Chapter 4 Study of solute-solute and solute-solvent interactions of l-histidine in aqueous-sucrose solutions at different temperatures using

Study of solute-solute and solute-solvent interactions of l-histidine in aqueous-sucrose solutions at different temperatures using volumetric, ultrasonic and viscometric methods

4.1. INTRODUCTION The physicochemical properties of amino acids in aqueous solutions provide valuable information on solute-solute and solute-solvent interactions [1-6]. These interactions are important in understanding the stability of proteins, and are implicated in several biochemical and physiological processes in a living cell [7-9]. In continuation to our earlier studies [10-12] on amino acids in aqueous-carbohydrate solutions, we report here the results of our study on volumetric, ultrasonic and viscometric behaviour of l- histidine in aqueous-sucrose solutions. It is known [13,14] that polyhydroxy compounds helps in stabilizing the native globular structure of protein and reduce the extent of their denaturation by other substances. Carbohydrates located at cell surfaces, are important as receptors for the bioactive structures of enzymes, hormones, viruses, antibodies, etc. [15]. The protein-carbohydrate interactions are important for immunology, biosynthesis, pharmacology, medicine and cosmetic industry [16,17]. Thus, the properties of amino acids in aqueous-carbohydrate solutions are essential for understanding the chemistry of biological systems [18,19]. In this chapter, the densities, ρ, ultrasonic speeds, u, and viscosities, η of l- histidine in aqueous-sucrose (5, 10, 15 and 20 % of sucrose, w/w in water) at 293.15, 298.15, 303.15, 308.15, 313.15, and 318.15 K and at atmospheric pressure, are reported. These experimental data have been used to calculate the apparent molar volume, apparent molar volume, V φ, limiting apparent molar volume, V φ and the slope, S v, apparent molar compressibiliity, Ks, φ, limiting apparent molar compressibility, Ks, φ and the slope, S k, transfer volume, V φ,tr, transfer compressibility, Ks, φ, tr, Falkenhagen Coefficient, A, Jones-Dole coefficient, B and temperature derivative of B-coefficient, db/dt. These parameters have been used to discuss the solute-solute and solute-solvent interactions in these systems. 4.2. RESULTS AND DISCUSSION The experimental values of density, ρ, ultrasonic speed, u, and viscosity, η of l- histidine solutions in aqueous-sucrose solvents as functions of l-histidine concentration and temperature are listed in Table 4.1. 92

4.2.1. Apparent Molar Volume and Compressibility The apparent molar volume, V φ and apparent molar compressibiliity, Ks, φ of these solutions were calculated by using the relations V φ 1000( ρo ρ) M = + (4.1) mρρ ρ o K s, φ o 1000( κ sρo κ s ρ) κ sm = + (4.2) mρρ ρ o where m is the molal concentration of the solute (l-histidine), ρ and ρ o are the densities of the solution and the solvent (aqueous-sucrose), respectively; M is the molar mass of the solute (l-histidine), and κ s and κ s are the isentropic compressibilities of the solution and the solvent (aqueous-sucrose), respectively, calculated using the relation κ s = 1/u 2 ρ (4.3) The values of V φ and Ks, φ as functions of l-histidine concentration and temperature are shown graphically in Fig. 4.1 and Fig. 4.2. It is observed that, for l- histidine in all the four aqueous-sucrose solvents, V φ and Ks, φ vs. m curves (Fig. 4.1 and Fig. 4.2) were almost linear in the studied concentration range and at each investigated temperature. 4.2.2. Limiting Apparent Molar Volume and Compressibility The values of limiting apparent molar volume, V φ and the slope, S v, limiting apparent molar compressibility, Ks, φ and the slope, S k have been obtained using method of linear regression of V φ and Ks, φ vs. m of l-histidine in sucrose + water solvents from the following relations [20] V = V + S m φ φ v (4.4) s, φ s, φ k K = K + S m (4.5) 93

K φ where the intercepts, V φ or s,, by definition are free from solute-solute interactions and therefore provide a measure of solute-solvent interactions, whereas the experimental slope, S v or S k provides information regarding solute-solute interaction. The values of V φ, S v, Ks, φ, and S k along with the standard deviations of linear regression, σ for l-histidine in aqueous-sucrose solutions at different temperatures are listed in Table 4.2. A perusal of Table 4.2 reveals that the V φ values are positive and S v values are negative for l-histidine in aqueous-sucrose solutions indicating the presence strong solute-solvent interactions and weak solute-solute interactions in these systems. The trends observed in V φ values can be due to their hydration behaviour [21 25], which comprises of following interactions in these systems: (a) The terminal groups of zwitterions of amino acids, NH + 3 and COO are hydrated in an electrostatic manner whereas, hydration of R group depends on its nature, which may be hydrophilic, hydrophobic or amphiphilic; and (b) the overlap of hydration co-spheres of terminal NH + 3 and COO groups and of adjacent groups results in volume change. The V φ values increase due to reduction in the electrostriction at terminals, whereas it decreases due to disruption of side group hydration by that of the charged end. The increase in V φ values (Fig. 4.3) with increase in temperature for l-histidine in aqueous-sucrose solutions can be explained by considering the size of primary and secondary solvation layers around the zwitterions. At higher temperatures the solvent from the secondary solvation layer of l-histidine zwitterions is released into the bulk of the solvent, resulting in the expansion of the solution, as inferred from larger V φ values at higher temperatures [26,27]. Similar trends in V φ values were obtained in our earlier study [10] on interactions of l-histidine in aqueous-glucose solutions, however V φ values are found larger in case of aqueous-sucrose solvents as compared to aqueous-glucose solvents. Similar trends in V φ have also been reported by Ali et al. [17] for amino acids in aqueous-sucrose solutions and Pal and Kumar [2] for l-alanine and l-valine in water + sucrose solutions. 94

The values of Ks, φ are negative (Table 4.2) for l-histidine in aqueous-sucrose solutions, indicating that the water molecules around ionic charged groups of amino acids are less compressible than the water molecules in the bulk solution [28,29]. This further supports the conclusion that there exist strong solute-solvent interactions and weak solute-solute interactions in these systems. The values of Ks, φ are negative (Fig. 4.4) and S k are positive (Table 4.2) for l-histidine in aqueous-sucrose solutions, indicating that there exist strong solute-solvent interactions and weak solute-solute interactions in these systems. This further supports the conclusion that the hydrophilic-ionic groups and hydrophilic-hydrophilic group interactions between OH groups of sucrose with l-histidine zwitterions dominate in these systems. The values K φ of s, increase with increase in temperature, indicating release of more water molecules from the secondary solvation layer of l-histidine zwitterions into the bulk, thereby, are making the solutions more compressible. 4.2.3. Transfer Limiting Partial Molar Volume Limiting apparent molar properties of transfer provide qualitative as well as quantitative information regarding solute-solvent interactions without taking into account the effects of solute-solute interactions [30]. The transfer volumes, V φ,tr of l- histidine from water to aqueous-sucrose solutions were calculated by using the relation V = V V (4.6) o o o φ, tr φ, aq. sucro s e φ, water where V φ,water is the limiting apparent molar volume of l-histidine in water (Table 4.2). The V φ,tr values for l-histidine from water to aqueous-sucrose solutions are included in Table 4.2 and represented graphically in Fig. 4.5. Fig. 4.5 indicates that V φ of l-histidine in aqueous-sucrose are more than those in pure water, i.e., V φ,tr values are positive. In general, the types of interactions occurring between l-histidine and sucrose can be classified as follows [23,24,31]: 95

(a) The hydrophilic-ionic interaction between OH groups of sucrose and zwitterions of l-histidine. (b) Hydrophilic-hydrophilic interaction the OH groups of sucrose and NH groups in the side chain of acid l-histidine mediated through hydrogen bonding. (c) Hydrophilic-hydrophobic interaction between the OH groups of sucrose molecule and non-polar ( CH 2 ) in side chain of l-histidine molecule. (d) Hydrophobic-hydrophobic group interactions between the non-polar groups of sucrose and non-polar ( CH 2 ) in side chain of l-histidine molecule. The V φ values increase due to reduction in the electrostriction at terminals by positive contribution from the interactions of type (a) and (b), whereas it decreases due to disruption of side group hydration by that of the charged end by negative contribution from the interactions of type (c) and (d) mentioned above. The observed positive V φ,tr values suggest that the hydrophilic-ionic group and hydrophilichydrophilic group interactions dominate in these systems. The V φ,tr values increase with increase in sucrose concentration in the solutions (Fig. 4.5). This may be due to greater hydrophilic-ionic groups and hydrophilic-hydrophilic group interactions with increased concentrations of sucrose. The Similar trends in V φ and V φ,tr with sucrose concentration were also observed by Zhao et al. [4] from volumetric properties of arginine in aqueous-carbohydrate solutions at 298.15 K. It is worth to compare the present results with those reported in chapter 3 on the behaviour of l-histidine in aqueous-glucose solutions [10]. The V φ and V φ,tr values are found much larger in case of aqueous-sucrose solvents as compared to aqueousglucose solvents [10]. This may be due to greater hydrophilic-ionic groups and hydrophilic-hydrophilic group interactions, with the presence of more hydroxyl groups in sucrose molecules as compared to glucose molecules. Zhao et al. [4] also reported similar results from volumetric properties of arginine in aqueousglucose/sucrose solvents at 298.15 K, wherein V φ and V φ,tr values were found larger in aqueous-sucrose solvents as compared to aqueous-glucose solvents. These authors also suggested similar order of interactions of arginine in aqueous-glucose/sucrose solvents. Our results are in agreement with the conclusions drawn by Zhao et al. [4]. 96

4.2.4. Transfer Limiting Partial Molar Compressibility The transfer compressibility of l-histidine from water to aqueous-sucrose solutions, were calculated by using the relation Ks, φ, tr s, φ, tr s, φ, aq sucros e Ks, φ, water K = K (4.7) where K s, φ, water 4.2). The Ks, φ, tr is the limiting apparent molar volume of l-histidine in water (Table values for l-histidine from water to aqueous-sucrose solutions are included in Table 4.2 and represented graphically in Fig. 4.6. Table 4.2 indicates that Ks, φ of l-histidine in aqueous-sucrose are more than those in pure water, i.e., Ks, φ, tr values are positive. The observed positive Ks, φ, tr values suggest that the hydrophilicionic groups and hydrophilic-hydrophilic group interactions dominate in these systems. The Ks, φ, tr values increase with increase in sucrose concentration in the solutions (Fig. 4.6). This may be due to greater hydrophilic-ionic group and hydrophilic-hydrophilic group interactions with increased concentrations of sucrose. The observed trends in Ks, φ and Ks, φ, tr further support the conclusions drawn from V φ and V φ,tr. The decrease in V φ,tr and Ks, φ, tr values with increase in temperature, indicate that release of water molecules from the secondary solvation layer of l- histidine zwitterions into the bulk, becomes difficult with addition of sucrose in the solution due to greater hydrophilic-ionic groups and hydrophilic-hydrophilic group interactions as compared to those in water. 4.2.5. Analysis of Viscosity Data The viscosity data were analyzed by using Jones-Dole [32] equation of the form η r η = = 1+ Am 1/ 2 + Bm (4.8) η o where η r is the relative viscosity of the solution, η and η o are the viscosities of solution and the solvent (sucrose + water), respectively, m is molality of l-histidine in sucrose + water solvent, A and B are the Falkenhagen [33,34] and Jones-Dole [34] coefficients, respectively. Coefficient A accounts for the solute-solute interactions and 97

B is a measure of structural modifications induced by the solute-solvent interactions [35,36]. The values of A and B have been obtained as the intercept and slope from 1/ 2 linear regression of [( η 1)/ m ] vs. m 1/2 curves, which were found almost linear for r these systems. The values of A and B along with the standard deviations of linear regression, σ are listed in Table 4.3. The values of A- and B-coefficients are positive, however, the A-coefficients are much smaller in magnitude as compared to B- coefficients, suggesting weak solute-solute and strong solute-solvent interactions in these solutions. Large and positive B-coefficients values, which increase with increasing concentration of sucrose, also indicate a structure to allow the co-solute (sucrose) to act on solvent [4]. B-coefficients increase (Fig. 4.7) when the water is replaced by sucrose, i.e., sucrose act as water structure-maker by H-bonding. B- coefficients increases (Fig. 4.7) with increasing concentration of sucrose, the reason may be that the friction increases to prevent water flow at increased sucrose concentration. The values of B-coefficients are found larger in case of aqueoussucrose solvents as compared to aqueous-glucose solvents [10], which may be due to greater hydrophilic-ionic group and hydrophilic-hydrophilic group interactions, with the presence of more hydroxyl groups in sucrose molecules as compared to glucose molecules. Thus, the values of coefficients A and B support the behaviours of V φ, Ks, φ, S v, S k, V φ,tr and Ks, φ, tr, which suggest stronger solute-solvent interactions as compared to solute-solute interactions in these solutions. The temperature derivatives of B-coefficient (db/dt) have also been calculated. The sign of db/dt values is found to provide important information regarding structure-making or structure-breaking ability of the solute in solvent media [35,37]. In general, the db/dt is negative for structure-maker and positive for structure-breaker solutes in solution [35,37]. The negative db/dt values for l-histidine in aqueoussucrose solvents indicate that l-histidine act as structure-maker in aqueous-sucrose solvents under study. Ali et al. [17] also reported similar structure-making behaviour of glycine in water + sucrose solutions and of l-histidine in aqueous-caffeine solvent [38]. Pal and Kumar [39] have also drawn similar conclusions for some amino acids in aqueous-urea solutions. 98

4.3. CONCLUSIONS The densities, ρ, ultrasonic speeds, u, and viscosities, η of solutions of l-histidine in aqueous-sucrose solvents (5, 10, 15 and 20 % of sucrose, w/w in water) were measured at different temperatures. From the experimental data, various parameters, K φ viz., V φ, V φ, Ks, φ, s,, V φ,tr, Ks, φ, tr, Falkenhagen Coefficient, A, Jones-Dole coefficient, B and db/dt were calculated. The results indicate that there exist strong solute-solvent (hydrophilic-ionic group and hydrophilic-hydrophilic group) interactions in these systems, which increase with increase in sucrose concentration. It is also observed that l-histidine act as structure-maker in these aqueous-sucrose solvents. 99

Table 4.1: Densities, ρ, ultrasonic speeds, u, and viscosities, η of solutions of l-histidine in sucrose + water (5, 10, 15 and 20 % sucrose, w/w in water) solvents as functions of molality, m of l-histidine in sucrose + water solvents and temperature. m (mol kg 1 ) T /(K) 293.15 298.15 303.15 308.15 313.15 318.15 l-histidine in 5 % aqueous-sucrose ρ /(kg m 3 ) 0.0000 1018.91 1017.19 1015.45 1013.72 1011.98 1010.23 0.0249 1020.19 1018.47 1016.74 1015.01 1013.28 1011.54 0.0498 1021.46 1019.75 1018.03 1016.31 1014.58 1012.84 0.0749 1022.75 1021.05 1019.32 1017.61 1015.89 1014.16 0.0999 1024.03 1022.34 1020.62 1018.91 1017.19 1015.47 0.1250 1025.32 1023.63 1021.92 1020.21 1018.50 1016.78 0.1499 1026.60 1024.91 1023.20 1021.50 1019.79 1018.07 0.1749 1027.89 1026.20 1024.49 1022.79 1021.08 1019.37 0.1999 1029.17 1027.48 1025.78 1024.08 1022.37 1020.66 u /(m s 1 ) 0.0000 1499.7 1514.3 1525.1 1535.7 1545.6 1554.5 0.0249 1503.9 1518.4 1529.0 1539.4 1549.1 1557.8 0.0498 1507.5 1521.8 1532.1 1542.3 1551.8 1560.2 0.0749 1510.5 1524.6 1534.5 1544.5 1553.6 1561.8 0.0999 1512.9 1526.7 1536.3 1546.0 1554.7 1562.6 0.1250 1514.6 1528.1 1537.3 1546.7 1555.0 1562.5 0.1499 1515.6 1528.8 1537.7 1546.7 1554.8 1561.9 0.1749 1515.9 1529.0 1537.3 1546.1 1553.8 1560.3 0.1999 1515.6 1528.4 1536.5 1544.8 1552.1 1558.4 10 3 η /(N s m 2 ) 0.0000 1.2137 1.0110 0.9129 0.8285 0.7457 0.6946 0.0249 1.2335 1.0264 0.9260 0.8394 0.7548 0.7026 0.0498 1.2513 1.0403 0.9372 0.8490 0.7627 0.7092 0.0749 1.2690 1.0539 0.9483 0.8582 0.7702 0.7155 0.0999 1.2865 1.0671 0.9592 0.8673 0.7778 0.7217 0.1250 1.3043 1.0809 0.9704 0.8764 0.7851 0.7278 0.1499 1.3216 1.0942 0.9815 0.8852 0.7923 0.7337 0.1749 1.3392 1.1078 0.9925 0.8941 0.7993 0.7396 0.1999 1.3574 1.1212 1.0032 0.9027 0.8062 0.7455 100

Table 4.1 (Continued) m (mol kg 1 ) T /(K) 293.15 298.15 303.15 308.15 313.15 318.15 l-histidine in 10 % aqueous-sucrose ρ /(kg m 3 ) 0.0000 1039.28 1037.45 1035.61 1033.76 1031.93 1030.09 0.0249 1040.42 1038.60 1036.76 1034.92 1033.10 1031.26 0.0499 1041.57 1039.75 1037.92 1036.09 1034.27 1032.44 0.0749 1042.72 1040.91 1039.09 1037.25 1035.44 1033.62 0.0999 1043.88 1042.07 1040.25 1038.43 1036.61 1034.80 0.1250 1045.04 1043.24 1041.42 1039.60 1037.79 1035.98 0.1499 1046.20 1044.40 1042.59 1040.77 1038.96 1037.15 0.1750 1047.37 1045.57 1043.76 1041.94 1040.14 1038.33 0.1999 1048.53 1046.73 1044.92 1043.11 1041.31 1039.50 u /(m s 1 ) 0.0000 1521.4 1530.6 1540.3 1550.2 1559.9 1568.4 0.0249 1525.4 1534.5 1544.0 1553.8 1563.4 1571.7 0.0499 1528.9 1537.8 1547.1 1556.7 1566.2 1574.4 0.0749 1531.8 1540.6 1549.7 1559.1 1568.4 1576.5 0.0999 1534.2 1542.8 1551.7 1561.0 1570.1 1578.1 0.1250 1536.0 1544.5 1553.2 1562.3 1571.2 1578.8 0.1499 1537.2 1545.6 1554.2 1563.0 1571.5 1579.1 0.1750 1537.8 1546.1 1554.6 1563.3 1571.8 1578.8 0.1999 1538.2 1546.4 1555.2 1563.3 1571.2 1578.0 10 3 η /(N s m 2 ) 0.0000 1.3765 1.1832 1.0606 0.9614 0.8804 0.0000 0.0249 1.4006 1.2028 1.0770 0.9754 0.8923 0.0249 0.0499 1.4227 1.2204 1.0915 0.9872 0.9023 0.0499 0.0749 1.4439 1.2376 1.1057 0.9989 0.9120 0.0749 0.0999 1.4656 1.2548 1.1198 1.0102 0.9215 0.0999 0.1250 1.4868 1.2720 1.1336 1.0220 0.9310 0.1250 0.1499 1.5081 1.2888 1.1476 1.0335 0.9405 0.1499 0.1750 1.5298 1.3060 1.1621 1.0451 0.9500 0.1750 0.1999 1.5515 1.3228 1.1752 1.0561 0.9595 0.1999 101

Table 4.1 (Continued) m (mol kg 1 ) T /(K) 293.15 298.15 303.15 308.15 313.15 318.15 l-histidine in 15 % aqueous-sucrose ρ /(kg m 3 ) 0.0000 1060.31 1058.49 1056.67 1054.84 1053.01 1051.20 0.0249 1061.33 1059.52 1057.70 1055.88 1054.05 1052.25 0.0499 1062.36 1060.55 1058.74 1056.92 1055.10 1053.30 0.0749 1063.40 1061.59 1059.78 1057.97 1056.15 1054.36 0.0999 1064.44 1062.63 1060.83 1059.02 1057.21 1055.41 0.1249 1065.48 1063.68 1061.88 1060.07 1058.26 1056.47 0.1500 1066.53 1064.73 1062.94 1061.13 1059.33 1057.54 0.1750 1067.58 1065.78 1063.99 1062.19 1060.39 1058.60 0.1999 1068.63 1066.83 1065.04 1063.24 1061.44 1059.65 u /(m s 1 ) 0.0000 1532.4 1542.5 1551.5 1560.5 1569.6 1577.2 0.0249 1536.2 1546.3 1555.2 1564.1 1573.1 1580.6 0.0499 1539.6 1549.6 1558.4 1567.3 1576.2 1583.6 0.0749 1542.6 1552.5 1561.2 1570.0 1578.8 1586.2 0.0999 1545.3 1555.1 1563.7 1572.3 1581.0 1588.2 0.1249 1547.5 1557.2 1565.6 1574.2 1582.9 1589.9 0.1500 1549.3 1558.8 1567.2 1575.6 1584.3 1591.0 0.1750 1550.5 1560.0 1568.1 1576.5 1585.1 1591.7 0.1999 1551.4 1560.6 1568.6 1576.8 1585.2 1591.9 10 3 η /(N s m 2 ) 0.0000 1.6088 1.4184 1.2523 1.1291 1.0250 0.9402 0.0249 1.6396 1.4440 1.2734 1.1467 1.0401 0.9531 0.0499 1.6672 1.4660 1.2914 1.1615 1.0525 0.9637 0.0749 1.6945 1.4874 1.3088 1.1758 1.0646 0.9738 0.0999 1.7218 1.5088 1.3265 1.1906 1.0765 0.9839 0.1249 1.7485 1.5306 1.3445 1.2051 1.0889 0.9942 0.1500 1.7756 1.5529 1.3625 1.2195 1.1010 1.0040 0.1750 1.8036 1.5750 1.3807 1.2340 1.1128 1.0139 0.1999 1.8320 1.5991 1.3985 1.2488 1.1248 1.0236 102

Table 4.1 (Continued) m (mol kg 1 ) T /(K) 293.15 298.15 303.15 308.15 313.15 318.15 l-histidine in 20 % aqueous-sucrose ρ /(kg m 3 ) 0.0000 1082.73 1080.77 1078.80 1076.84 1074.88 1072.93 0.0250 1083.64 1081.68 1079.72 1077.76 1075.81 1073.86 0.0499 1084.55 1082.60 1080.64 1078.69 1076.74 1074.80 0.0750 1085.47 1083.52 1081.57 1079.62 1077.68 1075.74 0.0999 1086.39 1084.45 1082.50 1080.55 1078.61 1076.67 0.1249 1087.32 1085.38 1083.43 1081.49 1079.55 1077.61 0.1500 1088.26 1086.32 1084.38 1082.43 1080.50 1078.56 0.1749 1089.19 1087.26 1085.31 1083.37 1081.44 1079.50 0.2000 1090.13 1088.20 1086.26 1084.32 1082.38 1080.45 u /(m s 1 ) 0.0000 1543.2 1553.3 1563.1 1573.5 1582.2 1591.2 0.0250 1546.8 1556.9 1566.7 1577.1 1585.8 1594.8 0.0499 1550.1 1560.2 1570.0 1580.3 1589.0 1597.9 0.0750 1553.1 1563.2 1572.9 1583.2 1591.8 1600.7 0.0999 1555.8 1565.8 1575.5 1585.8 1594.3 1603.1 0.1249 1558.2 1568.2 1577.8 1587.9 1596.4 1605.2 0.1500 1560.3 1570.2 1579.7 1589.8 1598.1 1606.7 0.1749 1562.1 1572.0 1581.3 1591.2 1599.4 1608.0 0.2000 1563.6 1573.3 1582.5 1592.4 1600.5 1608.9 10 3 η /(N s m 2 ) 0.0000 1.9318 1.7558 1.5489 1.3963 1.2495 1.1500 0.0250 1.9725 1.7899 1.5772 1.4198 1.2695 1.1671 0.0499 2.0078 1.8202 1.6012 1.4398 1.2858 1.1812 0.0750 2.0427 1.8492 1.6247 1.4595 1.3019 1.1948 0.0999 2.0773 1.8782 1.6485 1.4787 1.3178 1.2085 0.1249 2.1128 1.9077 1.6727 1.4984 1.3337 1.2220 0.1500 2.1488 1.9370 1.6966 1.5177 1.3499 1.2351 0.1749 2.1855 1.9675 1.7206 1.5373 1.3661 1.2485 0.2000 2.2215 1.9975 1.7446 1.5573 1.3820 1.2618 103

Table 4.2: Limiting apparent molar volume, V φ, slope, Sv, transfer volume, K φ K φ V φ,tr, Limiting apparent molar compressibility, s,, slope, S k, transfer compressibility, s,, tr and standard deviations of linear regression, σ for l-histidine in sucrose + water (5, 10, 15 and 20 % sucrose, w/w in water) solvents at different temperatures. Property l-histidine in water [10] T /(K) 293.15 298.15 303.15 308.15 313.15 318.15 10 5 V φ /m 3 mol 1 9.806 9.828 9.852 9.870 9.895 9.917 10 σ for equation (4.4) 0.033 0.021 0.037 0.036 0.037 0.033 10 5 S v /m 3 mol 1 kg 1-1.174-1.162-1.174-1.165-1.174-1.179 10 12 Ks, φ /m 5 N 1 mol 1-2.043-1.916-1.790-1.646-1.518-1.405 σ for equation (4.5) 0.004 0.005 0.013 0.011 0.012 0.008 10 12 S k /m 5 N 1 mol 1 kg 1 6.938 7.159 7.414 7.233 7.069 7.098 l-histidine in 5 % aqueous-sucrose 10 5 V φ /m 3 mol 1 9.913 9.929 9.947 9.959 9.977 9.993 10 σ for equation (4.4) 0.006 0.023 0.021 0.023 0.015 0.020 10 5 S v /m 3 mol 1 kg 1-1.101-1.062-1.029-0.953-0.899-0.868 10 6 V φ,tr /m 3 mol 1 1.076 1.013 0.952 0.890 0.821 0.760 10 12 Ks, φ /m 5 N 1 mol 1-1.461-1.406-1.340-1.286-1.230-1.179 σ for equation (4.5) 0.001 0.004 0.008 0.006 0.010 0.010 10 12 S k /m 5 N 1 mol 1 kg 1 2.991 3.056 3.151 3.205 3.305 3.409 10 12 Ks, φ, tr /m 5 N 1 mol 1 0.582 0.510 0.421 0.360 0.288 0.226 l-histidine in 10 % aqueous-sucrose 10 5 V φ /m 3 mol 1 9.987 10.002 10.020 10.033 10.052 10.069 10 σ for equation (4.4) 0.014 0.021 0.016 0.015 0.020 0.025 10 5 S v /m 3 mol 1 kg 1-1.167-1.115-1.067-1.012-0.980-0.927 10 6 V φ,tr /m 3 mol 1 1.810 1.736 1.679 1.627 1.578 1.523 10 12 Ks, φ /m 5 N 1 mol 1-1.249-1.210-1.150-1.115-1.088-1.050 σ for equation (4.5) 0.003 0.005 0.008 0.008 0.008 0.003 10 12 S k /m 5 N 1 mol 1 kg 1 2.386 2.355 2.239 2.299 2.394 2.408 10 12 Ks, φ, tr /m 5 N 1 mol 1 0.794 0.706 0.611 0.531 0.431 0.355 104

Table 4.2 (Continued) Property T /(K) 293.15 298.15 303.15 308.15 313.15 318.15 l-histidine in 15 % aqueous-sucrose 10 5 V φ /m 3 mol 1 10.036 10.053 10.070 10.084 10.103 10.119 10 σ for equation (4.4) 0.023 0.025 0.027 0.025 0.019 0.027 10 5 S v /m 3 mol 1 kg 1-1.175-1.113-1.088-1.033-1.003-0.945 10 6 V φ,tr /m 3 mol 1 2.302 2.244 2.184 2.135 2.079 2.026 10 12 Ks, φ /m 5 N 1 mol 1-1.083-1.062-1.038-1.014-0.984-0.961 σ for equation (4.5) 0.002 0.002 0.004 0.002 0.003 0.002 10 12 S k /m 5 N 1 mol 1 kg 1 1.670 1.708 1.743 1.741 1.685 1.715 10 12 Ks, φ, tr /m 5 N 1 mol 1 0.960 0.854 0.723 0.632 0.534 0.444 l-histidine in 20 % aqueous-sucrose 10 5 V φ /m 3 mol 1 10.084 10.101 10.118 10.130 10.150 10.167 10 σ for equation (4.4) 0.020 0.015 0.013 0.013 0.026 0.019 10 5 S v /m 3 mol 1 kg 1-1.107-1.068-1.036-0.944-0.907-0.824 10 6 V φ,tr /m 3 mol 1 2.783 2.724 2.662 2.599 2.553 2.504 10 12 Ks, φ /m 5 N 1 mol 1-0.933-0.924-0.913-0.902-0.893-0.880 σ for equation (4.5) 0.001 0.001 0.001 0.002 0.003 0.002 10 12 S k /m 5 N 1 mol 1 kg 1 1.171 1.203 1.254 1.299 1.351 1.370 10 12 Ks, φ, tr /m 5 N 1 mol 1 1.110 0.992 0.848 0.744 0.625 0.525 105

Table 4.3: Falkenhagen coefficient, A, Jones-Dole coefficient, B and standard deviations of linear regression, σ for l-histidine in sucrose + water (5, 10, 15 and 20 % sucrose, w/w in water) solvents at different temperatures. Property T /(K) 293.15 298.15 303.15 308.15 313.15 318.15 l-histidine in water [10] 10 5 A /kg 1/2 mol 1/2 1.221 1.480 1.598 1.704 1.868 2.236 10 4 B /kg mol 1 5.018 4.369 3.843 3.292 2.800 2.217 10 σ for equation (4.8) 0.005 0.014 0.007 0.005 0.010 0.010 l-histidine in 5 % aqueous-sucrose 10 5 A /kg 1/2 mol 1/2 1.470 1.604 1.808 2.026 2.138 2.399 10 4 B /kg mol 1 5.564 5.082 4.535 4.041 3.605 3.136 10 σ for equation (4.8) 0.008 0.006 0.008 0.005 0.008 0.003 l-histidine in 10 % aqueous-sucrose 10 5 A /kg 1/2 mol 1/2 1.627 1.794 1.905 2.099 2.244 2.481 10 4 B /kg mol 1 5.971 5.496 4.986 4.455 3.978 3.475 10 σ for equation (4.8) 0.007 0.003 0.006 0.008 0.004 0.008 l-histidine in 15 % aqueous-sucrose 10 5 A /kg 1/2 mol 1/2 1.743 1.933 2.017 2.139 2.390 2.549 10 4 B /(kg mol 1 ) 6.497 5.847 5.352 4.791 4.318 3.865 10 σ for equation (4.8) 0.014 0.026 0.016 0.011 0.010 0.005 l-histidine in 20 % aqueous-sucrose 10 5 A /kg 1/2 mol 1/2 1.974 2.089 2.178 2.274 2.477 2.605 10 4 B /kg mol 1 6.999 6.371 5.798 5.225 4.721 4.270 10 σ for equation (4.8) 0.023 0.015 0.015 0.010 0.018 0.004 106

V φ /10-5 m 3 mol -1 10.00 9.90 9.80 9.70 (a) 9.60 10.10 0.00 0.05 0.10 0.15 0.20 0.25 V φ /10-5 m 3 mol -1 10.00 9.90 9.80 (b) 9.70 10.15 0.00 0.05 0.10 0.15 0.20 0.25 V φ /10-5 m 3 mol -1 10.05 9.95 9.85 (c) 9.75 10.20 0.00 0.05 0.10 0.15 0.20 0.25 V φ /10-5 m 3 mol -1 10.10 10.00 9.90 (d) 9.80 0.00 0.05 0.10 0.15 0.20 0.25 m/(mol kg -1 ) Figure 4.1: Variations of apparent molar volume, V φ vs. molality, m of l-histidine in sucrose + water (w/w) solutions, (a) 5% sucrose, (b) 10% sucrose, (c) 15% sucrose, (d) 20% sucrose, at temperatures, At T/K = 293.15, ; T/K = 298.15, ; T/K = 303.15, ; T/K = 308.15, ; T/K = 313.15, ; T/K = 318.15,. The points represent experimental values and lines represent values calculated from equation (4.4). 107

-0.30 K s,φ / 10-12 m 5 N -1 mol -1-0.50-0.70-0.90-1.10-1.30-1.50 (a) 0.00 0.05 0.10 0.15 0.20 0.25-0.50 K s,φ / 10-12 m 5 N -1 mol -1-0.70-0.90-1.10 (b) -1.30-0.50 0.00 0.05 0.10 0.15 0.20 0.25 K s,φ / 10-12 m 5 N -1 mol -1-0.60-0.70-0.80-0.90-1.00 (c) -1.10-0.55 0.00 0.05 0.10 0.15 0.20 0.25 K s,φ / 10-12 m 5 N -1 mol -1-0.65-0.75-0.85-0.95 (d) 0.00 0.05 0.10 0.15 0.20 0.25 m/mol kg -1 Figure 4.2: Variations of apparent molar compressibility, Ks, φ vs. molarity, m of l-histidine in sucrose + water (w/w) solutions, (a) 5% sucrose, (b) 10% sucrose, (c) 15% sucrose, (d) 20% sucrose, at temperatures, T/K = 293.15, ; At T/K = 293.15, ; T/K = 298.15, ; T/K = 303.15, ; T/K = 308.15, ; T/K = 313.15, ; T/K = 318.15,. The points represent experimental values and lines represent values calculated from equation (4.5). 108

10.2 10.1 V φ /10-5 m 3 mol -1 10.0 9.9 9.8 0 5 10 15 20 25 Mass % of sucrose Figure 4.3: Variations of limiting apparent molar volume, V φ vs. mass % of sucrose for l- histidine in sucrose + water solutions at temperatures, T/K = 293.15, ; At T/K = 293.15, ; T/K = 298.15, ; T/K = 303.15, ; T/K = 308.15, ; T/K = 313.15, ; T/K = 318.15,. 109

-0.8-1.0 K s,φ /10-12 m 5 N -1 mol -1-1.2-1.4-1.6-1.8-2.0-2.2 0 5 10 15 20 25 Mass % of sucrose K φ Figure 4.4: Variations of limiting apparent molar compressibility, s, vs. mass % of sucrose for l-histidine in sucrose + water solutions at temperatures, T/K = 293.15, ; At T/K = 293.15, ; T/K = 298.15, ; T/K = 303.15, ; T/K = 308.15, ; T/K = 313.15, ; T/K = 318.15,. 110

2.4 V φ tr /10-5 m 3 mol -1 1.8 1.2 0.6 0 5 10 15 20 25 Mass % of sucrose Figure 4.5: Variations of transfer volume, V φ,tr vs. mass % of sucrose for l-histidine in sucrose + water solutions at temperatures, T/K = 293.15, ; At T/K = 293.15, ; T/K = 298.15, ; T/K = 303.15, ; T/K = 308.15, ; T/K = 313.15, ; T/K = 318.15,. 111

1.2 1.0 K s,φ tr /10-12 m 5 N -1 mol -1 0.8 0.6 0.4 0.2 0 5 10 15 20 25 Mass % of sucrose K φ Figure 4.6: Variations of transfer compressibility, s,, tr vs. mass % of sucrose for l- histidine in sucrose + water solutions at temperatures, T/K = 293.15, ; At T/K = 293.15, ; T/K = 298.15, ; T/K = 303.15, ; T/K = 308.15, ; T/K = 313.15, ; T/K = 318.15,. 112

7 6 B /10-4 kg mol -1 5 4 3 2 0 5 10 15 20 25 Mass % of sucrose Figure 4.7: Variations of Jones-Dole coefficient, B vs. mass % of sucrose for l-histidine in sucrose + water solutions at temperature, T/K = 293.15, ; At T/K = 293.15, ; T/K = 298.15, ; T/K = 303.15, ; T/K = 308.15, ; T/K = 313.15, ; T/K = 318.15,. 113

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