Biomedicine
International
Biomedicine International (2010) 1: 19-24
ORIGINAL ARTICLE
Improved Prediction of Drug Solubilities in Ethanol + Water
Mixtures at Various Temperatures
Abolghasem Jouyban,1* Shahla Soltanpour,2 William E Acree Jr3
1
Faculty of Pharmacy and Drug Applied Research Center, Tabriz University of Medical Sciences, Tabriz, Iran
2
Biotechnology Research Center, Tabriz University of Medical Sciences, Tabriz, Iran.
3
Department of Chemistry, University of North Texas, Denton, USA
ABSTRACT
Predicting the solubilities of drugs in ethanol + water mixtures has been improved using a trained version of the
Jouyban-Acree model. To check the accuracy of the improved model, solubility data for various drugs in ethanol + water
mixtures at different temperatures were collected from the literature and the predicted solubilities were compared to the
corresponding experimental values by computing the mean percentage deviations (MPDs). The overall MPDs for the
predicted solubilities (from a total of 113 data sets including 1318 data points) using the previous trained model and the
improved model were 52.9 (±44.2) % and 40.7 (±21.6) %, respectively; this mean difference was statistically significant
(P < 0.0005). Biomed. Int. 2010; 1: 19-24. ©2010 Biomedicine International, Inc.
Key words: solubility prediction; cosolvency; water-ethanol; Jouyban-Acree model
INTRODUCTION
The low solubility of drugs remains a challenge in
pharmacy. Ethanol is the most commonly used
cosolvent in the pharmaceutical industry; it has a reasonably high solubility capability and is used in liquid formulations at concentrations lower than 50%.
Previously, a number of formulations used ethanol at
higher concentrations, and pure ethanol has been
used as a solvent.1 Solubility in ethanol + water mixtures is essential information for drug discovery and
development studies, and can be used for drug recrystallization studies and drug formulation. In addition
to experimental measurements, a number of mathematical models have been used to predict the solubilities of drugs in cosolvent + water mixtures. The advantages and limitations of these models were reviewed recently.2
Of the numerous models developed in recent years,
the Jouyban−Acree model is one of the most versatile. It provides very accurate mathematical descriptions of the changes in solute solubility due to
changes in both temperature and solvent composition.
*
Address correspondence to Dr. A. Jouyban, Faculty of
Pharmacy, Tabriz University of Medical Sciences, Tabriz 51664,
Iran; E-mail: [email protected]
Submitted August 8, 2009; accepted in revised form October 15,
2009.
Advance Access Publication 15 December 2010 (see
www.bmijournal.org
The trained model for predicting drug solubility in
ethanol + water mixtures at various temperatures is3:Sat
log X mSat,T = f c log X cSat
,T + f w log X w,T
⎡ 724.21 485.17( f c − f w ) 194.41( f c − f w )2 ⎤
+ fc fw ⎢
+
+
⎥
T
T
⎣⎢ T
⎦⎥
(1)
Sat
where X m,T is the solubility of the solute in the
binary solvent mixture at temperature T (K), fc, and fw
are the fractions of ethanol and water in the absence
Sat
Sat
of solute, and X c ,T and X w,T denote the solubilities
of the solute in ethanol and water, respectively.3 In
combining solubility data for several solutes in ethanol + water mixtures, we assumed that the coefficients in Eq. (1) (the constant terms) were independent of solute structure. While this assumption holds
for structurally similar solute molecules, it is not applicable to drugs with different chemical structures
and functional groups. To provide a more accurate
predictive model, incorporating more structural information about the drug molecule, we added an additional term, the logarithm of the water-to-octanol
partition coefficient ( log P ) of the drug, and a
model constant B:-
20
Jouyban et al. / Biomedicine International (2010) 1: 19-24
mole/L and mole fraction; we used the units reported
in the original articles.
The predictive capacity of Eq. (1) was re-evaluated
by employing the additional data sets of Table 2.
In order to improve this capacity of the model, Eq.
(2) was trained using the data in Table 1 and then
used to predict the data in Table 2. The mean percentage deviation (MPD), used to check the accuracy
of the prediction methods, was calculated using the
following equation:
where N is the number of data points in each set.
Goodness of fit to each method was investigated by
plotting the predicted solubilities against the experimental values for the drugs.
Sat
log X mSat,T = f c log X cSat
,T + f w log X w,T
+
fc fw
T
2
∑A (f
j =0
j
(2)
− f w ) + Bf c f w log P
j
c
The log P values encompass information about
drug characteristics; the numerical values used in the
computations are either experimental and/or calculated using ACD software.
EXPERIMENTAL DATA AND
COMPUTATIONAL METHODS
Experimental solubility data for solutes in ethanol +
water mixtures covering all composition ranges (fc =
0-1) were collected from the literature.4-35 Data sets
previously used to obtain Eq. (1) were used as training sets in this work; their details are listed in Table
1. Other solubility data sets were collected from the
literature and were used as prediction sets in this investigation (see Table 2 for details). It should be
noted that the solubility sets in Tables 1 and 2 are
expressed using different solubility units - g/L,
⎧⎪ ( X mSat,T ) pred − ( X mSat,T ) ⎫⎪
⎬
∑⎨
( X mSat,T )
⎪⎩
⎪⎭
MPD =
N
(3)
RESULTS AND DISCUSSION
All the data in Table 1 were fitted to Eq. (2) and the
equation used for the trained model was:
Table 1. Details of solubility data in water + ethanol mixtures, temperature T (K), number of data points (N), references, logarithm of partition coefficient and mean percentage deviations (MPDs) for Eqs. (1), (4) and (5)
No.
Solute
T (K)
N
Reference
logP
MPD
Eq. (1)
Eq. (4)
Eq. (5)
1
Acetanilide
298
13
4
1.16
41.9
25.1
67.6
2
Alanine (Beta)
298
7
5
-2.96
50.5
41.0
85.2
3
Alanine (DL)
298
7
5
-2.96
24.9
16.5
84.6
4
Aminocaproic acid (ε)
298
7
5
2.95
55.4
47.9
85.4
5
Asparagine (L)
298
5
5
-3.41
20.4
12.0
80
6
Aspartic acid (L)
298
7
5
-2.41
25.6
25.4
84.9
7
Benzo [a] pyrene
296
6
6
6.12
43.3
36.5
70.4
8
Caffeine
298
11
7
-0.07
27.2
26.7
59.3
9
Chrysene
296
6
6
5.66
21.7
31.8
40.9
10
Furosemide
298
13
8
2.29
115.5
65.0
51.1
11
Glycine
298
7
5
-3.21
30.9
17.1
84.9
12
Glycylglycine
298
7
5
-2.92
41.6
27.7
85.2
13
Hexachlorobenzene
296
6
6
5.70
108.9
31.9
77.4
14
Leucine (L)
298
7
5
-1.52
22.9
35.2
82
15
Niflumic acid
298
9
7
4.43
335.4
138.8
474.3
16
Norleucine (DL)
298
7
5
-1.38
25.7
39.2
81.2
17
Oxolinic acid
293
11
9
0.20
19.3
19.3
72.8
18
Oxolinic acid
298
11
9
0.20
21.3
21.1
71.4
19
Oxolinic acid
303
11
9
0.20
23.4
23.1
70.5
20
Oxolinic acid
308
11
9
0.20
26.2
25.9
69.9
21
Oxolinic acid
313
11
9
0.20
29.4
29.0
68.7
22
Paracetamol
293
11
10
0.51
53.7
49.6
57.5
23
Paracetamol
298
11
10
0.51
32.2
27.7
67
24
Paracetamol
303
11
10
0.51
46.0
44.8
58.1
25
Paracetamol
308
11
10
0.51
30.9
33.2
85.2
26
Paracetamol
313
11
10
0.51
35.5
34.7
61.4
27
Pentachlorobenzene
296
6
6
5.18
138.3
59.8
76.3
28
Perylene
296
6
6
6.12
19.0
39.1
81.8
29
Salicylic acid
298
11
11
2.26
44.9
17.4
50.9
30
Sulphamethiazine
298
11
12
1.11
37.9
42.8
87.8
31
Sulphanilamide
298
12
12
-0.62
16.7
22.9
80.7
32
Valine (DL)
298
7
5
-2.26
12.7
27.9
83.5
49.4
35.5
85.6
Biomedicine International (2010) 1: 19-24 / Solubility Prediction
21
Table 2. Details of additional data set used to test the predictive capacity of the models including name of solute, temperature T (K), number of
data points (N), references, logarithm of partition coefficient, and mean percentage deviations (MPDs) for Eqs. (1), (4) and (5).
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
Solute
Acetaminophen
Acetaminophen
Acetanilide
Acetanilide
Acetanilide
Aminopyrine
Amobarbital
Barbital
Benzocaine
Benzoic acid
Benzoic acid
Benzoic acid
Butabarbital
Celecoxib
Cholordiazepoxide
Clindamycin phosphate
Clindamycin phosphate
Clindamycin phosphate
Clindamycin phosphate
Clindamycin phosphate
Clindamycin phosphate
Clindamycin phosphate
Clindamycin phosphate
Clindamycin phosphate
Clindamycin phosphate
Clindamycin phosphate
Clindamycin phosphate
Clindamycin phosphate
Clindamycin phosphate
Clonazepam
Diazepam
Diazepam
Diclofenac Na
Ethyl maltol
Ethyl maltol
Ethyl maltol
Ethyl maltol
Ethyl maltol
Ethyl maltol
Ethyl maltol
Ethyl maltol
Ethyl maltol
Ketoprofen
Ketoprofen
Lamivudine (polymorphs I and II)
Lamotrigine
Lorazepam
Meloxicam
Methabarbital
Naproxen
Naproxen
Naproxen
Naproxen
Naproxen
Nimesulide
Pentobarbital
Phenacetin
Phenobarbital
Phenyl salicylate
Phenytoin
Resveratrol (trans)
Resveratrol (trans)
Resveratrol (trans)
Resveratrol (trans)
Rofecoxib
Rofecoxib
Rofecoxib
Rofecoxib (S)
Rofecoxib (S)
Rofecoxib (S)
Salicylic acid
Salicylic acid
Sulphamethoxypridazine
Thiamylal
Thiopental
Valdecoxib
Valdecoxib
Valdecoxib
Valdecoxib
Vinbarbital
T (K)
298
303
293
298
303
298
298
298
298
288
293
298
298
298
303
278
283
288
293
298
303
308
313
318
323
328
333
338
343
298
298
303
298
293
298
303
308
313
318
323
328
333
298
310
298
298
303
298
298
293
298
303
308
313
298
298
298
298
298
298
293
303
313
323
298
303
308
298
303
308
298
298
298
298
298
298
303
308
310
298
N
11
11
8
11
13
11
41
41
11
11
11
11
41
8
11
7
7
7
7
7
7
7
7
7
7
7
7
7
7
11
11
11
19
9
9
9
9
9
9
9
9
9
11
11
12
11
11
7
41
10
11
11
11
11
8
40
11
41
10
11
11
11
11
11
14
6
6
6
6
6
11
17
13
40
40
6
6
6
7
41
Reference
13
14
4
15
4
16
17
17
15
18
18
18
17
19
20
21
21
21
21
21
21
21
21
21
21
21
21
21
21
22
22
20
23
24
24
24
24
24
24
24
24
24
25
25
26
22
20
19
17
27
27
27
27
27
19
17
15
17
4
28
29
29
29
29
19
30
30
31
31
31
15
32
33
17
17
34
34
34
35
17
logP
0.51
0.51
1.16
1.16
1.16
1.00
2.07
0.65
1.86
1.87
1.87
1.87
1.58
3.47
2.44
2.16
2.16
2.16
2.16
2.16
2.16
2.16
2.16
2.16
2.16
2.16
2.16
2.16
2.16
3.02
2.85
2.85
0.70
0.63
0.63
0.63
0.63
0.63
0.63
0.63
0.63
0.63
3.12
3.12
1.40
1.87
2.40
3.43
1.14
3.18
3.18
3.18
3.18
3.18
2.60
2.07
1.58
1.47
4.12
2.47
1.58
1.58
1.58
1.58
3.20
3.20
3.20
3.20
3.20
3.20
2.26
2.26
0.32
3.23
2.88
3.20
3.20
3.20
3.20
1.63
Eq. (1)
31.2
48.1
37.2
44.3
28.8
41.4
39.2
76.6
120.2
102.7
60.4
34.8
37.1
108.9
26.1
95.6
190.1
147.0
135.0
101.6
111.3
97.1
94.8
80.7
63.8
63.2
63.2
64.8
67.3
32.9
12.2
18.5
62.7
27.7
32.6
33.0
32.5
36.2
38.0
38.3
37.2
38.4
51.5
51.7
50.2
21.7
21.1
99.0
54.7
69.9
51.6
42.0
27.7
24.5
69.0
17.3
52.5
53.9
198.8
20.0
55.9
54.6
54.4
53.9
13.8
22.7
26.3
15.9
27.2
34.2
37.1
49.1
5.5
66.6
25.6
35.7
39.9
44.1
41.3
52.4
54.8
Eq. (4)
23.9
39.5
24.0
26.7
19.3
33.2
22.0
62.6
73.6
62.2
31.6
23.0
17.1
56.1
28.7
73.3
130.4
99.1
90.9
67.6
74.0
64.3
62.7
54.2
50.1
49.8
49.7
48.8
48.1
20.4
25.0
28.3
51.1
25.8
30.4
31.6
31.6
36.0
37.7
37.9
36.9
38.1
57.6
58.1
53.6
29.5
30.0
50.1
34.6
32.9
25.8
24.4
22.1
23.0
37.9
18.9
59.2
28.5
87.8
17.6
58.7
57.6
57.7
57.3
23.9
38.3
40.5
32.2
40.0
44.6
17.1
54.2
7.7
22.8
30.8
46.4
49.2
51.8
50.3
25.6
43.0
Eq. (5)
51.3
48.2
52
62.2
53.9
45.7
57.2
42.9
41.2
36
35.7
36.7
50
66.8
50.6
84.3
67.4
70.8
70.3
70.1
62.4
59.8
59.3
57
59.8
60.7
57.5
51.5
41.9
118.4
48.7
62.7
32.2
73
75.6
76.7
78.2
79
79.4
79.4
79.1
77.6
84.5
83.6
82.9
58.3
59.7
1589.8
33.7
53.3
52.1
52
52.4
54.1
41.8
68.5
96.1
51.9
302.6
52.8
89.9
89.7
89.5
89.4
638.5
710.5
702.4
749.6
674.4
665.3
56.4
73.1
86.5
47.8
46.3
73
66.6
66.5
63.4
44.6
132.0
22
Jouyban et al. / Biomedicine International (2010) 1: 19-24
Equations (1) and (4) were used to back-calculate the
solubility data of the training set; the results are listed
in Table 1. The niflumic acid, pentachlorobenzene
and furosemide data sets had the highest MPDs for
both Eqs. (1) and (4). The overall MPDs (± SD) for
Eqs. (1) and (4) were 49.4 (± 59.7) % and 35.5 (±
22.5) % respectively, and the reduction in MPD using
Eq. (4) (13.9 %) was statistically significant (paired ttest, P < 0.03).
The solubility data sets in Table 2 were predicted
using Eqs. (1) and (4); the computed MPDs are listed
in Table 2. Phenyl salicylate and clindamycin phosphate at 283 K and 288 K had the highest MPDs for
both Eqs. (1) and (4). The overall MPDs (±SD) were
54.8 (± 36.7) % and 43.0 (± 21.0) % for Eqs. (1) and
(4) respectively, and the improvement (11.8 %) in
accuracy using Eq. (4) was statistically significant
Sat
logX mSat,T = f c logX cSat
,T + f w log X w,T
⎡724.21 485.17( f c − f w ) 194.41( f c − f w )2 ⎤
+ fc f w ⎢
+
+
⎥
T
T
⎣⎢ T
⎦⎥
− 0.314f c f w logP
(4)
(paired t-test, P < 0.0005). It should be noted that
none of the solubility data for the binary solvents
listed in Table 2 were used in the training of Eq. (4);
the only data required for prediction were the solubilities in mono-solvents. Theoretically, there are a
Sat
Sat
number of possibilities for replacing X c ,T and X w,T
with the values predicted by relevant models from the
literature.36-38 However, these predictions have relatively high errors.2 Therefore, until more accurate
methods are available for predicting solubilities in
mono-solvents at various temperatures, we will conSat
tinue to use experimentally-determined X c ,T and
X wSat,T values.
The ideal MPD value is any value less than the
relative standard deviations (RSDs) for the experimental solubilities measured in the laboratory. The
reported RSDs for a single solute’s solubility measured in a laboratory using the same procedure, the
same drug powder, the same solvents, the same instruments and the same research group, vary between
4.4 %39 and 10 %.40 However, solubility data could
be affected by a number of parameters including; 1)
solute purity, 2) equilibration time, 3) temperature, 4)
method of analysis, 5) laboratory technique, 6) typographical error, 7) polymorphism and 8) enantiomeric
forms.2 A ring test conducted by the environment
agency of Japan41 demonstrated that the MPDs between the measured solubilities within 19 laboratories of the local government and universities in Japan
were approximately 51 %2, providing evidence of the
effect of some of the variables listed above on the
outcome of solubility determinations.
The literature also provides evidence for deviations
in reported solubilities (readers are referred to Table
7 of a previous review (reference 2) varying from 17
% to 988 %. The accepted MPD for correlation of
solubility data in mixed solvents is approximately 30
% in the pharmaceutical industry.42-43 However, this
MPD level concerns correlative data and greater
MPDs should be expected when using predictive
models. In addition, a comparison between the MPDs
of the proposed Eq. (4) and those of the wellestablished log-linear model of Yalkowsky44 reveals
that Eq. (4) improves the prediction of the solubility
of drugs in water-ethanol mixtures. The trained loglinear model of Yalkowsky45 for solubility prediction
of drugs in water–ethanol mixtures is:
log X mSat,T = log X wSat,T + f c (0.95logP + 0.30)
(5)
4
R = 0.9906
2
Calculated by Eq. (4)
-10
-8
-6
-4
-2
0
-2
-4
-6
-8
Experimental solubility
0
-10
Fig. 1. Plot of solubilities ( log
X m ,T ) calculated by Eq. (4) against the corresponding experimental values.
2
4
Biomedicine International (2010) 1: 19-24 / Solubility Prediction
23
4
R = 0.9355
2
Calculated by Eq. (5)
0
-8
-6
-4
-2
0
-2
-4
-6
-8
2
4
Experimental solubility
-10
-10
Fig. 2. Plot of solubilities ( log
X m ,T ) calculated by Eq. (5) against the corresponding experimental values.
MPDs for the solubility data sets investigated in
this study are listed in Tables 1 and 2, with overall
MPDs of 85.6 and 132.0 % respectively. These values are statistically different from the corresponding
values for Eq. (4) (paired t-test, P < 0.0005).
When the data sets in Tables 1 and 2 were considered together, the overall MPDs (±SD) for Eqs. (1)
and (4) were 52.9 (± 44.2) % and 40.7 (± 21.6) %
respectively, and the reduction in MPD using Eq. (4)
(12.2 %) was statistically significant (paired t-test, P
< 0.0005). There was a strong correlation (R=0.9907)
between the individual predicted solubilities and the
corresponding experimental values (Figure 1). By
adding one more term to the Jouyban-Acree model, a
12 % reduction in error may be achieved for predicting drug solubilities in ethanol + water mixtures at
various temperatures. The MPD of Eq. (5), calculated
for all data sets in Tables 1 and 2, was 118.7 %, significantly larger than the MPD of Eq. (4). In addition,
the plot of the calculated solubilities against experimental values (Figure 2) revealed that Eq. (4) is superior to Eq. (5). Since ethanol is one of the most common cosolvents in oral and parenteral pharmaceutical
formulations46, we propose that this version of the
model be used in the industry to facilitate and accelerate solubilization procedures.
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