POBLACIÓN Y MUESTRA POBLACIÓN

A point often neglected in correlations o f biological systems and SPRs in general, is that o f "bunching" or "clustering" o f datasets. This point has been amply discussed by Rekker"^^ in a recent paper, but is illustrated by eqs(4.30-4.32). If a given dataset is found to cluster into two distinct groups, it is possible that neither group will lead to a satisfactory general regression equation, whereas the two groups taken together will yield a satisfactory equation. For example, the A-W set o f solutes covers a Vx range o f 0.085-1.095, whereas the Y-M set covers a Vx range o f 1.138-3.178, in units of (cm^ mol" 1)/100. Only by combining both sets, or clusters, can a general equation be constructed. Instructive figures can be constructed for other descriptors. Thus the A-W set covers a range o f Z a"; o f only 0.00-0.37, whereas the Y-M set covers a range o f 0.00-1.28 units. It can be concluded that neither the A-W set nor the Y-M set can be used to construct a general equation for logBB, (see Section 4.4.5) and that only by combining the two sets o f data can any reasonably general equation for logBB be obtained.

4.11 Outliers

There are a number o f wild outliers in the Y-M dataset, that need to be considered. First o f all it is stressed that eq(4.32), and any similar predictive equation, will not be expected to hold for any compound that undergoes some conformational change or change in intramolecular H-bonding between the two phases concerned. Difficulty o f

b etw een calculated and observed values, and, fin ally, i f a com pound is m etab olised in either phase then the m easured lo g B B value m ight not refer to the correct equilibrium concentrations. It is therefore not surprising that out o f the 30 Y -M com pou n ds, so m e 8 com pou n ds are very strong outliers to eq (4 .32 ).

4 .1 1 .1 E x a m in a tio n o f O u tlie r s

The calculated lo g B B values using the Y -M A logP correlation, eq .(4 .6 ), and the Abraham correlation, (A C M -II, eq .(4 .3 2 )), are presented in T able 4.13

The fo llo w in g points are dem onstrated by Table 4 .1 3 , a) A ll m easured lo g B B valu es o f th ese outliers are m ore negative than those predicted by either the AC M -II m od el or the A logP m od el, excep t com pound 6 w hich is the least deviant com pound, b) The A log P m od el predicts m ore n egative values (and thus values clo ser to m easured lo g B B ), again exclu d in g com pound 6. H ow ever, even though A log P predictions are apparently better, they are still relatively poor; for exam ple the A logP prediction is alm ost 1.5 lo g units greater than the m easured lo g B B for com pound 13.

Table 4.13

Predictions o f lo g B B values for outlier com pounds using the Y -M A lo gP and the ACM - II correlations

C om pound N o Predicted lo g B B O bserved lo g B B AlogP Y -M A C M - l f 3 -1.62 -0 .7 4 -2 .0 0 4 -1 .1 0 -0.41 -1 .3 0 6 -0 .2 9 -0.41 0.11 9 N A -0 .2 6 -1.23 13 -0 .6 9 -0 .27 -2.15 24 -0 .62 -0 .3 6 -1.12 25 -0 .34 0.05 -0.73 45 N A -0.45 -1 .88 45 N A -0.45

A n a ly sis o f the Abraham equation sheds further light on th ese values. For com pou n d 13 the predicted value is alm ost 2 lo g units too high. S in ce the vo lu m e and e x c e ss m olar refraction term s, V x and Rj , have fixed determ inations, on ly n^2 , and can be in error. H ow ever, to explain this huge d ifference b etw een the ob served and predicted values w ou ld require m assive and unreasonable changes in the solute descriptor values.

It is u sefu l to contrast the ab ove outliers w ith com pounds 2 and 9, Table 4 .1 4

Table 4.14

C alculated and observed lo g B B values for com pounds 2 and 19 using the Y -M A lo gP and A C M -II correlations

C om pound N o Calc. lo g B B Calc. lo g B B O bserved AlogP Y -M “ A CM -II lo g B B

2 -1 .0 7 -0.43 -0 .0 4

19 -1.01 -0 .3 0 -0.18

‘^Calculated from eq(4.6) ^Calculated from eq(4.32)

For th ese tw o com pou n ds, the Y -M A logP predictions are resp ectively 1.03 and 0.83 log units to o n egative. H ow ever in both o f these ca ses the A C M -II predictions are more p o sitiv e and m uch clo ser to the m easured values.

A n oth er w ay that the outliers m ay be analysed is to com pare the observed and calculated v a lu es o f logP^ct and logP^yc using eq (4.1 6) and eq (4 .1 7 ) and the solute descriptors listed in T able 4 .1 1. The results o f this com parison are in T able 4 .1 5 . For sev en o f the eig h t outliers, there is reasonable agreem ent b etw een observed and calculated values**.

** Note, there is a discrepancy for Compound 4, which appears to be predicted by the Abraham methodology as a more hydrophilic compound, thus having lower predicted logP^c and logP^yc than the values given by Y-M. However the logP^^t value listed for this compound had been estimated by Y-M and the logP^yc has been determined by ionisation correction; so they are not wholly certain values. Examination o f the discrepancy in terms of incorrect Abraham solute descriptor determination did not yield any coherent reason. Furthermore, an important aspect to note regarding the current discussion of

T his su gg ests that the descriptors for these com pou n ds cannot be greatly in error and that large d ifferen ces b etw een observed and calculated lo g B B values m ust be due other factors. N o te that an error o f 0 .1 0 units in the descriptor Zp"; or ZpO^ w o u ld lead to an error in logPoct o f 0.35 units (eq 4 .1 7 ), but o n ly to an error o f 0 .0 7 units in lo g B B (eq 4 .3 2 ). Thus Table 4 .1 5 provides som e ju stification for the rem oval o f the outliers from the regression and point to eq (4 .3 2 ) as the m ost useful equation for the estim ation o f lo g B B values.

Table 4.15

C om parison o f observed and predicted log and lo g P^yc values for outlier com pounds.

C om pound N o logP^ct logP_eye

observed predicted" observed predicted

3 2.58 2.4 9 -2 .6 0 -2.41 4 4.57* 3.32 0.47 -0.9 5 6 1.59 1.30 -0.85 -1 .0 4 9 0.2 7 0.36 13 1.98* 1.57 -1.28 -1.53 24 1.64* 1.36 -1.48 -1 .8 6 25 3.6 5 * 3.52 1.11 0.53 45 3.57 3.56

^ used for these calculations ^ Estimated by Y-M

From the ab ove d iscu ssion the fo llo w in g argum ents can be sum m arised, the strong outliers are m ore n egative than predicted and that th ese com pounds are generally predicted w e ll using the determ ined Abraham descriptors for com parable partition co efficien t m easurem ents. Thus it is proposed that these outliers are due to the in v iv o m etabolism .

Abraham regression equations both of these are conflicting requirements (the logP requiring smaller descriptors for the negative coefficients and logBB requiring larger solute descriptors for the negative coefficients). It is therefore submitted that, at the present time, Compound 4 is an outlier, but that this issue requires further work including an actual determination o f logPo^t to find the cause o f the discrepancy.

M etabolites are generally more polar and hydrophilic that the parent drug molecule and therefore they are less likely to cross the Hence if metabolism is not corrected for in measurements o f logBB values, as was the case in the Y-M studytt, then the measured values will be underestimated. Therefore it is likely that this is the reason why the measured values for the outliers are more negative than predicted.

For completeness corresponding equations for all o f the 30 Y-M compounds (including the outliers) are given, both separately, eq(4.33), and together with the A-W set, eq(4.34),

logB B ry-# = 0.867 + 0.192R^ -0.68571» -0.636Ia»2 -1.177IP» + 0.848Vx (4.33) n = 30 p = 0.7758 sd = 0.567 F = 7.3

logBB(Comb.) = 0.044 +0.223Rz -0.61371» -0.486Sa» -0.986ZP», + 0.909Vx (4.34) n = 65 p = 0.8685 sd = 0.397 F = 36.2

It is important to remember that outliers are removed to obtain a useful and relevant correlation and not just to improve the statistics. Fig 4.6, a plot o f observed logBB values versus predicted values using the ACM-II equation, eq(4.32) illustrates this point. The points fall around a straight line, except where they tail o ff at the negative end where observed values are more negative than predicted. Graphically this suggests that these points are outliers.

Figure 4.6

A p lot o f calculated versus observed lo gB B values

1.5 0.5 _{» ■} S ' ■ -2.5 -2 -1.5 -1 -0.5

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