Approximating Blood-Tissue Partition Coefficient Measurements with Solubility Measurements

Researchers: Andrew SID Lang, William E Acree Jr., Caitlin Derricott, Emily Knight

Introduction

The Abraham model has been applied to blood-tissue partition coefficients [1]. For example, The blood-brain-barrier partition coefficient can be modeled using the equation:

Equation 1: log BB = 0.547 + 0.221 E -0.604 S -0.641 A -0.681 B + 0.635 V -1.216 Ic

where E, S, A, B, and V are the standard solute descriptors and Ic is taken to be one if the solute is a carboxylic acid and zero otherwise (because carboxylic acids undergo ionization. The pH of blood is 7.4 and carboxylic acids are ionized at this pH).

The above model gives us a way to approximate log BB for compounds with known Abraham descriptors [2]. If Abraham descriptors are not know, then we can either get them indirectly from models [3] - which is advantageous for virtual compound libraries, or for specific compounds, derive them from available solubility and partition measurements [4]. Sometimes measurements for a compound cannot be found in abundance. In the case where few measurements are known, a significant number of measurements have to be performed in order to approximate the descriptors with any degree of certainty.

Instead of deriving the solute descriptors through a series of measurements in order to approximate log BB, we propose a method to approximate log BB using only a couple (or a few) solubility measurements.

Procedure

We took all solvents with measured Abraham coefficients and normalized them by multiplying each coefficient by the average (mean) corresponding solute descriptor value ( Eave = 0.902, Save = 1.016, Aave = 0.144, Bave = 0.492, Vave = 1.330) for our set of compounds with known Abraham descriptors (not including those with nAcid > 0). We did this to account for the relative contributions that each coefficient makes towards the final partition value.

We then regressed the normalized coefficients for these solvents against the normalized coefficients in the Log BB equation using the following code in R:
mydata = read.csv(file="20141022Coefficients-NormalizedReadyForR.csv",head=TRUE,row.names="coefficient")
library(leaps)
attach(mydata)
leaps<-regsubsets(normalized ~ 0 + .,nvmax=2,data=mydata,nbest=5,really.big=TRUE,intercept=FALSE)
## summary(leaps)
for (n in 1:10)
{
print(coef(leaps,n))
}
 
[output]
(Intercept)         X74
-0.09548583  0.16409286
(Intercept)         X50
 -0.1057396   0.1664516
(Intercept)         X43
 -0.0981550   0.1654905
(Intercept)         X42
 -0.1011318   0.1665445
(Intercept)         X45
 -0.1020970   0.1671912
 (Intercept)          X40          X88
-0.001642993  0.683174473 -0.497378870
 (Intercept)          X45          X53
 0.001946871  0.448904998 -0.308778314
 (Intercept)          X51          X71
 0.002899478  0.370024092 -0.224092036
 (Intercept)          X45          X68
 0.001891418  0.455433153 -0.309829606
 (Intercept)          X46          X71
 0.004117552  0.360386611 -0.239561717
[output]
 
fit <- lm(normalized ~ 0 + X74,data=mydata)
summary(fit)
 
[output]
Call:
lm(formula = normalized ~ 0 + X74, data = mydata)
 
Residuals:
        e         s         a         b         v
-0.278023 -0.015804 -0.002069 -0.033820 -0.068669
 
Coefficients:
    Estimate Std. Error t value Pr(>|t|)
X74  0.15165    0.02068   7.332  0.00184 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 
Residual standard error: 0.1444 on 4 degrees of freedom
Multiple R-squared:  0.9307,    Adjusted R-squared:  0.9134
F-statistic: 53.75 on 1 and 4 DF,  p-value: 0.001842
[output]
 
fit <- lm(normalized ~ 0 + X40 + X88,data=mydata)
 summary(fit)
 
[output]
Call:
lm(formula = normalized ~ 0 + X40 + X88, data = mydata)
 
Residuals:
         e          s          a          b          v
 0.0001244 -0.0026766 -0.0011036 -0.0002149 -0.0001633
 
Coefficients:
     Estimate Std. Error t value Pr(>|t|)
X40  0.686187   0.002623   261.6 1.23e-07 ***
X88 -0.500414   0.002444  -204.7 2.57e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 
Residual standard error: 0.00168 on 3 degrees of freedom
Multiple R-squared:      1,     Adjusted R-squared:      1
F-statistic: 2.133e+05 on 2 and 3 DF,  p-value: 1.865e-08
[output]
The results show that we can approximate log BB as follows (X74 = methylcyclohexane), see the solvent datafile (xlsx)

Equation 2: log BB = 0.510 + 0.152 log P_mcy -1.216 Ic

with a predicted adjR2 value of 0.91 and where log P_mcy = log P_(methylcyclohexane/water) = log S_methylcyclohexane - log S_water under most reasonable conditions (note carboxylic acids may dimerize in methylcyclohexane) [4].

To test our model, we compared log BB values calculated using equation (1) to those calculated using equation (2) and the following data provided by Bill Acree (RMSE 0.168):
name
E
S
A
B
V
logP_mcy
AD logBB (1)
ONS logBB (2)
water
0.000
0.450
0.820
0.350
0.167
-4.01
-0.38
-0.10
ethanol
0.250
0.420
0.370
0.480
0.449
-1.78
0.07
0.24
1-propanol
0.240
0.420
0.370
0.480
0.590
-1.05
0.16
0.35
acetone
0.180
0.700
0.040
0.490
0.547
-0.90
0.15
0.37
t-butanol
0.180
0.300
0.310
0.600
0.731
-0.56
0.26
0.42
2-methyl-1-propanol
0.220
0.390
0.370
0.480
0.731
-0.41
0.26
0.45
1-butanol
0.220
0.420
0.370
0.480
0.731
-0.40
0.24
0.45
neon
0.000
0.000
0.000
0.000
0.085
0.60
0.60
0.60
argon
0.000
0.000
0.000
0.000
0.190
1.02
0.67
0.67
nitrogen
0.000
0.000
0.000
0.000
0.222
1.06
0.69
0.67
krypton
0.000
0.000
0.000
0.000
0.246
1.25
0.70
0.70
methane
0.000
0.000
0.000
0.000
0.250
1.34
0.71
0.71
xenon
0.000
0.000
0.000
0.000
0.329
1.61
0.76
0.75
sulphur hexafluoride
-0.600
-0.200
0.000
0.000
0.464
2.36
0.83
0.87
benzene
0.610
0.520
0.000
0.140
0.716
2.38
0.73
0.87
toluene
0.600
0.520
0.000
0.140
0.857
2.90
0.81
0.95
ethylbenzene
0.610
0.510
0.000
0.150
0.998
3.44
0.91
1.03
cyclohexane
0.310
0.100
0.000
0.000
0.845
4.07
1.09
1.13
methylcyclohexane
0.240
0.060
0.000
0.000
0.986
4.75
1.19
1.23
styrene
0.850
0.650
0.000
0.160
0.955
5.15
0.84
1.29

We see good results as illustrated in the figure below.

20141029logBB.png

We see log BB can be approximated fairly well just using logP_mcy values which in turn can be attained in most circumstances from simple solubility measurements in methylcyclohexane and water. We do note however that as the Abraham model for log BB improves our models will also need updating and it is feasible that in the future another solvent other than methylcyclohexane will be predicted as best for approxiamting logBB values.

Regressing against two solvents gave us the following eqution for log BB

log BB = 0.483 + 0.446 log P_(heptane/water) - 0.308 log P_(1-chlorobutane/water) -1.216 Ic

with a predicted adjR2 value of 0.99 and where log P_(heptane/water) = log S_heptane - log S_water and log P_(1-chlorobutane/water) = log S_1-chlorobutane - log S_water under most reasonable conditions (carboxylic acids may dimerize in these solvents).

Thus log BB can easily be approximated by measuring its solubility in two (or for a more accurate results three) solvents, namely methylcyclohexane and water (or pentane, carbon disulfide, and water). The results are so good for the two-solvent (X1, X2) approximation several other choices would give accurate results and solvents could thus be chosen for convenience sake. For example, it looks like that it is good to have one of the solvents be an alkane (see table below), so let's pick hexane and then see what solvents would be a good match for hexane (X41):

leaps<-regsubsets(normalized - X41 ~ 0 + .,nvmax=1,data=mydata,nbest=10,really.big=TRUE)
 
for (n in 1:10)
+ {
+ print(coef(leaps,n))
+ }
 
[output]
(Intercept)         X56
 0.04708982 -0.83915134
(Intercept)         X57
  0.2135541  -1.3039898
(Intercept)          X4
 0.08579438 -0.91845706
(Intercept)         X40
 -0.0662102  -0.8323128
(Intercept)         X48
-0.08385477 -0.84289618
(Intercept)         X46
-0.06944242 -0.81177586
(Intercept)         X72
-0.08579303 -0.81583914
(Intercept)         X47
-0.08768122 -0.83694456
(Intercept)         X91
 0.03366287 -1.11731138
(Intercept)         X59
  0.1396774  -0.8748496
[output]

We see hexane is a good pairing with: carbon tetrachloride, trifluoroethanol, isopropyl myristate, pentane, hexadecane, undecane, cyclohexane, dodecane, peanut oil, and dibutyl ether.

Results

The regression analysis was performed on other blood-tissue partition equations for in vivo processes, as log P, at 37 °C [5] without normalizing by the average descriptor values:
Process
c
e
s
a
b
v
Ic
Blood–brain
0.547
0.221
−0.604
−0.641
−0.681
0.635
−1.216
Blood–muscle
0.082
−0.059
0.010
−0.248
0.028
0.110
−1.022
Blood–liver
0.292
0.000
−0.296
−0.334
0.181
0.337
−0.597
Blood–lung
0.269
0.000
−0.523
−0.723
0.000
0.720
−0.988
Blood–kidney
0.494
−0.067
−0.426
−0.367
0.232
0.410
−0.481
Blood–heart
0.132
−0.039
−0.394
−0.376
0.009
0.527
−0.572
Blood–skin
−0.105
−0.117
0.034
0.000
−0.681
0.756
−0.816
Blood–fat
0.077
0.249
−0.215
−0.902
−1.523
1.234
−1.013
Water–skin
0.523
0.101
−0.076
−0.022
−1.951
1.652
0.000
Skin permeation
−5.420
−0.102
−0.457
−0.324
−2.608
2.066
0.000
Note: The skin permeation coefficients are for In vitro permeation with log Kp in cm s−1 all other coefficients are for in vivo processes.

In general, the blood-tissue partition coefficient is approximated using the following equation:

log P_blood/tissue = c_0 + c_1 X1 + c_2 X2 + Ic

where c_0 is the intercept and Ic is the carboxylic acid modifier; c1 is the coefficient multiplier for the log P value of compound X1, and c_2 is the coefficient multiplier for the log P value of compound X2 (c_2 = 0 for 1-variable approximations).

The top five results for log BB are as follows:

blood-brain 1-variable
0.547
solvent
c
c0
c1
p
R2
X74
methylcyclohexane
0.246
0.5054875
0.16875
0.00138
0.9401
X50
1,9-decadiene
0.104
0.52899032
0.17317
0.00251
0.9193
X43
octane
0.231
0.51007003
0.15987
0.00224
0.9237
X72
cyclohexane
0.159
0.52201315
0.15715
0.0028
0.9148
X45
decane
0.186
0.51718048
0.16032
0.00282
0.9145

Similarly, the top five results for the other processes are:

blood-muscle
0.082
solvent
c
c0
c1
p
R2
X57
trifluoroethanol
0.395
0.063356
0.0472
0.1955
0.3759
X55
chloroform
0.191
0.07672649
0.02761
0.1735
0.4061
X54
dichloromethane
0.319
0.0740888
0.0248
0.2132
0.3536
X56
carbon tetrachloride
0.199
0.0777215
0.0215
0.2275
0.3364
X65
iodobenzene
-0.192
0.08615104
0.02162
0.2428
0.3191

blood-liver
0.292
solvent
c
c0
c1
p
R2
X57
trifluoroethanol
0.395
0.24957305
0.10741
0.1513
0.4394
X74
methylcyclohexane
0.246
0.2809423
0.04495
0.2361
0.3266
X50
1,9-decadiene
0.104
0.28738136
0.04441
0.2644
0.296
X55
chloroform
0.191
0.28278234
0.04826
0.2805
0.2799
X49
2,2,4-trimethylpentane
0.32
0.2793408
0.03956
0.2926
0.2682

blood-lung
0.269
solvent
c
c0
c1
p
R2
X57
trifluoroethanol
0.395
0.1651545
0.2629
0.04008
0.6918
X74
methylcyclohexane
0.246
0.23886992
0.12248
0.05695
0.6372
X50
1,9-decadiene
0.104
0.2561404
0.12365
0.0693
0.6031
X55
chloroform
0.191
0.24312523
0.13547
0.07863
0.5797
X49
2,2,4-trimethylpentane
0.32
0.2327024
0.11343
0.07877
0.5793

blood-kidney
0.494
solvent
c
c0
c1
p
R2
X57
trifluoroethanol
0.395
0.4429818
0.12916
0.1746
0.4046
X74
methylcyclohexane
0.246
0.48103334
0.05271
0.2744
0.2859
X50
1,9-decadiene
0.104
0.48857016
0.05221
0.3008
0.2605
X55
chloroform
0.191
0.48345107
0.05523
0.3316
0.2335
X49
2,2,4-trimethylpentane
0.32
0.4792736
0.04602
0.3345
0.2311

blood-heart
0.132
solvent
c
c0
c1
p
R2
X57
trifluoroethanol
0.395
0.062
0.17744
0.03284
0.7193
X74
methylcyclohexane
0.246
0.113
0.07916
0.06759
0.6076
X50
1,9-decadiene
0.104
0.124
0.08062
0.07638
0.5851
X49
2,2,4-trimethylpentane
0.32
0.109
0.07273
0.09441
0.5437
X43
octane
0.231
0.115
0.07153
0.09471
0.543

blood-skin
-0.105
solvent
c
c0
c1
p
R2
X24
ethanol/water(10:90)vol
-0.173
0.1918161
1.7157
0.0001669
0.979
X12
DMF
-0.305
-0.05844175
0.15265
0.0001956
0.9773
X23
ethanol/water(20:80)vol
-0.252
0.09946272
0.81136
0.0003916
0.9679
X22
ethanol/water(30:70)vol
-0.269
0.03408914
0.51706
0.0006143
0.9598
X18
ethanol/water(70:30)vol
0.063
-0.11973255
0.23385
0.0005348
0.9625

blood-fat
0.077
solvent
c
c0
c1
p
R2
X88
carbon disulfide
0.047
0.064954605
0.256285
1.14E-06
0.9983
X67
ethylbenzene
0.093
0.0493604
0.2972
1.57E-05
0.9935
X70
p-xylene
0.166
0.0277727
0.29655
1.62E-05
0.9934
X69
o-xylene
0.083
0.05226932
0.29796
1.97E-05
0.9928
X91
peanut oil
0.574
-0.12834276
0.35774
0.0008404
0.953

water-skin
0.523
solvent
c
c0
c1
p
R2
X75
THF
0.223
0.43751295
0.38335
2.79E-06
0.9973
X81
N-formylmorpholine
-0.032
0.53818944
0.47467
2.84E-05
0.9913
X13
dibutylformamide
0.332
0.38916084
0.40313
1.56E-05
0.9936
X85
acetone
0.313
0.39460114
0.41022
2.59E-05
0.9917
X76
1,4-dioxane
0.123
0.47371144
0.40072
2.24E-05
0.9923

skin-permeation
-5.42
solvent
c
c0
c1
p
R2
X75
THF
0.223
-5.53170293
0.50091
0.0001648
0.9791
X60
methyl tert-butyl ether
0.341
-5.58776518
0.49198
2.34E-05
0.9921
X58
diethyl ether
0.35
-5.595987
0.50282
3.54E-05
0.9903
X22
ethanol/water(30:70)vol
-0.269
-4.9673268
1.6828
0.001522
0.937
X21
ethanol/water(40:60)vol
-0.221
-5.1467114
1.2366
0.001265
0.9425

2-variable coefficients

blood-brain 2-variables
0.547
solvent1
c
solvent2
c
c0
c1
p
R2
X42
heptane
0.297
X66
toluene
0.125
0.45117932
0.46044
0.000391
0.9947
X43
octane
0.231
X66
toluene
0.125
0.48459881
0.42974
7.92E-05
0.9982
X44
nonane
0.24
X66
toluene
0.125
0.47497705
0.48008
0.0004171
0.9944
X45
decane
0.186
X68
m-xylene
0.122
0.50038846
0.4592
1.79E-05
0.9993
X43
octane
0.231
X67
ethylbenzene
0.093
0.472768
0.44587
7.01E-05
0.9983

blood-muscle
0.082
solvent1
c
solvent2
c
c0
c1
p
R2
X49
2,2,4-trimethylpentane
0.32
X51
1-hexadecene
0.116
-0.0107512
0.4529
0.04075
0.8816
X36
1-heptanol
0.035
X84
ethylene glycol
-0.27
-0.0020195
0.1854
0.1483
0.7198
X30
1-butanol
0.165
X84
ethylene glycol
-0.27
-0.03736505
0.21589
0.1236
0.7518
X55
chloroform
0.191
X59
dibutyl ether
0.176
0.07475273
0.11273
0.006448
0.9654
X49
2,2,4-trimethylpentane
0.32
X44
nonane
0.24
0.000392
0.9388
0.04187
0.8794

blood-liver
0.292
solvent1
c
solvent2
c
c0
c1
p
R2
X19
ethanol/water(60:40)vol
-0.04
X80
N-methyl-2-piperidone
0.056
0.336086
0.60886
0.001459
0.9871
X18
ethanol/water(70:30)vol
0.063
X11
N-ethylformamide
0.22
0.36579914
0.80642
0.01333
0.9438
X17
ethanol/water(80:20)vol
0.172
X80
N-methyl-2-piperidone
0.056
0.22836036
0.47659
0.005441
0.9691
X39
octadecanol
-0.096
X79
N-methylpyrrolidinone
0.147
0.36228256
0.30679
0.02378
0.9173
X16
ethanol/water(90:10)vol
0.243
X80
N-methyl-2-piperidone
0.056
0.20549356
0.4286
0.007922
0.9603

blood-lung
0.269
solvent1
c
solvent2
c
c0
c1
p
R2
X32
3-methyl-1-butanol
0.073
X27
2-propanol
0.099
0.3218737
2.0713
0.00211
0.9835
X20
ethanol/water(50:50)vol
-0.142
X11
N-ethylformamide
0.22
0.7257252
1.7856
0.07541
0.8215
X21
ethanol/water(40:60)vol
-0.221
X80
N-methyl-2-piperidone
0.056
0.68674853
1.72937
0.001563
0.9865
X29
2-methyl-2-propanol
0.211
X6
N-ethylacetamide
0.284
0.3042222
0.9758
0.0003914
0.9946
X22
ethanol/water(30:70)vol
-0.269
X80
N-methyl-2-piperidone
0.056
0.9410796
2.36584
0.004666
0.9721

blood-kidney
0.494
solvent1
c
solvent2
c
c0
c1
p
R2
X23
ethanol/water(20:80)vol
-0.252
X87
DMSO
-0.194
0.92373252
2.03498
0.0001233
0.9975
X23
ethanol/water(20:80)vol
-0.252
X9
formamide
-0.171
1.0139219
2.5962
0.03288
0.8974
X31
2-butanol
0.127
X90
tributyl phosphate
0.022
0.40783367
0.79943
0.001471
0.9871
X22
ethanol/water(30:70)vol
-0.269
X87
DMSO
-0.194
0.75434917
1.26831
0.001073
0.9895
X21
ethanol/water(40:60)vol
-0.221
X87
DMSO
-0.194
0.61679969
0.91581
0.001315
0.988

blood-heart
0.132
solvent1
c
solvent2
c
c0
c1
p
R2
X39
octadecanol
-0.096
X79
N-methylpyrrolidinone
0.147
0.21453465
0.38488
0.006347
0.9657
X19
ethanol/water(60:40)vol
-0.04
X80
N-methyl-2-piperidone
0.056
0.1851036
0.76094
0.0002552
0.996
X18
ethanol/water(70:30)vol
0.063
X11
N-ethylformamide
0.22
0.2098766
0.9478
0.02701
0.91
X53
1-chlorobutane
0.222
X71
nitrobenzene
-0.196
-0.0693916
0.4976
0.2066
0.6506
X18
ethanol/water(70:30)vol
0.063
X80
N-methyl-2-piperidone
0.056
0.11141671
0.67863
0.0005619
0.9932

blood-skin
-0.105
solvent1
c
solvent2
c
c0
c1
p
R2
X12
DMF
-0.305
X79
N-methylpyrrolidinone
0.147
0.0072516
0.29355
8.51E-05
0.9981
X23
ethanol/water(20:80)vol
-0.252
X84
ethylene glycol
-0.27
0.22089576
1.54723
0.0002055
0.9965
X18
ethanol/water(70:30)vol
0.063
X84
ethylene glycol
-0.27
-0.20430483
0.46661
0.0005899
0.993
X31
2-butanol
0.127
X33
1-pentanol
0.15
-0.1116483
0.8469
0.0002163
0.9964
X20
ethanol/water(50:50)vol
-0.142
X84
ethylene glycol
-0.27
-0.09356472
0.64464
0.0003629
0.9949

blood-fat
0.077
solvent1
c
solvent2
c
c0
c1
p
R2
X30
1-butanol
0.165
X27
2-propanol
0.099
-0.14452933
2.90901
1.67E-06
0.9999
X46
undecane
0.058
X50
1,9-decadiene
0.104
0.0795048
0.6
0.000768
0.9916
X88
carbon disulfide
0.047
X67
ethylbenzene
0.093
0.0715957
0.3647
4.58E-05
0.9987
X88
carbon disulfide
0.047
X57
trifluoroethanol
0.395
0.07875685
0.2703
3.27E-05
0.999
X88
carbon disulfide
0.047
X66
toluene
0.125
0.073668
0.3435
4.59E-05
0.9987

water-skin
0.523
solvent1
c
solvent2
c
c0
c1
p
R2
X27
2-propanol
0.099
X89
sulfolane
0
0.502735789
0.204689
8.08E-07
0.9999
X83
acetonitrile
0.413
X90
tributyl phosphate
0.022
0.45830486
0.141688
3.98E-08
1
X6
N-ethylacetamide
0.284
X86
butanone
0.246
0.417296244
0.147212
5.50E-07
0.9999
X3
butyl acetate
0.248
X48
hexadecane
0.087
0.407784123
0.504905
5.57E-08
1
X5
N-methylacetamide
0.09
X71
nitrobenzene
-0.196
0.52935714
0.26483
1.61E-05
0.9994

skin-permeation
-5.42
solvent1
c
solvent2
c
c0
c1
p
R2
X16
ethanol/water(90:10)vol
0.243
X83
acetonitrile
0.413
-5.6188514
0.3992
0.002202
0.9831
X16
ethanol/water(90:10)vol
0.243
X78
cyclohexanone
0.038
-5.4961234
0.2646
0.003174
0.9784
X1
methyl acetate
0.351
X17
ethanol/water(80:20)vol
0.172
-5.5907014
0.3698
0.00236
0.9823
X29
2-methyl-2-propanol
0.211
X77
propylene carbonate
0.004
-5.4934282
0.3434
0.001826
0.9851
X22
ethanol/water(30:70)vol
-0.269
X71
nitrobenzene
-0.196
-5.0966903
1.0577
0.006749
0.9643

Calculating the coefficients for methylcyclohexane and 1,9-decadiene for all processes gives:

Partition Coefficients for Methylcyclohexane
Process
p
R2
c_1
0_0
Blood-brain
0.0014
0.94
0.169
0.505
Blood-muscle
0.2401
0.32
0.021
0.077
Blood-liver
0.2361
0.33
0.04495
0.281
Blood-lung
0.05695
0.64
0.122
0.239
Blood-kidney
0.2744
0.29
0.053
0.481
Blood-heart
0.06759
0.61
0.079
0.113
Blood-skin
0.05174
0.65
0.111
-0.132
Blood-fat
0.000858
0.95
0.285
0.007
Water-skin
0.03418
0.71
0.289
0.452
Skin permeation
0.01667
0.8
0.403
-5.519

Blood Brain EquationVariables for 1,9-decadiene (X50)
Process
p
R2
c_1
c_0
Blood-brain
0.0025
0.92
0.173
0.529
Blood-muscle
0.2697
0.29
0.021
0.080
Blood-liver
0.264
0.3
0.044
0.287
Blood-lung
0.0693
0.6
0.124
0.256
Blood-kidney
0.3008
0.26
0.0502
0.489
Blood-heart
0.07638
0.59
0.08
0.124
Blood-skin
0.03598
0.71
0.12
-0.117
Blood-fat
0.0005379
0.96
0.297
0.046
Water-skin
0.02297
0.76
0.311
0.491
Skin permeation
0.01016
0.84
0.43
-5.465
1,9- Decadiene was a decent blood-partition coefficient.

Blood-Muscle
X90
X289
X108
X2
X277
co
-0.019
-0.033
-0.020
-0.018
-0.018
c1
0.026
0.044
0.023
0.023
0.022
mult r2
0.38
0.37
0.3214
0.3159
0.3025

Blood-Liver
X289
X224
X14
X90
X91
co
-2.6E-02
0.017
0.013
0
0.015
c1
-0.099
0.046
0.045
0.047
0.041
mult r2
0.408
0.320
0.291
0.269
0.264

Blood-Lung
X289
X224
X14
X90
X91
co
-0.048
0.001
-0.003
-0.018
-0.002
c1
0.246
0.121
0.122
0.131
0.114
mult r2
0.681
0.615
0.583
0.560
0.5563

Blood-Kidney
X289
X224
X14
X90
X91
c0
-0.048
0.001
-0.003
-0.018
-0.002
c1
0.12
0.052
0.052
0.053
0.046
mult r2
0.381
0.269
0.245
0.218
0.214

Blood-heart
X289
X224
X14
X91
X26
c0
-0.061
0.013
0.009
0.013
0.019
c1
0.167
0.08
0.081
0.075
0.074
mult r2
0.706
0.596
0.573
0.533
0.532


Conclusion

Several blood-tissue processes have been approximated using just a few solvent/solvent partition coefficients or common solvent solubility measurements. Several blood-tissue coefficients (blood-skin, blood-fat, water-skin, and skin-permeation) had very good (R2 > 0.97) models using just 1-variable approximations and gained relatively little improvement when 2-variable were used.

In the case of blood-brain, we have a very good 1-varibale model with an R2-value of 0.91 that can be improved to 0.99 when a 2-variable model is used. This case is borderline and whether you use the 1-variable or a 2-variable model should depend upon circumstances.

For the other processes (blood-muscle, blood-liver, blood-lung, blood-kidney, and blood-heart) the R2-value for the 1-variable models ranged from 0.58 for blood-kidney to 0.82 for blood-lung. All of the R2 values for these processes increased to at least 0.94 when 2-variables were used. Thus it seems that 2-variable models are more appropriate in these case. However, in a pinch, the 1-variable models are attractive because they all share the same three solvents (methylcyclohexane, trifluroethanol, and 1,9-decadiene). That is, with just one logP_mcy measurement, 5 blood-tissue partition values can be estimated with reasonable accuracy. This is not surprising, as the actual processes are similar in nature. It is also not surprising that the blood-fat partition coefficient can be approximated using the peanut oil-water coefficient.

All the 2-variable models had very good R2 values and there should not be a need to step up to 3-variable models. The models do so well that we can get good approximations from many different logP combinations. This adds to the convenience of our method.

References

1. Abraham MH, Gola JM, Ibrahim A, Acree WE Jr, Liu X. The prediction of blood-tissue partitions, water-skin partitions and skin permeation for agrochemicals. Pest Manag Sci. 2014 Jul;70(7):1130-7. doi: 10.1002/ps.3658. Epub 2013 Oct 13.
2. Bradley, Jean-Claude; Acree, William; Lang, Andrew (2014): Compounds with known Abraham descriptors. figshare. doi: 10.6084/m9.figshare.1176994 Retrieved 19:12, Oct 22, 2014 (GMT)
3. Lang ASID. Modeling Abraham model solute descriptors. Open Notebook
4. Abraham MH, et al. 2009. Prediction of Solubility of Drugs and Other Compounds in Organic Solvents. Journal of Pharmaceutical Sciences. doi: 10.1002/jps.21922
5. Abraham, Michael H., et al. A simple method for estimating in vitro air-tissue and in vivo blood-tissue partition coefficients. Chemosphere 120 (2015): 188-191. doi: 10.1016/j.chemosphere.2014.06.037|