# Physicochemical analysis of αS₁⁻, β⁻- and κ-casein solubility in 45% ethanol

By S. MEZDOUR<fnref n="1" />, P. BOYAVAL<fnref n="2" />, and J. KOROLCZUK<fnref n="3" />*

The casein fractions solubility in 45% ethanol at T = 293 K as a function of pH and the electrostatic surface energy (V<sub>E</sub>) can be represented by an equation describing the ionisation process. The half solubility of αS₁⁻, β⁻- and κ-caseins is observed respectively at pH: 6.54, 6.85 and 6.85 at V<sub>E</sub>: 38, 19 and 0.3 k<sub>B</sub>·T. The solubility increases from 10% to 90% for the change in pH by 0.78, 0.84 and 1.08, and in V<sub>E</sub> by 22, 11 and 0.6 k<sub>B</sub>·T, respectively. For the solubility presented as a function of the reduced V<sub>E</sub>, the behaviour of κ-casein is different from αS₁⁻, β-caseins. The fraction of an industrial sodium caseinate, soluble in 45% ethanol at pH 6.4 and 293K is enriched to about 60% in αS₁⁻-casein. This fraction could be used as an emulsifying agent or for cream liqueur production.

## Physikochemische Analyse der αS₁⁻, β⁻- und κ-Casein-Löslichkeit in 45%igem Ethanol

Die Löslichkeit der Caseinfraktionen in 45%igem Ethanol bei T = 293 K als Funktion des pH-Wertes und der elektrostaticischen Oberflächenenergie (V<sub>E</sub>) kann mit einer Gleichung dargestellt werden, die den Ionisierungsprozess beschreibt. Die Halblöslichkeit von αS₁⁻, β⁻- und κ-Casein wird bei pH-Werten von 6,54, 6,85 bzw. 6,85 und V<sub>E</sub>-Werten von 38, 19 bzw. 0.3 k<sub>B</sub>·T ermittelt. Die Löslichkeit erhöht sich von 10 % auf 90 % bei Veränderungen im pH-Wert um 0,78, 0,84 und 1,08 und bei V<sub>E</sub> um 22, 11 bzw. 0.6 k<sub>B</sub>·T. Für die Löslichkeit, dargestellt als Funktion eines reduzierten V<sub>E</sub>, unterscheidet sich das Verhalten von κ-Casein gegenüber den αS₁⁻, und β-Caseinen. Die Fraktion eines industriellen Natriumcaseinats, löslich in 45 % Ethanol bei pH 6,4 und 293 K, ist auf etwa 60 % beim αS₁⁻-Casein angereichert. Diese Fraktion kann als Emulgator für die Herstellung von Sahnelikör eingesetzt werden.

**58 Casein solubility (physicochemical analysis)**

**58 Casein-Löslichkeit (physikochemische Analyse)**

## 1. Introduction

Several articles have been published on milk protein stability in ethanol solutions. This subject has been reviewed recently (1-3). In a previous study (3) we analysed the solubility of αS₁⁻, β⁻- and κ-casein as a function of the ethanol volume fraction and temperature and found the highest selectivity of αS₁⁻-caseine extraction from the sodium caseinate dissolved in 45-50% ethanol. The aim of this work is to analyse the solubility of αS₁⁻, β⁻- and κ-caseins in 45% ethanol as a function of pH and electrostatic surface energy.

## 2. Materials and methods

Industrially produced, spray-dried sodium caseinate (Armor Proteines, 35466 Saint Brice en Cogles, France) was used in this study. The pH of sodium caseinate solutions in water was adjusted to values in the 5.2-6.8 range, with 0.5 mol·L⁻<fnref n="1" /> HCl and left for 1 hour at room temperature. Subsequently, ethanol was slowly added and continuously stirred, to reach the final ethanol volume fraction of 0.45. The solutions were then kept for 1 h in a water bath at a specified temperature. The casein concentration in final solutions was 10 g·L⁻<fnref n="1" />. The pH of water and ethanol solutions was measured with a pH meter equipped with a combination electrode. Calibration was performed with buffers in aqueous solution.

Soluble caseins were separated from the precipitate by centrifugation at 2000×g for 30 min. Casein content in the initial sodium caseinate samples, solutions and supernatants was estimated from nitrogen determinations

using Kjeldahl techniques with 6.38 as a nitrogen to protein conversion coefficient (4, 5).

Supernatants were evaporated under vacuum to eliminate alcohol and the concentrates were freeze-dried and kept at -20 °C until analysed. Casein fractions content in supernatants were determined by reverse phase high performance liquid chromatography - RP-HPLC (3, 6).

The solubility of a given casein fraction (x) was calculated as follows:

Solubility of x-casein = x-casein concentration in the supernatant / x-casein concentration in the initial solution

- Selectivity or purity = x-casein in the supernatant / (αS₁⁻-casein + αS₂⁻-casein + β-casein + κ-casein) in the supernatant.

The relative dielectric constants of aqueous ethanol solutions were calculated according to ÅKERLÖF (7), HARVEY and PRAUSNITZ (8) and SMITH *et al.* (9).

Casein and casein fractions solubility as a function of pH can be represented by equation [1], representing the ionisation process (1, 10-14):

$$S = \frac{S_{\text{min}} + S_{\text{max}} \cdot 10^{\left(\frac{\varphi H - \varphi H_0}{D}\right)}}{1 + 10^{\left(\frac{\varphi H - \varphi H_0}{D}\right)}} \quad [1]$$

where: pHᵢ is the pH of the inflexion point or the pH corresponding to 50% casein solubility; D is the slope of the straight line in pH vs. Log₁₀[(S - Smin)/(Smax - S)] coordinates. It also is the pH increase to cause the Log₁₀[(S - Smin)/(Smax - S)] to rise by 1 unit. Smin = 0% and Smax = 100% are respectively the minimal and

<footnote n="1">¹UMR 1145 Ingénierie Procédés Aliment, AgroParisTech, Cnam, INRA, 1 avenue des Olympiades, 91300 Massy cedex, France</footnote>

<footnote n="2">²Danisco France SAS, Zone d'Activités de Buxières, F-86220 Dangé Saint Romain, France</footnote>

<footnote n="3">³INRA-Agrocampus Rennes, UMR1253 Science et Technologie du Lait et de l'Œuf, 65 rue de Saint-Brieuc, 35042 Rennes cedex, France. *Corresponding author: jozef.korolczuk@gmail.com</footnote>
maximal casein solubility and S is the solubility at a given pH and ethanol concentration.

The electrostatic energy of casein molecules was estimated by the relation (15):

$$V_E = 2 \cdot \pi \cdot \epsilon_0 \cdot \epsilon \cdot r \cdot \psi_0^2 \cdot \ln[1 + \exp(-d / \lambda_D)] \quad [2]$$

where: $V_E$ = electrostatic energy in $k_B \cdot T$, $k_B = 1.381 \cdot 10^{-23} \text{ J} \cdot \text{K}^{-1}$ is the Boltzmann constant, $T$ = absolute temperature in K, $\pi = 3.14...$, $\epsilon_0 = 8.854 \cdot 10^{-12} \text{ J}^{-1} \cdot \text{C}^2 \cdot \text{m}^{-1}$ = dielectric permittivity of vacuum, $\epsilon$ = relative dielectric constant, $r$ = molecule radius in metres, $\psi_0$ = electrostatic surface potential in Volts, $d$ = distance from the surface of the molecule in metres, $\lambda_D$ = Debye length in meters. The values of $\epsilon$, $\psi_0$ and $\lambda_D$ were calculated as described previously (2).

### 3. Results and discussion

<figure><img src="image_1.png" /><figcaption>Fig. 1: The solubility and the selectivity profile of $\alpha_{S1-}$, $\beta-$ and $\kappa$-casein as a function of pH. Solid lines represent the solubility calculated by Equation [1] or by the polynomial curves with their coefficients, correlation coefficient ($R^2$) and standard error (Err) given in the figure. Experimental conditions: ethanol volume fraction $E = 0.45$, $T = 293\text{K}$, stirring time = 1 h). Number of experimental points $N = 7$.</figcaption></figure>

In 45% ethanol and for a pH range between 6.0 and 6.7, the most soluble is $\alpha_{S1-}$-casein (Fig. 1). $\kappa$-Casein is slightly more soluble than the $\beta$-casein. According to Equation [1], solubility profiles (solid lines in Fig. 1) correspond quite closely to our experimental results. The $pH_i$ from Equation [1] is 6.54, 6.85 and 6.85 for $\alpha_{S1-}$, $\beta-$ and $\kappa$-caseins respectively. For $\alpha_{S1-}$, $\beta-$ and $\kappa$-caseins, 10% solubility is reached respectively at pH 6.15, 6.43 and 6.31 and its increase by 0.79, 0.84 and 1.09 augments their solubility from 10% to 90%.

The coefficient $D$ from Equation [1] is 0.41, 0.44 and 0.56 respectively for $\alpha_{S1-}$, $\beta-$ and $\kappa$-casein. When pH is reduced from $pH_i$ by $D$ the solubility drops from 50% to 100/11 ≈ 9.09% and when it increases from $pH_i$ by $D$, the solubility increases from 50% to 100/1.1 ≈ 90.9%. The pH of a chosen level of protein solubility (S in %) can be calculated from the relation:

$$pH_S = D [\text{Log}_{10}(S) + pH_i / D - \text{Log}_{10}(100 - S)].$$

The highest selectivity of $\alpha_{S1-}$-casein soluble in 45% ethanol at 20°C (~57%) is at pH 6.4 (Fig. 1). We previously observed (3) the maximal purity (~68%) at 30°C and at pH 6.4 for the ethanol volume fraction $E = 0.47$. HIPP et al. (16) obtained 80% pure $\alpha$-casein from the ammonium caseinate, soluble in 50% ethanol with 0.2 mol.L$^{-1}$ of ammonium acetate at pH 6.5 and at 20-28°C but insoluble at pH 5.7.

<figure><img src="image_2.png" /><figcaption>Fig. 2: The solubility of $\alpha_{S1-}$, $\beta-$ and $\kappa$-casein as a function of the electrostatic surface energy ($V_{E0}$) calculated by Equation (2) or of reduced electrostatic surface energy ($V_{E0R} = V_{E0} / V_{E0i}$). Solid lines represent the solubility calculated by modified Equation (1). Experimental conditions: ethanol volume fraction = 0.45, temperature = 293K, stirring time = 1 h). Number of experimental points $N = 7$.</figcaption></figure>

The half solubility of $\alpha_{S1-}$, $\beta-$ and $\kappa$-caseins corresponds, respectively, to 38, 19 and 0.3 $k_B \cdot T$ of the electrostatic surface energy (Fig. 2). When the electrostatic surface energy is decreased or increased from $V_{E0i}$ by 10.3, 5.6 or 0.28 $k_B \cdot T$ respectively $\alpha_{S1-}$, $\beta-$ and $\kappa$-caseins, their solubility drops to 10% or rises to 90%.

Two statistically different master curves are obtained for the solubility presented as a function of the reduced electrostatic surface energy ($V_{E0R} = V_{E0} / V_{E0i}$)
as shown in Fig. 2. For all three analysed caseins, the half solubility is at $V_{EORI} = 1.00$. The significant difference is in $DV_{EOR}$, which is about 0.3 for $\alpha_{S1}$- and $\beta$-casein while it is about 0.9 for $\kappa$-casein.

The same protein fraction solubility level is observed for very different levels of the electrostatic surface energy ($V_{E0}$). These properties are governed by pH, dielectric constant, ionic strength and temperature. For constant $\epsilon$, I and T, the pH is responsible for the ionisation level and thus the electrostatic properties of protein molecules. On the other hand, within the pH range studied (6.0 – 6.7) in 45% ethanol, caseins form aggregates and the soluble fraction represents smaller aggregates enriched in the $\alpha_{S1}$-casein, having the highest electrostatic surface energy with smaller participations from the other two fractions. The aggregation of caseins and the formation or the dissociation of casein micelles as a function of different factors has already been observed (17-23).

At pH 6.4 in 45% ethanol and at 20°C, the number of dissociated positive charges is 21, 17 and 16 and negative charges is 40, 28, and 16 for the $\alpha_{S1}$-, $\beta$- and $\kappa$-caseins respectively (2). The residues charged in caseins are not uniformly distributed in the amino acid sequence of the molecules (24-25). The clusters of positive and negative charges facilitate the formation of intermolecular aggregates within the same fraction as well as between different caseins. The centrifugation at 2000×g, used in this work, separates smaller aggregates from the precipitate. The so-called soluble fraction is richer in $\alpha_{S1}$-casein, while the precipitate is enriched in $\beta$- and $\kappa$-caseins, as was also observed by ZITTLE and CUSTER (26). The higher solubility of $\kappa$-casein at low electrostatic surface energy can also be attributed to the more hydrophilic character of this protein due to the presence of the galactosylated threonyl residues and of N-acetylneuraminic acid (24, 25, 27). In the experimental conditions of this work, $\kappa$-casein is almost electrically uncharged and so its repulsive electrostatic surface energy is smaller than the attractive van der Waals interaction. For this reason the molecules of $\kappa$-casein would stick to other $\kappa$-casein and to $\alpha_{S1}$- and $\beta$-casein molecules.

## 4. Conclusions

The electrostatic properties, governed by pH, ionic strength, temperature and the solvents' dielectric constant are responsible for the aggregation or dissociation of casein molecules.

Among the three fractions analysed, within the 6 to 7 pH range, $\alpha_{S1}$-casein has the highest electrostatic surface energy. For these reasons, the soluble fraction is enriched in $\alpha_{S1}$-casein.

Taking into account the very high electrostatic properties, $\alpha_{S1}$-casein enriched fraction could be used as an emulsifying agent or for cream liqueur production.

Equations describing the ionisation phenomenon as a function of pH and the electrostatic surface energy, quite satisfactorily represent the solubility of casein fractions in water ethanol mixtures.

## 5. References

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