Prediction of the permeability of neutral drugs inferred from their solvation properties

Abstract

Motivation: Determination of drug absorption is an important component of the drug discovery and development process in that it plays a key role in the decision to promote drug candidates to clinical trials. We have developed a method that, on the basis of an analysis of the dynamic distribution of water molecules around a compound obtained by molecular dynamics simulations, can compute a parameter-free value that correlates very well with the compound permeability measured using the human colon adenocarcinoma (Caco-2) cell line assay.

Results: The method has been tested on twenty-three neutral drugs for which a consistent set of experimental data is available. We show here that our method reproduces the experimental data better than other existing tools. Furthermore it provides a detailed view of the relationship between the hydration and the permeability properties of molecules.

Contact: anna.tramontano@uniroma1.it

Supplementary information: Supplementary data are available at Bioinformatics online.

1 Introduction

The study of drug absorption is of critical importance in the development of effective drugs. The path of a drug from the site of administration to its target cells or compartments implies the crossing of several semipermeable cell membranes, therefore it is relevant to be able to predict whether and to which extent a molecule can pass through the cell membranes.

Passive permeation of drugs through the biological cell membranes is obviously strongly dependent on the molecule physicochemical properties (Meanwell, 2011). It has been established that the acid–base character of the molecule (which influences the charge of the molecule at the specific pH), its lipophilicity (which affects its partition between aqueous and lipid environments) and solubility are the most relevant parameters to take into account. These parameters are well described by the molecule hydropathy profile (Siew et al., 2012; Smith et al., 2010). A more lipophilic drug is more likely to effectively cross the hydrophobic phospholipid bilayer. On the other hand, extremely hydrophobic molecules, insoluble in aqueous body fluids, might be poorly absorbed (Frenkel et al., 2005). In summary, there should be an appropriate balance between the hydrophobicity and hydrophilicity of a molecule (Ghuman et al., 2005; Seelig et al., 1994; Waring, 2009).

From an experimental point of view, data on permeability can be obtained by in situ and/or in vivo animal studies, but these are time consuming and expensive experiments and therefore only performed towards the end of the drug development process. Efforts have therefore focused on the development of in vitro permeability assays that can mimic the relevant characteristics of in vivo absorption. Among these, there are the Parallel Artificial Membrane Permeability Assay (PAMPA) (Avdeef et al., 2007), the human colon adenocarcinoma (Caco-2) cell line assay (Artursson et al., 2001), the Madin-Darby Canine Kidney (MDCK) cell assay (Irvine et al., 1999), the rat duodenal immortalized cell line assay (2/4A1 cell) (Tavelin et al., 2003), and the rat everted gut sac assay (Bohets et al., 2001). All of them are routinely used for the preliminary assessment of drug permeability. In particular, the Caco-2 cell is probably the most extensively characterized cell-based model and the most popular both in the pharmaceutical industry and in academia (Balimane et al., 2006). It has been shown that this model can effectively predict the human initial drug absorption (Artursson and Karlsson, 1991) because it reflects the transport of the drug across a cell membrane rather than the interaction of the drug with the lipid bilayer (Hou et al., 2006).

The membrane permeability for a given compound is usually estimated from its partition coefficient, logP, defined as the logarithm of the relative concentration of the molecule when it partitions between a two-phase system, usually water and octanol, where the latter is assumed to have a lipophilicity comparable to that of a cell membrane (Artursson et al., 2001; Seddon et al., 2009).

From the theoretical point of view, many computational approaches have been developed to infer drug properties, such as bioavailability, aqueous solubility, initial absorption, plasma-protein binding and toxicity (van de Waterbeemd and Gifford, 2003). These are often related to features such as molecular size, hydrophobicity, or number of hydrogen bonds established by the compound with water molecules (since these bonds need to be broken to allow the molecule to pass the membrane) (Hou et al., 2004).

In general, permeability may be estimated in terms of the free energy barrier that the drug should overcome when crossing the membrane, which is usually predicted from computationally intensive molecular dynamics simulations of the translocation process (Carpenter et al., 2014; Meng and Xu, 2013). Some methods compute the Polar Surface Area (PSA) of the drug to predict its permeability under the assumption that this parameter correlates with the hydrogen-bonding pattern in the aqueous solvent of the molecule and therefore with the energy cost of transferring the molecule from the solvent to the membrane (Kelder et al., 1999; Stenberg et al., 1999).

Other popular methods are the Quantitative Structure-Property Relationship (QSAR) analysis (Yu and Adedoyin, 2003), Multiple Linear Regression (MLR), Partial Least Square (PLS), Linear Discriminant Analysis (LDA), Artificial Neutral Networks (ANNs), Genetic Algorithms (Gas), Support Vector Machines (SVMs) and the ‘Lipinski rule of five’ (Lipinski, 2000). In particular, the Lipinski's rule takes into account different features to assess whether a compound is likely to be cell membrane permeable and easily absorbed by the body on the basis of the following criteria: molecular weight of the compound lower than 500; logP lower than 5; number of hydrogen bond donors (usually the number of hydroxyl and amine groups in a drug molecule) lower than 5; number of groups that can accept hydrogen atoms to form hydrogen bonds (estimated by the number of oxygen and nitrogen atoms) lower than 10.

In this work we describe a new method based on an estimate of the hydropathy and charge distribution of a compound deduced from the distribution and orientation of the water molecules around it. We have already successfully used a similar approach to estimate the hydrophobicity of the twenty natural amino acids (Bonella et al., 2014). Here we show that, when applied to a set of 23 drugs, neutral at physiological pH, to compute their hydrophobicity and charge distribution, the method can effectively predict their ability to cross the plasma membrane.

Our dataset only includes neutral compounds since these are well known to mainly use passive transport to cross the phospholipid bilayer of the cell membrane (Neuhoff et al., 2003, 2005; Seelig, 2007) and therefore their diffusion and permeability is essentially related to their chemico-physical properties that is what our method can infer.

2 Methods

We analyzed the hydration of small solutes by investigating the changes in the structure of the dynamic hydrogen bond network formed by the water molecules surrounding them as well as their orientation as obtained by Molecular Dynamics (MD) simulations.

2.1 Molecular dynamics

All simulations were performed using NAMD 2.7b1 (Phillips et al., 2005) and the CHARMM force field was used for the investigated compounds (MacKerell et al., 1998). In each simulation a single solute molecule was located in a cubic simulation box (with imposed periodic boundary conditions) filled with TIP4P rigid water molecules (Abascal and Vega, 2005). Each simulation contained a single copy of the compound and the size of the box varied in a range of 56–62 Å depending on the compound considered. The topologies and parameters for the small molecule compounds were obtained via the SwissParam server (Zoete et al., 2011) [www.swissparam.ch] that generates molecules topologies and parameters for small organic compounds in a functional form that is compatible with the CHARMM force field.

The Particle Mesh Ewald (PME) method was used to calculate the electrostatic interactions. Each simulation was run for 1.5 ns. A 1 fs time step was used and the coordinates were retrieved every 0.5 ps. All simulations were performed at T = 310 K, and the system was thermostated using Langevin dynamics. The simulations were performed also at constant pressure using a modified Nosé-Hoover method in which Langevin dynamics is used to control fluctuations in the barostat (Hoover, 1985). More details about the molecular dynamics simulation parameters are available at: http://arianna.med.uniroma1.it/neutraldrugs/.

2.2 Dataset

We used a sample set of structurally diverse, small molecular weight drugs analyzed by Yazdanian et al. (1998) for which in vitro Caco-2 cell permeability data is available. We selected 23 neutral drugs at pH 7.4 from this dataset.

The advantage of selecting this specific dataset is that the data have been obtained in the same experimental conditions. To verify how representative our dataset is, we collected data for 131 compounds available in the literature for a total of 277 Caco-2 cell permeability values (different values have been obtained for a number of these drugs in different experimental conditions) (Artursson, 1990; Artursson and Karlsson, 1991; Artursson and Magnusson, 1990; Augustijns et al., 1996; Aungst et al., 2000; Chong et al., 1997; Collett et al., 1996; Gres et al., 1998; Haeberlin et al., 1993; Hilgendorf et al., 2000; Hou et al., 2004; Hovgaard et al., 1995; Lentz et al., 2000; Liang et al., 2000; Rubas et al., 1993; Ruiz-Garcia et al., 2002; Saha and Kou, 2002; Schipper et al., 2001; Wu et al., 2000; Yee 1997; Zhu et al., 2002) and compared both their Caco2 experimental values (Supplementary Figure S1) and their structural features.

To estimate the latter, we computed the structural dissimilarity of our selected compounds and compared it with that of the 131 compounds. To this end, we used the ChemMine tool (Backman et al., 2011) that takes into account parameters such as partition coefficient, rule-of-five, partial charges, fingerprint calculation and more (for a detailed description of the features see ‘http://www.ra.cs.uniuebingen.de/software/joelib/tutorial/descriptors/descriptors.html’). We used these values to perform a clustering analysis, using the ‘hclust’ function of R software package (Ihaka and Gentleman, 1996) [http://www.R-project.org], the results of which are shown in Supplementary Figure S2.

As it can be seen, the 23 compounds from the Yazdanian et al. (1998) dataset, selected for the analysis, span quite uniformly about 85% of the available range both in terms of Caco2 values and of structural features. Some regions of the feature space are less well represented in our dataset (left most branch of the tree in Supplementary Figure S2). These are all compounds with a rather large molecular weight (above 500 Da). This might imply that our method might behave differently for very large compounds (that in any case are usually excluded a priori as leads because of their size).

All compound three-dimensional coordinates were downloaded from the free public database ZINC (Irwin et al., 2012) [zinc.docking.org]. For this study the following small molecule compounds were chosen: Griseofulvin, Aminopyrine, Piroxicam, Diazepam, Nevirapine, Phenytoin, Testosterone, Progesterone, Clonidine, Corticosterone, Estradiol, Hydrocortisone, Dexamethasone, Scopolamine, Zidovudine, Urea, Uracil, Sucrose, Hydrochlorothiazide, Mannitol, Ganciclovir, Acyclovir and Chlorothiazide (Table 2). Of importance, they cover a wide range of permeability values (Pcaco-2), from 36.6 × 10⁻⁶ cm/s to 0.19 × 10⁻⁶ cm/s and are as evenly distributed as possible (see Table 2).

Table 2.

Experimental and predicted permeability values

Drug	Pcaco-2	Ppred	Ppred_CV
Griseofulvin	36.6	31.07	29.96 ± 1.09
Aminopyrine	36.5	37.41	37.62 ± 1.53
Piroxicam	35.6	24.52	23.46 ± 0.65
Diazepam	33.4	29.87	29.26 ± 1.03
Nevirapine	30.1	31.52	31.81 ± 1.04
Phenytoin	26.7	24.53	24.27 ± 0.75
Testosterone	24.9	21.89	21.64 ± 0.63
Progesterone	23.7	29.20	30.78 ± 1.12
Clonidine	21.8	21.94	21.90 ± 2.33
Corticosterone	21.2	15.67	15.01 ± 0.74
Estradiol	16.6	15.57	14.39 ± 1.88
Hydrocortisone	14	10.55	10.17 ± 0.81
Dexamethasone	12.2	10.51	10.33 ± 0.81
Scopalamine	11.8	21.93	22.79 ± 0.53
Zidovudine	6.9	13.61	14.12 ± 0.66
Urea	4.56	4.64	4.67 ± 0.98
Uracil	4.24	8.61	9.01 ± 0.77
Sucrose	1.7	−2.35	−3.31 ± 1.45
Hydrochlorothiazide	0.51	5.20	5.85 ± 0.91
Mannitol	0.38	−8.10	−11.42 ± 1.20
Ganciclovir	0.38	2.38	2.64 ± 1.10
Acyclovir	0.25	9.33	10.16 ± 0.65
Chlorothiazide	0.19	5.03	5.64 ± 0.91

The first column reports the drug name, the second reports the experimental values, the third (Ppred) the values obtained using Eq. (1). The last column reports the predicted values obtained in the cross validation test (P_{pred_CV}).

2.3 Data analysis

The results of the molecular dynamics simulations of each molecule are used to evaluate the orientation of the water molecules in the first and second hydration shell, being the first related to the hydrophilic and the second to the hydrophobic characteristics of the compound, respectively (see ref (Bonella et al., 2014) for details).

We represent each water molecule as a tetrahedron, where an sp3-hybridized oxygen atom lies at the center and two hydrogen atoms and two lone pair electrons point to the vertices. Each water molecule can then form up to four hydrogen bonds with other water molecules. According to this model of the water molecule, we can define four Hydrogen Bond Vectors (HBVs) and one dipole vector (Fig. 1). The HBVs are defined as the lines connecting the oxygen atom and the vertices of the tetrahedron (in blue in the Fig. 1). The dipole vector (in red in the Fig. 1) lies along the bisectrix of the angle formed by the oxygen and the two hydrogen atoms.

Fig. 1.

Definition of the angles used in the analysis. We connect each solute atom (S in the figure) to the oxygen atom (red circle) of the closest water molecule and the same oxygen atom to each vertex of the water tetrahedron, thus defining the four angles, ${\theta }_{h1}$, ${\theta }_{h2}$, ${\theta }_{h3}$and ${\theta }_{h4}$ (for clarity only one, in green, is shown in the figure). Hydrogen atoms are represented as dark grey circles. We also define the dipole vector of the water molecule (red arrow) and compute the angle ${\theta }_d$ between this vector and the line connecting the solute atom and the oxygen (in blue)

We can define the angles related to hydrogen bond orientations (${\theta }_{h1}$, ${\theta }_{h2}$, ${\theta }_{h3}$and ${\theta }_{h4}$) as those formed by the straight line linking the solute atom with the oxygen atom of the nearest water molecule and the hydrogen bond vector (for clarity, only one of the four angles is represented in blue in Fig. 1). Similarly, we can define the angle ${\theta }_d$ related to the orientation of the dipole vector as the angle formed by the straight line connecting a solute atom (S in Fig. 1) to the oxygen atom of the closest water molecule (in black) and the dipole vector of the molecule itself (in red). The different orientations of the water molecules around a solute can be used to analyze the compound hydrophilicity and hydrophobicity. In fact a water molecule in the vicinity of a hydrophobic solute positions one of the faces of the tetrahedron toward the solute. On the other hand, for a hydrophilic solute, a water molecule reorients to point toward the compound with one of its vertices. We need to take the dipole vector into account because the four vertices of the tetrahedron representing the waters are equivalent in our model and therefore it would be impossible to distinguish between positive and negative partial charges without considering ${\theta }_d$.

At each step of the molecular dynamics simulation, we can measure the values of the five angles (${\theta }_{h1}$, ${\theta }_{h2}$, ${\theta }_{h3}$, ${\theta }_{h4}$ and ${\theta }_d$) and the distance R (Å) between each water molecule and the nearest solute atom and compute the probability of finding a water molecule with a given orientation and around at a given distance from the solute atoms.

The hydropathy and charge distribution properties are computed from the conditional probability density of the waters in the appropriate intervals of the angles and distances described before. We can build two three-dimensional histograms for each simulation; the first reports the conditional probability density P(${\theta }_{hi}$|R) (for i = 1, 2, 3, 4), the second is the conditional probability density P(${\theta }_d$|R). R is defined as the distance between each solute atom and the oxygen atom of the nearest water molecule. The histogram distance and angle bins were set to 0.05 Å and 1°, respectively (Bonella et al., 2014).

2.4 Molecular descriptors

The analysis of the conditional probability density distributions allows us to compute four indices, named $I_y$, $I_n$, $I_{+}$ and $I_{-}$, obtained by summing the intensity of the peaks in the appropriate angle and distance range.

As described in more detail in our previous work (Bonella et al., 2014), the distribution P(${\theta }_{hi}$|R) permits to distinguish between the hydrophilicity and hydrophobicity of a compound on the basis of the probability values observed in the first and second hydration shell, respectively. Intuitively, this is justified by the fact that a polar solute will establish Coulomb interactions with the closest water molecules and this situation will contribute to the peaks observed in the first hydration shell of the hydrogen bond histogram, while a hydrophobic (or apolar) solute will cause the waters to orient themselves as to maximize the number of hydrogen bonds with neighboring waters, forming a cage around the solute, and will contribute to peaks in the second hydration shell in the hydrogen bond histogram.

The dipole probability density P(${\theta }_d$|R) in the first hydration shell takes into account which of the vertices of the tetrahedron representing the waters (all equivalent in our model) is oriented towards the solute and therefore provides information about the electric charge (positive or negative) of the interacting solute atoms.

We define the compound hydrophilicity $I_y$ and hydrophobicity $I_n$ as the sum of the hydrogen bond probability densities, computed over the appropriate distance and angle range (Δθ and ΔR) in the first and second shell of hydration, respectively. The charge indices $I_{+}$ and $I_{-}$ are defined as the sum, in the appropriate range, of the probability densities in the first shell of the distribution related to dipole moment (see Fig. 2). For more details, see ref. (Babiaczyk et al., 2010; Bonella et al., 2014).

Fig. 2.

Histograms of P(${\theta }_{hi}\mathrm{ }|R)\mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }P({\theta }_d$|R) for Diazepam. In both histograms the cells highlighted in grey are used to calculate the sum of the conditional probability densities at each given angle and distance. In the P(${\theta }_{hi}$|R) histogram, the yellow arrows indicate the first and second component of the hydrophilic index related to the two peaks in the first hydration shell. The green arrows show the first and the second component of the hydrophobic peaks that are localized in the second hydration shell. In the P(${\theta }_d$|R) histogram, the blue arrow indicates the contribution of positive charge distribution. The pink arrow indicates the contribution of the negative charge distribution

As shown in Supplementary Figure S3a–c, the length of the MD simulation (1.5 ns) is sufficient to ensure convergence of the indices.

The scheme used to select the boundaries of the region (Δθ and ΔR) is based on Guassian fits. In particular, we performed a Gaussian fit of the probability distribution for both the first and second hydration shell along the θ axis (see Supplementary Fig. S4) and determined the average and standard deviation of the Guassian distributions for each of the compounds. The average of these values is used to compute the volume of each peak. A similar approach has been used to determine the range of integration along the R axis.

The analytical details of the scheme used to select the boundaries of the region (Δθ and ΔR) are described in the supporting information. The scripts for running the simulations and perform the analysis are available at: http://arianna.med.uniroma1.it/neutraldrugs/.

2.5 Statistical analysis and comparison with other methods

The program used to analyze the molecular dynamics trajectories and to build the histograms was written in Fortran90. The R package (Ihaka and Gentleman, 1996) [http://www.R-project.org] was used to analyze the histograms. The same package was used to calculate the indices, perform the Gaussian fitting and the Multiple Regression Analysis (MRA), compute the Pearson’s correlation coefficient, (r) and perform the cross validation analysis. The clustering analysis was performed using the Euclidean distance and via the ‘hclust’ function from the ‘Stats’ package of R (in particular, the ‘average’ method of the ‘hclust’ function was used).

We compared our results with those of several other methods. In particular we computed, for each of the 23 compounds, the predicted permeability values according to the two methods described in ref. (Fujiwara et al., 2002), based on a linear combination of molecular descriptors (Fuij_1), or including quadratic terms (Fuij_2). We also compared our results with those obtained by a linear regression (Hou) and a multiple linear regression (Guangli and Yiyu, 2006) (Gua_1) method. Finally we also used for comparison the Support Vector Machine based method (Gua_2) described in ref. (Guangli and Yiyu, 2006)

3 Results

In silico permeability prediction is consistent with available published data. We computed four indicators ($I_y$, $I_n$, $I_{+}$ and $I_{-}$) described in the Methods section for each of the drugs in our dataset. As explained in detail in the Methods section, these indices are derived from the conditional probability of finding a water molecule with a given orientation around the solute atoms estimated from the results of molecular dynamics simulations. In particular, the first two ($I_y$ and $I_n$) provide information about the hydrophilic and hydrophobic properties of the compound and are computed from the probability values of finding water molecules in the first and second hydration shells, respectively. $I_{+}$ and $I_{-}$ are related to the dipole orientation of the water molecules surrounding the analyzed compound and therefore to the effect of its positive and negative charges.

The values of the indices for the analyzed molecules are reported in Supplementary Table S1. Three of these parameter-free indicators ($I_n$, $I_{+}$ and $I_{-}$) correlate remarkably well with the permeability data while the $I_y$ index shows a lower level of correlation.

We tested whether a combination of these indices can represent a good proxy for estimating the permeability of a molecule. To this end, we used a multiple linear regression algorithm as implemented in the R function ‘lm’ (Ihaka and Gentleman, 1996) to find the weights providing the best correlation with the Caco-2 experimental data. The tool also provides the probability P-value of a computed coefficient to be different from 0. We tested both linear and quadratic terms in the regression. The best correlation is obtained by a linear fit of the $I_n$ and $I_{-}$ indices (P-value < 0.001), while $I_y$ and $I_{+}$ were found to contribute very little to the overall correlation (P-value > 0.05). This is consistent with the values of their correlation coefficients (see Table 1).

Table 1.

Correlation between the values of the indices in our dataset

	$${\mathit{I}}_{\mathit{y}}$$	$${\mathit{I}}_{\mathit{n}}$$	$${\mathit{I}}_{+}$$	$${\mathit{I}}_{-}$$	Caco-2
$${\mathit{I}}_{\mathit{y}}$$	1	−0.05	−0.39	0.89	0.28
$${\mathit{I}}_{\mathit{n}}$$		1	0.76	0.33	0.85
$${\mathit{I}}_{+}$$			1	−0.76	−0.81
$${\mathit{I}}_{-}$$				1	0.59

Also the correlation value between each index and Caco-2 experimental value is reported.

The regression model corresponding to the best fit is:

$$P_{pred}=\left(a\mathrm{*}{I}_n\right)+\left(b\mathrm{*}{I}_{-}\right)+c$$ (1)

where a = 3.06 (P-value = 4.7 × ${10}^{-7}),$b = 0.04 (P-value = 2.6 × ${10}^{-3}$) and c = 3092 (P-value = 4.0 × 10⁻⁷).

In Table 1 we also report the correlation between each index and the Caco-2 permeability values. As aspect the highest linear correlation value is between $I_n$ index (hydrophobic index) and Caco-2 permeability value because a more lipophilic drug is more likely to effectively cross the hydrophobic phospholipid bilayer. More interesting is the correlation linked to positive charge distribution index $I_{+}$. It can be observed that the index with the highest value of negative correlation is $I_{+}$, indicating that most likely positive groups prevent uptake of compounds more than negative ones (see also Supplementary Fig. S5).

Table 2 reports the predicted Ppred permeability values obtaining using Eq. (1) for all the drugs considered and shows that they reproduce very well the experimental Caco-2 permeability values (Pearson’s correlation coefficient, r = 91%). We also performed a cross validation analysis by repeatedly leaving out 20% of the compounds (testing sets) and re-computing the coefficients of Eq. (1) on the remaining ones (training sets) as described in the Methods section. We iterated this procedure 10 000 times, randomly choosing the training set at each step. The predicted average values (P_{pred_CV}) obtained for each drug in the test set are reported in Table 2. Once again, the correlation between prediction and experiment is very satisfactory (88%) (Fig. 3).

Fig. 3.

Scatter plot correlating the predicted permeability values in the cross validation (P_{pred_CV}) and their experimental Caco-2 values. For each compound the average predicted value and the standard deviation are reported

The coefficients of Eq. (1) are also very stable. Their average value and standard deviation obtained in the 10 000 cross validation runs are: a = 3.064 ± 0.194, b = 0.043 ± 0.005 and c = −3091.866 ± 195.453.

The average difference between the predicted and experimental values is 4.7 × 10⁻⁶ cm/s. It is relevant to mention here that the threshold used to discriminate between low absorbance and high absorbance compounds is usually set to 8.0 × 10⁻⁶ cm/s (Castillo-Garit, et al., 2008) and the data shown in Table 1 demonstrate that only in two cases (Acyclovir and Zidovudine) our method would significantly misclassify the compound.

In summary, Eq. (1) describes well the permeability properties of neutral compounds. It is worth noticing that the P_pred value is well balanced in the sense that it overestimates and underestimates the experimental values in a similar number of cases (11 and 12 respectively).

We compared our results with those of several other methods (as described in the Methods section) and the results are reported in Table 3 and Supplementary Figure S6a–e. It can be appreciated that the correlation between predicted and experimental values is higher for our method. The average error is lower than all other tested methods, but for the Gua_2 method (Guangli and Yiyu, 2006) that shows a very similar value.

Table 3.

Comparison of the results of the P_pred method with those obtained by a number of other predictors (described in Experimental section). P_{pred_CV} (using the test set data) also has been reported

	Fuij_1	Fuij_2	Hou	Gua_1	Gua_2	Ppred	Ppred_CV
r	0.66	0.62	0.80	0.85	0.79	0.91	0.88
R2	0.43	0.39	0.64	0.72	0.63	0.83	0.78
Average error	8.2	9.9	4.8	6.2	4.8	4.3
Ref.	(59)	(59)	(18)	(60)	(60)

The goodness of fit parameters (r and $R^2$) are also shown.

4 Conclusion

We have shown here that an approach based on the simultaneous analysis of molecule hydrophobicity and charge distribution has the potential to accurately predict the passive plasma membrane permeability of neutral drugs. This method may be useful for investigating the mechanism of passive permeation of small neutral compounds since it can easily provide information on the role that every single atom plays on the hydration process.

Our P_pred indicator correlates very well with the experimentally determined Caco-2 permeability values and performs better than other available methods. Furthermore, it only requires the knowledge of the chemical structure of the compound. Given the cost and impact of late stage failures in drug development we believe that the relatively high computational cost of running the molecular dynamics simulations (an average of 48 hours on a 20 CPU server for each molecule) is not necessarily a relevant drawback of the approach.

As is the case also for several in vitro methods, our method cannot estimate the permeability of drugs that use an active uptake system. In these cases, additional techniques, such as docking the compounds to efflux/influx protein models, should be explored.