Abstract: The modified Wilson model have been used to correlate the activity coefficients of amino acids and simple peptides in aqueous solutions. In the models studied in this reserch only the binary interaction parameters for amino acid-water molecules were taken into account. This treatment was based on this phenomenon that amino acid molecules are in their zweitter ionic in aqueous solutions. The results obtained from the model were compared with the experimental data of the activity coefficients in the literature. It is shown that this model can accurately correlate the experimental data for activity coefficients. The models were also used to correlate the solubility of amino acids in aqueous solutions. The results show that this model can accurately correlate the solubility experimental data over a wide range of temperature. The values for Δh, Δs and Δg of the solutions were calculated from the results of this model.
Introduction
Separation processes based on precipitation and crystallization has proven to be useful techniques for the concentration and separation of various biomolecules, such as amino acids (Belter et al .,1998). Amino acids are the basic units of proteins. Nass developed a model for the activity coefficient of many amino acids using the chemical reaction equilibrium constant of amino acids in aqueous solution (Nass, 1998). Gupta and Heidemann (1990) used the modified UNIFAC (Larsen et al., 1987) model to evaluate of the activity coefficients of amino acids in aqueous solutions and used some group parameters in predicting the solubility of antibiotic in water. Chen et al. (1989) modeled the activity coefficient of amino acids using the electrolyte NRTL model (Renon and Prausnitz, 1968; Chen et al., 1986). Khoshkbarchi and Vera (1996,1998) developed a perturbed hard-sphere model for the activity coefficient of amino acids in aqueous solutions. Recently Pazuki et al. (2005) proposed a new model based on the perturbation theory to predict the activity coefficients and solubility of amino acids in pure water. In this research the modified Wilson model that predicted by Novak et al. (1987) were used to correlate the experimental activity coefficients data of amino acids and simple peptides. The model was also used to correlate the solubility of amino acid in aqueous solution over a wide temperature range. The values for Δh, Δs and Δg of the solutions were calculated from the results of this model.
The Modified Wilson Model
Among several forms of the Wilson model modified for binary partially miscible mixtures, Novak et al. (1987) proposed the following form:
| (1) |
where, b12 is the empirical parameter. The binary parameter is expressed in terms of molar energy parameter and the molar volumes of pure components and:
| (2) |
A new ternary extended form of Eq. 1, which is not identical with the ternary modification proposed by Nagata (1995), has shown good applicability in the correlation of ternary liquid-liquid equilibrium. The activity coefficient for component (1) in binary mixture obtained from Gibbs energy of modified Wilson model as below:
| (3) |
Then activity coefficient of component 1 is given by:
| (4) |
where, in Eq. 4 X1 and X2 are mole fraction of component 1 and 2, respectively.
Evaluation of the Parameters
The modified Wilson models were employed to correlate the experimental data of water-amino acids systems. For aqueous solutions of amino acids the data reported in Handbook of Biochemistry and Molecular Biology was used (Fasman, 1976). This model contains three adjustable parameters and for prediction the activity coefficient with this model we assumed. Λ12 = Λ21. Therefore, this model contains two parameters Λ12 and b12. Subscripts 1 and 2 refer to amino acid and water, respectively.
Parameters of amino acids and peptides were evaluated by fitting the experimental activity data. For all the cases, the following objective function was used:
| (5) |
Results and Discussion for the Activity Coefficient
The activity coefficients of amino acids and peptide should be converted from the molality scale to the mole fraction scale base using the following relation (Khoshkbarchi and Vera, 1998):
| (6) |
Where, Mw is the molar mass of solvent and superscripts and, represent the molality and mole fraction scale, respectively.
For prediction of the activity coefficients of amino acids and peptides, considered the dissociation of amino acids in pure water is insignificant and the zwitterionic species are predominant, no term has been introduced in binary amino acid-water model to take into account the presence of ionic species in solution. The consideration of the terms that take into account the effect of ionic forms of amino acid molecules other than their zwitterionic form only makes the modeling more complex. Since the available experimental data for the activity coefficient of amino acids and peptides do not include the ionization of amino acids and peptides in water, consideration of the ionization term seems unnecessary at this point. The Fig. 1 and 2 shows that this model can accurately correlate the experimental activity coefficient data of amino acids and peptides in aqueous solutions. The binary interaction energy of model and the root mean square deviation of the correlation of the experimental data for amino acids and peptides are presented in Table 1. The root mean square deviations (rms) of this model are compared with those obtained by Chen et al. (1989), Gupta and Heidemann (1990), Pinho et al. (1994) and Khoshkbarchi and Vera, (1996,1998). These results show that the modified Wilson model a more accurate correlation than other models for the amino acids and peptides in aqueous solutions.
Solubility of Amino Acids in Water
When an amino acid dissolved in water, solid-liquid equilibrium of the amino acids is given by terms of fugacities:
| (7) |
By definition:
| (8) |
where, Xi is the mole fraction of the amino acid, γi
is the unsymmetrical activity coefficient of amino acid based on mole fraction
scale and
| (9) |
The ratio
| (10) |
Therefore:
| (11) |
Combining Eq. 9 and 11, one obtains:
| (12) |
Knowing the activity coefficient, Eq. 12, relates the solubility of amino acids to the temperature.
Results of Solubility of Amino Acids in Water
Equation 12 can predict the solubilities of amino acids in water at various temperatures by use of the adjustable parameters presented in Table 1.
| Table 1: | Parameters of the modified Wilson model for amino acids and peptides and the root mean square deviation |
| aThis work; b Khoshkbarchi and Vera (1998); c Khoshkbarchi and Vera (1996); d Chen et al. (1989);e Gupta and Heidemann (1990); f Pinho et al. (1994). | |
| Table 2: | Regressed values of parameter for the modified Wilson model of several amino acids in aqueous solutions and the root mean square |
| a This Work, b Khoshkbarchi-Vera (1998), c Fasman (1976) | |
| Table 3: | Calculated and experimental values of, Δg/RT0, To = 298.15 |
| aThis Work, b Khoshkbarchi-Vera(1998), c Fasman (1974) | |
| Fig. 1: | Activity coefficient of the modified Wilson model for two amino acids plotted vs. molality: (–) result of the modified Wilson model; (♦) experimental data of Alanine; (●) experimental data of Threonine |
| Fig. 2: | Activity coefficient of the modified Wilson model for two amino acids plotted vs. molality: (–) result of the modified Wilson model; (♦) experimental data of Glycine; (●) experimental data of Serine |
In Eq. 12 Δs'R and Δh′R are the standard entropy and enthalpy changes in aqueous solutions. These values are two adjustable parameters. In the calculation, the activity coefficients of optical isomers of amino acids are assumed to be equal. The results of calculation for the solubility of two amino acids with the modified Wilson model in aqueous solution are shown in Fig. 3. As shown in this figure this model can accurately predict the solubility of amino acids in aqueous solution over a wide range of temperature.
| Fig. 3: | Solubility of three amino acids for the modified Wilson model plotted vs. temperature: (–) result of the modified Wilson model; (♦) experimental data of DL-Serine; (▲) experimental data of Glycine; (●) experimental data of L-Alanine |
| Fig. 4: | Solubility of Proline plotted vs. temperature: (–) result of the modified Wilson model; (●) experimental data of Proline. |
Figure 4 shows the correlation of Proline which is much more soluble in water than the other amino acids. As shown in this figure the accuracy of the modified Wilson model in correlating the experimental solubility data of Proline is as an amino acid in water. The value of Δs/R and Δh/R of Eq. 12 are presented in Table 2.
To make sure the capability of this model in predicting the other independent thermodynamic properties, it is interesting to compare the values for the dimensionless Gibbs free energy change of the solute. As seen in Table 3 the modified Wilson model accurately represents the values of Δg/RT0 in comparison with the experimental data reported in the literature and the Khoshkbarchi-Vera model (1996).
Conclusions
The modified Wilson model has been applied for prediction of phase behavior of amino acids and peptides in pure water. The adjustable parameters of this model for amino acids and peptides were calculated by fitting the experimental activity coefficients of amino acids and peptides. Using these parameters for the activity coefficients, the solubilities of several amino acids in aqueous solution can be determined with the experimental values of standard enthalpy changes in solution. The predictions are acceptable a wide range of temperatures. The results of solubility of amino acids for Gibbs free energy change of the solute at temperature 298.15 K are in agreement with the experimental data available in the literature.
List of symbols
| a | : | Molar energy parameter |
| b | : | Empirical parameter |
| f | : | Fugacity |
| g | : | Molar excess Gibbs free energy |
| m | : | Molality |
| M | : | Molar mass |
| OF | : | Objective function |
| rms | : | Root mean square |
| R | : | Universal constant of gas |
| T | : | Temperature |
| V | : | Molar volume of pure component |
| x | : | Mole fraction of liquid phase |
| Δg | : | Gibbs free energy change in the solution |
| Δh | : | Enthalpy energy change in the solution |
| Δs | : | Entropy energy change in the solution |
Greek letters
| γ | : | Activity coefficient |
| Λ | : | Binary interaction for Wilson model |
Subscripts
| i,j | : | Species |
| A | : | Amino acid |
| W | : | Water |
Superscripts
| exp | : | Experimental |
| cal | : | Calculation |
| ° | : | Reference |
| L | : | Liquid |
| S | : | Solid |
| x | : | Mole fraction scale |
| m | : | Molality scale |