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. 2019 Feb 8;4(2):2883–2892. doi: 10.1021/acsomega.8b03242

Solvation Descriptors for Zwitterionic α-Aminoacids; Estimation of Water–Solvent Partition Coefficients, Solubilities, and Hydrogen-Bond Acidity and Hydrogen-Bond Basicity

Michael H Abraham †,*, William E Acree Jr ‡,*
PMCID: PMC6648601  PMID: 31459518

Abstract

graphic file with name ao-2018-03242e_0001.jpg

The literature data on solubilities and water–solvent partition coefficients have been used to obtain properties or “Absolv descriptors” for zwitterionic α-aminoacids: glycine, α-alanine (α-aminopropanoic acid), α-aminobutanoic acid, norvaline (α-aminopentanoic acid), norleucine (α-aminohexanoic acid), valine (α-amino-3-methylbutanoic acid), leucine (α-amino-4-methylpentanoic acid), and α-phenylalanine. Together with equations that we have previously constructed, these descriptors can be used to estimate further solubilities and partition coefficients in a variety of organic solvents and in water–methanol and water–ethanol mixtures. It is shown that equations for neutral solutes are inadequate for the description of solubilities and partition coefficients for these α-aminoacids, and our equations developed for use with both neutral and ionic solutes must be used. The Absolv descriptors include those for hydrogen-bond acidity, A, and hydrogen-bond basicity, B. We find that both of these descriptors are far smaller in value than those for compounds that contain the corresponding ionic groups. Thus, A for α-alanine is 0.28, but A for the ethylammonium cation is 1.31; B for α-alanine is 0.83, and yet B for the acetate anion is no less than 2.93. The additional descriptors that we developed for equations that involve ions, J+ and J, are very significant for the α-aminoacids, although numerically smaller than for ionic species such as EtNH3+ and CH3CO2.

Introduction

The α-aminoacids are one of the most important series of compounds in the chemical and biological sciences, and there has been a very large number of experimental and theoretical studies on this series. Campen et al.1 have shown that there are some 517 distinct scales of aminoacid properties. Even so, there are notable omissions in α-aminoacid properties. The most common methods24 for the estimation of water–solvent partition coefficients only apply to the water–wet octanol system and not to any other water–solvent system. The EPI method for the estimation of solubility4 applies only to solubility in water and not to any other solvent. Most surprisingly, there are no estimations of the hydrogen-bond acidity or of the hydrogen-bond basicity of α-aminoacids. The hydrogen-bond acidity of glycine might be supposed to be close to that of the ethylammonium cation, and the corresponding hydrogen-bond basicity close to that of the acetate anion, but no information on these important hydrogen-bond properties is available.

It is our aim to use known physicochemical properties of zwitterionic α-aminoacids such as water–solvent partitions and solubilities in a range of solvents to obtain “descriptors” of these aminoacids. Together with equations that we have previously obtained, these descriptors can be used to estimate further partition coefficients in various water–solvent systems and further solubilities in various solvents. Crucially, these descriptors include the hydrogen-bond acidity and hydrogen-bond basicity so that it will then be possible to compare values for α-aminoacids with those for other species, both charged and uncharged.

Methods

Over the past few years, we have developed a system of properties or descriptors of solute molecules, known as Abraham descriptors or as Absolv descriptors,5 and have constructed a data base of these solute properties, now available in the public domain.6 In conjunction with this data base, we have assembled a complementary set of equations for physicochemical and biological properties of solutes, so that a combination of solute descriptors and equation coefficients can be used to predict various physicochemical and biological properties, as set out in a number of reviews.711 This work311 dealt only with neutral species, but was extended to cover charged solutes, specifically ions such as K+ and Cl and ionic species, defined as protonated base cations and deprotonated acid anions,1221 as recently reviewed.22 The total method, for neutral and ionic species, has already been applied to a number of systems.2330 Although we had descriptors for a large number of charged species,22 we have not investigated the α-aminoacids that are electrically neutral but with an internal charge separation, that is, zwitterions. Our study on betaine, Me3N+CH2CO2, showed31 that it could not be treated as a “neutral” molecule, but that it was essential to include ionic descriptors. Since our analysis of betaine was reasonably successful, we applied the same method to the α-aminoacids.

Our general method for the analysis of neutral solutes makes use of the two linear free energy relationships, eqs 1 and 2.

graphic file with name ao-2018-03242e_m001.jpg 1
graphic file with name ao-2018-03242e_m002.jpg 2

Equation 1 is used when the dependent variable, SP, refers to a property such as a water–solvent partition coefficient, as log P, for a series of solutes in a given system. Equation 2 is used when SP refers to a gas to system partition, as a log K value, where K is the gas to system partition coefficient.

The independent variables in eqs 1 and 2 are solute descriptors as follows:711E is the solute excess molar refractivity in units of (cm3 mol–1)/10, S is the solute dipolarity/polarizability, A and B are the overall or summation hydrogen-bond acidity and basicity, V is the McGowan characteristic volume in units of (cm3 mol–1)/100, and L is the logarithm of the gas–hexadecane partition coefficient, at 298 K. The coefficients in eqs 1 and 2 are obtained by multiple linear regression analysis and serve to characterize the system under consideration. In the case of ionic solutes, we could not use eq 2 and so only eq 1 is relevant. This equation can be extended to ionic solutes by incorporation of two new terms, as in eq 3. The j+J+ term refers to cations, and the jJ term refers to anions. Cations have J = 0, anions have J+ = 0 and neutral compounds have J = J+ = 0, so that the equation coefficients c, e, s, a, b, and v are the same for neutral molecules, ions, and ionic species. Thus, for neutral molecules, eq 3 reverts to eq 1.

graphic file with name ao-2018-03242e_m003.jpg 3

To apply eqs 1 or 3 to a given α-aminoacid, values of the dependent variable, SP are needed. The most direct source is a directly determined water–solvent partition coefficient, P, as log P, although for many α-aminoacids, partition coefficients are restricted to the water–wet octanol system, Poct/w. Partition coefficients can also be obtained indirectly from solubilities, in mol dm–3, in water, Cw, and a given (usually dry) solvent, Cs, through eq 4.

graphic file with name ao-2018-03242e_m004.jpg 4

Then, if enough values of log P, direct or indirect, are available for a given α-aminoacid, they can be combined with the corresponding equations, eq 3, and the unknown descriptors calculated by solving the set of simultaneous equations. The Microsoft “Solver” add-on is particularly useful, and any set of simultaneous equations can be solved to give a “best-fit” solution. Coefficients in eq 3 for the ionic equations that we have obtained so far are given in Table 1.

Table 1. Coefficients in Equation 3 for Water–Solvent Partitions; SP = log P.

  coefficients
   
solvents c e s a b v j+ j
methanol 0.276 0.334 –0.714 0.243 –3.320 3.549 –2.609 3.027
ethanol 0.222 0.471 –1.035 0.326 –3.596 3.857 –3.170 3.085
propan-1-ol 0.139 0.405 –1.029 0.247 –3.767 3.986 –3.077 2.834
butan-1-ol 0.165 0.401 –1.011 0.056 –3.958 4.044 –3.605 2.685
hexan-1-ol 0.115 0.492 –1.164 0.054 –3.971 4.131 –3.100 2.940
propan-2-ol 0.099 0.344 –1.049 0.406 –3.827 4.033 –3.896 2.889
t-butanol 0.211 0.171 –0.947 0.331 –4.085 4.109 –4.455 2.953
ethylene glycol –0.270 0.578 –0.511 0.715 –2.619 2.729 –1.300 2.363
1,2-propylene glycol –0.149 0.754 –0.966 0.684 –3.134 3.247 –1.381 3.057
butan-1-ol, wet 0.369 0.426 –0.719 0.091 –2.346 2.689 –2.050 2.370
octan-1-ol, wet 0.088 0.562 –1.054 0.034 –3.460 3.814 –3.023 2.580
formamide –0.171 0.070 0.308 0.589 –3.152 2.432 –3.152 2.432
dimethylformamide –0.305 –0.058 0.343 0.358 –4.865 4.486 –3.605 0.415
dimethylacetamide –0.271 0.084 0.209 0.915 –5.003 4.557   0.286
acetonitrile 0.413 0.077 0.326 –1.566 –4.391 3.364 –2.234 0.101
nitromethane 0.023 –0.091 0.793 –1.463 –4.364 3.460   –0.149
N-methylpyrrolidinone 0.147 0.532 0.275 0.840 –4.794 3.674 –1.797 0.105
dimethylsulfoxide –0.194 0.327 0.791 1.260 –4.540 3.361 –3.387 0.132
propylene carbonate 0.004 0.168 0.504 –1.283 –4.407 3.424 –1.989 0.341
sulfolane 0.000 0.147 0.601 –0.318 –4.541 3.290 –1.200 –0.792
propanone 0.313 0.312 –0.121 –0.608 –4.753 3.942 –2.288 0.078
tetrahydrofuran 0.223 0.363 –0.384 –0.238 –4.932 4.450 –2.278 –2.132
NPOEa 0.121 0.600 –0.459 –2.246 –3.879 3.574 –2.314 0.350
dichloromethane 0.319 0.102 –0.187 –3.058 –4.090 4.324 –3.984 0.086
1,2-dichloroethane 0.183 0.294 –0.134 –2.801 –4.291 4.180 –3.429 –0.025
nitrobenzene –0.152 0.525 0.081 –2.332 –4.494 4.187 –3.373 0.777
benzonitrile 0.097 0.285 0.059 –1.605 –4.562 4.028 –2.729 0.136
chlorobenzene 0.065 0.381 –0.521 –3.183 –4.700 4.614 –4.536 –1.486
a

NPOE is o-nitrophenyloctylether.

Results

We first studied the homologous series of α-amino-n-carboxylic acids, because we thought that it is reasonable to expect that the various solute descriptors would vary regularly with the number of carbon atoms in the aminoacids, and that this would help in the assignment of descriptors.

Glycine

Values of directly determined water to (wet) octan-1-ol and water to (wet) butan-1-ol are available.2,32 We have the coefficients in eq 3 for partition into both of these solvents, see Table 1. There are a large number of recorded solubilities for glycine in water and various dry solvents, as given in Table 2(2,3246) in terms of log C, where C is the molar solubility. There are some very large discrepancies among the recorded solubilities. For example, values of log C vary from −1.959 to −3.638 in solvent propan-1-ol and from −2.40 to −3.745 for in solvent propan-2-ol. In Table 2, we give the corresponding partition coefficients derived through eq 4, with log Cw taken as 0.49; Cw is the molar solubility in water at 298 K.3239 The values of log P obtained through eq 4 are also in Table 2, and it is these values that we use to derive descriptors for glycine.

Table 2. Solubilities of Glycine in Water and Organic Solvents, as log C, and Water–Solvent Partition Coefficients, as log P, at 298 K.

      log P
 
solvent log C refs obsa taken calc
water 0.460 (32)      
water 0.462 (33, 34)      
water 0.522 (35)      
water 0.522 (36)      
water 0.460 (37, 38)      
water 0.497 (39)      
methanol –2.045 (34) –2.535 –2.66 –2.18
methanol –1.939 (36) –2.429    
methanol –2.370 (38) –2.860    
methanol –2.345 (40) –2.835    
ethanol –2.400 (34) –2.890 –3.31 –3.15
ethanol –2.071 (36) –2.561    
ethanol –3.409 (38) –3.899    
ethanol –3.026 (39) –3.516    
ethanol –3.188 (40) –3.678    
propan-1-ol –1.959 (34) –2.449 –3.30 –3.34
propan-1-ol –2.826 (39) –3.316    
propan-1-ol –3.638 (40) –4.128    
propan-2-ol –4.824 (36) –5.314 –3.55 –3.89
propan-2-ol –2.400 (34) –2.890    
propan-2-ol –3.030 (39) –3.520    
propan-2-ol –3.745 (34) –4.235    
butan-1-ol –4.018 (38) –4.508 –4.45b –3.78b
butan-1-ol –3.921 (40) –4.411    
tert-butanol –2.400 (34) –2.890 –4.25 –4.12
tert-butanol –4.886 (35) –5.376    
tert-butanol –4.000 (40) –4.490    
ethylene glycol –0.711 (41) –1.201 –1.20 –1.40
ethylene glycol –0.709 (42) –1.199    
DMSO –1.338 (41) –1.828 –1.83 –1.34
dioxane –2.710 (43) –3.200 –3.20  
acetonitrile –1.453 (42) –1.943 –1.94 –1.83
propanone –4.516 (38) –5.006 –5.01b –2.48b
formamide –1.077 (38) –1.567 –1.57 –1.46
dimethylformamide –1.362 (44) –1.852 –1.85 –2.49
2-methoxyethanol –0.627 (45) –1.117 –1.12  
1,2-dimethoxyethane –0.728 (46) –1.218 –1.22  
octan-1-ol, wet   (2) –3.21c –3.21 –3.34
butan-1-ol, wet   (2, 32) –1.81c –1.81 –1.76
a

With log C in water taken as 0.490.

b

Not used in the calculations.

c

Direct determination.

In addition to solubilities in pure solvents, there are also available solubilities in aqueous methanol25,27,34,36 and aqueous ethanol,25,2830,33,37,39 for which we have the coefficients in the ionic equation, eq 3, see Table 3. We combined the various solubilities to obtain log P values from methanol to water–methanol mixtures and from water to water–ethanol mixtures, using our selected log P values for partition to 100% methanol and 100% ethanol, for consistency. The log P values that we obtained are in Table 4.

Table 3. Coefficients in Equation 3 for Water–Methanol and Water–Ethanol Partitions, SP = log P; Composition of Mixtures Given as Volume %.

  coefficients
solvents c e s a b v j+ j
methanol 0.276 0.334 –0.714 0.243 –3.320 3.549 –2.609 3.027
95% 0.270 0.278 –0.520 0.230 –3.368 3.365 –2.661 2.909
90% 0.258 0.250 –0.452 0.229 –3.206 3.175 –2.629 2.707
80% 0.172 0.197 –0.319 0.241 –2.912 2.842 –2.540 2.421
70% 0.098 0.192 –0.260 0.266 –2.558 2.474 –2.267 2.164
60% 0.053 0.207 –0.238 0.272 –2.157 2.073 –1.978 1.872
50% 0.023 0.223 –0.222 0.264 –1.747 1.662 –1.588 1.569
40% 0.020 0.222 –0.205 0.218 –1.329 1.259 –1.329 1.259
30% 0.016 0.187 –0.172 0.165 –0.953 0.898 –0.823 0.930
20% 0.022 0.142 –0.138 0.088 –0.574 0.559 –0.465 0.599
10% 0.012 0.072 –0.081 0.026 –0.249 0.266 –0.185 0.287
ethanol 0.222 0.471 –1.035 0.326 –3.596 3.857 –3.170 3.085
96% 0.238 0.353 –0.833 0.297 –3.533 3.724 –3.020 2.970
95% 0.239 0.328 –0.795 0.294 –3.514 3.697 –2.985 2.943
90% 0.243 0.213 –0.575 0.262 –3.450 3.545 –2.794 2.837
80% 0.172 0.175 –0.465 0.260 –3.212 3.323 –2.466 2.722
70% 0.063 0.085 –0.368 0.311 –2.936 3.102 –2.203 2.550
60% –0.040 0.138 –0.335 0.293 –2.675 2.812 –1.858 2.394
50% –0.142 0.124 –0.252 0.251 –2.275 2.415 –1.569 2.051
40% –0.221 0.131 –0.159 0.171 –1.809 1.918 –1.271 1.676
30% –0.269 0.107 –0.098 0.133 –1.316 1.414 –0.941 1.290
20% –0.252 0.042 –0.040 0.096 –0.823 0.916 –0.677 0.851
10% –0.173 –0.023 –0.001 0.065 –0.372 0.454 –0.412 0.401

Table 4. Values of log P for Glycine from Water to Water–Methanol and Water–Ethanol Mixtures.

methanol (%) obs calc ethanol (%) obs calc
      96 –2.925 –2.750
95 –2.177 –1.999 95 –2.856 –2.670
90 –1.973 –1.902 90 –2.538 –2.218
80 –1.631 –1.723 80 –2.009 –1.865
70 –1.404 –1.525 70 –1.594 –1.612
60 –1.150 –1.355 60 –1.259 –1.437
50 –0.967 –1.130 50 –0.980 –1.233
40 –0.710 –0.962 40 –0.739 –0.997
30 –0.461 –0.645 30 –0.522 –0.770
20 –0.300 –0.400 20 –0.324 –0.551
10 –0.125 –0.185 10 –0.148 –0.322

There were a number of solvents, 2-methoxyethanol, dioxane, and 1,2-dimethoxyethane, for which we had coefficients only for neutral species. However, we were still left with log P values for 35 solvents or solvent mixtures. The log P values for water to propanone and water to butan-1-ol (and hence the corresponding solubilities) were quite out of line, and so we were left with 33 values. We obtained a value of E = 0.476 for the neutral species NH2CH2CO2H from a refractive index calculated by the ChemSketch program.3 Judging from our results on base cations and acid anions, we can take E for the zwitterionic species as that for the neutral species. Similarly, we take V = 0.5646 for the neutral species as that for the zwitterion. Then, we have five descriptors, S, A, B, J+, and J to obtain from 33 simultaneous equations. The descriptors in Table 5 yield a standard deviation SD = 0.241 log units between observed and calculated log P values. The number of data points used is N. In view of the large discrepancies in the solubilities of glycine, the SD value is as small as could reasonably be expected. The calculated log P values for the water–methanol and water–ethanol mixtures are in Table 4, and the calculated log P values for the organic solvents are in Table 2. We also used exactly the same 33 equations to obtain descriptors through the neutral eq 1, that is with j+ and j taken as zero. The SD now rises considerably to 0.348 log units, see Table 5.

Table 5. Solute Descriptors Obtained from Equation 3.

descriptors E S A B V J+ J N SD
glycine 0.476 2.12 0.27 0.72 0.5646 0.5854 0.2483 33 0.241
α-alanine 0.460 2.58 0.28 0.83 0.7055 0.6226 0.4186 30 0.206
α-aminobuta 0.455 2.63 0.28 0.94 0.8464 0.5170 0.3871 17 0.180
norvalineb 0.454 2.20 0.33 0.92 0.9873 0.5106 0.2001 27 0.138
norleucinec 0.449 2.10 0.32d 0.96 1.1282 0.5227 0.2356 17 0.155
valine 0.439 2.38 0.32d 0.95 0.9873 0.5804 0.2897 27 0.204
leucine 0.438 2.61 0.32d 0.96 1.1282 0.3397 0.1336 13 0.074
α-phenylalanine 1.150 2.48 0.77 1.70 1.3133 0.1907 0.5312 30 0.144
glycine 0.476 1.92 0.19 1.05 0.5646 0 0 32 0.348
α-alanine 0.460 2.14 0.30 1.09 0.7055 0 0 29 0.345
α-aminobutanoic 0.455 2.18 0.49 1.14 0.8464 0 0 16 0.331
norvaline 0.454 2.05 0.34 1.20 0.9873 0 0 27 0.214
α-phenylalanine 1.150 1.58 1.00 1.65 1.3133 0 0 30 0.330
a

α-Aminobutanoic acid.

b

α-Aminopentanoic acid.

c

α-Aminohexanoic acid.

d

Value of A fixed.

α-Alanine (α-Aminopropanoic Acid)

For α-alanine, there is also a substantial data available. As for glycine, water to (wet) octan-1-ol and water to (wet) butan-1-ol partition coefficients are known.2,32 The solubilities of l-α-alanine and dl-α-alanine in water are almost the same, with log Cw = 0.260.3437,39,4448 Solubilities are also known in organic solvents,3436,38,39,4148 water–methanol mixtures33,36 and water–ethanol mixtures.33,36,37 We used log Cw = 0.260 to convert solubilities into values of log P through eq 4, see Tables 6 and 7. We obtained E = 0.460 and V = 0.7055 as for glycine and then had five descriptors to obtain from 30 simultaneous equations. The best-fit descriptors are in Table 5. Together with the corresponding equations for log P, these yield the calculated log P values in Tables 6 and 7. The descriptors in Table 5 give SD = 0.206 log units between observed and calculated log P values. If the neutral equation, eq 1 is used, the SD is considerably increased to 0.345 log units, see Table 5.

Table 6. Solubilities of α-Alanine in Organic Solvents, as log C, and Water–Solvent Partition Coefficients, as log P, at 298 K.

      log P
 
solvents log C refs obs taken calc
methanol –1.921 (34) –2.181 –2.30 –1.95
methanol –3.119 (37) –3.379    
methanol –2.045 (36) –2.305    
ethanol –2.700 (34) –2.960 –2.96 –3.06
ethanol –2.301 (36) –2.561    
ethanol –2.694 (39) –2.954    
propan-1-ol –2.700 (34) –2.960 –3.56 –3.31
propan-1-ol –2.588 (39) –2.848    
propan-1-ol –3.297 (47) –3.557    
propan-2-ol –2.400 (34) –2.660 –3.86 –3.88
propan-2-ol –2.523 (36) –2.783    
propan-2-ol –2.458 (39) –2.718    
propan-2-ol –3.607 (44) –3.867    
tert-butanol –2.401 (34) –2.660 –2.94a –4.09a
tert-butanol –2.680 (35) –2.940    
ethylene glycol –0.824 (44) –1.076 –1.08 –1.19
ethylene glycol –0.816 (42) –1.084    
ethylene glycol –0.814 (41) –1.074    
DMSO –1.339 (41) –1.599 –1.12 –1.10
DMSO –0.859 (48) –1.119    
dioxane –3.873 (43) –4.133 –4.13  
acetonitrile –1.443 (42) –1.693 –1.69 –1.77
dimethylformamide –1.319 (44) –1.579 –1.58a –2.29a
2-methoxyethanol –0.678 (45) –0.938 –0.94  
1,2-dimethoxyethane –0.833 (46) –1.093 –1.09  
octan-1-ol, wet   (2) –2.96 –2.96 –3.35
butan-1-ol, wet   (32) –1.60 –1.60 –1.65
a

Not used in the calculations.

Table 7. Values of log P for α-Alanine from Water to Water–Methanol and Water–Ethanol Mixtures.

methanol (%) obs calc ethanol (%) obs calc
      96 –2.58 –2.61
95 –2.16 –1.74 95 –2.50 –2.51
90 –2.01 –1.66 90 –2.14 –1.98
80 –1.67 –1.47 80 –1.60 –1.59
70 –1.33 –1.29 70 –1.25 –1.31
60 –1.01 –1.17 60 –0.99 –1.15
50 –0.74 –0.98 50 –0.78 –0.97
40 –0.52 –0.86 40 –0.59 –0.76
30 –0.35 –0.58 30 –0.39 –0.58
20 –0.22 –0.36 20 –0.20 –0.41
10 –0.12 –0.17 10 –0.05 –0.24

α-Aminobutanoic Acid

There is less data for α-aminobutanoic acid, but log P values into wet octan-1-ol2 and wet butan-1-ol are available,32 and solubilities in water,45,46,49,50 organic solvents,41,42,44,45 and water–ethanol37 mixtures have been determined for dl-α-aminobutanoic acid. Values of log C and derived values of log P are in Table 8, the latter using a value of 0.333 for log Cw for water. There are 17 values of log P, for which we have the corresponding equation coefficients. We take E = 0.455 and V = 0.8464, obtained as for glycine and α-alanine. If we omit the value for dimethyl sulfoxide (DMSO), we are left with a set of 17 simultaneous equations. These yield the descriptors given in Table 5 and the calculated values of log P, as shown in Table 8. The observed and calculated log P values yield SD = 0.180 log units. If the set of 17 simultaneous equations is solved using the neutral equations, the SD rises to 0.331 log units, with the descriptors given in Table 5.

Table 8. Solubilities of dl-α-Aminobutanoic Acid in Water and Organic Solvents, as log C, and Water–Solvent Partition Coefficients, as log P, at 298 K.

      log P
 
solvents log C refs obs taken calc
ethanol –2.507 (37) –2.84 –2.84 –2.73
ethylene glycol –0.584 (42) –0.92 –0.93 –1.06
ethylene glycol –0.604 (44) –0.94    
ethylene glycol –0.606 (41) –0.94    
DMSO –1.171 (41) –1.50 –1.50a –0.74a
acetonitrile –1.284 (42) –1.62 –1.62 –1.53
dimethylformamide –1.372 (44) –1.71 –1.71 –1.81
2-methoxyethanol –0.664 (45) –1.00 –1.00  
ethanol          
96%   (37) –2.48 –2.48 –2.29
95%   (37) –2.37 –2.37 –2.20
90%   (37) –1.99 –1.99 –1.69
80%   (37) –1.43 –1.43 –1.33
70%   (37) –1.07 –1.07 –1.07
60%   (37) –0.84 –0.84 –0.95
50%   (37) –0.66 –0.66 –0.79
40%   (37) –0.50 –0.50 –0.62
30%   (37) –0.36 –0.36 –0.47
20%   (37) –0.22 –0.22 –0.33
10%   (37) –0.09 –0.09 –0.19
octan-1-ol, wet   (2) –2.53 –2.53 –3.01
butan-1-ol, wet   (32) –1.34 –1.34 –1.28
a

Not used in the calculations.

Norvaline (α-Aminopentanoic Acid)

Values of log P from water to wet butan-1-ol and wet octan-1-ol are known for norvaline,2,32 and solubilities of dl-norvaline are available in water, log Cw = −0.168,44,45 and in a limited number of organic solvents,41,42,4446 as shown in Table 9. Wang et al.51 have determined solubilities of l-norvaline in methanol, ethanol, and their aqueous mixture but not in water itself. Klimov and Deshcherevsky52 determined that log Cw = −0.153 for l-norvaline, and we obtain values of log P using log Cw = −0.168 and −0.153 for dl-norvaline and l-norvaline, respectively, see Table 9. We take E = 0.454 and V = 0.9873; if the datum in DMSO is neglected, we have 27 equations and derive the remaining descriptors, see Table 5, with an SD of 0.138 log units. If the neutral equations are used to obtain descriptors, the SD rises to 0.214 log units, see Table 5.

Table 9. Solubilities of Norvaline in Water and Organic Solvents, as log C, and Water–Solvent Partition Coefficients, as log P, at 298 K.

        log P
solvents isomer log C refs obs calc
water dl –0.166 (44)    
water dl –0.169 (45)    
ethylene glycol dl –0.811 (42) –0.643 –0.812
DMSO dl –1.334 (41) –1.166a –0.483a
acetonitrile dl –1.348 (42) –1.180 –1.207
dimethylformamide dl –1.520 (44) –1.352 –1.298
2-methoxyethanol dl –0.836 (45) –0.668  
1,2-dimethoxyethane dl –1.014 (46) –0.846  
water l –0.153 (52)    
ethanol l   (51) –2.359 –2.253
96% l   (51) –2.135 –1.885
95% l   (51) –2.069 –1.809
80% l   (51) –1.265 –1.097
70% l   (51) –0.979 –0.879
60% l   (51) –0.801 –0.789
50% l   (51) –0.656 –0.671
40% l   (51) –0.525 –0.551
30% l   (51) –0.396 –0.438
20% l   (51) –0.268 –0.324
10% l   (51) –0.138 –0.192
methanol l   (51) –1.447 –1.364
95% l   (51) –1.327 –1.249
90% l   (51) –1.196 –1.187
80% l   (51) –0.972 –1.070
70% l   (51) –0.808 –0.955
60% l   (51) –0.684 –0.878
50% l   (51) –0.580 –0.755
40% l   (51) –0.479 –0.677
30% l   (51) –0.374 –0.455
20% l   (51) –0.261 –0.286
10% l   (51) –0.139 –0.130
octan-1-ol, wet     (2) –2.11 –2.43
butan-1-ol, wet     (32) –0.98 –1.09
a

Not used.

Norleucine (α-Aminohexanoic Acid)

Values of log P from water to wet butan-1-ol and wet octan-1-ol are known for norleucine,2 and solubilities are available for dl-norleucine in water–ethanol mixtures38 and in a few organic solvents,38 as set out in Table 10. We took E = 0.449 and V = 1.1282, calculated as before. Then, using log Cw = −1.062, we obtained the given log P (obs) values. The log P value for propanone was considerably out of line, but the remaining log P values yielded 17 simultaneous equations from which we could calculate the descriptors shown in Table 5. The set of equations and calculated solute descriptors yield observed and calculated values of log P with SD = 0.153 log units.

Table 10. Solubilities of dl-Norleucine in Water and Organic Solvents, as log C, and Water–Solvent Partition Coefficients, as log P, at 298 K.

      log P
solvents log C refs obs calc
water –1.062 (38)    
formamide –1.762 (38) –0.70 –0.72
propanone –4.101 (38) –3.04a –1.26a
methanol –2.068 (38) –1.01 –0.90
butan-1-ol –3.474 (38) –2.41 –2.33
ethanol –2.982 (38) –1.92 –1.73
96% –2.663 (38) –1.60 –1.40
95% –2.593 (38) –1.53 –1.33
90% –1.888 (38) –0.83 –0.96
80% –1.671 (38) –0.61 –0.69
70% –1.563 (38) –0.50 –0.50
60% –1.504 (38) –0.44 –0.44
50% –1.450 (38) –0.39 –0.38
40% –1.378 (38) –0.32 –0.32
30% –1.279 (38) –0.22 –0.26
20% –1.165 (38) –0.10 –0.21
10% –1.162 (38) –0.10 –0.14
octan-1-ol, wet   (2) –1.54 –1.92
butan-1-ol, wet   (2, 32) –0.51 –0.76
a

Not used.

Valine (α-Amino-3-methylbutanoic Acid)

log P values for partition to wet octan-1-ol (−2.26) and to wet butan-1-ol (−1.14) are known,2,32 and solubilities are available in water, organic solvents,34,35,37,43 water–methanol,34,36,45 and water–ethanol mixtures.37,53 The solubilities of l-valine and dl-valine differ somewhat. In water, values of log C are −0.122,35,36,43 and −0.243.37 However, log P values to water–ethanol mixtures as calculated from solubilities of l-valine and dl-valine in water and water–ethanol mixtures37,53 are essentially the same for both isomers, as expected. In Table 11 are given values of log P as obtained from solubilities of l-valine in water and organic solvents or from solubilities of dl-valine in water and organic solvents. The total of log P values is in Table 11. We took E = 0.439 and V = 0.9873, as before, and used 27 simultaneous equations to obtain the descriptors given in Table 5; the value of A = 0.32 was fixed by comparison to other aminoacids. For the 27 observed and calculated values of log P in Table 11, SD = 0.204 log units.

Table 11. Water–Solvent Partition Coefficients, as log P, at 298 K for Valine at 298 K.

    log P
solvents refs obs calc
methanol (34) –1.63 –1.50
propan-1-ol (34) –2.40 –2.67
propan-2-ol (34) –3.53 –3.21
tert-butanol (35) –3.58 –3.43
dioxane (43) –2.48  
ethanol (37) –2.65 –2.48
96% (37) –2.27 –2.08
95% (37) –2.18 –2.00
90% (37, 53) –1.81 –1.54
80% (37, 53) –1.30 –1.20
70% (37, 53) –0.99 –0.96
60% (37, 53) –0.81 –0.84
50% (37, 53) –0.67 –0.71
40% (37, 53) –0.55 –0.57
30% (37, 53) –0.40 –0.44
20% (37, 53) –0.25 –0.33
10% (37, 53) –0.10 –0.19
methanol      
90% (34) –1.28 –1.30
80% (34, 45) –1.05 –1.17
60% (34, 45) –0.71 –0.95
50% (34) –0.59 –0.82
40% (34, 36, 45) –0.46 –0.74
30% (34, 36) –0.36 –0.49
20% (34, 36, 45) –0.21 –0.31
10% (34, 36) –0.11 –0.14
octan-1-ol, wet (2) –2.26 –2.69
butan-1-ol, wet (2, 32) –1.14 –1.61

Leucine (α-Amino-4-methylpentanoic Acid)

Dey and Lahiri36 report solubilities of l-leucine in water, water–methanol, water–ethanol, and water-propan-2-ol mixtures. The derived log P values for water to pure solvents are in Table 12. Cohn et al.37 also determined solubilities of l-leucine in water–ethanol mixtures, but the value of log P from water to ethanol is −2.13, as compared to that of −1.54 by Dey and Larhiri.36 Pal et al.35 listed similar data in water-tert–butanol mixtures, and the log P value from water to tert-butanol itself is in Table 12. Also given2,32 are log P values from water to wet octan-1-ol and wet butan-1-ol. Gekko54 has determined solubilities in water–methanol mixtures, and his values in water and pure methanol lead to a log P value of −1.05, as compared to the value of −1.48 from Dey and Lahiri.36

Table 12. Solubilities of Leucine in Water and Organic Solvents, as log C, and Water–Solvent Partition Coefficients, as log P, at 298 K.

solvents refs obs calc
methanol (36) –1.48  
methanol (54) –1.05 –0.94
90% methanol (54) –0.79 –0.69
80% methanol (54) –0.55 –0.55
70 % methanol (54) –0.49 –0.49
60% methanol (54) –0.47 –0.49
50% methanol (54) –0.37 –0.46
40% methanol (54) –0.35 –0.45
30% methanol (54) –0.29 –0.33
20% methanol (54) –0.18 –0.23
10% methanol (54) –0.13 –0.11
ethanol (37) –2.13 –1.83
ethanol (36) –1.54  
propan-2-ola (36) –1.63 –2.33
tert-butanola (35) –1.65 –2.40
octan-1-ol, wet (2) –2.06 –2.03
butan-1-ol, wet (2, 32) –0.74 0.88
a

Not used.

The derived log P values in Table 12 for partition from water to methanol and ethanol are very inconsistent. In addition, those for partition into propan-2-ol and tert-butanol are far out of line by comparison with those for the other α-aminoacids. The only way that we could assign descriptors to leucine was on the basis of the already obtained descriptors for the other α-aminoacids listed in Table 5. The suggested descriptors for leucine are in Table 5 and lead to the calculated log P values in Table 12. Clearly, more data on leucine are needed.

Phenylalanine

Solubilities have been determined for both l-phenylalanine and dl-phenylalanine. In water, at 298 K, values of log Cw are −0.762 for l-phenylalanine3336,54,55 and −1.065 for dl-phenylalanine.5659 We use the values of log Cw = −0.762 and −1.065 to convert solubilities of l-phenylalanine33,54 and dl-phenylalanine40 in solvents to the corresponding log P values; details are in Table 13. Gomaa60 has determined solubilities of phenylalanine in several solvents. There is no indication of which isomer was used, but we have simply calculated log P values from the given solubilities in solvents and in water, see Table 13. There should be no difference in the log P values for l-phenylalanine and dl-phenylalanine for transfer to a given solvent. Also included in Table 13 are recent determinations of solubilities and hence log P values in dimethylsulfoxide,61 methanol,62 and ethanol.63 Where necessary, we have averaged the various values. Also, given2 are experimental values of log P for partition into wet octan-1-ol and wet butan-1-ol.

Table 13. Partition Coefficients for either l-Phenylalanine or dl-Phenylalanine, as log P, at 298 K.

solvents obs refs taken calc
methanol –1.040 (40) –0.950 –0.796
methanol –0.893 (33)    
methanol –0.844 (54)    
methanol –0.919 (60)    
methanol –1.053 (62)    
ethanol –1.830 (40) –1.887 –1.534
ethanol –1.934 (33)    
ethanol –1.891 (60)    
ethanol –1.895 (62)    
propan-1-ol –2.250 (40) –2.093 –2.007
propan-1-ol –1.936 (33)    
butan-1-ol –2.360 (40) –2.360 –2.517
propan-2-ol –2.440 (40) –2.338 –2.213
propan-2-ol –2.236 (33)    
tert-butanol –2.790 (40) –2.515 –2.515
tert-butanol –2.240 (33)    
90% ethanol –1.089 (33) –1.089 –0.972
80% ethanol –0.499 (54) –0.499 –0.700
70% ethanol –0.536 (33) –0.536 –0.495
60% ethanol –0.336 (54) –0.336 –0.424
50% ethanol –0.311 (33) –0.311 –0.337
40% ethanol –0.267 (54) –0.267 –0.242
30% ethanol –0.240 (33) –0.240 –0.161
20% ethanol –0.157 (54) –0.157 –0.102
10% ethanol –0.080 (33) –0.080 –0.054
90% methanol –0.679 (33) –0.679 –0.743
80% methanol –0.499 (54) –0.499 –0.623
70% methanol –0.390 (33) –0.390 –0.504
60% methanol –0.336 (54) –0.336 –0.417
50% methanol –0.311 (33) –0.311 –0.324
40% methanol –0.267 (54) –0.267 –0.256
30% methanol –0.240 (33) –0.240 –0.172
20% methanol –0.157 (54) –0.157 –0.101
10% methanol –0.080 (33) –0.080 –0.043
octan-1-ol, wet –1.630 (2) –1.630 –1.930
butan-1-ol, wet –0.580 (2) –0.580 –0.443
dimethylformamide –1.793 (60) –1.793 –2.092
acetonitrile –3.457 (60) –3.457 –3.315
dimethylsulfoxide –1.299 (60) –1.000 –0.766
dimethylsulfoxide –1.000 (61)    
propanone –2.132a (60)   –3.394
a

Not used.

We calculated E = 1.15 in the same way as for glycine, and we took V = 1.3133 the same as the corresponding neutral species. We have data for 30 solvents, including aprotic solvents, and derive the descriptors in Table 5 with an SD of 0.144 log units as between observed (taken) and calculated log P values. If the analysis is carried out with the neutral equations, SD rises to 0.330 log units.

Discussion

There are a number of other zwitterionic α-aminoacids to those in Table 5 for which solubility data are available. The latter invariably refer only to hydroxylic solvents and water–solvent mixtures. In these cases, the set of simultaneous equations for a given aminoacid can still be solved, but there then exists numerous solutions that have nearly the same statistical quality, so that no definite set of descriptors can be obtained. Unless data in a number of aprotic solvents such as dimethylsulfoxide, dimethylformamide, acetonitrile, and also propylene carbonate are available, it is difficult to use our method of simultaneous equations to determine descriptors. Exceptions are norleucine, valine, and leucine that are structurally so close to other α-aminoacids, Table 5, that it is possible to estimate some of their descriptors.

One complication is that many α-aminoacids exist as optical isomers (especially as the l- or dl-forms). Although the l- and d-isomers will have the same solubilities, the dl-form may have different solubilities to the l- and d-forms. Then, application of eq 4 requires that log Cs and log Cw refer to the same isomer. Of course any value of log P obtained through eq 4 or directly determined will be the same for an l- or dl-isomer.

An objective of this work was to establish if the properties of α-aminoacids could reasonably be estimated using our simple equation for neutral species, eq 1, or whether the more complicated “ionic” equation, eq 3 should be used. For the five α-aminoacids in Table 5 for which we have reliable descriptors, the average SD as between observed and calculated values of log P is 0.182 log units, which suggests that we can predict further values of log P to about 0.20 log units. Once a given value of log P has been estimated through a combination of descriptors and equation coefficients, the corresponding value of log Cs can be obtained from log Cw, eq 4. If the neutral equation eq 1 is used, the average SD for the five α-aminoacids rises to 0.314 log units. However, we expect that the SD from an equation with five descriptors will be larger than the SD from an equation with seven descriptors. We, therefore, carried out a multiple linear regression of the 33 log P values for glycine against the five solvent descriptors E, S, A, B, and V and found that the Fisher F-statistic was 172.2. For a regression against the seven solvent descriptors E, S, A, B, V, J+, and J, we found that F = 206.0, so that even when taking into account the extra two descriptors, the equation with J+ and J is preferred. We conclude that use of eq 3 with the J+ and J descriptors is necessary for the analysis of partition and solubility of α-aminoacids by our method.

In the solution of a set of simultaneous equations for a given solute, the solute descriptors are all determined in the same analysis, so that the individual errors in the descriptors are not obtained. However, the overall errors in the analyses, Table 5, are larger than the errors we usually find with neutral compounds for which we have estimated descriptor errors to be around 0.02 units. We suggest that descriptor errors for the α-aminoacids could be 0.03–0.04 units. The obtained descriptors for α-aminoacids, Table 5, are of some interest, especially in that the α-aminoacids appear to have remarkably small values of the hydrogen-bond descriptors A and B. It is useful to compare some of the α-aminoacid descriptors with those for other charged species, as shown in Table 14, with α-alanine as an example. There are some very notable differences between the α-alanine descriptors and those for charged species that might be suitable models. Both α-alanine and the ethylammonium cation contain the C-NH3+ group, and yet A is only 0.28 for α-alanine as against 1.31 for the cation. α-Alanine, betaine, and the acetate ion all contain the C-CO2 group, and yet B values are 0.83, 2.00, and 2.93, respectively. The hydrogen-bond acidity and hydrogen-bond basicity of α-alanine are far less than expected by comparison to these particular charged species. Alagona et al.63 have used the Monte Carlo simulation to show that glycine has an intramolecular hydrogen bond and a quantum mechanics, molecular mechanics simulation by Tuňón et al.64 yields a similar result. The existence of an intramolecular hydrogen bond would at least partially explain the relatively small values of A and B for the α-aminoacids. It is interesting that betaine, which would not be expected to have an intramolecular bond, has a much larger value of B than have the α-aminoacids. Tsai et al.65 have suggested that zwiterionic α-aminoacids are far less hydrophilic than expected from the presence of two charged groups; the small values of A and B would certainly lead to this result. α-Phenylalanine has substantially larger values of A and B than the other aminoacids in Table 14. Possibly, the presence of the phenyl group interrupts the intramolecular bond that reduces the values of A and B in the other α-aminoacids. This interruption results in a B-value just short of that in betaine, which can have no intramolecular bond.

Table 14. Solute Descriptors for Aminoacids and Other Species.

descriptors E S A B V J+ J
glycine 0.476 2.12 0.27 0.72 0.5646 0.5854 0.2483
α-alanine 0.460 2.58 0.28 0.83 0.7055 0.6226 0.4186
α-aminobutanoic acid 0.455 2.63 0.28 0.94 0.8464 0.5170 0.3871
norvaline 0.454 2.20 0.33 0.92 0.9873 0.5106 0.2001
norleucine 0.449 2.10 0.32 0.96 1.1282 0.5227 0.2356
valine 0.439 2.38 0.32 0.95 0.9873 0.5804 0.2897
leucine 0.438 2.61 0.32 0.96 1.1282 0.3397 0.1336
α-phenylalanine 1.150 2.48 0.77 1.70 1.3133 0.1907 0.5312
betaine 0.315 1.57 0.00 2.00 0.9873 –0.3240 0.8760
ethylammonium cation 0.086 2.50 1.31 0.00 0.5117 0.7680 0.0000
acetate anion 0.415 2.19 0.00 2.93 0.4433 0.0000 2.0750
ethylamine 0.236 0.35 0.16 0.61 0.4902 0.0000 0.0000
acetic acid 0.265 0.64 0.62 0.44 0.4648 0.0000 0.0000

As we have shown, above, the ionic descriptors J+ and J are very significant for the α-aminoacids, although they are numerically smaller than those for the ionic species EtNH3+ and MeCO2. This parallels the situation with the descriptors A and B and suggests again that the charged groups in the α-aminoacids cannot be compared directly with those in typical anionic and cationic species.

A feature of the log P values for the α-aminoacids is that the observed log P is more negative than calculated in mixtures with a high proportion of alcohols and the observed log P is more positive than calculated in mixtures with a high proportion of water. It is worth pointing out that these differences are quite small. For the glycine/methanol/water system, the errors between observed and calculated log P are −0.18 log units (95% methanol) and + 0.06 log units (10% methanol), see Table 4. For methanol itself, observed values of log P range from −2.43 to −2.86, a difference of 0.43 log units, and for ethanol itself, observed values range from −2.56 to −3.90, a difference of no less than 1.34 log units (Table 2). In view of the errors in observed values, we just note the (rather small) variation of log P with alcohol/water content.

The authors declare no competing financial interest.

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