Biochemistry @ Copyright 1971 by the American Chemical Society
Volume 10, Number 23
Nouember 9, 1971
Equilibrium Casein Micelle Systems* David F. Waught and Bernard Talbot$
ABSTRACT: A casein micelle consists of a core of essentially insoluble as-and/or @-caseinates stabilized by a coat layer containing K-casein. In a system, cores occur in a variety of sizes, thus producing a micelle distribution. Ultracentrifugation is used t o characterize reconstituted micelle systems containing as-and K-caseins with respect to the weight fractions of total protein in particles of different size. At final environmental conditions of 37', pH 6.6, a monovalent ionic strength of 0.05 and 0.012 M calcium chloride, it is concluded that a system is in equilibrium when a particular micelle distribution is present and that the distribution is determined by the system weight ratio of a,-:K-casein. (A) Micelle systems develop spontaneously as calcium chloride is increased progressively from zero. Using initial weight ratios, RI, from 20 t o 3, the micelle radius of the maximum weight fraction decreases as RIis decreased, respectively, from -425 to -36 nm. Concomitantly, the concentration of nonmicellar protein (including coat) slowly increases; a t 8 mg/ml of a,-casein, from 0.15 to 0.4 mg per ml. (B) Colloid particles of Ca-
C
asein micelles of bovine milk are nearly spherical and exist in a distribution of sizes. Average radii, by electron microscopy, range from about 10 t o 400 nm, with over 95 of the micelle mass in particles from 30 to 150 nm (Nitschmann, 1949; Hostettler and Imhof, 1951; Dyachenko et al., 1955; Knoop and Wortman, 1960; Adachi, 1963; Saito and Hashimoto, 1964; Rose and Colvin, 1966; Carroll et al., 1968). Size distributions obtained by reconstituting with calcium and other divalent cations have been shown (Adachi, 1963) t o resemble closely size distributions found in milk. Casein micelles may be obtained using K-casein and a,-casein (Zittle, 1961; Noble and Waugh, 1965; Waugh and Noble, 1965),
* From the Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. Receiced April 28, 1971. This work has been supported by U. s. Public Health Service Grant GM 05410. To whom to address correspondence. $ Special Fellow of the National Institutes of Health. A portion of this work was submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Massachusetts Institute of Technology, 1967.
a,-caseinate having radii >440 nm can be stabilized as micelles a t original size, or spontaneously transformed into micelles of smaller size, by adding appropriate amounts of x-casein. (C) After mixing aliquots of micelle systems at different RI, spontaneous rearrangement leads to a size distribution characteristic of the weight ratio of the mixture. (D) A micelle system at R I = 4 can stabilize as micelles all a,-casein added t o give Rs = 8.4. The required x-casein comes mainly from preexisting micelles. For equilibrium systems, population surface area and %-caseincontent yield 3400 A2/K-caseinmonomer of 20,000. Thus, t KCI. These stock solutions were stored at - 1 5 " . Absorbunce and Extinction Coejj'icients. In 0.05 sodium 2s,)i!m values citrate at pH 7.0 (standard diluent) the are 10.0 for as-and K-caseins and 4.7 for $-casein (Waugh et id,, 1970). Observed absorbances were corrected by subtracting 1.7 times the apparent absorbance at 1 320 nm. One absorbance unit is the amount of protein per milliliter required to give unit corrected absorbance for 1-cm path. ionic Strength. In what follows the symbol "I" is used for the ionic strength contribution due to monovalent ions, and calcium chloride concentrations are specified separately. Addjtion (if C a k i i m . Calcium was usually brought to a predetermined concentration by dialysis of protein solutions against large volumes of buffer. In instances a single aliquot of a solution containing CaCl,! and monovalent ions was added with rapid mixing (Noble and Waugh, 1965). The added volume was 0.1 1 of the volume of the protein solution. Weight Ratios. The weight ratio of a system is (a,-plus p-) : K-casein = R. Subscripts indicate particular applications : R I , a ratio established before micelle formation is initiated, and Ra,a ratio established after CaCI, has been introduced at some prior point of an experiment, for example, if two micelle systems established at different R Iare mixed. Coiilescerzt iinil Prrrriculiite Pellets. Sufficient calcium precipitates ci,-casein alone. Particles spontaneously coalesce, and on gentle contrifugation form a pellet of bulk phase. In contrast, pellets obtained by ultracentrifuging micelle systems are piirticulatr. They redisperse spontaneously in their supernatants (Waugh and Noble, 1965). Micelles may be sufficiently large so that they settle in quiescent systems, giving a micelle sediment . Col/oidcrl Crr-a,-Caseinate. Spherical colloidal particles of Ca-oc,-caseinate, about 1 p in diameter by electron microscopy are formed at low I and low calcium chloride concentrations (e.g., I = 5 X 0.0045 11 CaCI,!). Such colloids are unstable: particles coalesce irreversibly on centrifugation, and the introduction of 0.01 M CaCll leads to immediate precipitation. Electron Microscopy. Systems were fixed by the addition of a n equal volume of 1 formaldehyde adjusted to pH 7.0. They were then diluted tenfold with water and a drop immediately applied t o a parloidin-coated grid. Electron micrographs were taken on an RCA E M U 3B, which was generously made available by Professor Cecil Hall. Cmtrifiigntinn. The objective is to characterize a micelle system. To do so it is assumed that the system contains particles in a set of discrete sizes referred to as classes. The classes include micelles and smaller nonmicellar association products, such as coat, which will mainly appear in the supernatant of a suitable ultracentrifugation. Particles in the ith class have a sedimentation coefficient, s,, and a radius, r i rand represent a fraction,f,, of the total protein mass, W . TheJ are the quan-
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BIOCHEhlISTRY,
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AND
T A L B O T
tities to be derived. The fraction of total mass in a particular class, ,f,W ? which is removed by a particular centrifugation step is + , , d . The fraction of W so removed is FCI.The subscript "d" specifies the centrifugation step and includes w,the rotor angular velocity; t , the time; and xm and x1,, the radial distances to meniscus and cell base. The F,, are determined experimentally. The particle sedimentation coefficient is defined by
For a sector-shaped cell, eq 1 yields an exact expression for the + l , d . The swinging-bucket rotor employed in this work holds cylinders, and some mass flow along the walls to the base of the tube is expected. It was known that this is compensated (to a n unknown extent) by the formation of a viscous layer, just above the pellet, in which particle velocity is decreased. It was also observed that pellets have sharp centripetal surfaces. We have tested (see Centrifugation of Fresh Skim Milk) and used the approximation for which it is assumed that the tube has constant cross section and that + , , ( I is given by the ratio of the distance between the meniscus and the centripetal micelle boundary to the total length of solution in the tube. Then by eq 1
and for a population of 12 classes
where the restriction 0 5 + i , d 5 1 holds for each class. Micelles are nearly spherical. The coat-core model (Waugh and Noble, 1965) requires that the total micelle population surface area be determined by the amount of adsorbed K casein. Let the solvated micelle radius, r , , include an increment A due to K-casein. Since as- and K-caseins have essentially equal density, it follows that s, =
-
,
T
r,3
- (r, 1
1)J
7Qk
and
In eq 4 and 5 , pp is the protein density (approximately ( ~ ) - l ) , F is the protein partial specific volume, p.. is the solution density, 7 is the solution viscosity, Qa and Q,, are the solvation of cyb- and ti-caseins, respectively, in cubic centimeters of solvent per cubic centimeters of protein, and R is the system weight ratio. We take p = 0.728 g/cm3 (McMeekin et al., 1949; McKenzie and Wake, 1959), pp = 1.37 gf'cm3, pi = 1.0 g/cm3, 7 = 0.0069 P at 37", and Q, = 2.3 (Noble and Waugh, 1965; Creamer and Waugh, 1966). Q, is taken as 3.0 from an extrapolation of the data of Waugh and Noble (1965). A value of A = 2.85 nm is obtained from the average area of Table 111 and eq 5 ; the average area per gram of
EQUILIBRIUM CASEIN MICELLE SYSTEMS ~
~~~
TABLE I :
Centrifugation of Skim Milk:
Min
Milk I
Milk I1
Micelle Class
2 4 8 12 16 20 24 28
0.13 0.26 0.52 0.72 0.85 0.94 1 .oo 1 .oo X cm2/g of K-casein
0.105 0.21 0.42 0.59 0.72 0.83 0.93 1 .oo
1 2 3 5 5 6 7 8
si (10-2 S)
75 37 19 12 9.3 7.5 6.2 5.3
ri (nm)
Milk I
Milk I1
144 102 72 59 51 46 42 39
0.02 0.03 0.16 0.21 0.16 0.14 0.28
0.01 0.02 0.11 0.13 0.10 0.08 0.17 0.38 10.0
8.9
Conditions are 37', 25 krpm, xm = 5.2 cm, x b = 9.6 cm, and centrifugation times given in column 1. Columns 2 and 3 refer to two milks and give F d , the fraction of the total micelle absorbance removed by centrifugation. Column 4 gives the micelle class (i.e., micelles just completely removed by the coiresponding centrifugation), and columns 5 and 6 give, respectively, the class sedimentation coefficient (Svedbergs) and radius. Columns 7 and 8, give, for the two milks,f,, the fractions of total micellar protein in the micelle classes. Q
+
K-casein multiplied by A should equal tj(l Q x ) = 2.91 g/cm3. Calculations were made using either an Olivetti-Underwood Programma 101 or an IBM Model 360 computer. Procedures for statistical analysis are given in Bennett and Franklin (1963). The standard deviation (std dev) will be given as such, or in per cent of the average value of the measurement. Averages are indicated by a bar. Assay centrifugation was carried out for 1 min at 3800 rpm in a n International Model CL centrifuge maintained at 37". A 1-ml aliquot gave xm = 12.0 cm and Xh = 13.3 cm. Assay centrifugation removes all particles having s, = >108,000 S by eq 2, thus r , = >545 nm by eq 4. The fraction of Wappearing in the pellet after assay centrifugation will be referred to as F,. Preparatice uhacentrifugations were carried out using polyethylene tubes, a Spinco Model L ultracentrifuge, and the SW 39 rotor controlled at 37" (Waugh et al., 1962; Noble and Waugh, 1965). A small correction for tube end curvature gives x b = 9.6 cm. Analytical ultracentrifugations were carried out using the Spinco Model E equipped with schlieren optics. Results Centrifugation of Fresh Skim Milk. To determine the applicability of eq 2, a n examination was first made of centrifugates of skim milk. For constant xmand x b , eq 2 and 3 predict that equal removal of particles from a distribution will be obtained whenJw2dt has a particular value, independent either of w or t (i.e., centrifugation at 5 krpm for 40 min should give the same Fd as centrifugation a t 10 krpm for 10 min). T o test this, the following sequence of three equivalent pairs of (krpm, min) were examined: ( 5 , 40) and (10, lo), ( 5 , 20) and (10, 5 ) , and (10, 20) and (20, 5). A volume of 5.2 ml gave xm = 5.2 cm and x b = 9.6 cm. Each ultracentrifugation, carried out at 37", gave a triplicate. Each pellet was drained of supernatant and dissolved in 3.0 ml of buffer containing 4.5 M urea and 0.1 M sodium citrate at pH 7.0. Absorbance was determined using two aliquots. Centrifugations of equivalent pairs were carried out on two
different milks, and in three instances sequences were repeated. The average standard deviation of the single absorbance determination, 6 . 4 z , accounts for the variance between averages within a triplicate, std dev = 3 . 9 z , to > 7 5 z confidence limits. The equivalent pairs of centrifugations of the sequences gave an average std dev of 4.9 By F test t o 2 75 confidence limits, variance between the averages of triplicates accounts for variance between the equivalent pairs of centrifugations. It is concluded that constant u2t produces constant removal and that eq 2 is a reasonable approximation. Evidently, inaccessible experimental conditions such as large w and small t can be replaced by small w and large f , and results can be referred to a single w . Of the proteins present in milk micelles, @-casein is the only significant component which has a low extinction coefficient. According to Rose and Colvin (1966), micelles of different size contain the same fractional content of pcasein ; therefore, the absorbance contributed to a pellet by micelles of different size will be proportional to micelle mass. Micelle distributions have been determined by ultracentrifugation. It was observed that pellet absorbances become a constant maximum after centrifugation at 25 krpm for times greater than 24-32 min, depending on the milk lot. Pellet absorbances were converted to Fd using the average maximum, and thus neglecting the small fraction of total casein protein in the supernatant. As a n approximation t o distribution, milk is considered to contain micelles in eight classes: those just completely removed at 25 krpm at 2, 4, 8, 12, 16, 20, 24, and 28 min. The micelle class, class sedimentation coefficient, and radius by eq 4 are given in Table I. I n order to obtain the of columns 7 and 8, a series of calculations based on eq 3 was used. Here, x m / ( x b - x,) = 1.18 and w = 9.42 X lo6. For example, for milk I1
z
z.
FT = 0.93 BIOCHEMISTRY,
= 1.l8(ewzdsatd VOL.
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+ i=
7 fi
1
23, I 9 7 1
(7)
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WAUGH
TABLE 11:
AND
TALBOT
Characteristics of Differential Centrifugation: _-
-
--
__
- _~
-_
~~
Centrifugation krpm
min
Vol (ml)
xmh(cm)
C,f
4.8 4.5 4.2 3.9 3.6
8.3 5.6 5.9 6.2 6.6
1.66 1.40 1.59 1.82 2.20
3.8 1 5 5 10 10 20 20 30 30 Final supernatant
-
~
~.
''8, or ' ' y d 1 2 3 4
S -~
6
A,
(10-2 S,)
r , (nm)
4963 655 74 8.3 2.1 0.8
1169 42 5 143 48.5 24.8 15.5
~~
-~ _ -
~~
~-
The mixed supernatant of one centrifugation contributes the material t o be centrifuged at the next. IJ stl is 13.3 cm for the first centrifugation (International CL), and 9.6 cm for the others (Spinco Model L). C,, = [.u,/(x,, - x,)],,.d The subscripts in this column are used as follows: for Fd, 1-5 designate fractions of the total initial protein in the pellet of the corresponding centrifugation step, and F6 that in the final supernatant; for s, (and r , ) , 1-5 specify the sedimentation coefficient (and radius) of a micelle class just completely removed at the corresponding centrifugation step, and s6 (and r 6 )values for particles in the final supernatant. s6 was obtained from experimental data.
Combination of these equations and substitution of a,,, and &? = 532 X 10 - 1 3 yields A = 0.383. The sequence of L were obtained by successive applications of eq 3. The last row of Table I gives cm2,'g of K-casein for the total micelle population surface area, calculated by eq 5 using the $, of Table I and R = 5.7 (Waugh and von Hippel, 1956; Sullivan et al., 1959; Marier et al., 1963; Rose and Colvin, 1966). The calculated distributions of Table I are in agreement with the electron microscopic studies of Saito and Hashimot0 (1964) and of Rose and Colvin (1966). There is a variation in micelle distribution between milks, but in each milk 9 5 z of the micelle mass is in particles of radius 30-120 nm . Effects of Ionic Strength mid p H on Path Dependency of Micelle Formation. At p H 7.1 and I = 0.075, using mixtures of as-and K-caseins, Noble and Waugh (1965) observed that coalescent pellets of Ca-a,-caseinate form at CaCL concentrations below those required for complete micelle formation. Systems were found to be strongly path dependent: F, was found to depend on the way in which CaClz was added (single aliquot cs. incremental addition) as well as on [
