Article pubs.acs.org/molecularpharmaceutics
Stability of Sugar Solutions: A Novel Study of the Epimerization Kinetics of Lactose in Water Rim Jawad,† Alex F. Drake,† Carole Elleman,‡ Gary P. Martin,† Frederick J. Warren,§ Benjamin B. Perston,∥ Peter R. Ellis,⊥ Mireille A. Hassoun,† and Paul G. Royall*,† †
Institute of Pharmaceutical Science, King’s College London, Franklin-Wilkins Building, 150 Stamford Street, London SE1 9NH, U.K. The Reading Science Centre, Reading Scientific Services, Ltd., Whiteknights Campus, Pepper Lane, Reading RG6 6LA, U.K. § Centre for Nutrition and Food Sciences, Queensland Alliance for Agriculture and Food Innovation, The University of Queensland, St. Lucia, Brisbane, Queensland 4072, Australia ∥ PerkinElmer, Chalfont Road, Seer Green, Buckinghamshire HP9 2FX, U.K. ⊥ Biopolymers Group, Diabetes and Nutritional Sciences Division, King’s College London, Franklin-Wilkins Building, 150 Stamford Street, London SE1 9NH, U.K. ‡
ABSTRACT: This article reports on the stereochemical aspects of the chemical stability of lactose solutions stored between 25 and 60 °C. The lactose used for the preparation of the aqueous solutions was α-lactose monohydrate with an anomer purity of 96% α and 4% β based on the supplied certificate of analysis (using a GC analytical protocol), which was further confirmed here by nuclear magnetic resonance (NMR) analysis. Aliquots of lactose solutions were collected at different time points after the solutions were prepared and freeze-dried to remove water and halt epimerization for subsequent analysis by NMR. Epimerization was also monitored by polarimetry and infrared spectroscopy using a specially adapted Fourier transform infrared attenuated total reflectance (FTIR-ATR) method. Hydrolysis was analyzed by ion chromatography. The three different analytical approaches unambiguously showed that the epimerization of lactose in aqueous solution follows first order reversible kinetics between 25 to 60 °C. The overall rate constant was 4.4 × 10−4 s−1 ± 0.9 (± standard deviation (SD)) at 25 °C. The forward rate constant was 1.6 times greater than the reverse rate constant, leading to an equilibrium constant of 1.6 ± 0.1 (±SD) at 25 °C. The rate of epimerization for lactose increased with temperature and an Arrhenius plot yielded an activation energy of +52.3 kJ/ mol supporting the hypothesis that the mechanism of lactose epimerization involves the formation of extremely short-lived intermediate structures. The main mechanism affecting lactose stability is epimerization, as no permanent hydrolysis or chemical degradation was observed. When preparing aqueous solutions of lactose, immediate storage in an ice bath at 0 °C will allow approximately 3 min (180 s) of analysis time before the anomeric ratio alters significantly (greater than 1%) from the solid state composition of the starting material. In contrast a controlled anomeric composition (∼38% α and ∼62% β) will be achieved if an aqueous solution is left to equilibrate for over 4 h at 25 °C, while increasing the temperature up to 60 °C rapidly reduces the required equilibration time. KEYWORDS: lactose, stability, epimerization, anomer purity, first order reversible kinetics, NMR, polarimetry, FTIR-ATR
1. INTRODUCTION Lactose is one of the most frequently used excipients present in marketed medicines and hence a complete understanding of its stability in solution should be regarded as vital for improving the pharmaceutical reproducibility of both previously developed and new drug delivery systems. The epimerization of lactose, © 2014 American Chemical Society
Received: Revised: Accepted: Published: 2224
August 23, 2013 February 13, 2014 May 9, 2014 May 9, 2014 dx.doi.org/10.1021/mp400509t | Mol. Pharmaceutics 2014, 11, 2224−2238
Molecular Pharmaceutics
Article
Figure 1. α-Lactose (A) and β-lactose (B) images captured by an optical microscope-using plane polarized light (25× magnification).
typically used in the manufacture of tablets is very dependent on anomer composition5 and the fine particle fraction of inhaled drugs from DPIs increases in the order of αmonohydrate > β anhydrous > α anhydrous when these forms of lactose are used as carrier particles.6 Lactose, a disaccharide that consists of β-D-galactose and α/ β-D-glucose fragments bonded through a β-1,4 glycosidic linkage, is isolated typically from aqueous emulsions (e.g., milk).17 It is often used as a component with the active pharmaceutical ingredient in water-based pharmaceutical processing methods including, for example, wet granulation or spray-drying.10,18−21 The two isomeric forms of lactose differ in the configuration of the hydroxyl group at the anomeric
which is used in half of all tablets and three-quarters of all dry powder inhalers (DPIs) dispensed worldwide,1−4 is not frequently considered or is incorrectly described in terms of the interchange between polymorphic forms within the pharmaceutical literature.5−8 The anomers, α- and β-lactose, are different molecular species, which may exist both in the solid-state and in solution. Recent work9,10 as well as that described in earlier literature,11−16 has shown that the isomeric composition of the solid forms of lactose is greatly influenced by the properties of the solution before the crystallization or the drying step is initiated. These different isomers have a major bearing on the critical quality attributes of the final drug product.9 For example, the compressibility of lactose samples 2225
dx.doi.org/10.1021/mp400509t | Mol. Pharmaceutics 2014, 11, 2224−2238
Molecular Pharmaceutics
Article
Table 1. Summary of the Previously Reported Parameters Relating to the Epimerization of Lactose under the Conditions Specified; All Were Obtained Using Polarimetry ref
concentration and source of water used
Kendraw et al. (1940)51
6% w/v in distilled water
Haase et al. (1966)29
5% w/v in distilled water
Patel et al. (1970)27
4−5% w/v (no information concerning purity of water)
equilibrium constant K T (°C) 25 30 35 40 45 49
forward k1/reverse k2 rate constant s−1
K 1.64 1.65 1.73 1.73 1.77 1.80
6% w/v (no information concerning purity of water)
Majd et al. (1978)41
1−8% w/v in distilled water 1.7
carbon C1 of the glucopyranose ring.22 The equilibrium between the α- and β-forms will influence the molecular species present when lactose is isolated from water (Figure 1 and refs 8 and10). Lactose may exist in one of 3 crystalline forms, which are α-lactose monohydrate, α-lactose anhydrous, and β-lactose anhydrous, and the α- and β-anomers will be present in the amorphous solid forms of lactose. It is very difficult to isolate the pure forms of the amorphous anomers; however, some authors have achieved this but only rarely, for example, Willart et al.32 However, in these cases, the anomeric purity is always dependent on the means of manufacture, and the work of Willart et al.32 and Jawad et al.10 has shown that the production method will influence the β/α ratio, with solution-based methods suffering more chance of the epimerization ratio changing. The different anomeric forms of lactose show distinct properties, for example, the crystalline α- and β-anomers of lactose have different solubilities. The solubility of α-lactose monohydrate is 7 g/100 mL, whereas the solubility of β-lactose is 50 g/100 mL. This may explain the difference in sweetness between both forms23,24 and is likely to account for some of the batch-to-batch differences in the dissolution rates of lactosecontaining tablet formulations.25,26 The transformation of one anomer into its chiral counterpart is called epimerization and when monitored by polarimetry the term mutarotation is used.22 As a result of epimerization, the final anomer equilibrium for aqueous solutions of lactose obtained typically after 4 h is reported to be 40% α-lactose and 60% β-lactose at room temperature.10 Other workers have reported slight differences in this ratio, for example, 37% αlactose and 63% β-lactose at room temperature.17 Such differences can be attributed to variability in lactose purity, pH, source of water, and the analytical methods employed. The literature data presented in Table 1 shows that lactose epimerization is often considered to be a first order process
k1 = 0.8 × 10−4; k2 = 0.5 × 10−4
overall rate constant k s−1 T (°C) 25 30 35 40 45 49 T (°C) 0.5 15 25 45 55 T (°C) 25 30 35 T (°C) 25 30 35 T (°C) 25
k (s−1) 1.9 × 10−4 3.1 × 10−4 4.8 × 10−4 7.5 × 10−4 11.4 × 10−4 16.0 × 10−4 k (s−1) 0.2 × 10−4 1.2 × 10−4 3.0 × 10−4 17.2 × 10−4 37.9 × 10−4 k (s−1) 1.2 × 10−4 2.2 × 10−4 3.8 × 10−4 k (s−1) 1.3 × 10−4 2.2 × 10−4 3.8 × 10−4 k (s−1) 1.3 × 10−4
having been investigated solely using polarimetry. However, the reversible nature of lactose epimerization is seldom investigated as indicated by the lack of reported forward and reverse rate constants.27−29 This paucity of important information is caused by the difficulty in separating the forward and reverse rate constants from polarimetric results since the analysis of the data is cumbersome. Without knowledge of the α/β ratio at the beginning and at the end of the reaction, it is impossible to determine accurately both the forward and the reverse rates constants. Jenness et al. 30 reported that the rate of epimerization increases 2.8-fold with a 10 °C increase in temperature. These workers also referred to the early work of Hudson,31 who reported that the conversion from the α- to the β-anomer in aqueous solution is 51.1% complete after 1 h at 25 °C, 17.5% complete after 1 h at 15 °C, and 3.4% complete after 1 h at 0 °C.31 All of these studies also relied on the application of polarimetry, without the utilization of any alternative technique to confirm the findings. Moreover, none of the previous studies have analyzed the β/α ratios of the starting material, which may have biased the results. In all these previous studies, it was declared or assumed that the starting material was 100% α. However, Jawad et al.10 have successfully determined that the purest commercially available forms of αlactose monohydrate contained a 4% impurity of the β-anomer, as determined by nuclear magnetic resonance (NMR). Accordingly a study employing a known starting molecular composition of lactose would be expected to improve the accuracy of stability determinations. There is no contemporary or historical paper available that has reported the influence of temperature on the equilibrium constant and the forward, reverse, and overall rate constants for the epimerization of lactose in aqueous solution (Table 1). The aim of the work described in this article was to investigate the epimerization kinetics of α-lactose monohydrate 2226
dx.doi.org/10.1021/mp400509t | Mol. Pharmaceutics 2014, 11, 2224−2238
Molecular Pharmaceutics
Article
Table 2. Optical Rotation Values of Solutions Employed in the Calibration of the Chirascan Spectrometer at Temperatures of 25, 45, and 60 °C; Experiments Were Performed on the Same Day and 1% w/v Sucrose Aqueous Solution (Freshly Prepared) Was Used (Values Are Reported at a Wavelength λ = 589 nm) optical rotation (n = 3, ±SD) sucrose air water
25 °C
45 °C
60 °C
66.2 ± 0.02 deg −9.0 ± 0.4 mdeg −16.0 ± 0.14 mdeg
62.1 ± 0.05 deg −10.2 ± 0.15 mdeg −17.9 ± 0.36 mdeg
61.7 ± 0.06 deg −9.3 ± 0.4 mdeg −17.8 ± 0.07 mdeg
epimerization or possible chemical degradation. The resulting samples were analyzed by ion chromatography (IC) for the detection of any potential inversion products, i.e., galactose and glucose formed after irreversible hydrolysis.33,34 As the amounts of inversion products were expected to be low, the sample preparation involved adding 1 mL of water to 40 mg of the lactose material (in powder solid form) and then injecting the obtained solution into the IC. Samples from the derived freezedried lactose batches after incubation at the two respective temperatures were compared to samples from the α-lactose monohydrate as received. 2.4. PerkinElmer Polarimeter 343 Measurements. A PerkinElmer 343 polarimeter equipped with a sodium lamp (λ = 589 nm) was used with the proprietary 10 cm sample cell. The polarimeter was prepared for calibration by zeroing the instrument with an empty cell compartment. Any (ideally negligible) optical rotation for a cell full of water was taken as a baseline and subtracted from all optical rotations measurements. The polarimeter was calibrated with a 1% w/v sucrose solution and measuring the rotation in triplicate as recommended by the instrument manufacturer.35−37 The temperature was kept constant at room temperature (25 ± 2 °C) by circulating water through the cell jacket; temperature was monitored by a Comark C9003 thermometer. Lactose solutions (4% w/v) were prepared by weighing 0.4 g of α-lactose monohydrate into a 10 mL volumetric flask and made up with water. In practice, the actual weight of the αanomer is 0.384 g corresponding to the 96% α-lactose content confirmed by NMR.10 The samples were prepared at room temperature (25 ± 2 °C). The zero time point was recorded as the initial time of mixing, i.e., when the first drop of water touched the lactose powder. The α-lactose monohydrate solution was shaken for 3 min (180 s) to ensure complete dissolution of the lactose powder and to obtain a clear lactose solution. Each solution was prepared and measured in triplicate at room temperature (25 ± 2 °C). The optical rotation readings were recorded over a period of 4 h with a final measurement recorded on the following day. 2.5. Chirascan Spectrometer Measurements. The current article discusses lactose epimerization kinetics followed at higher temperatures (45 and 60 °C). The PerkinElmer polarimeter equipped with a relatively large volume, long path length 10 cm cell and having a slow instrumental response is not ideal for monitoring higher temperature, faster processes. Accordingly, optical rotation measurements were transferred to the Chirascan. The Chirascan is a polarization modulation spectrometer fitted with variable temperature facilities and able to measure optical rotation at any wavelength in the UV/vis wavelength region.38 Set to 100 kHz linear polarization modulation with a calcite polarizer prism as the analyzer, the Chirascan becomes a very sensitive polarimeter capable of measuring optical rotation at any wavelength in the UV/vis region. Chirascan set up and
as a function of temperature by determining unambiguously the forward, reverse, and overall rate constants using a range of analytical techniques.
2. MATERIALS AND METHODS Lactose used for the preparation of the aqueous solutions was α-lactose monohydrate (SigmaUltra). The stated anomer purity from the suppliers was 96% α and 4% β based on the supplied certificate of analysis using a gas chromatography (GC) analytical protocol. The α-lactose monohydrate was used as received with anomer purity confirmed by proton NMR analysis. High-performance liquid chromatography (HPLC) grade water was used throughout (Fisher Scientific). Phosphorus pentoxide P2O5 (≥98.5%) was supplied by Sigma-Aldrich. 2.1. Freeze-Drying of α-Lactose Monohydrate Solutions. Stock aqueous 4% w/v solutions of α-lactose monohydrate were prepared, with the point of mixing the solid lactose with the HPLC grade water taken as time zero. A 4% w/v lactose concentration was used as the solubility of lactose (at 25 °C) is limited to 7 g/100 mL.17 The stock solutions were held for 4 h at each of the following temperatures: 25, 45, and 60 °C using temperature controlled water baths. Aliquots of lactose solution (2 mL) were collected at different time points and placed in 7 mL glass sample jars. These were freeze-dried using a Varian freeze-dryer Girovac model GVD4. The freeze-drying process involved a prefreezing step at −80 °C, a primary drying step for 72 h employing a temperature of −50 °C, and vacuum pressure of 0.06 mbar, then secondary drying over P2O5 for 48 h at 25 °C. 2.2. NMR of Freeze-Dried Lactose. NMR samples were prepared by dissolving 3−4 mg of lactose in 0.7 mL of dimethyl sulfoxide-d 6 (DMSO) 99.9% at %D with 0.05% v/v trimethylsilane (TMS) (Goss Scientific instruments Ltd.). One-dimensional 1H spectra were recorded on a Bruker Avance 400 MHz spectrometer equipped with a QNP probe. The temperature was maintained at 298 K. Scans (n = 16) were recorded using a standard zg 30 pulse sequence with a 1 s recycle delay. The 30° pulse length was 3.43 μs. The sweep width was set to 20.69 ppm, and the acquisition time was 3.96 s. Spectra were processed and analyzed using the Bruker Topspin software. The free induction decay was multiplied with an exponential function corresponding to a line broadening of 0.3 Hz, and spectra were phase corrected manually prior to an automatic baseline correction. Peaks were integrated using the β-lactose peak as a reference by defining its peak area as 1. The ratios of the two areas were compared.32 2.3. Chemical Purity of Lactose. Prior to investigating the epimerization kinetics of lactose, it was essential to detect any possible chemical degradation upon exposure to the relatively high temperatures for long periods of time (∼4 h). Therefore, 4% w/v lactose solutions were held at 45 and 60 °C for 4 h and then freeze-dried to remove water and halt any further 2227
dx.doi.org/10.1021/mp400509t | Mol. Pharmaceutics 2014, 11, 2224−2238
Molecular Pharmaceutics
Article
2.6. Fourier Transform Infrared Spectroscopy Measurements with Attenuated Total Internal Reflectance (FTIR-ATR). All FTIR-ATR measurements were obtained using a PerkinElmer Spectrum 2 spectrometer fitted with a resistively heated Pike MIRacle single reflection ATR device, with a ZnSe crystal. Data were collected using a PC running PerkinElmer Timebase software, and the same PC was used to run Pike TempPro software, which controlled the temperature of the ATR crystal. All samples were prepared by weighing 0.04 g of lactose into a microfuge tube and adding 1 mL of double deionized Milli-Q water (18.2 MΩ·cm) at 4 °C. The samples were mixed for 2.5 min (150 s), when clear solutions were formed. A sample of 100 μL was pipetted into a PTFE well such that the solution was in direct contact with the ATR crystal, and a glass microscope slide was clamped in place on top of the well to minimize water loss. The Timebase software collected data (one spectrum every ∼7.5 s) as the sample was added to the crystal; so that spectra were collected from the moment the sample came into contact with the crystal. Spectra were collected from 4000 to 650 cm−1 at a resolution of 4 cm−1. A background spectrum of 8 coadded scans was collected after cleaning the crystal with water and isopropanol. A calibration set of lactose samples with differing β/α ratios were prepared by weight, using samples of α- and β-lactose. The β/α ratios of the “pure” α and β initial samples were determined by 1H NMR as described above. Spectra were measured for each of the calibrants at 25, 45, and 60 °C. A solution of each calibrant was prepared as described above, and the first 6 stable spectra after adding solution to the crystal were collected and coadded. Each calibrant was measured in triplicate at each temperature. A partial least-squares (PLS) calibration model was then developed for the data at each temperature, using PerkinElmer Quant+ software. First derivative (13 point smoothing) spectra were standard normal variate (SNV) normalized (without detrending), and the PLS1 algorithm was applied to the data within the spectral range 1200 to 900 cm−1. This resulted in the generation of calibration models for a range of lactose β/α ratios at 25, 45, and 60 °C. These were used to predict β/α ratios for solutions of α-lactose monohydrate over time at 25, 45, and 60 °C using the Quant feature in PerkinElmer Spectrum 10 software.
calibration with 1% w/v sucrose were according to the spectrometer manual. With an empty sample compartment, the calcite prism analyzer was rotated to produce an optical rotation signal as close to zero as reasonably possible (≤5 mdeg). Subsequent measurements of water in the measurement cell were taken as the baselines for associated measurements. Air measurements continued until stability had been reached, while all the calibration measurements (water and sucrose) were performed in triplicates at 25, 45, and 60 °C at the beginning of each working session. The temperature variations had no significant impact on the optical rotations of both air and water. However, the optical rotation of sucrose demonstrated a modest decreasing trend as the temperature increased (Table 2). Conventionally, lactose optical rotation values found in the literature have been determined with respect to a 10 cm cell and refer to ambient temperature (20 to 25 °C) and the NaD line (λ = 589 nm) of a sodium lamp.35−37 The Chirascan spectrometer is equipped with a xenon lamp and a sample cell thermosetting facilities. To ensure good fastresponding thermal properties for faster kinetics studies, a 2 mm path length cell was chosen. This implies a measured optical rotation at 589 nm, 50 times less than that obtained with the dedicated benchtop PerkinElmer polarimeter. However, optical rotation increases significantly at shorter wavelengths. The wavelength of 313 nm (with a spectral bandwidth of 2 nm) matches the Hg line often used in benchtop instruments. The optical rotation of equilibrated 4% w/v lactose solutions measured on the Chirascan spectrometer with λ = 589 nm was found to be 165°, while the optical rotation signal value at 313 nm was found to be 750°, a 4.5-fold increase in optical rotation signal. The choice of 313 nm as the analytical wavelength and 2 mm as the sample cell path length results in a ∼10-fold reduction in the magnitude of the optical rotation signal compared with the PerkinElmer polarimeter with a 10 cm path length and λ = 589 nm. However, this is well compensated for by the inherent greater detectability of the Chirascan. The Applied Photophysics software was used to drive the Chirascan, and the associated Pro-Data viewer was used to analyze the results. All previously published polarimetry data associated with lactose solutions were obtained at λ = 589 nm. Therefore, the optical rotation values obtained at λ = 313 nm using the Chirascan were divided by a factor of 4.5 to produce an optical rotation value that was equivalent to values measured at λ = 589 nm and thus could be compared with values reported in the literature (at the same wavelength). The rate of epimerization was expected to increase with temperature and so the following protocol was used to minimize data loss at the beginning of each experiment. An empty cuvette was placed in the instrument to incubate at the desired set temperature. The aqueous lactose solution was prepared using HPLC grade water equilibrated in a fridge (4 °C) with the container surrounded by an ice bath (∼0 °C). This was done to slow the mutarotation process at the early stages of mixing.39 The solution was mixed for 2.5 min (150 s) to ensure complete dissolution. A 300 μL aliquot of this solution was pipetted into the prewarmed cuvette, and once the temperature probe indicated that the contents of the cuvette had reached the required temperature, the optical rotation was recorded as a function of time. The length of time from solution preparation to the first data point recorded was approximately 3 min (180 s).
3. RESULTS 3.1. Chemical Purity of Lactose. The amounts of the monomers glucose and galactose present in all of the samples of lactose analyzed by IC were minimal, all below 0.02% w/w (Table 3). Thus, negligible irreversible hydrolysis or degradation had taken place over the range of temperatures investigated, even up to 60 °C. 3.2. NMR of Freeze-Dried Lactose. A plot of the αanomer content (% w/w) vs time produced an exponential decay where all samples produced similar final equilibrium of β/α anomeric ratio (Figure 2; Table 4) independent of storage temperature. However, the rate of decay varied between the three storage temperatures. To confirm similarity in the equilibrium β/α ratio of α-lactose monohydrate at 25, 45, and 60 °C, three solutions (in duplicate) of 4% w/v α-lactose monohydrate were stored, each set of duplicates at 25, 45, and 60 °C, respectively, for 4 h prior to the prefreezing stage of freeze-drying. Once freeze-drying was completed, the NMR spectra of the lactose samples in DMSO were recorded immediately. The equilibrium β/α ratios, determined using the 2228
dx.doi.org/10.1021/mp400509t | Mol. Pharmaceutics 2014, 11, 2224−2238
Molecular Pharmaceutics
Article
where k1 is defined as the forward rate constant and k2 is the reverse rate constant. The rate of the decomposition of the reactant A can be expressed as follows:42,43
Table 3. Analysis by Ion Chromatography of Lactose Degradation Products (Glucose and Galactose) at 25 °C and the Freeze-Dried Products after Incubation of Solutions at 45 and 60 °C for 4 h lactose lactose as-received (25 °C) lactose (freeze-dried 45 °C) lactose (freeze-dried 60 °C)
sugars
content mg/kg of lactose sample
content (%w/w)
glucose galactose glucose galactose glucose galactose
123 115 135 133 148 129
0.0123 0.0115 0.0135 0.0133 0.0148 0.0129
−d[A] d[B] = = k1[A] − k 2[B] dt dt
(1)
[B]eq k1 = =K [A]eq k2
(2)
where [A] is the concentration of the reactant, in this case αlactose monohydrate; [B] is the concentration of the product βlactose. K is the equilibrium constant calculated as the ratio of the forward and reverse rates.10,42 ln
[B]eq [B]eq − [B]t
= (k 1 + k 2 )t
(3)
Equation 3 is an integrated form of eq 1, where [B]t is the % w/ v concentration of β-anomer at time t and [B]eq is the % w/v concentration of β-anomer at equilibrium. These values were easily determined from the NMR data (Figure 2) by acknowledging that the percentage content w/w of both anomers must equal 100% because the percentage impurities measured by IC were minimal, i.e., 0.02% w/w. Plots of ln ([B]eq/([B]eq − [B]t)) versus time produced straight lines, for example, the plot using the 25 °C data produced a correlation coefficient r2 value of 0.996. Therefore, the epimerization kinetics of lactose fits the reversible first order rate equation. For the 25 °C data, the slope of the straight lines obtained (k1 + k2) and thus the overall rate constant for epimerization at 25 °C determined by NMR was 6 × 10−4 s−1 (SD < 0.1, n = 3). The forward and reverse rate constants were calculated using both the overall rate constant (k1 + k2) and the equilibrium constant K by substituting these into a rearranged version of eq 2 creating 2 simultaneous equations. The same approach was applied to the NMR data gathered from the 45 and 60 °C experiments, and the equilibrium constants, overall, forward and reverse rates constants are reported in Tables 5 and 6. 3.3. Optical Rotation of Lactose at 25 °C. The optical rotation of lactose solutions was determined at 25 ± 2 °C using both a PerkinElmer polarimeter and Chirascan spectrometer (Figure 3). The specific rotation of α-lactose was calculated using the observed optical rotation by employing the following equation:
Figure 2. α-Anomer content of freeze-dried lactose (determined by NMR) for a 4% w/v α-lactose solution prepared at 25 °C (black ●), 45 °C (blue ▲), and 60 °C (red ■).
method reported earlier,10 are listed in Table 4, and these values indicated that the equilibrium constant for the epimerization of lactose is approximately 1.5 by NMR over the temperature range studied, e.g., K at 25 °C = 1.43 ± 0.08 (mean ± standard deviation (SD)). The epimerization mechanism of lactose has been reported by many authors to follow first order kinetics.28,29,40 However, the hypothesis applied here and by Majd et al.,41 is that the mechanism should be represented by first order reversible kinetics as follows:
[αObs]D =
k1
A⇌B k2
OR × 100 lC
(4)
where [αObs]D is the specific rotation in degrees recorded by the PerkinElmer polarimeter at wavelength of sodium lamp light source λ = 589 nm, OR is the observed optical rotation, l is the path length in dm, and C is the concentration in % w/v. When
k1
α ‐lactose ⇌ β ‐lactose k2
Table 4. Equilibrium β/α Anomeric Ratio of Freeze-Dried Lactose Samples, as Removed from Solutions Incubated at Different Temperatures, as Determined by NMR (3 Batches at Each Temperature Were Prepared and Each Batch Was Sampled 3 Times Using NMR) 25 °C mean SD
45 °C
60 °C
β%
α%
β/α
β%
α%
β/α
β%
α%
β/α
59.0 1.3
41.0 1.3
1.43 0.08
60.9 0.5
39.1 0.5
1.55 0.03
60.6 0.14
39.4 0.14
1.53
