4

"~0 0.20

lI

//I

i//

i **

0

0

0

0.2

0.15

0 0

o 0.0 o 100

0 K2/1014m-2 200

300 Diameter (nm)

400

FIG. 2. Size distribution of casein micelles in the skim milk plotted as the cumulative weight fraction against the hydrodynamic diameter measured by PCS.

FIG. 3, Angular variation of the measured intensityweighted average diffusion coefficient of casein micelles before (O) and after (O) treatment with chymosin. Sample temperature was 4°C. Values f o r / % were corrected for temperature as described in the text. Journal of Colloid and Interface Science, Vol. 115,No. 2, February 1987

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MARY C. AMBROSE GRIFFIN

in shape (P > 0.1). The displacement was 8.0 ___ 1.3 nm. The calculations represented by the solid line in Fig. 1 were carried out using a range of relative refractive indices, 1.033-1.18, the latter corresponding to the refractive index of 1.57 measured for the nonaqueous part of the casein micelles (26). The smaller value was estimated from a linear combination of the products of the volume fraction and the refractive index of each constituent of the casein micelle, 1 basing the estimate on values of 3.9 ml/g for the voluminosity of the micelles (27), 0.73 for the apparent specific volume of the protein (28), and 7% for the weight percentage of mineral constituents (2). In fact, varying the relative refractive index did not make an appreciable difference in the calculations. The angular variation was also calculated in the same way using RGD theory; differences between the two sets of calculations were two orders of magnitude less than the experimental standard deviation. At K = 0 the intercept is the z-average value for the distribution (11, 12). A further set of calculations used another model, based on the "hairy" micelle models of Holt (29) and of Walstra (27), for the casein micelles. In these calculations the para-casein micelle centers, which remain after cleavage of K-casein by chymosin, were conceived as homogeneous spheres; the macropeptide portion contributed viscous drag to the micelles, increasing the effective hydrodynamic size of the micelles by 5-10 nm, without contributing to the mass or to the density of light scattering. Using this model the angular variation of the diffusion coefficient of the casein micelles before and after cleavage by chymosin could be compared. This model gave a slightly better fit to the experimental data for intact micelles than the homogeneous sphere model. The effect of removal of the hairs was a decrease in the intensity-weighted average hydrodynamic Suggested as an approximation by Kerker (24, p. 201) for calculating scattering efficiencies.

Journal of Colloid and Interface Science, Vol. 115,No. 2, February 1987

radius by approximately the length of the hairs used in the calculations. DISCUSSION

The size distribution for the casein micelles in the skim milk (given in Fig. 2) used for calculating the angular dependence of the intensity-weighted average diffusion coefficient of two samples is approximate. One systematic error in the distribution is expected, arising from imperfections of the fractionation procedure. Although measurements of hydrodynamic diameter from individual fractions showed little variation with scattering angle (30) each fraction does contain a distribution of sizes. The hydrodynamic diameter measured by PCS will, therefore, be weighted on the large side. In view of this, the calculated curve should lie below the experimental values for the diffusion coefficient, whereas the reverse is true. This might be explained by a variation of the refractive index of the casein micelles with size, the larger micelles having a higher value of m. The degree of light scattering by the larger micelles would be correspondingly higher. The dotted line in Fig. 1 is given as an example calculation to illustrate this point: here m varies as 1.015 + 0.015a, where c~ = ~rdhn/Xo. The voluminosity of casein micelles has, in fact, been found to decrease with increasing size, indicating a decreasing degree of hydration (31). An increase in the overall particle refractive index with size is, therefore, expected because its value is determined by contributions from both aqueous and nonaqueous constituents.2 The range of voluminosities given in (31), 3.58-5.03 ml/g, is consistent with a range of m values similar to that employed in the example calculation here. Horne (13), in his study of the angular variation of the diffusion coefficient of casein mi2 The method described in (26) for measuring the refractive index of the n o n a q u e o u s part of casein micelles is not sufficiently accurate to detect the small contribution due to the inorganic constituents (M. C. A. Griffin, unpublished data).

STRUCTURAL STUDIES OF CASEIN MICELLES celles, used only data for K 2 > 2.88 X 1014 m -2 to fit a S c h u l z - Z i m m distribution. Below this value o f K 2 (corresponding to 0 = 80 °) his data gave values for the diffusion coefficient which were significantly lower than the theoretical fit to the S c h u l z - Z i m m distribution. He ascribed the difference between his experimental points and the theoretical line as being due to residual c o n t a m i n a t i o n by fat globules. In earlier work from this laboratory (9) we found that there was a measurable fraction o f casein micelles o f h y d r o d y n a m i c diameter greater than 300 n m in skim milk, and, although electron microscopy revealed the presence of m e m b r a n e material in the void volume peak from C P G chromatography, there was no evidence for fat contamination. This m e m b r a n e material, moreover, was not significantly turbid. The data presented here indicate that even at K 2 > 2.88 X 1014 m -2 we need to postulate a weighting for the larger micelles higher than that afforded by a model of homogeneous spheres o f the same refractive index in order to reconcile the measured size distribution with the diffusion coefficient; such a postulate would explain the significant curvature o f / ) toward the K 2 axis as K 2 ~ 0 (Fig. 1). The diffusion coefficients obtained for the samples used in these experiments were the same at 4 and 20°C, and in other experiments (not described here) we have found that raising the temperature to 30°C has not caused any change in h y d r o d y n a m i c diameter. W e may, therefore, c o m p a r e the effect o f c h y m o s i n action on the h y d r o d y n a m i c diameter at 4 ° C with the results o f Walstra et al. (15) at 30°C and o f H o m e (16) at 20°C. O u r m o r e detailed results give a drop in diameter o f 8.0 + 1.3 n m which is in reasonable agreement with their figure o f 10 nm. IH N M R experiments (32) have provided evidence consistent with there being a hairy layer c o m p o s e d o f the macropeptide section o f K-casein. F r o m the results described here we c o n d u d e that the thickness o f this layer does not expand on decreasing the tempera-

505

ture, which might have been predicted from entropic effects (27). ACKNOWLEDGMENTS I thank Miss C. Moore for technical assistance, Dr. S. V. Morant for advice on statistics, Mr. C. Bishop for assistance with computer programs, and Dr. W. G. Griffin for valuable discussion and for criticizing the manuscript. I also thank Dr. R. L. J. Lyster for continually helpful discussion. This work was supported by the Agriculture and Food Research Council of Great Britain. REFERENCES 1. Jenness, R., in "Milk Proteins, Chemistry and Molecular Biology I" (H. A. McKenzie, Ed.), p. 17. Academic Press, New York, 1970. 2. Schmidt, D. G., in "Developments in Dairy Chemistry. 1. Proteins" (P. F. Fox, Ed.), p. 61. Applied Science Pub., London, 1982. 3. Davies, D. T., and Law, A. J. R., J. Dairy Res. 50, 67 (1983). 4. Stothart, P. H., and Cebula, D. J., J. MoL BioL 160, 391 (1982). 5. McGann, T. C. A., Donnelly, W. J., Kearney, R. D., and Buchheim, W., Biochim. Biophys. Acta 630, 261 (1980). 6. Schmidt, D. G., Walstra, P., and Buchheim, W., Neth. Milk Dairy J. 27, 128 (1973). 7. Holt, C., Kimber, A. M., Brooker, B., and Prentice, J. H., J. Colloid Interface Sci. 65, 555 (1978). 8. Lin, S. H. C., Dewan, R. K., Bloomfield, V. A., and Morr, C. V., Biochemistry 10, 4788 (1971). 9. Griffin, M. C. A., and Anderson, M., Biochim. Biophys. Acta 748, 453 (1983). I0. Berne, B. J., and Pecora, R., "Dynamic Light Scattering with Applicationsto Chemistry, Biologyand Physics." Wiley-Interscience, New York, 1976. 11. Brown, J. C., Pusey, P. N., and Dietz, R., J. Chem. Phys. 62, 1136 (1975). 12. Brehm, G. A., and Bloomfield,V. A., Macromolecules 8, 663 (1975). 13. Home, D. S., J. Colloid Interface Sci. 98, 537 (1984). 14. Waugh, D. F., and Noble, R. W., J. Amer. Chem. Soc. 87, 2246 (1965). 15. Walstra, P., Bloomfield,V. A., Wei, G. J., and Jenness, R., Biochim. Biophys. Acta 669, 258 (1981). 16. Home, D. S., Biopolymers 23, 989 (1984). 17. Berridge, N. J., Nature (London) 149, 194 (1942). 18. Berridge, N. J., DairyEng. 80, 161 (1963). 19. Anderson, M., Griffin, M. C. A., and Moore, C., J. Dairy Res. 51, 615 (1984). 20. Lang, C. A., Anal Chem. 30, 1692 (1958). 21. Jenness, R., and Koops, J., Neth. Milk Dairy J. 16, 153 (1962). Journal of Colloid and Interface Science, Vol. 115, No. 2, February 1987

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22. Chu, B., in "The Application of Laser Light Scattering to the Study of Biological Motion" (J. C. Earnshaw and M. W. Steer, Eds.), NATO ASI A59, p. 53. Plenum, New York, 1983. 23. Pusey, P. N., and van Megen, W. J., J. Phys. Chem. 80, 3513 (1984). 24. Kerker, M., "The Scattering of Light and Other Electromagnetic Radiation," Chap. 8. Academic Press, New York, 1969. 25. Van de Hulst, H. C., "Light Scattering in Small Particles," Chap. 9. Wiley, New York, 1957. 26. Griffin, M. C. A., and Griffin, W. G., aT. Colloid Interface Sci. 104, 409 (1985). 27. Walstra, P., J. DairyRes. 46, 317 (1979).

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28. McMeekin, T. L., Groves, M. L., and Hipp, N. J., J. Amer. Chem. Soc. 71, 3298 (1949). 29. Holt, C., in "Proceedings, International Conference on Colloid and Surface Science, Budapest" (E. Wolfram, Ed.), p. 641. Akademai Kiado, Budapest, 1975. 30. Griffin, M. C. A., and Anderson, M., in "The Application of Laser Light Scattering to the Study of Biological Motion" (J. C. Earnshaw and M. W. Steer, Eds.), NATO ASI A59, p. 347. Plenum, New York, 1983. 31. Sood, S. M., Sidhu, K. S., and Dewan, R. K., N.Z. aT. Dairy Sci. TechnoL 11, 79 (1976). 32. Griffin, M. C. A., and Roberts, G. C. K., Biochem. J. 228, 273 (1985).