We have seen that methylcyclohexane can be used to approximate log BB using Eq. (4). In general, we approximate the blood–tissue partition coefficient using the following
equation
(6)
where c
0
is the intercept, c
1
is the coefficient multiplier for the log P system corresponding to solvent X
1
, and I
c
is the carboxylic acid flag. Performing a similar analysis as described above and
regressing the water–solvent system Abraham coefficients against the blood–tissue
systems given in Table 1, we find the following results, presented in tables, see Tables 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, where the p-values are the standard p-values from linear regression—calculated using
the ‘lm’ command in R.
Table 3. Top five solvents for blood–brain
Table 4. Top five solvents for blood–muscle
Table 5. Top five solvents for blood–liver
Table 6. Top five solvents for blood–lung
Table 7. Top five solvents for blood–kidney
Table 8. Top five solvents for blood–heart
Table 9. Top five solvents for blood–skin
Table 10. Top five solvents for blood–fat
Table 11. Top five solvents for water–skin
Table 12. Top five solvents for skin-permeation
Examining the results presented in the Tables 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, we see that the blood–brain barrier system can be modeled well with multiple solvents,
including methylcyclohexane, octane, and 1,9-decadiene.
The results for blood–muscle and blood–liver were similar, with similar solvents,
but very poor R
2
values overall. The highest R
2
was 0.44, exhibited by 2,2,2-trifluoroethanol for the blood–liver system.
The results for modeling the blood–lung, blood–kidney, and blood–heart partition coefficients
were interesting as the top three suggested replacement solvents were identical, namely:
2,2,2-trifluoroethanol, methylcyclohexane, and 1,9-decdiene. The R
2
values for these systems ranged between 0.41 for blood–kidney to 0.72 for blood–heart.
The blood–skin barrier model showed very strong results, with all of the top 5 R
2
values above 0.95, which is very good. Some previously unseen solvents came up, the
various ethanol–water mixtures composed four of the top five solvents.
Modeling the blood–fat system also had some very promising results. The highest was
carbon disulfide with an R
2
of 0.998. The lowest of the top 5 values was still very good, an R
2
value of 0.95 for peanut oil. We suggest using the water/peanut oil system as a replacement
system for blood–fat partition coefficients.
The water–skin solvents tested also produced strong results; the lowest of the top
five R
2
values is over 0.9, much higher than several of the earlier systems. Tetrahydrofuran
resulted in the highest R
2
value at 0.997.
The top five suggested replacement water–solvent systems for skin-permeation, like
many previous blood–tissue systems, show great promise. The top three solvents being
methyl tert-butyl ether, tetrahydrofuran, and diethyl ether.
Whilst most blood–tissue systems can be modeled with a single water–solvent system,
blood–muscle, blood–liver, and blood–kidney had poor results, with R
2
values all below 0.45. This is due to these three solvents having the smallest v values
(0.110, 0.337, and 0.410) and highest b values (0.028, 0.181, 0.232) taking them out
of the chemical space for single solvents. For these systems we modeled the blood–tissue
coefficients using two measured water–solvent partition coefficient values X
1
and X
2
as follows
(7)
where again c
0
is the intercept. The results of these models are again presented in table form, see
Tables 13, 14, 15.
Table 13. Top five results for two-variable blood–kidney partition coefficient
Table 14. Top five results for two-variable blood–liver partition coefficient
Table 15. Top five results for two-variable blood–muscle partition coefficient
Blood–kidney regression with 1-variable produced very poor results, the top R
2
value was 0.4 for 2,2,2-trifluoroethanol. Two variables can be used to increase the
R
2
value. This greatly improved all values for blood–kidney, the top value produced by
a mixture of ethanol/water (20:80) and DMSO, with an R
2
value of 0.997.
Blood–liver also produced very poor 1-variable results, so 2-variables were used to
improve the R
2
value. The highest R
2
with 1-variable was 0.44 with 2,2,2-trifluoroethanol. The highest R
2
with 2-variables was 0.99 by ethanol/water (60:40) and N-methyl-2-piperidone.
For the blood–muscle process, the overall 2-variable correlation coefficients were
fairly good. The solvents that are best are chloroform and dibutyl ether with an R
2
value of 0.97.
Combining two measured water/solvent partition coefficients can also improve the models
for approximation the other blood–tissue partition coefficient values. See the Wiki
page in the references for a complete list of all two-variable data tables 11].
When looking at the results, we note that the standard 1-octanol/water partition coefficient
(log P) does not appear as a top solvent for any of the blood–tissue processes. This
is interesting because log P has for a long time been assumed to be useful in estimating
the distribution of drugs within the body and is a standard descriptor used in most
QSAR modeling. Since the use of log P is prevalent throughout the chemistry community,
we calculated how well the Abraham model for every blood–tissue partition coefficient
can be modelled by the Abraham model for log P, see Table 16.
Table 16. Equation (6) coefficients for 1-octanol against multiple processes
Examining Table 16, we see that log P can be used to approximate all blood–tissue partition coefficients
and actually performs moderately well for estimating log BB, but poorly for blood–muscle
and all other organs. However, log P seems like a reasonable measure for processes
to do with chemicals entering into the body: blood–skin, blood–fat, water–skin, and
skin-permeation. The latter observation is in accord with the published results of
Cronin and coworkers 12], 13] who noted that the percutaneous adsorption of organic chemicals through skin is mediated
by both the hydrophobicity (log P) and the molecular size of the penetrant.
The water/solvent systems that included methylcyclohexane and 1,9-decadiene were in
the top 5 results for multiple regressions. In Tables 17 and 18 we present the Eq. (6) coefficients for methylcyclohexane and 1,9-decadience respectively. In some case
the coefficients have low R
2
values. Keeping that in mind, we have a two more ways (with better performance than
log P for predicting the important log BB partition coefficient) that all blood–tissue
partition coefficients can be approximated by a single water–solvent partition coefficient
measurement.
Table 17. Equation (6) coefficients for methylcyclohexane against multiple processes
Table 18. Equation (6) coefficients for 1,9-decadiene against multiple processes
As we have seen, methylcyclohexane is a good solvent when used to model the blood–brain
barrier process. For other processes, blood–fat and skin-permeation, it showed a reasonably
good R
2
value (over 0.80). However, blood–muscle, blood–liver, and blood–kidney showed really
poor R
2
values (all less than 0.33).
1,9-Decadiene was just as good of a solvent as methylcyclohexane for approximating
multiple blood–tissue coefficients. Blood–brain, blood–fat, and skin-permeation all
showed good R
2
values over 0.80. Just as in the methylcyclohexane case, the processes blood–muscle,
blood–liver, blood–kidney were not well modeled and 2-solvent models are needed for
more accurate approximations.
The research presented in this paper was performed under standard Open Notebook Science
conditions, where day-to-day results were posted online in as near to real time as
possible. For addition details, the data files, and the R-code used to find model
systems, see the Open Lab Notebook page 11].