Effect of Solvent on Protonation Equilibria of L-Proline and L-Valine in 1 , 2-Propanediol-Water Mixtures

Protonation equilibria of L-proline and L-valine in varying compositions (0.0-60.0% v/v) of 1, 2-Propanediol-water mixtures were investigated pH-metrically. Titrations were performed at 303.0 K and the ionic strength of the medium was maintained at 0.16 mol L using sodium chloride. The best fit chemical models of the protonation equilibria were based on crystallographic R-factor, χ, skewness, and kurtosis. All the protonation constants of proline and valine increased with increasing propanediol content. This is attributed to the dielectric constant of the medium.


Introduction
L-proline is an imino acid containing pyrrole type nitrogen rather than the amino nitrogen of the amino acids 1 .Proline is one of the main components of the collagen.It promotes the formation of bone, skin and cartilage.It is extremely important for the proper functioning of joints and tendons.L-valine is an essential amino acid and not synthesized in mammals.Valine participates in the detoxification of ammonia and works along with α-ketoglutarate.It is an important amino acid in the prevention of muscle wasting in diabetes.
1,2-Propanediol also known as propylene glycol (PG) is a clear, viscous, colorless, odorless liquid with a dielectric constant of 30.2 2 .It is fully miscible with water.The dielectric constant of the medium decreases with increase in mole fraction of PG.This solvent is selected to provide the similar physiological conditions where the concept of equivalent solution dielectric constant for protein cavities is applicable 3 .
Study of dissociation and solvation processes in solutions of amino acids is important to elucidate the connection between chemical ability and biological activity.Protonation constants of α-amino acids can be determined by analysis of acid-base titrations.The methods have been critically reviewed [4][5][6] .In the present investigation we studied the protonation constants of L-proline and L-valine in PG-water mixtures.The data obtained would be useful to those working in biomedicine.

Experimental
Solutions (0.05 mol L -1 ) of L-proline (SRL, India) and L-valine (Qualigens, India) were prepared in triple-distilled water by maintaining 0.05 mol L -1 hydrochloric acid concentration to increase the solubility.1, 2-Propanediol (Qualigens, India) was used without further purification.Carbonate free sodium hydroxide (Qualigens, India) pellets were used for the preparation of 0.4 mol L -1 solution.Hydrochloric acid (Qualigens, India) of 0.2 mol L -1 was prepared.Sodium chloride (Qualigens, India) of 2.0 mol L -1 was prepared to maintain 0.16 mol L -1 ionic strength in the titrand.Triple distilled water was used throughout the experiment.The strengths of acid and alkali were determined using Gran plot method 7 .To assess the errors that might have crept in to the determination of the concentrations, the data were subjected to analysis of variance of one way classification (ANOVA) 8 .

Alkalimetric Titrations
Alkalimetric titrations were carried out with varying composition of PG (0.0-60.0%v/v) maintaining an ionic strength of 0.16 mol L -1 with sodium chloride at 303.0±0.1 K. Amounts of L-proline and L-valine in the titrands ranged between 0.25 and 0.50 mmols.Systronics MK-VI digital pH meter was used.Potassium hydrogen phthalate (0.05 mol L -1 ) and borax (0.01 mol L -1 ) solutions were used to calibrate the pH meter.The glass electrode was equilibrated in a well stirred PG-water mixture containing inert electrolyte for several days.At regular intervals strong acid was titrated against alkali to check the complete equilibration of the glass electrode.The calomel electrode was refilled with PG-water mixture of equivalent composition of the titrand.The details of the experimental procedure and titration assembly have been detailed elsewhere 9 .

Modeling Strategy
The approximate protonation constants of L-proline and L-valine were calculated with the computer program SCPHD 10 .The best fit chemical model for each system investigated was arrived at using non-linear least-squares computer program, MINIQUAD75 11 .

Results and Discussion
Normal biochemical processes occur in aqueous solutions at about neutral pH.Physiological pH is about 7.2 to 7.4.Amino acids present in biomolecules can gain or lose protons depending on the availability of hydrogen ions in the solution.This situation results in the simultaneous existence of a number of protonation-deprotonation equilibria in solution.
Secondary formation functions like average number of protons bound per mole of ligand (n H ) and number of moles of alkali consumed per mole of ligand (a) are useful to detect the number of polymeric species and equilibria.Plots of n H versus pH (formation curves) for different concentrations of the ligand should overlap if there is no formation of polymeric species.Overlapping formation curves for L-proline and L-valine (Figure1) rule out the polymerization of the ligand molecules.The pH values at half integral values of n H correspond to the protonation constants of the ligands.Two half integrals (0.5 and 1.5) in the case of both the ligands (Figure 1) emphasize the presence of two protonation-deprotonation equilibria in the pH range of present study.The plots of a versus pH for L-proline and L-valine were given in Figure 2. The negative values of a correspond to the number of moles of free acid present in the titrand and the number of associable protons.The positive values of a indicate the number of dissociable protons in the ligand molecules.The maximum value of a in Figure 2 is +1, which indicates that both L-proline and L-valine have one dissociable proton.The best fit models containing the type of species and log values of overall formation constants (log β) along with some of the important statistical parameters of the present study are given in Table 1.These values are close to the reported values [12][13][14][15][16] , after allowing for changes in experimental conditions as well as methods of calculation.A very low standard deviation (SD) in log β values and U corr (sum of the squares of deviations in concentrations of ligand and hydrogen ion at all experimental points corrected for degrees of freedom) indicate that the experimental data can be represented by the model.Small values of mean, standard deviation and mean deviation for the systems corroborate that the residuals are around a zero mean with little dispersion.

Residual Analysis 17
In data analysis with least squares methods, the residuals (the differences between the experimental data and the data simulated based on the model parameters) are assumed to follow Gaussian distribution.When the data are fit into the models, the residuals should be ideally equal to zero.Further, a model is considered adequate only if the residuals do not show any trend.Respecting the hypothesis of the least squares analysis, the residuals are tested for normal distribution.Such tests are χ 2 , skewness, kurtosis, and R-factor.These statistical parameters of the present data show that the best fit models portray the acido-basic equilibria of L-proline and L-valine in PG-water mixtures, as discussed below.
χ 2 test χ 2 is a special case of gamma distribution, whose probability density function is an asymmetrical function.This distribution measures the probability of residuals forming a part of standard normal distribution with zero mean and unit standard deviation.If χ 2 calculated is less than the table value, the model is accepted.

Crystallographic R-Test
Hamilton's R factor ratio test 18 is applied in complex equilibria to decide whether inclusion of more species in the model is necessary or not.In pH-metric method, the readability of pH meter is taken as the R

Skewness
It is a dimensionless quantity indicating the shape of the error distribution profile.A value of zero for skewness indicates that the underlying distribution is symmetrical.If the skewness is greater than zero, the peak of the error distribution curve is to the left of the mean and the peak is to the right of the mean if skewness is less than zero.The values of skewness recorded in Table 1 are between -0.15 and 0.98.These data evince that the residuals form a part of normal distribution; hence, least-squares method can be applied to the present data.9) 88 0.966 0.98 5.45 10.64 0.0054 1.9-3.6&8.4-9.9 20.0 9.46(8) 12.13(12) 109 1.972 1.42 6.96 12.24 0.0079 1.9-3.8&8.4-10.

Kurtosis
It is a measure of the peakedness of the error distribution near a model value.For an ideal normal distribution kurtosis value should be three (mesokurtic).If the calculated kurtosis is less than three, the peak of the error distribution curve is flat (platykurtic) and if the kurtosis is greater than three, the distribution shall have sharp peak (leptokurtic).The kurtosis values in the present study indicate that the residuals form leptokurtic pattern in the case of L-valine and close to mesokurtic in the case of L-proline.
Alkalimetric titration data are simulated using the model parameters given in Table 1.These data are compared with the experimental alkalimetric titration data, to verify the sufficiency of the models.The overlap of the typical experimental and simulated titration data indicates that the proposed models represent the experimental data.

Effect of Systematic Errors in Concentrations on Best Fit Model
MINIQUAD75 does not have an inbuilt provision to study the effect of systematic errors in the concentration of ingredients like mineral acid, alkali and ligand.In order to rely upon the best fit chemical model for critical evaluation and application, a brief investigation was made by introducing pessimistic errors in the ingredients.This type of investigation is useful because the data acquisition was done under varied experimental conditions with different accuracies.The results of a typical system given in Table 2 emphasize that the errors in the concentrations of alkali and mineral acid affect the protonation constants more than that of the ligand.

Effect of Dielectric Constant of Medium
When the ionization of an acid gives a net increase of ions, a decrease in the dielectric constant of the solvent should be accompanied by an increase in the protonation constant of a weak acid dissolved in it.The variation of protonation constant or change in free energy with co-solvent content depends upon two factors, viz, electrostatic and non-electrostatic forces.Born's classical treatment holds good in accounting for the electrostatic contribution to the free energy change 19 .According to this treatment, the energy of electrostatic interaction or the logarithm of step-wise protonation constant (log K) should vary linearly as a function of the reciprocal of the dielectric constant (1/D) of the medium.Such linear variation of protonation constants of L-proline and L-valine (Figure 3) in PG-water mixtures shows the dominance of electrostatic interactions.These amino acids can exist in anionic, zwitterionic and cationic forms in different equilibria investigated.The cation stabilizing nature of co-solvents, specific solvent-water interactions, charge dispersion, and specific interactions of co-solvent with solute, account for the deviation of classical linear relationship of log K with 1/D.K 1 and K 2 are step-wise protonation constants for the reactions mentioned in Figure 3.

Distribution Diagrams
The distribution plots (Figure 5) produced using the protonation constants from the best fit models (Table 1) show the existence of LH2 + , LH ± , and L -in the case of both L-proline and L-valine in different pH ranges.The corresponding protonation-deprotonation equilibria are shown in Figure 4.As the alkali is added to the titrand containing the ligands, the protonated forms of the ligands lose their protons.In the pH range of present study L-proline and L-valine lose carboxylic and amino protons successively.

Conclusion
1. L-proline and L-valine have one dissociable proton and one amino group which can associate with a proton.Both the ligands exist as LH 2 + at low pH and get deprotonated with the formation of LH ± and L -successively with increase in pH. 2. Secondary formation functions detected two protonation equilibria for both the ligands.3. The log values of protonation constants of L-proline and L-valine increased linearly with decreasing dielectric constant of PG-water mixtures indicating the dominance of electrostatic forces in the protonation-deprotonation equilibria.4. The effect of systematic errors in the influential parameters showed that the errors in the concentrations of alkali and mineral acid will affect the protonation constants more than that of ligand.

Figure 2 .
Figure 2. Variation of a with pH in 30% v/v PG-water mixture: (A) L-proline and (B) Lvaline.
limit' which represents the upper boundary of R beyond which the model bears no significance.When different values are obtained for models containing different number of species, models whose values are greater than R-table are rejected.The low crystallographic R-values given in Table 1 indicate the sufficiency of the model.

Table 2 .
Effect of errors in influential parameters on the protonation constants in 30% v/v PG-water mixture.