Hoang Tam
Do‡
a,
Yeong Zen
Chua‡
*bc,
Jonas
Habicht
a,
Marcel
Klinksiek
a,
Moritz
Hallermann
a,
Dzmitry
Zaitsau
cd,
Christoph
Schick
bce and
Christoph
Held
*a
aLaboratory of Thermodynamics, TU Dortmund University, Emil-Figge-Str. 70, 44227 Dortmund, Germany. E-mail: christoph.held@tu-dortmund.de
bInstitute of Physics, University of Rostock, Albert-Einstein-Str. 23-24, 18051 Rostock, Germany. E-mail: yeong.chua@uni-rostock.de
cCompetence Centre CALOR, University of Rostock, Albert-Einstein-Str. 25, 18051 Rostock, Germany
dInstitute of Chemistry, University of Rostock, Dr-Lorenz-Weg 2, 18051 Rostock, Germany
eChemical Institute A. M. Butlerov, Kazan Federal University, 18 Kremlyovskaya Street, Kazan 420008, Russian Federation
First published on 14th October 2019
Melting properties (melting temperature, melting enthalpy and heat capacity difference between liquid and solid phase) of biomolecules are indispensable for natural and engineering sciences. The direct determination of these melting properties by using conventional calorimeters for biological compounds is often not possible due to decomposition during slow heating. In the current study this drawback is overcome by using fast scanning calorimetry (FSC) to directly measure the melting properties of five dipeptides (glycyl-glycine, glycyl-L-alanine, L-alanyl-glycine, L-alanyl-L-alanine and cyclo(L-alanyl-glycine)). The experimental melting properties were used as inputs into a thermodynamic solid–liquid equilibrium relation to predict solubility of the dipeptides in water. The required activity coefficients were predicted with PC-SAFT using solubility-independent model parameters. PC-SAFT predicted different solubility profiles (solubility vs. temperature) of isomers. The predictions were validated by new experimental solubility data, and the crystal structure of the dipeptides in saturated solution was verified by X-ray diffraction. The different water solubility profiles of isomers (glycyl-L-alanine and L-alanyl-glycine) were found to be caused by the big difference in the melting enthalpy of the two dipeptides. To conclude, combining the PC-SAFT and FSC methods allows for accurate prediction of dipeptide solubility in water in a wide temperature range without the need to fit any model parameters to experimental solubility data.
Among such thermodynamic models, gE models and equations of state (EoS) are widely used for engineering purposes to calculate the activity coefficients. Models such as the modified Wilson model (Xu et al.7) with two adjustable parameters per system has already been used to calculate the activity of polymer aqueous solutions as well as the aqueous solubility of several amino acids and dipeptides. Pazuki et al. used perturbation theory,8 M-Wilson and M-NRTL9 models based on three adjustable parameters to predict the activity coefficients of aqueous solutions containing an amino acid or a small peptide. Mortazavi-Manesh et al.10 used a two-parameter model based on the perturbation theory of a hard-sphere reference to correlate the activity coefficients of some amino acids and peptides in aqueous solutions. Held et al.11 calculated the activity coefficients based on the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) of aqueous amino-acid and peptide solutions. It has been shown that in comparison to other models, PC-SAFT provides accurate modeling results of activity coefficients and prediction of solubility even in complex mixtures.12–15
Thermodynamic models make use of an equilibrium condition between the solid dipeptide and the dipeptide in the saturated liquid phase. No mixed solids (pure compound in single solid phase) were assumed. The temperature dependency of the melting enthalpy was taken in account resulting in the term of the difference of the heat capacities of the solid and liquid state. The difference of heat capacities itself was assumed to be temperature dependent in a linear function. The mole fraction of the dipeptide in the liquid phase at saturation conditions xL,sati can be calculated according to ref. 16 and 17 by eqn (1), and by assuming a linear temperature dependence of eqn (2).
(1) |
(2) |
The common strategy to model solubility of amino acids and peptides is to adjust simultaneously all model parameters including melting properties to experimental solubility data in any chosen solvent (in most cases water). This method is physically unsound as so-determined melting properties include information of the mixture. This is forbidden from a physical perspective as melting properties are pure-component properties. As a consequence, so-determined melting properties from literature for several amino acids (Ji and Feng et al.22 and Ferreira et al.23) and for dipeptides (Held et al.11) largely deviate from each other and cannot be considered as reliable data.24 The only physically correct procedure to predict solubility is the use of experimentally determined melting properties that are universally valid and do not depend on unphysical treatments. However, the melting properties for amino acids and dipeptides are mostly inaccessible due to the thermal decomposition during slow heating in conventional Differential Scanning Calorimetry (DSC).25 However, in our recent work24 we have shown that it is possible to use the Fast Scanning Calorimetry (FSC) to avoid thermal decomposition before and during melting. FSC has been successfully applied to accurate study of meting of amino acids glycine and L-alanine,24 bio-polymers,26–28 low molecular mass compounds29 and nucleobases.30,31 Further, for glycine and L-alanine we have shown that it is possible to predict the temperature-dependent solubility in water on the basis of the FSC-determined melting properties.24
Within this work the temperature-dependent aqueous solubilities of glycyl-glycine (Gly–Gly), glycyl-L-alanine (Gly–Ala), L-alanyl-glycine (Ala–Gly), L-alanyl-L-alanine (Ala–Ala) and cyclo(L-alanyl-glycine) (cyclo(Ala–Gly)) were measured gravimetrically and photometrically. To determine the activity coefficients properly the knowledge about the melting properties are desired according to eqn (1). Due to the decomposition of these dipeptides before melting in common DSC, the melting properties were determined with FSC. The experimental results were used to predict the solubility with PC-SAFT. The predicted solubilities were compared to new experimental solubility data. As cyclization of dipeptides can occur both in solution32–34 and in the solid phase35–37 during thermal treatment, we have proven that the obtained results corresponded to the dipeptides instead of to their cyclic pendants.
Substance | Abbrev. | Supplier | CAS no. | Purity |
---|---|---|---|---|
a Cyclo(alanyl-glycine)((S)-3-methyl-2,5-piperazinedione). | ||||
Glycyl-glycine | Gly–Gly | Sigma A. | 556-50-3 | ≥99% |
Glycyl-L-alanine | Gly–Ala | Sigma A. | 3695-73-6 | ≥99% |
L-Alanyl-glycine | Ala–Gly | Sigma A. | 687-69-4 | ≥99% |
L-Alanyl-L-alanine | Ala–Ala | Bachem | 1948-31-8 | ≥99% |
a | Cyclo(Ala–Gly) | Bachem | 4526-77-6 | ≥99% |
Dipeptides might undergo thermally induced cyclization upon heating, as shown in the literatures for L-leucyl-L-leucine35 and diphenylalanine.36 In order to exclude that cyclization of the dipeptides occurred in our FSC measurements, both Ala–Gly and cyclo(Ala–Gly) were characterized and their melting properties and solubility profiles were compared.
Substance | DF | Absorbance maximum |
---|---|---|
Ala–Gly | 14000 | 192 nm |
Ala–Ala | 15000 | 190 nm |
LHA,tot = LHA[1 + 10pKa,1−pH + 10pH−pKa,2 + 102pH−pKa,2−pKa,3] | (3) |
LHA,tot = LHA[1 + 10pH−pKa,1 + 102pH−pKa,2−pKa,1] | (4) |
The conversion from the molar fraction x [mol mol−1] to molality [mol kgwater−1] is done according to the following equation:
(5) |
The measurement procedure is divided into three measurement stages, as shown in the temperature–time profile in Fig. 1. In the first stage, the initial mass of the sample was determined as m0 = CSp0i/cSp0i, where CSp0i is heat capacity of the solid sample on the sensor [J K−1] obtained from the heating and cooling cycles in scanning steps #1 to #4, and cSp0i is specific heat capacity [J g−1 K−1] obtained from the measurement with conventional DSC (Pyris 1, PerkinElmer, USA). The temperature range and constant scanning rate, β = 2000 K s−1, were selected as such that the sample undergoes no mass loss, e.g. no sublimation and no decomposition.24,27,28,30 The starting temperature was set to 303 K.
Fig. 1 Temperature–time profile with three measurement stages: (i) 1st stage: sample mass determination (red segment), (ii) 2nd stage: sample melting and fast-quenching (green segment), and (iii) 3rd stage: re-heating of supercooled sample (blue segment). After cooling step #4 in 1st stage, the sample can be coated with silicon oil. In the heating step #5, the scanning rate, β, varied from 2000 K s−1 to 20000 K s−1 [reprinted from ref. 24 with modifications]. |
The properties TSL0i and ΔhSL0i are determined in the heating step #5 in the second stage. The ΔhSL0i is defined as
(6) |
In order to ensure good thermal contact between sample and surface of sensor, as well as to decrease the mass loss due to sublimation and evaporation, the sample was coated with silicon oil before the heating step #5. The scanning rate of heating step #5 was varied from 2000 K s−1 to 20000 K s−1 used for the extrapolation of the measured properties to zero heating rate. Silicon oil was commonly used to improve the thermal contact in FSC measurements, e.g. for polymers42–45 and for organic compounds.24,46 Nevertheless in order to ensure that there is no interaction between the dipeptides and silicon oil, the melting properties, TSL0i and ΔhSL0i, for samples coated with and without silicon oil were determined and presented in Fig. 2 and 3.
Fig. 3 Enthalpy, ΔHSL0i, of Gly–Gly, Gly–Ala, Ala–Gly, Ala–Ala and cyclo(Ala–Gly) in respect to initial sample mass, m0, regardless of the scanning rates. The symbols used were as described in Fig. 2. The dashed line was linear fit through zero origin, where the slope denoted as ΔhSL0i. The scanning rates used were 2000 K s−1 (circles), 4000 K s−1 (up-triangles), 5000 K s−1 (hexagonals), 6000 K s−1 (down-triangles), 8000 K s−1 (diamonds), 10000 K s−1 (stars). The melting enthalpy for Gly–Gly, Gly–Ala, Ala–Gly, Ala–Ala and cyclo(Ala–Gly) is ΔhSL0Gly–Gly = (40 ± 6) kJ mol−1, ΔhSL0Gly–Ala = (41 ± 5) kJ mol−1, ΔhSL0Ala–Gly = (52 ± 7) kJ mol−1, ΔhSL0Ala–Ala = (45 ± 7) kJ mol−1 and ΔhSL0cyclo(Ala–Gly) = (24 ± 4) kJ mol−1, respectively. The values are already given in the figures, same for Fig. 2. |
After melting in heating step #5, the sample without silicon oil was cooled rapidly with a programmed rate of 20000 K s−1 (cooling step #6 in third stage) to minimize the sample mass loss due to evaporation at high temperature. If crystallization in cooling steps #6 and #7 took place, the ultra-fast quenching of the melted sample was applied allowing the sample to retain in the liquid state below the melting temperature (supercooled liquid). The glass transition of the sample (supercooled liquid to glass and vice versa) was denoted as a step change in the specific heat capacity.
In the third stage for sample without silicon oil, the glassy sample was heated/cooled in temperature range similar to that in the first stage. The initial scanning rate used in this stage was 2000 K s−1, however accessible temperature range for accurate determination of the glass transition with this scanning rate was too narrow. The limitation on the accessible temperature arises due to device response depending on the scanning rate. The accessible temperature range can be increased by (i) decreasing starting temperature below 303 K, and (ii) decreasing the scanning rates of heating and cooling cycles. The first solution is not favorable, as this would increase the measuring time due to increasing required equilibrating time of the device at low temperatures below 303 K. Thus, as in second solution, a range of lower scanning rates was used in heating and cooling cycles in the third stage. By decreasing the scanning rates, the temperature range needed to achieve constant scanning rates decreases. Therefore the accessible temperature range in heating and cooling curves increases. An example of heating and cooling cycles for glassy Gly–Gly in the third stage that shows that the accessible temperature range for glass transition evaluation increases with decreasing scanning rate are shown in Fig. S1 in ESI.†
(7) |
ares = ahc + adip + aassoc | (8) |
(9) |
(10) |
The binary interaction parameter kij is a fit parameter that describes deviations from the geometric mean of the dispersion–energy parameters of components i and j.
The dipeptides used in this work were modeled with the 2B association scheme.48 Both, the amino group and the carboxylic group were characterized with one association site each. The PC-SAFT pure-component parameters for the dipeptides were taken from literature.11 The parameters were fitted to thermodynamic properties of aqueous solution, and, therefore, depend on the chosen water parameters. Water was modeled as well with the 2B association scheme with a temperature-dependent segment diameter introduced by Cameretti and Sadowski.49 The same water parameters used in ref. 24 were also used in the present work. The PC-SAFT parameters used in this work are listed in Table 3.
Component | m segi [−] | σ i [Å] | u i/kB [K] | ε AiBi/kB [K] | κ AiBi [−] | k ij to water |
---|---|---|---|---|---|---|
a For water, a temperature-dependent segment diameter σ = 2.7927 + 10.11exp(−0.01775T) − 1.417exp(−0.01146T) was used. | ||||||
Gly–Gly11 | 7.3374 | 2.327 | 216.96 | 2598.06 | 0.0393 | −0.080 |
Gly–Ala11 | 9.2047 | 2.411 | 279.32 | 2912.21 | 0.0392 | −0.075 |
Ala–Gly11 | 9.2047 | 2.411 | 279.32 | 2912.21 | 0.0392 | −0.075 |
Ala–Ala11 | 10.230 | 2.522 | 287.59 | 3176.59 | 0.0819 | −0.074 |
Cyclo(Ala–Gly)this work | 5.8185 | 2.780 | 278.48 | 1029.07 | 0.0157 | −0.053 |
water49 | 1.2047 | a | 353.94 | 2425.67 | 0.0451 | — |
One binary interaction parameter was applied between dipeptide and water according to eqn (10). In this work, the values for kij were fitted to activity-coefficient data of dipeptides in water at (298.15 ± 0.1) K. For cyclo(Ala–Gly) osmotic coefficients in water solutions at (273.15 ± 0.1) K were determined. The Gibbs–Duhem equation was used to convert these values in activity coefficients where the value for kij was fitted to. For comparison, the PC-SAFT modelled and experimental activity coefficients are illustrated in Fig. S3 in the ESI.† The values are listed in Table S2 in the ESI.† Furthermore, the experimental dipeptide-water density data was used to confirm the binary interaction parameter kij values. The result of the parameter fit can be observed in Fig. S4† and the values are listed in Table S3 in the ESI.† It can be seen that PC-SAFT and experimental results are in good agreement. Additionally, it can be observed that the segment number of cyclo(Ala–Gly) as well as the association energy and volume is smaller in comparison with linear Ala–Gly. The molecule Ala–Gly consists of one primary amine group, of one carboxyl group, and of the peptide bond that contains a secondary amine group and a carbonyl group. The molecule cyclo(Ala–Gly) has two peptide bonds, so two secondary amine groups and two carbonyl groups. Thus, the association behavior of cyclo(Ala–Gly) is weaker than of Ala–Gly, which can be seen also from the association parameters listed in Table 3.
The extrapolated onset temperatures, TSL0i(β), were plotted in respect to heating rates, β, as shown in Fig. 2. The value for the thermodynamic melting temperature, TSL0i, is defined as TSL0i = TSL0i(β → 0),50 which considers such device dependent effects as the thermal lag50,51 and possible superheating.51–53 As described above in eqn (6) ΔHSL0i should linearly depend on the sample mass m0, regardless of the scanning rate and this was demonstrated for both samples with and without silicon oil in Fig. 3. This also indicates no interaction between dipeptides and silicon oil. The slopes of the dashed red lines in Fig. 3 provides the specific melting enthalpies.24,27,28
Fig. 4 shows the glass transition step (solid line) in specific heat capacity for Gly–Gly, Gly–Ala, Ala–Gly and Ala–Ala. The heat capacity of solid phase, cSp0i, measured with conventional DSC, as well as the heat capacity of liquid phase, cLp0i, determined from the glass transition step were linearly fitted in order to extrapolate to melting temperature. The heat capacity difference between liquid and solid phase were determined at glass transition temperature, ΔcSLp0i (TG0i) and at melting temperature, ΔcSLp0i (TSL0i). It should be mentioned that we assumed the heat capacity of glass and crystal state equal to each other. This assumption is reasonable, while the heat capacity difference between glass and crystal phases often lower than the uncertainty of heat capacity determination with FSC technique (approx. 10%).54–59
Fig. 4 Specific heat capacity for Gly–Gly, Gly–Ala, Ala–Gly and Ala–Ala. The heat capacity of solid, cSp0i, of the dipeptides was measured with conventional DSC (dotted lines). The solid line denotes the glass transition step of ultra-fast quenched melted dipeptides without silicon oil. Both cSp0i and cLp0i (dashed lines) were linearly fitted to extrapolate to TSL0i. The heat capacity difference between liquid and solid phase were determined at glass transition temperature, ΔcSLp0i (TG0i) and at melting temperature, ΔcSLp0i (TSL0i). Gly–Gly: ΔcSLp0Gly–Gly (TG0Gly–Gly) = (84 ± 6) J mol−1 K−1 and ΔcSLp (TSL0Gly–Gly) = (51 ± 6) J mol−1 K−1; Gly–Ala: ΔcSLp0Gly–Ala (TG0Gly–Ala) = (91 ± 6) J mol−1 K−1 and ΔcSLp0Gly–Ala(TSL0Gly–Ala) = (55 ± 6) J mol−1 K−1; Ala–Gly: ΔcSLp0Ala–Gly (TG0Ala–Gly) = (82 ± 3) J mol−1 K−1 and ΔcSLp (TSL0Ala–Gly) = (57 ± 3) J mol−1 K−1; Ala–Ala: ΔcSLp0Ala–Ala (TG0Ala–Ala) = (84 ± 18) J mol−1 K−1 and ΔcSLp0Ala–Ala (TSL0Ala–Ala) = (62 ± 18) J mol−1 K−1. The solid squares depict specific heat capacity of solid Gly–Gly from literature.60 In order to avoid crystallization on cooling, higher scanning rates are required and might be able to achieved with ultra-fast scanning nanocalorimetry.61,62 |
Unfortunately, no heat capacity difference for cyclo(Ala–Gly) can be determined as cyclo(Ala–Gly) crystallizes on cooling from melted state, even at cooling rate 20000 K s−1.
The experimental melting temperatures, melting enthalpy, and heat capacity differences at glass transition temperature and at melting temperature of dipeptides, as well as the melting properties implemented in PC-SAFT, are listed in Table 4. The melting properties of Ala–Gly differs considerably from that of cyclo(Ala–Gly). This implies that Ala–Gly does not undergo cyclization into cyclo(Ala–Gly) upon heating in FSC conditions and allows determining the melting properties of dipeptides without accounting for this chemical process. So, the big difference in the melting properties justifies the observed difference in the solubility data of Ala–Gly and cyclo(Ala–Gly).
FSC | |||||
---|---|---|---|---|---|
M [g mol−1] | T SL0i [K] | ΔhSL0i [kJ mol−1] | ΔcSLp0i (TG0i) [J mol−1 K−1] | ΔcSLp0i (TSL0i) [J mol−1 K−1] | |
Gly–Gly | 132.12 | 593 ± 7 | 40 ± 6 | 84 ± 6 | 51 ± 6 |
Gly–Ala | 146.15 | 551 ± 7 | 41 ± 5 | 91 ± 6 | 55 ± 6 |
Ala–Gly | 146.15 | 611 ± 7 | 52 ± 7 | 82 ± 3 | 57 ± 3 |
Ala–Ala | 160.17 | 606 ± 7 | 45 ± 7 | 84 ± 18 | 62 ± 18 |
Cyclo(Ala–Gly) | 128.13 | 526 ± 7 | 24 ± 4 | — | — |
Fig. 5 Experimental dipeptide solubility at pH = 7 in water as molality vs. temperature. Full symbols present data measured by photometric method; empty symbols by gravimetric method. Gly–Ala (squares + “x”-filled square38); Ala–Ala (up-triangles); Gly–Gly (circles);11 Ala–Gly (down-triangles) and cyclo(Ala–Gly) (diamonds). The experimentally determined values are given in Tables S5 and S6 (pH 7) and Tables S7 and S8 (pH at saturated solutions) in the ESI.† |
As expected, the solubility of all dipeptides increases with increasing temperature. Some literature works have already reported solubility data of dipeptides in water. The temperature-dependent solubility of Gly–Gly as well as Gly–Ala in water are listed in the literature ref. 11 and 38, respectively. These solubility data were repeated in the present work accounting also for pH correction using eqn (3) and (4). In addition to the already existing data, the temperature-dependent solubility of Gly–Ala in water was determined gravimetrically in the current work. Overall, Fig. 5 illustrates that the data agree well with each other.
(1) The solubility of the dipeptides are lower than of the respective amino-acids constituents,
(2) The solubility of the isomeric dipeptides Gly–Ala and Ala–Gly is expected to be equal and
(3) the solubility of Gly–Ala and of Ala–Gly is assumed to be in between the solubilities of Gly and Ala and
(4) The solubility is expected to decrease with the increase in alkyl chain length as in the case of amino acids. That, Gly–Gly is expected to have a larger solubility than Gly–Ala and larger than Ala–Gly, which in turn are expected to have a higher solubility than Ala–Ala.
Unexpectedly, none of these expected behaviors were found experimentally. The comparison of the solubilities of the four dipeptides compared to the amino acids Gly and Ala is illustrated in Fig. 6.
Fig. 6 Solubility in water. Bars: mean values of the photometric and gravimetric determined dipeptide solubility data at T = 298.15 K and pH = 7. Lines represent the corresponding amino-acid solubility at T = 298.15 K and pH = 7: solid line: Gly24 and dashed line: Ala.24 |
First, it becomes clear from Fig. 6 that amino acids are not necessarily more soluble in water than dipeptides. In the following, only those dipeptides are considered that possess the amino acid Gly in the first place of the primary structure. As soon as another Gly with a dipeptide binding is placed in the second place (Gly–Gly), the solubility decreases. However, if an Ala is present at second place (Gly–Ala), the solubility is increased and even exceeds the solubility of the glycine.
Now, we consider peptides that possess the amino acid Ala at the first place of the primary structure. Combining this with Gly at the second place (Ala–Gly) causes a strong decrease in the water solubility that it is even lower than the solubility of the Ala. However, as soon as Ala occurs at second place again (Ala–Ala), the solubility is increased compared to the amino acid Ala.
As observed the order of the sequence has an important role for the observed solubility data. In total as shown in Fig. 8 the dipeptides solubility follows the order
Gly–Ala > Gly > Ala–Ala > Gly–Gly > Ala > Ala–Gly > cyclo(Ala–Gly) |
Fig. 7 Influence of the difference of the heat capacities on the solubility behaviour for Gly–Gly (circles11) in water as molality vs. temperature. Lines represent PC-SAFT predictions with the parameters from Table 3 and FSC-measured melting properties from this work (Table 4). Dotted line: eqn (1) with ΔcSLp0i = 0, dotted-dashed line: eqn (1) with ΔcSLp0i = const. = 51 J mol−1 K−1, solid line: eqn (1) with eqn (2). |
Fig. 8 Influence of the activity coefficient on the solubility in molality in water expressed as difference between ideal and experimental solubility. Black (Ideal): calculated solubility at T = 298.15 K from eqn (1) based on the FSC-measured melting properties in experimental uncertainty assuming an ideal mixture γ = 1. Shaded (Exp.): mean value of the photometric and gravimetric determined solubility data at T = 298.15 K and pH = 7. Grey (PC-SAFT): calculated solubility at T = 298.15 K from eqn (1) based on the PC-SAFT used melting properties from Table 4 including the activity coefficient. |
Besides the chemical structure and the kind of polymorphic solid form that has been produced upon dissolution, the dipeptide-water interactions (activity coefficient) and the melting properties of the solid dipeptide (TSL0i, ΔhSL0i and ΔcSLp0i) determine the exact values of solubility according to eqn (1). This is discussed in the following.
The solubility data at pH = 7 between Ala–Gly and cyclo(Ala–Gly) are compared with each other. Due to different melting properties as mentioned in advance as well as different solubility, a thermally induced cyclization can be excluded. It is assumed that no cyclization has been occurred for all the other dipeptides.
The solubility of the isomeric dipeptides Gly–Ala and Ala–Gly are very different (Fig. 5). In contrast, the activity coefficients of Gly–Ala and Ala–Gly in water are the same within experimental uncertainties (Fig. S2 in the ESI†). Thus, a difference in the melting properties is the only explanation for the observed solubility between Ala–Gly and Gly–Ala are the different crystal structures which yield to different melting properties.
The general effect of the melting properties on solubility modeling using eqn (1) is discussed briefly in the following. Decreasing melting temperature TSL0i, melting enthalpy ΔhSL0i as well as increasing heat capacity difference of ΔcSLp0i lead to higher solubility values. Based on the experimental data the melting temperature of dipeptides appears to be about TSL0dipeptides ≈ 600 K (except for Gly–Ala with TSL0Gly−Ala = 551 + −7 K), while ΔSLp0dipeptides ≈ 55 J mol−1 K−1. Thus, it can be concluded that the main reason for the solubility difference is the enthalpy of melting which is different for Ala–Gly and Gly–Ala (ΔhSL0Ala−Gly = (52 ± 7) kJ mol−1 and ΔhSL0Gly−Ala = (41 ± 5) kJ mol−1). The lower the value for the melting enthalpy the higher the solubility according to eqn (1) given that activity coefficients play a minor role. As we found that the activity coefficients of Ala–Gly and Gly–Ala in water are equal, the difference in the melting enthalpy mainly explains the higher solubility of Gly–Ala over Ala–Gly.
It can be concluded from the experimental melting properties that the uncertainty of TSL0i and of ΔcSLp0i measured with FSC is sufficiently high. Changing TSL0i and of ΔcSLp0i within their uncertainty values only slightly influences the solubility according to eqn (1). In contrast, changing the FSC-measured melting enthalpy within its error bars strongly influences solubility according to eqn (1).24
Fig. 7 shows the influence of ΔcSLp0i on the solubility predictions using the melting properties of Gly–Gly (see Table 5, PC-SAFT). The dotted line represents eqn (1) with the approach of ΔcSLp0i = 0. The solubility prediction is lower than the experimentally determined aqueous solubility of Gly–Gly. The dashed-dotted line represents the assumption of ΔcSLp0i = const. = 51 J mol−1 K−1. The solubility increases compared to ΔcSLp0i = 0. The solid line takes in account the temperature dependency of ΔcSLp0i as described in eqn (2). The solubility increases again and is in good agreement to the experimental data of Gly–Gly in a broad temperature range. Based on the heat capacity results (Fig. 4) the ΔcSLp0i is neither equal to zero nor constant over the temperature range. Thus, all the PC-SAFT calculations in this work have been done with the approach of the linear temperature-dependent ΔcSLp0i(T) expressed by eqn (2). The individually slope and interceptions of the heat capacity of the liquid and solid phase are listed in Table 5.
Fig. 8 shows the solubility (in molality units) for ideal and experimental conditions. First, the ideal (=ideal mixture) solubility was calculated by setting activity coefficient equal to one at T = 298.15 K using eqn (1). The error bars of this calculation are based on using the FSC-measured melting properties within their uncertainty limits. It can be seen that the calculation of solubility assuming ideal mixture leads to very small solubility values. Thus, assuming ideal solution does not allow matching the experimentally determined solubility data. Therefore, the dipeptide-water interaction was accounted for by means of PC-SAFT. The success of the predictions shown in Fig. 8 mean that it is crucially important to take the interactions between dipeptide and water into account in order to predict solubility successfully. Note, that the FSC-measured melting properties were modified within their experimental uncertainty (see Table 4) by adjusting them to the experimental data shown in Fig. 8, and the melting properties are listed in Table 5. In the following, these were used to predict the experimental solubility data as shown in Fig. 9. It can be observed that PC-SAFT allows for quantitative prediction of the experimental solubility behavior. The used melting properties agree very well with the FSC-determined melting properties, and the methods cross-validate the experimental melting properties as well as the accuracy of activity-coefficient predictions and the experimental solubility data.
Fig. 9 Dipeptides solubility at pH = 7 in water as molality vs. temperature. Symbols represent experimental data. Solid symbols present measurements using photometric method; open symbols present measurements using gravimetric method. Gly–Ala (squares + "x" filled square38); Ala–Ala (up-triangles); Gly–Gly (circles11); Ala–Gly (down-triangles); cyclo(Ala–Gly) (diamonds). Lines represent PC-SAFT predictions with the parameters from Table 3 and FSC-measured melting properties from this work. Gly–Ala (solid line), Ala–Ala (dashed line), Gly–Gly (dashed-dotted line), Ala–Gly (dashed-double dotted line) and cyclo(Ala–Gly) (dotted line). The experimental determined values are given in Tables S5 and S6 (pH = 7) and Tables S7 and S8† (pH at saturated solutions). |
In sum, it can be concluded the FSC-measured melting properties as well as the PC-SAFT refined melting properties do not deviate much, which can be considered as an excellent result. It could be shown that both the FSC-measured melting data and the use of a thermodynamic model for the solvent–solute interactions are indispensable for the correct temperature-dependent solubility prediction of dipeptides.
Finally, PC-SAFT parameters were fitted to solubility-independent thermodynamic properties (activity coefficients, osmotic coefficients and mixture densities). Based on these parameters and the FSC-determined melting properties (TSL0i, ΔhSL0i and a linear temperature-dependent ΔcSLp0i(T)) the solubility of the dipeptides in water was predicted with PC-SAFT. The predicted solubility was found to be in very good agreement with the experimental determined solubility data. This cross-validates PC-SAFT as method to quantitatively predict activity coefficients at saturation as well as FSC to accurately measure the melting properties of compounds that usually decompose before melting upon measuring in conventional DSC apparatuses. The availability of our new experimental melting properties will improve also other predictive models in the future up to high temperatures.
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9ra05730g |
‡ Shared first authors. |
This journal is © The Royal Society of Chemistry 2019 |