On Quantitative Relationships Between Drug-Like Compound Lipophilicity and Plasma Free Fraction in Monkey and Human

Abstract

Drug interactions with plasma proteins influence their pharmacokinetics and pharmacodynamics. We aimed to test whether a strong quantitative relationship exists between plasma free fraction (f_P) and lipophilicity for low molecular weight nonacidic drug-like compounds. We measured the n-octanol-buffer distribution coefficients at pH 7.4 (^mlogD) of 18 diverse radiotracers (<470 Da) used for brain imaging with positron emission tomography in vivo. Lipophilicities were also computed as ^clogD with two software packages. The f_P values for monkeys and humans were determined by ultrafiltration and transformed into ^mlogD_pr/pl values representing the log₁₀ of the within phase partition of the radiotracers between plasma proteins and remaining plasma. ^mlogD_pr/pl correlated strongly with mlogD for human (mlogD_pr/pl = 0.733^mlogD−0.780, r² = 0.74) and monkey (^mlogD_pr/pl = 0.780mlogD−1.15, r² = 0.83), but less strongly with ^clogD. These relationships were significantly different between species (P = 0.006). Removal of eight fluorinated compounds from the datasets raised r² to 0.81 and 0.91 for humans and monkeys, respectively. For the tested compounds, we conclude that n-octanol-buffer (pH 7.4) distribution strongly models that between plasma proteins and remaining plasma and moreover that ^mlogD accounts for over 74% of compound ^mlogD_pr/pl and is a strong determinant of f_P.

INTRODUCTION

The interaction of administered drugs with plasma proteins has long been of interest, since essentially only unbound drug is capable of traversing biological membranes to exert pharmacological action.^1,2 Furthermore, the extent to which a drug binds to plasma proteins will influence its distribution, rate of metabolism, and excretion.^1,2 In our laboratory, we are primarily interested in developing and applying radiotracers (radiopharmaceuticals) for imaging protein targets within brain with the technique of positron emission tomography (PET). Commonly, such radiotracers are structurally related to central nervous system drugs. The penetration of such radiotracers across the blood–brain barrier after intravenous administration depends on many factors,^3–5 including the plasma free fraction (f_P), which may be defined as the fraction of drug in plasma that is not bound to plasma proteins.⁶ For detailed pharmacokinetic analysis of the behavior of PET radiotracers aimed at deriving important imaging output parameters, accurate unbiased measurement of f_P may be required in subjects under study, whether animal or human.⁶ In view of the aforementioned considerations, the interaction of drug-like compounds with plasma proteins^7,8 and the prediction of these interactions^9,10 have merited considerable study. Lipophilicity has long been recognized as an important property influencing many aspects of drug–protein interactions, and consequently drug pharmacokinetic and pharmacodynamic behavior.¹ The most widely used index of drug lipophilicity is the n-octanol-water partition coefficient P, usually expressed as log₁₀ of this value (logP).^11,12 As many drugs also exist in ionized forms at physiological pH (pH 7.4), the log₁₀ of the partition of all forms of the drug between n-octanol and buffer at pH 7.4 (logD) is usually considered more relevant to physiological phenomena. Nowadays, estimates of lipophilicity may be computed from simple depictions of drug structure with various commercially available software packages to give the corresponding parameters ^clogP and ^clogD.^* Because of the great ease of these computations, ^clogP and ^clogD values have become quite prevalent in the literature, especially for large datasets where alternative experimental determinations would be laborious.

The extent to which logD can represent the interactions of drugs with plasma proteins is a fundamental and well-discussed question.¹⁰ Many experimental studies have observed or have derived different relationships between logD and f_P for various types of dataset. For example, Lázníček et al.¹³ studied the plasma protein binding of organic acids across three animal species and humans and established relationships of the type f_p = 1/(1 + aD^b), where a depends on species and b is approximately equal to 1. van de Waterbeemd et al.¹⁴ found sigmoidal relationships between plasma protein binding (i.e., 1−f_p) and logD that were appreciably dissimilar among acidic, basic, and neutral compounds. Laruelle et al.⁴ reported a strong linear relationship between f_p and logP for a small set (n = 4) of congeneric imaging radiotracers. However, Saiakhov et al.¹⁵ found a poor linear relationship (r² = 0.279) between 1−f_p and logP (logK_ow) for a large dataset (n = 154) of diverse drugs. Yamazaki and Kanaoka¹⁶ found strong nonlinear relationships between ^clogD and plasma protein binding among quite large datasets of diverse basic, neutral, and acidic pharmaceuticals. By contrast, Kratochwil et al.¹⁷ found poor correlations among a large set of both acidic and basic drugs between logD and binding affinity to human serum albumin, the most prevalent protein in plasma.

We are interested in testing the extent to which lipophilicity accounts for f_P among nonacidic PET radiotracers produced for brain imaging in our laboratory, because an understanding of the quantitative relationship between lipophilicity and its possible species dependence could be useful in further PET radiotracer development. Moreover, reliable quantification of the role of lipophilicity in drug–plasma protein interactions may be generally useful for drug design, and also facilitate the development of in silico predictive methods.^10,15,18,19

In this study, we examined the relationship between f_P and lipophilicity for a moderately sized set of well-diversified low molecular weight nonacidic compounds. These compounds serve in our laboratory as radiotracers for brain molecular imaging with PET and their availability in radioactive form and in high radiochemical purity facilitated f_P and lipophilicity measurements, and provided opportunity to study the relationships between these two parameters. We found that the log₁₀ of compound partition between plasma proteins and the remainder of plasma correlates strongly with measured logD value in both the human and the monkey. Accordingly, logD is the major determinant of f_P in both species, and may be considered a useful parameter for the prima facie estimation of f_P for candidate nonacidic low molecular weight drugs or indeed brain imaging radiotracers.

MATERIALS AND METHODS

Statistics

Linear regression analysis between one dependent and one independent variable was performed by the least squares method with GraphPad Prism for Windows software (GraphPad Software; San Diego, California). Statistical significance for the uppertail F-test was set at the 5.0% level (α = 0.05) for the appropriately calculated degrees of freedom. Regression lines and associated 95% confidence intervals were plotted with GraphPad Prism for Windows software. Analysis of covariance was used to test the hypothesis of whether two regression lines were equivalent. Significance of the test was performed at the 5% level (α = 0.05). Student’s t-test was used to test for differences in means of two samples.

Compound Selection and Preparation

Eighteen compounds for study were selected from among the radiotracers being produced in our laboratory for PET brain imaging experiments in monkey and human subjects. These compounds were labeled with either short-lived carbon-11 (t_1/2 = 20.4 min) or fluorine-18 (t_1/2 = 109.7 min) and obtained in high radiochemical purity (>99%), as described previously.^20–36 All were radiochemically stable in monkey and human plasma, except [¹⁸F]SP203, which is unstable in monkey plasma.²³ The radiotracers are all low molecular weight (260–470 Da) nonacidic compounds with low total polar surface area (tPSA; range: 30–65 Å) (Table 1). They span a wide range of lipophilicity (Table 1), and represent 12 distinct core structural classes (Chart 1). Eight of the compounds contain one or more fluorine atoms. Most of the compounds are quite basic (Table 1) and exist as interconverting neutral (non-zwitterionic) and positively charged species at physiological pH (pH 7.4).

Table 1.

Measured and Computed Properties of Radiotracers 1 – 18, Listed in Ascending Order of ^mlogD

Entry	Radiotracer	M. wt.a	tPSA b (Å)	pKac	clogP		clogD		mlogDd	fP		mlogDpr/pl
					Pallas	ACD	Pallas	ACD		Monkeye	Humane	Monkeye	Humane
1	[11C]CUMI-101	372.5	56	9.25 9.13	1.49	0.00	−0.47	−0.19	1.13 ± 0.02	0.594 ± 0.016	0.442 ± 0.003*	−0.165 ± 0.029	0.101 ± 0.006*
2	[11C]RX-1	320.5	65	8.47	2.16	2.62	1.06	2.39	1.77 ± 0.01	0.450 ± 0.0289	ND	0.087 ± 0.051	ND
3	[11C](R)-Rolipram	275.3	48	7.61	2.35	1.41	1.93	1.41	2.16 ± 0.01	0.238 ± 0.0545	0.0580 ± 0.0327*	0.512 ± 0.132	1.26 ± 0.26*
4	[18F]SP203	260.2	36	0.39	3.66	2.97	3.66	2.97	2.18 ± 0.22	ND	0.0550 ± 0.0165	ND	1.25 ± 0.13
5	[11C]DASB	283.4	34	7.28	2.37	2.87	2.12	1.49	2.47 ± 0.02	0.120 ± 0.015	0.109 ± 0.029	0.868 ± 0.063	0.921 ± 0.124
6	[18F]SL702	385.4	54	8.39	2.70	2.69	1.67	2.68	2.50 ± 0.01	0.238 ± 0.052	ND	0.511 ± 0.122	N.D.
7	[11C]dLop	463.0	53	8.05	4.51	3.71	3.77	3.04	2.60 ± 0.04	0.154 ± 0.018	0.123 ± 0.015	0.742 ± 0.063	0.853 ± 0.060
8	[18F]FECNT	325.8	30	6.99	3.47	3.31	3.33	2.28	2.64 ± 0.02	0.0873 ± 0.0255	0.0577 ± 0.0045	1.03 ± 0.14	1.21 ± 0.04
9	[18F]XB-1	351.4	30	9.29	4.79	4.84	2.90	2.28	2.95 ± 0.01	0.0193 ± 0.0044	0.0175 ± 0.0014f	1.71 ± 0.11	1.75 ± 0.03f
10	[11C]PBR28	348.4	51	6.58	2.56	3.30	2.50	3.29	3.01 ± 0.00	0.0560 ± 0.0125	0.0367 ± 0.0060	1.24 ± 0.11	1.42 ± 0.07
11	[11C]Loperamide	477.0	44	8.01	4.55	4.26	3.85	3.53	3.04 ± 0.00	0.0512 ± 0.0036	ND	1.27 ± 0.11	ND
12	[11C](R)-WAY	435.6	36	8.66	4.29	5.00	3.01	4.83	3.16 ± 0.35	0.0273 ± 0.0097	0.0063 ± 0.0015*	1.57 ± 0.15	2.20 ± 0.10*
13	[11C]NOP-1A	420.5	42	7.47	3.61	5.21	3.27	4.36	3.41 ± 0.07	0.114 ± 0.005	0.0977 ± 0.0152	0.892 ± 0.02	0.969 ± 0.074
14	[11C]PBR01	375.4	56	4.40	3.29	4.06	3.29	4.06	3.90 ± 0.02	0.0098 ± 0.0075	0.0072 ± 0.0086	2.15 ± 0.49	2.41 ± 0.620
15	[11C](R)-PK11195	352.9	33	3.53	4.89	4.58	4.89	4.58	3.97 ± 0.18	0.0207 ± 0.0085	0.0047 ± 0.0006*	1.71 ± 0.21	2.33 ± 0.06*
16	[18F]FBR	395.4	48	4.99	3.96	4.09	3.95	4.09	4.05 ± 0.02	0.0217 ± 0.0078	0.0040 ± 0.0030*	1.68 ± 0.18	2.52 ± 0.44*
17	[18F]S14506	392.5	33	8.39	4.14	4.08	3.11	3.93	4.14 ± 0.06	0.0059 ± 0.0023	0.0037 ± 0.0009f	2.25 ± 0.17	2.44 ± 0.11f
18	[18F]FMPEP- d2	474.5	42	6.86	4.74	5.36	4.63	5.32	4.24 ± 0.08	0.0041 ± 0.0001	0.0050 ± 0.0017	2.39 ± 0.01	2.31 ± 0.14

^*Significantly lower than monkey value (P < 0.05).

ND, not determined.

^aFor nonradioactive compound.

^bTotal polar surface area from Chem-Draw Ultra 11.0.

^cComputed with Pallas 3.70; compound 1 has 2 values.

^dMean ± SD for n = 6.

^eMean ± SD for n = 3.

^fMeasured on pooled human plasma that had been stored at −70°C.

Chart 1.

Structures of radiotracers (1 – 18) used in this study. References to the radiotracers are given in parentheses.

Estimation of Compound pK_a

Estimates of compound pK_a were obtained with Pal-las 3.70 software (Compudrug, S. San Francisco, California).

Computation and Measurement of Compound Lipophilicity

Pallas 3.70 software and also ACD software (version 9.04; Advanced Chemistry Development, Inc.; Toronto, Canada) were used to compute two compound lipophilicity parameters, ^clogD (the log₁₀ of compound partition between n-octanol and buffer at pH 7.4), and ^clogP (the partition of the neutral compound microspecies between n-octanol and water). Each software uses the depicted two-dimensional structure of the compound as input for computation.

Compound lipophilicity was also measured using the radiotracer as the log₁₀ of its partition between n-octanol and sodium phosphate buffer (pH 7.4, 0.15 M) (^mlogD) at room temperature, according to a previously published method.²⁹ The mean and standard deviation of six lipophilicity measurements are reported for each compound (Table 1). Computed (^clogD) and measured (^mlogD) values were each correlated to ^mlogD_pr/pl by regression analysis.

Measurement of Compound Plasma Free Fraction

All animal studies were performed in accordance with the Guide for the Use of Laboratory Animals³⁷ and the National Institutes of Health Animal Care and Use Committee. Thirteen rhesus monkeys (Macaca mulatta) were used. All experiments involving humans were approved by the Institutional Research Board of the NIH. The f_p of each compound was measured with a radiotracer of greater than 99% radiochemical purity at room temperature in either arterial monkey or human plasma, or both. Monkey plasma was prepared from blood taken from fasted male animals that had been immobilized with ketamine and that were maintained in anesthesia with about 1.5% isoflurane in oxygen in readiness for PET imaging experiments. Human plasma was prepared from blood taken from consenting conscious adults preceding radiotracer injection for PET imaging experiments, or, in a few exceptional cases, from pooled human blood that had been stored at −70°C, as indicated in Table 1. Each determination of f_p entailed addition of radiochemically pure radiotracer (20–70 μCi), as a solution in saline or saline–ethanol (2–10 μL), to a prepared non-radioactive plasma sample (≈650 μL) followed by mixing and measure ments of f_p on three aliquots (200 μL each) by ultrafiltration (Centrifree; Millipore, Billerica, Massachusetts), as detailed previously.³⁸ The mean value constituted one measurement. This procedure was performed thrice for each radiotracer and the results expressed as mean ± SD for the three measurements (Table 1). Except where pooled blood was used, no animal or human contributed to more than one of the three measurements. Because of the frequency of PET experiments, f_p data were sometimes available for some radiotracers in more than three subjects. In such cases, in order to achieve equal weighting of data between radiotracers, three values were selected randomly, that is, by lottery with replacement.

Relationship of Within-Phase Partition of Compound Between Plasma Proteins and Remaining Plasma to Lipophilicity

Compound f_p values for monkey and human were transformed into within-phase partition coefficients between plasma proteins and remaining plasma (D_pr/pl), where D_pr/pl = (1−f_p)/f_p and expressed as log₁₀ of this value (^mlogD_pr/pl) (Fig. 1). For each species, these values were then correlated by regression analysis with ^clogP, ^clogD, or ^mlogD as independent variables. Compound datasets were also divided into those for fluorine-containing (n = 8) and nonfluorine-containing radiotracers (n = 10), and the data reanalyzed.

Figure 1.

Diagram illustrating the analogy between logD (partition of radiotracer between n-octanol and pH 7.4 buffer) and logD_pr/pl (partition of radiotracer between dissolved plasma proteins and remaining plasma) for neutral radiotracer (panels A and B) and for a basic radiotracer having protonated species at pH 7.4 (panels C and D). The models assume that charged species are excluded from n-octanol and from binding to plasma proteins.

RESULTS AND DISCUSSION

In this study, our main findings were strong quantitative but species-distinct linear relationships between measured compound lipophilicity (^mlogD) and the parameter ^mlogD_pr/pl derived from our measurements of f_p in both human and nonhuman primate plasma. ^mlogD_pr/pl represents the log₁₀ of the equilibrium partition of compound between plasma proteins and remaining plasma and is a parameter that may be considered analogous to the log₁₀ of the equilibrium partition of compound between n-octanol and pH 7.4 buffer (logD) (Fig. 1).

At the outset of this study, we were interested in how well commercial software might predict logD as a measure of compound lipophilicity, because computations are easily performed from simple two-dimensional structural representations. Use of the radiotracers generally allowed compound lipophilicities to be measured with high precision across a wide range of values as evident from the associated relatively small standard deviations, except for compounds 4 and 12, which gave 10% and 11% coefficient of variance, respectively (Table 1). Compound logD values, when computed with either Pallas or ACD software and compared with measured values, showed regression lines with regression coefficients (slopes) greater than unity, but only moderately strong correlations (Fig. 2; Table 2, entries 1 & 2). Lipophilicity (logD) computed from ACD software correlated somewhat more strongly with measured lipophilicity (^mlogD) (r² = 0.740) than did lipophilicity computed from Pallas software (r² = 0.619). (It should be noted that the results from each software package are not expected to correspond because they apply different methods to calculate lipophilicity from two-dimensional structure). Although these correlations may be considered to be strong, these computational methods clearly fail to predict very accurate values. In fact, for ACD and Pallas software, the root mean squared errors were 0.76 and 0.80 log₁₀ units, respectively. Our observations are similar to those of Tetko and Poda³⁹ who, with the use of versions of Pallas, ACD and other software packages, found high root mean squared errors of 1.0 to 1.5 log₁₀ units in the estimation of logD among very large datasets (17,861 and 640) of diverse organic compounds.

Figure 2.

Plots of ^clogD from Pallas software (panel A) and ACD software (panel B) versus ^mlogD for the radiotracers 1 – 18 showing the regression lines and bounds of 95% confidence. The regression lines are defined in Table 2.

Table 2.

Data from Regression Analyses of Dependent Variables Y and Independent Variables X, Where the Line is Defined as Y = mX + c, with m Representing Slope and c the Value of Y at X = 0

Entry	X	Y	na	mb	cb	r2 b	Pb
1	mlogD	clogD (Pallas)	18	1.17 ± 0.23	−0.544 ± 0.706	0.619	0.0001
2	mlogD	clogD (ACD)	18	1.31 ± 0.19	−0.736 ± 0.600	0.740	<0.0001
3	clogD (ACD)	mlogDpr/pl (human)	15	0.384 ± 0.053	0.352 ± 0.184	0.553	<0.0001
4	clogD (ACD)	mlogDpr/pl (monkey)	17	0.394 ± 0.045	−0.0365 ± 0.0498	0.561	<0.0001
5	clogD (Pallas)	mlogDpr/pl (human)	15	0.393 ± 0.070	0.394 ± 0.229	0.426	<0.0001
6	clogD (Pallas)	mlogDpr/pl (monkey)	17	0.428 ± 0.053	−0.0283 ± 0.168	0.569	<0.0001
7	clogP (ACD)	mlogDpr/pl (human)	15	0.351 ± 0.062	−0.292 ± 0.241	0.430	<0.0001
8	clogP (ACD)	mlogDpr/pl (monkey)	17	0.407 ± 0.050	−0.268 ± 0.193	0.574	<0.0001
9	clogP (Pallas)	mlogDpr/pl (human)	15	0.461 ± 0.089	−0.0674 ± 0.333	0.385	<0.0001
10	clogP (Pallas)	mlogDpr/pl (monkey)	17	0.504 ± 0.070	−0.571 ± 0.256	0.519	<0.0001
11	mlogD	mlogDpr/pl (human)	15	0.733 ± 0.067	−0.651 ± 0.212	0.738	<0.0001
12	mlogD	mlogDpr/pl (monkey)	17	0.780 ± 0.050	−1.15 ± 0.16	0.832	<0.0001
13	mlogD	mlogDpr/pl (human; fluoro)	7	0.635 ± 0.120	−0.364 ± 0.416	0.595	<0.0001
14	mlogD	mlogDpr/pl (monkey; fluoro)	7	0.784 ± 0.130	−1.19 ± 0.45	0.659	<0.0001
15	mlogD	mlogDpr/pl (human; nonfluoro)	8	0.824 ± 0.084	−0.870 ± 0.246	0.814	<0.0001
16	mlogD	mlogDpr/pl (monkey; nonfluoro)	10	0.798 ± 0.049	−1.17 ± 0.14	0.906	<0.0001

^an = number of data points used in regression analysis, with one data point per compound; means were used for measured values.

^bValues computed with GraphPad Prism for Windows software.

Nevertheless, we proceeded to test whether ^clogD from either software program might correlate with ^mlogD_pr/pl in monkey and human plasma. The use of the radiotracers allowed for quite precise determinations of compound f_P and the derived parameter ^mlogD_pr/pl across a wide range of values as evident from the associated relatively small standard deviations (Table 1). From either program, significant correlations were found between ^clogD and ^mlogD_pr/pl for monkey and human (Fig. 3, Table 2, entries 3–6). Slopes of the regression lines were much lower than unity and the correlation coefficients were not especially high (Table 2). The ACD software gave a somewhat stronger correlation (r² = 0.553; Table 2, entry 3) for the human data than the Pallas software (r² = 0.426; Table 2, entry 5).

Figure 3.

^mlogD_pr/pl versus ^clogD and ^mlogD showing regression lines along with the 95% confidence intervals for human and monkey plasma samples. Where error bars are not visible they are within the symbol size. The regression lines are defined in Table 2.

Because the partition coefficient of uncharged compound between n-octanol and water (logP) is also readily computed from a two-dimensional representation of compound structure, and without the need for an additional uncertain internal estimation of compound pK_a, we also tested for correlation between ^clogP and ^mlogD_pr/pl in each species. Significant correlations were found. However, correlation coefficients were found to be weaker than for ^clogD (Table 2, c.f. entries 7 & 8), except in the case of monkey ^mlogD_pr/pl versus clogP from ACD software, which gave an almost negligible improvement (r² = 0.574 versus 0.569; Table 2, c.f. entries 8 and 6). Only in the single case of lipophilicity calculated with Pallas software and for the monkey data did we find that ^clogP was appreciably more sensitive than ^clogD to changes in ^mlogD_pr/pl (Table 2, c.f. entries for m in 10 and 6). Overall, we concluded that ^clogD gave stronger correlations than ^clogP with ^mlogD_pr/pl for our datasets. Our findings may be compared with those of Lobell and Sivarajah¹⁸ for human and uncharged (i.e., neutral) and positively charged sets of compounds with molecular weights <825 Da. They found linear relationships between ^mlogD_pr/pl and AlogP98, where the latter was a logP value computed with QSAR+ module of Cerius2 (version 4.6, Acclerys Inc. San Diego, California). Regression lines had similar regression coefficients (m ≈ 0.45) to those found in this study for neutral and basic compounds (Table 3). Their large datasets gave somewhat higher correlation coefficients (r² ≤ 0.67) (Table 3).

Table 3.

Comparison of m and c Values for Relationships ^mlogD_pr/pl = m^clogP + c in Human and Monkey for Different Sources of ^clogP and Organic Compound Classes

Entry	Species	Source of clogP	Compound class	n	r2	m	c
1a	Human	Cerius2 (version 4.6)	Uncharged	78	0.63	0.449	−0.416
2a	Human	Cerius2 (version 4.6)	Positively charged	63	0.67	0.463	−1.097
3b	Human	ACD	Neutral/basic	15	0.430	0.351	−0.834
4b	Monkey	ACD	Neutral/basic	17	0.574	0.407	−0.268
5b	Human	Pallas 3.0	Neutral/basic	15	0.385	0.461	−0.067
6b	Monkey	Pallas 3.0	Neutral/basic	17	0.519	0.504	−0.571

^aFrom Ref. 18.

^bFrom this study.

We proceeded to test whether ^mlogD_pr/pl might correlate more strongly with measured lipophilicity (^mlogD). For both monkey and human, strong and highly significant linear correlations were found between ^mlogD_pr/pl and ^mlogD (Fig. 3; Table 2, entries 11 and 12). For human, the quantitative relationship was found to be

$${}^m\text{l}\text{og}{D}_{\text{pr}/\text{pl}}=0.733{}^m\text{l}\text{og}D-0.651(r^2=0.738;P<0.0001)$$ (1)

and for monkey,

$${}^m\text{l}\text{og}{D}_{\text{pr}/\text{pl}}=0.780{}^m\text{l}\text{og}D-1.15(r^2=0.832;P<0.0001)$$ (2)

Therefore, the use of ^mlogD in place of computed values resulted in much improved sensitivity (higher slope or correlation coefficient) and also in much stronger correlation (higher r²). Equations 1 and 2 may be algebraically transformed to give the following relations between f_P and D for human and monkey, respectively.

$$f_{\text{P}}=1/(1+0.243D^{0.733})$$ (3)

$$f_{\text{P}}=1/(1+0.0708D^{0.780})$$ (4)

Species differences are important considerations in drug development and also in our research area of PET radiotracer development, where results in animals, usually rodents or monkeys, inform decisions on whether to advance radiotracer evaluations into humans. Only a few previous studies have compared f_P for drug-like compounds among species.^13,19,40,41 Comparison of the monkey and human f_P data for 14 of the 18 compounds in this study showed statistically significant species differences (P < 0.05) for five compounds (Table 1). In all five cases, f_P was lower in human than in monkey. The small set of other published studies also consistently reported lower f_P in human than in other species.^13,19,40,41 We found that the regression lines from the ^mlogD and ^mlogD_pr/pl values for human and monkey were significantly different by covariance analysis (P < 0.006). The monkey data show the higher coefficients of regression and correlation and this may have a strong biological basis. Thus, the managed monkey population, from which the data in this study were obtained, is more homogeneous with regard to factors that include genetics, gender, diet, fasting state, absence of disease, and exposure to medications than the sampled humans. Such factors are well known to affect the binding of drugs to plasma proteins.^7,8 Moreover, there are documented intrinsic species differences in the nature of drug binding sites for serum albumin,^42–44 the most abundant drug-binding protein in blood,^7,8 and also for serum α₁-acid glycoprotein.45 Table 4 compares the linear relationships between ^mlogD_pr/pl and ^mlogD established in this study for neutral and basic compounds in monkey and human (Eqs 1 and 2) with those established by Lázníček et al.¹³ for low molecular weight carboxylic acids in several species (mouse, rat, rabbit, and human). The regression coefficients (slopes m) for the relationships established by Lázníček et al.¹³ (Table 4, entries 1–4) are approximately 1 and significantly higher than for the relationships that we obtained for neutral and basic compounds in monkey and human (Table 4, entries 5 & 6). Acidic compounds are generally considered to bind preferentially to serum albumin whereas basic compounds are considered to bind preferentially to the much less abundant serum α₁-acid glycoprotein.^2,7,8 The differences in slopes between the equations obtained by Lázníček et al.¹³ for acid compounds and those for the regression lines expressed in Eqs. 1 and 2 may reflect these general differences in acid/base binding preference as well as species differences in protein binding sites.

Table 4.

Comparison of m and c Values for Relationships ^mlogD_pr/pl = m^mlogD + c in Various Species and for Different Organic Compound Classes

Entry	Species	Compound class	n	r2	m	c
1a	Mouse	Acidic	11	0.884	1.04	−2.15
2a	Rat	Acidic	11	0.931	1.01	−1.75
3a	Rabbit	Acidic	11	0.945	1.02	−1.28
4a	Human	Acidic	11	0.970	0.994	−1.10
5b	Monkey	Neutral/basicc	17	0.832	0.780	−1.15
6b	Human	Neutral/basicc	15	0.738	0.733	−0.651
7b	Monkey	F-noncontaining neutral/basic	10	0.906	0.798	−1.17
8b	Monkey	F-containing neutral/basic	7	0.659	0.784	−1.10
9b	Human	F-noncontaining neutral/basic	8	0.814	0.824	−0.870
10b	Human	F-containing neutral/basic	7	0.595	0.635	−0.364

^aFrom Ref. 13.

^bFrom this study.

^cIncludes fluorine-containing and nonfluorine-containing compounds.

A high proportion of our set of neutral/basic compounds, eight from 18, contains one or more fluorine atoms. Fluorine atoms are known to confer unusual and even unexpected partition properties in small organic molecules.⁴⁶ Highly fluorinated molecules tend to be neither oil nor water soluble, and are often therefore described as fluorophilic. Because the presence of fluorine atoms in a molecule may cause lipophilicity and hydrophobicity to diverge, logP may not truly reflect lipophilicity.⁴⁷ Even incorporation of a low number of fluorine atoms into a drug-like molecule may have major consequences for disposition or protein binding. In view of these considerations, we examined the impact of removing the eight fluorine-containing compounds from our datasets. For both human and monkey, this removal resulted in enhanced correlations of ^mlogD_pr/pl with ^mlogD (Fig. 4; Table 2, entries 11 & 12), with the monkey data again showing the stronger correlation. The correlations for the dataset of fluorine-containing compounds were much weaker (Fig. 4; Table 2, entries 13 & 14). The data for the fluorine compounds happen to appear mainly on the high side of the range of ^mlogD_pr/pl and ^mlogD values and show more dispersion about the regression line than for the nonfluorine-containing compounds. This may explain the observed differences in the strength of correlations of fluorine-containing and nonfluorine-containing compounds. Covariance analysis showed no statistical difference between the regression lines for fluorine-containing and non-fluorine-containing compound datasets (P = 0.563 for monkey and P = 0.482 for human).

Figure 4.

Regression lines for human and monkey ^mlogD_pr/pl versus ^mlogD for fluorine-containing radiotracers and nonfluorine-containing radiotracers. Where error bars are not visible they are within the symbol size. The regression lines are defined in Table 2.

The correlation coefficient for the relationship between monkey ^mlogD_pr/pl and ^mlogD for the structurally noncongeneric dataset of nonfluorinated compounds is remarkably high (r² = 0.906; n = 10) (Table 2). This implies that the two-phase n-octanol-pH 7.4 buffer system is an exceptionally robust model for the single-phase partition of compounds between plasma proteins and the remainder of plasma, and accounts for about 90% of this partition. It is useful to reflect on the meaning of the parameter logD_pr/pl. In the hypothetical case of a compound binding to a single binding site in only one protein in plasma, D_pr/pl would relate by the law of mass action to the equilibrium binding constant K_A, according to the expression:

$$K_{\text{A}}=D_{\text{pr}/\text{pl}}/[\text{protein}]$$ (5)

where [protein] is the protein concentration and therefore with f_P by:

$$K_{\text{A}}=((1-f_{\text{P}})/f_{\text{P}})/[\text{protein}]$$ (6)

In pharmacology, ligand affinity to a protein is usually expressed as the equilibrium dissociation constant K_D, the reciprocal of K_A, with a low value representing high affinity binding. From Eqs. 5 and 6, it follows that K_D relates to D_pr/pl by the expression:

$$K_{\text{D}}=[\text{protein}]/D_{\text{pr}/\text{pl}}$$ (7)

and therefore with f_P by:

$$K_{\text{D}}=[\text{protein}]/((1-f_{\text{P}})/f_{\text{P}})$$ (8)

For a low f_P value of 0.01 for a compound binding to a protein present at 0.6 mM, such as albumin in blood,^7,8 the K_D would be 6 μM¹⁶ and for binding to the much less prevalent serum α₁-acid glycoprotein, with a typical blood concentration of ~20 μM,⁸ the K_D would be 0.2 μM. These equilibrium dissociation constants are consistent with being due to relatively weak nonspecific interactions compared with the strong specific interactions of ligands that are needed for binding to proteins with K_D values in the nanomolar or even subnanomolar range. For example, in an extreme case, SP203 (4) binds specifically to metabotropic glutamate subtype five receptors with 37 pM affinity.²³ Of the ligands listed in Table 1, all f_P values exceed 0.0037, and they therefore bind to blood proteins with relatively low affinity.

As mentioned in the Introduction, different studies have reported different mathematical relationships between lipophilicity and f_p. Some are linear^4,15 and some are sigmoidal,¹⁴ plus some are of the logarithmic type reported here (Eqs. 1 and 2).¹³ The sigmoidal relationships between f_P (or 1−f_P) and logD are in fact congruent with the logarithmic relationships because a plot of log₁₀[(1−f_p)/f_p] versus f_p is sigmoidal.¹⁰ The linear relationship reported by Laruelle et al.⁴ is for only four structurally congeneric and similarly basic compounds ([¹¹C]DASB (5) and congeners) covering a narrow logD range of 2.44–3.31. Re-expression of the data as ^mlogD_pr/pl versus logD actually improves the correlation coefficient (from r² = 0.93 to 0.98) and the statistical significance of the correlation from P = 0.035 to 0.011. In fact, there is no physical basis for expecting a linear relationship between f_P and lipophilicity (logD or logP). Therefore, the poor linear relationship reported by Saiakhov et al.¹⁵ (r² = 0.29, n = 154) is, in fact, as would be expected.

Do the quantitative relationships between compound logD and f_P, derived from our model, have practical value? The relationships have some practical limitations. First, at least 10% of the variance in f_p is not accounted for by lipophilicity (logD). Second, small errors in the estimation or measurement of logD can lead to sizable errors in the estimation of f_p. Because of the sigmoidal relationship between f_P and logD, the relative magnitude of the error in f_p depends on the true value of logD. Our set of PET brain-imaging radiotracers has f_p values in human that range widely from 0.44 for radiotracer 1 to 0.0037 for radiotracer 18 (Table 1). By Eq. 3, a compound with a logD value of 0.816 would be expected to give an f_p value in human of 0.5. A +0.1 log₁₀ unit error in the logD value would predict an f_p value of 0.4999, that is, a negligible error in f_p. However, for very low values of f_p, errors become much more appreciable for the same error in logD. Thus, a compound with a logD value of 3.869 would be expected to give an f_p value of 0.005. A +0.1 log₁₀ unit error in the logD value would predict an f_p value of 0.0042, that is, a −16% error in f_p. In most cases, we measured logD with errors of <0.1 log10 unit (Table 1). Hence, ^mlogD values might be used to estimate f_p with reasonable accuracy, especially for moderate values. Although, from a practical standpoint, it may be just as easy to measure f_p as to measure logD, even with a nonradioactive compound, measurement of logD may be more convenient because f_P measurement requires regulatory approvals for animal or human blood sampling. As experienced here, present computational methods for estimating logD give sizeable root mean squared errors (≈0.8 log₁₀ units). Major advances are therefore still needed in the accuracy of computational estimations of logD for f_p in any species of interest to be predictable with good reliability.

CONCLUSIONS

For the set of structurally diverse nonacidic drug-like compounds studied here, ^mlogD accounts for over 73% of ^mlogD_pr/pl in humans and over 83% in monkey, despite the great structural dissimilarity between n-octanol and plasma proteins. The derived linear relationships (Eqs. 1 and 2) are statistically different between species. With the exception of one value among 13, monkey f_P values were consistently higher than human values. The much weaker correlation of ^mlogD_pr/pl with ^clogD reflects appreciable errors intrinsic to computation of ^clogD and points to the present limited value of computed lipophilicity for the development of in-silico methods for the prediction of f_P.