Thermodynamics of Dissolution of Calcium Hydroxycarboxylates in

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Thermodynamics of Dissolution of Calcium Hydroxycarboxylates in Water Martina Vavrusova,† Ran Liang,‡ and Leif H. Skibsted*,† †

Food Chemistry, Department of Food Science, University of Copenhagen, Rolighedsvej 30, DK-1958 Frederiksberg C, Denmark Department of Chemistry, Renmin University of China, Beijing 100872, China

‡

ABSTRACT: Aqueous solubility of calcium L-lactate, calcium D-gluconate, and calcium D-lactobionate increases with temperature (10−30 °C investigated), most significantly for the least soluble D-gluconate, while the calcium ion activity of the saturated solutions decreases with temperature, as measured electrochemically, most significantly for the most soluble Dlactobionate. This unusual behavior is discussed in relation to dairy processing and explained by endothermic binding of calcium to hydroxycarboxylate anions determined to have ΔH°ass = (31 ± 3) kJ·mol−1 for L-lactate, (34 ± 2) kJ·mol−1 for D-gluconate, and (29 ± 3) kJ·mol−1 for D-lactobionate in 1:1 complexes with thermodynamic binding constants at 25 °C of Kass = 49 (Llactate), 88 (D-gluconate), and 140 (D-lactobionate). Quantum mechanical calculations within density functional theory (DFT) confirm the ordering of strength of binding. The complex formation is entropy driven with ΔS°ass > 0, resulting in decreasing calcium ion activity in aqueous solutions for increasing temperature, even for the saturated solutions despite increasing solubility. KEYWORDS: calcium L-lactate, calcium D-gluconate, calcium D-lactobionate, calcium ion activity, endothermic calcium binding

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supersaturated calcium salt solutions.6,16 Accordingly, we now report the results of investigations of calcium speciation in saturated solutions of calcium L-lactate, calcium D-gluconate, and calcium D-lactobionate combining electrochemical determination of calcium ion activity at varying temperature with quantum mechanical calculations of calcium binding to hydroxycarboxylate anions.

INTRODUCTION Dairy products are an important source of dietary calcium, and calcium binding to the caseins and to proteins, peptides, and anions of the serum phase of milk prevents precipitation on calcium salts in the intestines during digestion ensuring high bioavailability of calcium.1−4 Calcium is also important for structure development in fermented milk products and in cheeses as calcium binds electrostatically to caseins initiating protein network formation for conditions of decreasing pH and during enzymatic protein hydrolysis.5−9 An understanding of calcium binding to other milk components and to components added to dairy products or formed during milk processing accordingly is important both for improvement of dairy technology and for optimizing calcium bioavailability of dairy products.10,11 Notably, it was recently shown that cooling of acidified skim milk for cheese production resulted in increased concentration of free calcium at the expense of complex bound calcium in the milk serum phase indicating that calcium binding is an endothermic process most likely involving carboxylate groups of peptides or of hydroxycarbolylates.9 Mixtures of hydroxycarboxylates of relevance for dairy products have further been shown to result in increased solubility of sparingly soluble calcium salts like calcium lactate otherwise known to precipitate in some cheeses during maturation.11−14 Such synergistic effects on calcium hydroxycarboxylate solubility may for certain conditions of relevance for biomineralization even result in spontaneous formation of supersaturated solutions during isothermal dissolution.15 Such phenomena, which at a first glance seem to violate thermodynamics, invite further investigations of the dissolution processes of calcium hydroxycarboxylates. It seems also of importance to make distinctions not only between bound and free calcium, but for the free calcium also between calcium ion concentration and calcium ion activity for the saturated and © 2014 American Chemical Society

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MATERIALS AND METHODS

Chemicals. Calcium L-lactate pentahydrate, calcium D-gluconate monohydrate, calcium D-lactobionate monohydrate, anhydrous calcium chloride, and ammonium purpurate 5,5-nitrilodibarbituric acid were all from Sigma-Aldrich (Steinheim, Germany). Ethylenediaminetetraacetic acid disodium salt dihydrate (EDTA), sodium chloride, and sodium hydroxide were all from Merck (Darmstadt, Germany). All aqueous solutions were made from purified water from Milli-Q Plus (Millipore Corporation, Bedford, MA). Solubility Determination. Saturated aqueous solutions of calcium L-lactate pentahydrate and calcium D-gluconate monohydrate were prepared by combining 15.0 and 10.0 g with 100 mL of water, respectively, while 40.0 g of calcium D-lactobionate monohydrate was combined with 50 mL of water at 10 and 20 °C and with 35 mL at 30 °C. Equilibration time for each of the calcium salts to reach saturation was found to be less than 2 h under constant stirring at 10 °C, 20 °C, or 30 °C in a thermostated water bath. Samples were filtered (589/3, Whatman, Dassel, Germany) prior to each analysis. Total calcium concentration was determined by EDTA titration, and the calcium ion activity was determined by a calcium ion selective electrode for solutions of each of the three salts saturated at each of the three temperatures. pH was measured in the saturated solutions at the specified temperatures. All samples were prepared in duplicate. Received: Revised: Accepted: Published: 5675

March 31, 2014 May 26, 2014 May 28, 2014 May 28, 2014 dx.doi.org/10.1021/jf501453c | J. Agric. Food Chem. 2014, 62, 5675−5681

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EDTA Titration. Standardization of the EDTA solution for titration with the concentration of 0.0500 mol·L−1 was obtained against a 0.0200 mol·L−1 aqueous solution of CaCl2. 1.000 mL of sample was transferred to a titration flask and diluted with 40 mL of water. 2.0 mL of 2.0 mol·L−1 solution of NaOH was added to each sample to maintain basic pH, and 0.30 mL of 0.50% murexid solution was used as an indicator. Samples were titrated until the initial pink color changed to dark purple, indicating the end point. Electrochemical Measurement of Calcium Ion Activity. A calcium ion selective electrode ISE25Ca with a reference REF251 electrode from Radiometer (Copenhagen, Denmark) was calibrated using aqueous 1.00 × 10−4, 1.00 × 10−3, and 1.00 × 10−2 mol·L−1 CaCl2 solutions prepared from a 1.000 mol·L−1 CaCl2 stock solution at 10 °C, 20 °C, or 30 °C. Calcium ion activity, aCa2+, in the standard solutions was calculated based on the relationship between activity and concentration according to

aCa 2 + = cCa 2 +·γ 2 +

(1)

where γ2+ is the activity coefficient calculated from the Davies equation:17

⎛ ⎞ I log γ 2 + = − ADH z 2⎜ − 0.30I ⎟ ⎝1 + I ⎠

Figure 1. Calcium ion activity standardization of calcium selective electrode using the standard solutions of Table 1 based on the Davies equation. Slope of regression line at 10 °C is −29.6 mV−1 and at 30 °C −32.7 mV−1.

(2)

where ADH is the Debye−Hückel constant with the numerical value of ADH = 0.498, 0.506, or 0.515 at 10 °C, 20 °C, or 30 °C, respectively.17 For aqueous solution, z (=2) is the charge of the calcium ion, and I is the ionic strength. The ionic strength was calculated as follows, taking all ions present in the solution into account including the calcium hydroxycarboxylate complexes: I=

1 2

∑ cz 2

solubility.11,12,19−21 The solubility of calcium L-lactate at 10, 20, and 30 °C, as determined by complexometric titration, is presented in Table 2, and the solubility of calcium D-gluconate and calcium D-lactobionate in Tables 3 and 4, respectively. The overall dissolution process for each of the three calcium hydroxycarboxylates is accordingly endothermic with ΔH°dissol > 0, as for most food related calcium salts in water, except calcium sulfate, where a solid state phase transition around 40 °C makes the temperature dependence more complicated.22 Calcium D-gluconate, the least soluble of the three hydroxycarboxylates investigated, showed a solubility ratio of 1.9 for the temperature interval of 20 °C investigated, the highest temperature sensitivity, while calcium D-lactobionate as the most soluble showed the lowest temperature sensitivity corresponding to a factor of 1.3. The solubility ratio for calcium D-gluconate and for calcium D-lactobionate was calculated by dividing the highest solubility by the lowest solubility to give an impression how much the solubilities of the investigated calcium hydroxycarboxylates will change with temperature. The calcium ion activity of the saturated aqueous solutions of the three calcium hydroxycarboxylates showed opposite trends. The measured activities were based on activity standards correcting the calcium ion concentration according to the Debye−Hückel theory using the Davies equation for single ion activity.17,23 Notably, activity standardization has to be performed at the actual temperature of measurement, and it is encouraging that the electrode response is in agreement with the Nernst equation and with an increasing slope for increasing temperature, see Figure 1. For each of the three calcium hydroxycarboxylates, the calcium activity in the saturated solution decreased with increasing temperature, which is remarkable, since the solubility increased. For the most soluble calcium D-lactobionate the effect was the largest, but still for calcium L-lactate and calcium D-gluconate, the effect is significant, compares Table 2, 3, and 4. In order to understand this unusual effect of decreasing calcium ion activity for increasing calcium hydroxycarboxylate concentration, the calcium speciation needs to be considered. The dissolution of each of the three calcium hydroxycarboxylates occurs stepwise,11,17,23

(3)

The calcium ion activities of the standard solutions at 10 °C, 20 °C, or 30 °C may be found in Table 1. In the samples, the calcium ion

Table 1. Calcium Ion Activities in Standard Solutions at 10, 20, And 30 °C As Calculated According to Davies’ Equation.17 pCa = −log aCa2+ cCa2+/mol·L−1 −4

1.00 × 10 1.00 × 10−3 1.00 × 10−2

10 °C

20 °C

30 °C

4.034 3.102 2.276

4.034 3.103 2.281

4.035 3.105 2.286

activity, aCa2+, was calculated from the linear relationship according to the Nernst equation between the electrode potential (in mV) measured for the calibration solutions and pCa (=−log aCa2+) of the calibration solution, see Figure 1. DFT Calculation. Geometries of calcium hydroxycarboxylates in aqueous solutions were optimized using the Gaussian 09 package18 on the basis of the B3LYP method combined with polarizable continuum model (PCM) at the 6-31G** level. Calcium binding enthalpies were calculated on the basis of stationary point energies of the calcium complexes and the hydroxycarboxylate anions at their optimized geometries, respectively, and relative association rate constants were calculated based on the approximation of

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ΔHbinding ≈ ΔG binding = − RT ln K rel

(4)

RESULTS AND DISCUSSION The aqueous solubility of the three calcium hydroxycarboxylates investigated for the temperature interval 10 to 30 °C in relation to calcium speciation and calcium salt precipitation in dairy products increased for increasing temperature and was in fair agreement with previous reports of calcium salt 5676

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Table 2. Solubilities and the Thermodynamic Association Constants of Calcium L-Lactate in Aqueous Solutions at 10, 20, and 30 °Ca temp (°C)

pH

solubility (g/ 100 mL)

cCa2+ (mol·L−1)

aCa2+

I

γCa2+

[Ca2+] (mol· L−1)

[CaLact+] (mol· L−1)

[Lact−] (mol· L−1)

Kass

10 20 30

6.3 6.2 6.2

4.8 ± 0.1 5.8 ± 0.1 8.50 ± 0.02

0.219 ± 0.003 0.266 ± 0.004 0.390 ± 0.001

0.021 ± 0.002 0.016 ± 0.001 0.013 ± 0.001

0.36 0.38 0.48

0.294 ± 0.001 0.28767 ± 0.00002 0.2844 ± 0.0002

0.07 ± 0.01 0.056 ± 0.002 0.047 ± 0.002

0.149 ± 0.004 0.21 ± 0.01 0.342 ± 0.003

0.29 ± 0.01 0.323 ± 0.001 0.437 ± 0.002

25 ± 4 40 ± 3 59 ± 4

Calcium ion activity, aCa2+, was determined electrochemically. Free calcium ion concentration, [Ca2+], activity coefficient, γCa2+, free lactate concentration, [Lact−], the calcium complex concentration [CaLact+], and the resulting ionic strength, I, were calculated by an iterative procedure.

a

CaL 2(s) ⇌ CaL+ + L−

(5)

CaL+ ⇌ Ca 2 + + L−

(6)

speciation seen for the three calcium hydroxycarboxylates in Tables 2, 3, and 4. The temperature dependence of the three thermodynamic association constants further allows determination of ΔH°ass and ΔS°ass for the complex formation reaction using the van’t Hoff equation.

with the reaction of eq 5 resulting in a complete dissociation into CaL+ and L−, where L− is L-lactate, D-gluconate, or Dlactobionate, and CaL+ the 1:1 complex of each of these anions with Ca2+. The reaction of eq 6 corresponds to the dissociation of the complex, for which the association constant is defined as K ass =

γ +[CaL+] aCaL+ [CaL+] = CaL − ≈ − γL−[L ]aCa 2+ a L−aCa 2+ [L ]aCa 2+

ln K ass = −

(7)

and a concentration of complex of aCa 2+ γCa 2+

(9)

2+

based on correction of aCa to free calcium concentration, [Ca2+], using eqs 1 and 2. A new estimate of the ionic strength was made according to I=

1 (4[Ca 2 +] + [L−] + [CaL+]) 2

(11)

The linearity of the plot of Figure 2 confirms the validity of the iterative calculation procedure and leads to the thermodynamic values of Table 5 including Kass at 25 °C using standard regression methods. Since the complex formation is endothermic corresponding to ΔH°ass > 0, the complex formation must be entropy driven with ΔS°ass > 0. The increasing entropy resulting from binding seems related to release of water bound both to the calcium ion and to the carboxylic group of the hydroxycarboxylate. The association constants were determined for the natural pH around 6 of the saturated solutions, see Tables 2, 3, and 4. The pKa values of the hydroxycarboxylic acids are around 3.6, and acid/base equilibria will accordingly not affect the calcium binding in the pH region of relevance for normal foods.23 The thermodynamic association constants for the three hydroxycarboxylate complexes of calcium and the derived thermodynamic parameters were determined in saturated aqueous solutions of each of the calcium hydroxycarboxylates. However, they should be of more universal use for aqueous solutions, since they are based on calcium ion activity rather than on calcium ion concentration as previously used.11 Values available for Kass are for other solution conditions, but for calcium L-lactate, a value of Kass = 35 has been reported, which is comparable to the value of 49 of Table 2.24 For D-gluconate a value Kass = 77 was previously obtained by extrapolation of Kass valid at varying ionic strength to infinite dilution.23 Also this value for Kass based on calcium ion activity compares well with the value of Kass = 88 of Table 2. A more recent value based on 13 C NMR spectra is somewhat lower, with Kass = 63.25 Binding of calcium to sugar derived ligands is of general interest for sugar metabolism, and structural assignment of the functional groups in the partly metabolized sugars binding calcium has been attempted.25,26 Calcium seems to bind to a carboxylic group but also with involvement of hydroxylic groups apparently with equilibration between five- and sixmembered rings.25 In order to understand the structural effects on calcium binding for the three hydroxycarboxylates, quantum mechanical calculations within DFT were used to obtain optimized structures of the three calcium complexes in aqueous solution followed by calculation of ΔHbinding for the reaction correcting for solvent interaction:

The approximation included in eq 7 is based on the assumption that the activity coefficient only depends on the charge of the ion as is also an assumption for the Davies equation.17,23 An iterative calculation procedure was used for each of the three salts for each of the three temperatures. From an initially estimated ionic strength neglecting complex formation (I = 3cCa2+, where cCa2+ is the concentration of calcium hydroxycarboxylate), γCa2+ was calculated according to eq 2 leading to a concentration of free ligand of a 2+ [L−] = c Ca 2+ + [Ca 2 +] = c Ca 2+ + Ca γCa 2+ (8) [CaL+] = c Ca 2+ − [Ca 2 +] = c Ca 2+ −

ΔH °ass ΔS°ass + RT R

(10)

and the calculation procedure repeated until the ionic strength, I, was not influenced further, and the final values for the ion concentrations of the three calcium hydroxycarboxylates were calculated at each of the three temperatures. The speciation for calcium L-lactate, calcium D-gluconate, and calcium D-lactobionate, resulting from measurement of total calcium, cCa2+, and calcium ion activity, aCa2+, and the iterative calculation procedure, is found in Tables 2, 3, and 4, respectively. Included in these tables are values for Kass for the calcium complexes of L-lactate (Table 2), D-gluconate (Table 3), and D-lactobionate (Table 4), each at three temperatures as calculated from eq 7. D-Lactobionate forms the strongest complex with calcium, Llactate the weakest, with D-gluconate being intermediate according to the thermodynamic association constant for all of the three temperatures. The binding is, however, for each hydroxycarboxylate significant especially for the high concentrations of the saturated solutions, as evident from the

Ca 2 + + L− → CaL+ 5677

(12)

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Calcium ion activity, aCa2+, was determined electrochemically. Free calcium ion concentration, [Ca2+], activity coefficient, γCa2+, free gluconate concentration, [Gl−], the calcium complex concentration [CaGl+], and the resulting ionic strength, I, were calculated by an iterative procedure.

The values of ΔHbinding are included in Table 5. The ordering of affinity of calcium ion to hydroxycarboxylates is D-lactobionate > D-gluconate > L-lactate, in agreement with the experimentally determined values for Kass. Moreover, the relative strength of binding of calcium to D-gluconate and L-lactate is 1.6, as obtained from the theoretical calculations, which is surprisingly close to the ratio of 1.8 indicated by the experimentally determined values for Kass at 25 °C, see Table 5. The optimized structures of the calcium complexes are presented in Figures 3, 4, and 5. For L-lactate, calcium ion binds solely to the oxygen atoms of the carboxylate with equal bond lengths. For D-gluconate, calcium ion binds also to the two carboxylate oxygens but also to the hydroxyl group of C-3 of Dgluconate for the optimized (lowest energy) structure. However, separated by only 8.3 kJ·mol −1 is another conformation where calcium is bound to only one of the two carboxylic oxygens, but also to the hydroxyl groups both at C-2 and C-3, see Figure 4a. Calcium binding to D-lactobionate follows a similar pattern with the lowest energy conformation characterized by binding to the two carboxylic oxygens and to a hydroxyl group (C-5). As for D-gluconate, another conformation of the calcium complex of D-lactobionate is only 10.4 kJ· mol−1 above the optimized structure, with binding to only the two carboxylic oxygens as for L-lactate and not involving any hydroxyl groups, compare Figures 4 and 5. In the view of the small energy separation between the two local minima of calcium complexes of D-gluconate, it is suggested that they coexist in solution. The strongest binding of calcium is characterized by three calcium-to-oxygen bonds as for D-gluconate and D-lactobionate, while the weaker binding of calcium for L-lactate only involves two oxygens. For D-lactobionate, an easy shift between binding to two carboxylic oxygens and binding including an additional hydroxyl group may explain the higher affinity for calcium by Dlactobionate than by D-gluconate. The speciation of calcium in the saturated calcium hydroxycarboxylate solutions presented in Tables 2, 3, and 4 provides the information required to calculate the solubility product: K sp = aCa 2+a L−2 ≈ aCa 2+[L−]2 γL−2

(13)

The values for K sp for each of the three calcium hydroxycarboxylates at three temperatures are presented in Table 6 applying the Davies equation for calculation of γL− at the ionic strength of the saturated solutions. For the more soluble calcium L-lactate and calcium D-lactobionate, the uncertainty is rather large for these calculations, and since solubility products normally only are considered as a thermodynamic parameter for sparingly soluble salts, the temperature dependence on Ksp is only analyzed for the least soluble calcium D-gluconate as seen in Figure 6. Based on the van’t Hoff equation as presented in eq 11, values of ΔH°sol = (16 ± 1) kJ·mol−1 and ΔS°sol = −(26 ± 5) J·mol−1·K−1 were calculated, see Figure 6. The solubility product obtained for 20 °C, log Ksp = −4.26, is in good agreement with the value obtained by others, log Ksp = −4.19, also corrected for complex formation and based on activity standard.21 The dissolution of calcium hydroxycarboxylates in water involves the two reactions of eqs 5 and 6. While the thermodynamic parameters obtained for complex formation solely are associated with the process of eq 6, ΔH°sol and ΔS°sol obtained for calcium D-gluconate are valid for the hypothetical

a

43 ± 3 66 ± 1 110 ± 1 0.083 ± 0.001 0.099 ± 0.001 0.131 ± 0.001 0.033 ± 0.001 0.053 ± 0.001 0.092 ± 0.001 0.025 ± 0.001 0.02291 ± 0.0004 0.0194 ± 0.0002 0.11 0.12 0.15 0.0583 ± 0.002 0.076 ± 0.001 0.112 ± 0.001 5.9 5.8 5.9 10 20 30

2.51 ± 0.01 3.27 ± 0.04 4.80 ± 0.04

0.0093 ± 0.003 0.00813 ± 0.0004 0.0064 ± 0.0001

0.373 ± 0.001 0.355 ± 0.001 0.3290 ± 0.0004

[CaGl+] (mol·L−1) [Ca2+] (mol·L−1) γCa2+ I aCa2+ cCa2+ (mol·L−1) solubility (g/100 mL) pH temp (°C)

Table 3. Solubilities and the Thermodynamic Association Constants of Calcium D-Gluconate in Aqueous Solutions at 10, 20, and 30 °Ca

[Gl−] (mol·L−1)

Kass

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Table 4. Solubilities and the Thermodynamic Association Constants of Calcium D-Lactobionate in Aqueous Solutions at 10, 20, and 30 °Ca temp (°C)

pH

solubility (g/ 100 mL)

cCa2+ (mol·L−1)

aCa2+

I

γCa2+

[Ca2+] (mol·L−1)

[CaLacto+] (mol·L−1)

[Lacto−] (mol· L−1)

Kass

10 20 30

5.7 5.7 5.6

42.8 ± 0.5 45.2 ± 0.5 56.8 ± 0.3

0.57 ± 0.01 0.60 ± 0.01 0.752 ± 0.004

0.012 ± 0.001 0.0077 ± 0.0001 0.006 ± 0.001

0.64 0.65 0.79

0.315 ± 0.002 0.310 ± 0.001 0.330 ± 0.000

0.038 ± 0.002 0.0248 ± 0.002 0.018 ± 0.002

0.529 ± 0.005 0.57 ± 0.01 0.73 ± 0.01

0.61 ± 0.01 0.62 ± 0.01 0.770 ± 0.002

73 ± 5 120 ± 2 162 ± 16

Calcium ion activity, aCa2+, was determined electrochemically. Free calcium ion concentration, [Ca2+], activity coefficient, γCa2+, free lactobionate concentration, [Lacto−], the calcium complex concentration [CaLacto+], and the resulting ionic strength, I, were calculated by an iterative procedure. a

Figure 3. Calcium binding to L-lactate: DFT-optimized geometry with PCM solvent model (water).

Figure 2. Effect of temperature on thermodynamic association constant of 1:1 complexes, Kass, of calcium with (■) L-lactate, (●) D-gluconate, and (▲) D-lactobionate in water.

process of dissolving 1 mol of calcium D-gluconate in an already saturated solution of the specified temperature corresponding to the differential enthalpy and entropy of dissolution for a saturated solution as partial molar quantities. In order to assign the thermodynamic parameters directly to the dissolution process of eq 5, where a solid is dissolved in pure water to obtain integral enthalpy and entropy of dissolution, other types of experiments based on dissolution calorimetry are needed. For a more practical use of the results in the food industry, the calcium ion activity in aqueous solutions was calculated for increasing concentration of each of the three calcium hydroxycarboxylates for 25 °C based on the association constants and correcting for the effect on the activity coefficient of calcium from the increasing ionic strength using iterative methods similar to those described for determination of the complex constants. The calculations were extended to concentrations above the saturation for each calcium hydroxycarboxylate as seen in Figure 7. The result is striking: up to saturation, the calcium ion activity continues to increasing steadily, but the continuing increase in activity is far less significant, when the concentration approaches the solubility limit especially for D-lactobionate and D-gluconate. For calcium

Figure 4. Calcium binding to D-gluconate: DFT-optimized local minima with PCM solvent model (water). Energy difference between two local minima: Ea − Eb = 8.3 kJ·mol−1. D-gluconate, the calcium ion activity is rather constant for up to 10 times supersaturation and the driving force for precipitation becomes small. This seem to be part of the explanation for the well-known phenomenon that calcium D-gluconate forms a supersaturated solution which may stay supersaturated for years before precipitation starts.15 D-Gluconate also protects against calcium L-lactate precipitation in cheeses during maturation, and similar effects of supersaturation may be involved.14

Table 5. Thermodynamic Association Constants of 1:1 Calcium Hydroxycarboxylate Complexes in Water at 25 °C and Thermodynamic Parameters (ΔG°ass, ΔH°ass, ΔS°ass) for Complex Formation from Electrochemical Measurement, Binding Enthalpy, ΔHbinding, and Relative Stability Constant, Krel, of Complexes Based on DFT Calculations

calcium L-lactate calcium D-gluconate calcium D-lactobionate

Kass

ΔG°ass (kJ·mol−1)

ΔH°ass (kJ·mol−1)

ΔS°ass (J·mol−1·K−1)

ΔHbinding (kJ·mol−1)

Krel

49 88 140

−9.7 −11.1 −12.2

31 ± 3 34 ± 2 29 ± 3

135 ± 11 150 ± 6 137 ± 9

−126.2 −127.3 −133.6

1 1.6 20

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Figure 7. Calcium ion activity in calcium hydroxycarboxylate aqueous solutions of increasing concentration at 25 °C. Calcium concentration was corrected to calcium activity using the Davies equation based on an iterative calculation procedure correcting for complex formation. Solubilities (↑) of calcium L-lactate, calcium D-gluconate, and calcium −1 −1 −1 D-lactobionate are 0.286 mol·L , 0.080 mol·L , and 0.620 mol·L , respectively, in water at 25 °C.11,19

Figure 5. Calcium binding to D-lactobionate: DFT-optimized local minima with PCM solvent model (water). Energy difference between two local minima: Ea − Eb = 10.4 kJ·mol−1.

Table 6. Thermodynamic Solubility Product, Ksp, of Calcium L-Lactate, Calcium D-Gluconate, and Calcium DLactobionate, Calculated from Experimental Data of Tables 2, 3, and 4 temp (°C) 10 20 30 10 20 30 10 20 30

Calcium L-lactate, calcium D-gluconate, and calcium Dlactobionate also find use as calcium supplements because of their nonbitter taste in contrast to calcium chloride. Calcium bound in the hydroxycarboxylates is not bitter tasting, and in the mouth the increasing temperature will even mask any bitter taste after intake due to the entropy driven lowering of the calcium ion activity.

Ksp Calcium L-Lactate 0.00090 ± 0.00010 0.00090 ± 0.00003 0.0014 ± 0.0001 Calcium D-Gluconate 0.000039 ± 0.000002 0.000047 ± 0.000001 0.000063 ± 0.000001 Calcium D-Lactobionate 0.0025 ± 0.0002 0.00166 ± 0.00001 0.0020 ± 0.0002

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +45-35333221. Fax: +4535283344. Funding

Danish Dairy Research Foundation and Arla Food Ingredients are thanked for supporting the project “Calcium during whey processing”. Notes

The authors declare no competing financial interest.

■ ■

ABBREVIATIONS USED DFT, density functional theory; PCM, polarizable continuum model REFERENCES

(1) Holt, C. An equilibrium thermodynamic model of the sequestration of calcium phosphate by casein micelles and its application to the calculation of the partition of salts in milk. Eur. Biophys. J. Biophys. Lett. 2004, 33, 421−434. (2) Gaucheron, F. The minerals of milk. Reprod. Nutr. Dev. 2005, 45, 473−483. (3) Parker, T. G.; Dalgleish, D. G. Binding of calcium-ions to bovine β-casein. J. Dairy Res. 1981, 48, 71−76. (4) Hansen, C.; Werner, E.; Erbes, H. J.; Larrat, V.; Kaltwasser, J. P. Intestinal calcium absorption from different calcium preparations: Influence of anion and solubility. Osteoporosis Int. 1996, 6, 386−393. (5) Ozcan, T.; Horne, D.; Lucey, J. A. Effect of increasing the colloidal calcium phosphate of milk on the texture and microstructure of yoghurt. J. Dairy Sci. 2011, 94, 5278−5288.

Figure 6. Effects of temperature on thermodynamic solubility product, Ksp, for calcium D-gluconate in water. Experimental data from Table 3. 5680

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dx.doi.org/10.1021/jf501453c | J. Agric. Food Chem. 2014, 62, 5675−5681