Aspartame kinetics in 0.1 M phosphate buffer solutions with and without added polyols
Sodium phosphate buffer solutions (0.1 M) were prepared at pH values of 4.8, 5.0, 5.2, 5.4, 5.6, and 5.8 by mixing appropriate volumes of bulk 0.1 M sodium monobasic and dibasic phosphate buffer solutions. At each pH level, the phosphate buffer solution was divided into three 101.2-g aliquots, containing 100 g water and 1.2 g buffer salts. Glycerol (18.4 g) was added to 1 aliquot to give 2 molal glycerol in the buffer solution. Similarly, 68.4 g of sucrose were added to a 2nd aliquot to obtain 2 molal sucrose in the buffer solution. The 3rd aliquot, to which no polyol was added, was the phosphate buffer control. The pH values of the solutions were measured before and after the addition of the polyols. In addition, the water activities of the polyol-containing solutions were measured using an Aqualab CX2 (Decagon Devices, Pullman, Wash., U.S.A.).
Aspartame degradation is a well-studied chemical reaction, which is subject to acid-base catalysis. As such, aspartame was selected as the model reaction to evaluate the effect of polyol-induced pKa and pH changes. Aspartame was added to each solution to obtain a final concentration of approximately 10 mg/100 mL solution. Each solution was passed through a 0.2-μm nylon filter. Aliquots (2 to 3 mL) were placed into screw-capped vials and incubated at 25 °C. The sampling intervals depended on the pH of the solution; single samples were removed once or twice per week for a period of up to 49 d. A total of 8 to 10 samples were analyzed throughout the course of the experiment.
The concentration of aspartame in each sample was determined using the isocratic reverse-phase high-performance liquid chromatography (HPLC) method described by Stamp and Labuza (1989) and modified by Bell and Labuza (1991a). The analysis utilized a 3.9 × 150 mm Nova-Pak C18 column (Millipore Corp., Milford, Mass., U.S.A.). The mobile phase consisted of 80/20 (v/v) deionized water/acetonitrile solution, containing 7 mM sodium heptanesulfonate and 5 mM sodium monobasic phosphate. The pH of the mobile phase was adjusted to pH 3 using 85% phosphoric acid. The sample (20 μL) was injected into the mobile phase flowing at a rate of 1 mL/min. Detection occurred at a wavelength of 214 nm using a UV/Visible detector.
The rate constants for aspartame degradation were determined using pseudo-1st-order kinetics, where the natural log of percent aspartame remaining was plotted as a function of time. The rate constants (that is, the slope) with 95% confidence intervals were determined using computerized least squares analysis, as described by Labuza and Kamman (1983).
Aspartame kinetics in sodium monobasic phosphate solutions
Sodium monobasic phosphate solutions (0.05, 0.075, 0.10, and 0.125 M) were prepared in deionized water. Aspartame (13.5 to 14.2 mg) was added to 100 mL of each solution, and the pH was measured. The solutions were filtered using a 0.2 μm nylon filter, and 2 to 3 mL aliquots were placed into cryovials, which were incubated at 25 °C. Samples were removed from the incubator approximately every 10 to 22 d, for up to 150 d. Samples were frozen at −80 °C until analysis.
Samples were thawed rapidly in lukewarm water, vortexed thoroughly, and analyzed for aspartame using the previously described HPLC method. The rate constants of aspartame loss were again determined using pseudo-1st-order kinetics. This experiment allowed for the catalytic effect of the monobasic phosphate anion (H2PO−4) to be determined for the kinetic model.
Development of the aspartame degradation kinetic model
In the current study, aspartame degradation was used as a model acid-base catalyzed reaction to evaluate the effect of nonionic polyols on its kinetics in phosphate buffer solutions. These aqueous solutions of phosphate buffer exist as an equilibrium mixture of several different species (that is, the acid [H3PO4], the monobasic anion [H2PO−4], the dibasic anion [HPO−24], and the tribasic anion [PO−34]), present in varying proportions depending on the pH of the medium (Christian 1980). Of phosphoric acid's 3 pKa values, the equilibrium concentrations of the monobasic and dibasic anions are governed by the 2nd pKa value (pK2) between approximately pHs 4.5 and 9. Because buffer type and concentration influence the rates of aspartame degradation (Tsoubeli and Labuza 1991; Bell and Wetzel 1995), it is important to take into account the catalysis by the buffer salts when evaluating the effect of pH and pKa on the rate constant.
Based on the above-mentioned degradation pathways, the pseudo-1st-order rate constant for aspartame degradation, kobs, can be expressed using the following equation for an acid-base catalyzed reaction
where ko (rate constant for the uncatalyzed reaction) equals 1 × 10−7 min−1, k[H+] (rate constant for catalysis by hydronium ions) equals 0.00146 M−1 min−1, and k[OH−] (the rate constant for catalysis by hydroxyl ions) equals 79.8 M−1 min−1, as previously determined at 25 °C by Bell and Wetzel (1995). In addition, [H+], [OH−], [H2PO−4], and [HPO−24] are the molar concentrations of hydronium ions, hydroxyl ions, monobasic phosphate ions, and dibasic phosphate ions, respectively. Using the measured pH, [H+] and [OH−] are calculated, assuming an activity coefficient (γ) equal to one. Because pH actually measures hydrogen ion activity (aH), γ is required to convert these into hydrogen ion concentrations ([H+]= aH/γ) for the kinetic expressions. From the pH and the apparent pKa value of phosphate buffer, [H2PO−4] and [HPO−24] can be calculated using the Henderson–Hasselbach equation. The terms kA1 and kA2 are the rate constants for the formation of α-AP catalyzed by the monobasic and dibasic phosphate ions, respectively, while kD1 and kD2 are the rate constants for the formation of DKP catalyzed by the monobasic and dibasic phosphate ions, respectively. The term fNH2 is the fraction of aspartame having the amine group unprotonated (the required molecular conformation leading to DKP formation). This term is calculated using the pKa value of 7.9 for aspartame's amine group (Skwierczynski and Connors 1993) and the measured pH of the system; algebraic rearrangement of the Henderson–Hasselbach equation yields the following equation
As mentioned previously and verified experimentally, DKP was the only measurable degradation product in the dibasic phosphate buffer solutions (pH > 7). This finding is consistent with those reported in the literature for solutions having alkaline pH values (Prudel and others 1986; Gaines and Bada 1988; Pattanaargson and Sanchavanakit 2000). The amount of α-AP was negligible, so kA2, the rate constant for the formation of α-AP catalyzed by the dibasic phosphate anion, was taken as zero and omitted from Eq. 1. Thus, the kinetic equation for aspartame degradation in dibasic phosphate buffer becomes
Defining k′ as (ko+k[H+][H+]+k[OH−][OH−]), substituting into Eq. 3, and rearranging the equation, one arrives at
A plot of (kobs−k′) as a function of (fNH2[HPO−24]) gave a straight line with a slope of 0.271 (that is, kD2= 0.271 M−1 min−1) and an R2 value of 0.999. The standard error associated with kD2 was 2.0 × 10−5.
Similarly, the rate constants for the formation of α-AP (kA1) and DKP (kD1) catalyzed by monobasic phosphate buffer were determined using the following equation
Using nonlinear regression to fit the experimental data to Eq. 5, the values of kA1 and kD1 were determined to be 3.98 × 10−5 and 2.33 × 10−2 M−1 min−1, respectively. The R2 value for this nonlinear regression model was 0.995. The standard errors associated with kA1 and kD1 were 3.4 × 10−6 and 6.7 × 10−3, respectively.
Substituting the values of the rate constants for catalysis by dibasic and monobasic phosphate buffer into Eq. 1, the final mathematical equation for modeling aspartame degradation in phosphate buffer at 25 °C becomes
It should be pointed out that this equation is unique to aspartame degradation in phosphate buffer at 25 °C. Equation 6 is not applicable to the reaction occurring in a different buffer type or at a different temperature. The above-mentioned kinetic model will be used to evaluate how the polyol-induced changes in buffer pKa and pH values affect aspartame degradation, an acid-base catalyzed reaction; this discussion will be presented in detail subsequently.
The experimentally determined rate constants were compared to those predicted from Eq. 6 using linear regression to determine slopes and R2 values. Pearson's product moment correlation coefficient and the significance of the correlations between experimental and predicted kinetic data were then evaluated.