cΔlog kwIAM: can we afford estimation of small molecules’ blood-brain barrier passage based upon in silico phospholipophilicity? doi: http://dx.doi.org/10.5599/admet.1034 267 ADMET & DMPK 9(4) (2021) 267-281; doi: https://doi.org/10.5599/admet.1034 Open Access : ISSN : 1848-7718 http://www.pub.iapchem.org/ojs/index.php/admet/index Original scientific paper cΔlog kw IAM : can we afford estimation of small molecules’ blood- brain barrier passage based upon in silico phospholipophilicity? Lucia Grumetto 1 , Giacomo Russo 2 * 1 Pharm-Analysis & Bio-Pharm Laboratory, Department of Pharmacy, School of Medicine and Surgery, University of Naples Federico II, Via D. Montesano, 49, I-80131, Naples, Italy. 2 School of Applied Sciences, Sighthill Campus, Edinburgh Napier University, 9 Sighthill Ct, EH11 4BN Edinburgh, United Kingdom. *Corresponding Author: E-mail: G.Russo@napier.ac.uk; Tel.: +44 (0) 131 455 3464; Fax: +44 (0) 131 455 3555 Received: June 27, 2021; Revised: November 27, 2021; Published: December 15, 2021 Abstract 56 compounds, whose log BB values were known from the scientific literature, were considered and their phospholipophilicity values were calculated in silico. These values, along with either experimentally determined or calculated lipophilicity values, were used to extract cΔ/Δ’log kw IAM parameters. cΔ/Δ’log kw IAM values were found inversely related to data of blood-brain barrier passage, especially in the < -0.20 log BB range and on the IAM.PC.DD2 phase (r 2 = 0.79). In multiple linear regression, satisfactory statistic models (r 2 (n-1) = 0.76), based on c/’log kw IAM.MG along with other in silico calculated descriptors, were achieved. This method brings the potential to be applied, along with other methodologies, to filter out solutes whose BBB permeation is foreseen to be substandard, thus allowing pharmaceutical companies/research institutes to focus on candidates that are more likely to concentrate in the brain. ©2021 by the authors. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/). Keywords immobilized artificial membrane; biochromatography; blood brain barrier; brain targeting; phospholipophilicity. Introduction Combinatorial chemistry involves the generation of a large array of structurally diverse compounds, i.e., a chemical library, through systematic, repetitive and covalent linkage of various “building blocks” [1]. This technique can be exploited in parallel, delivering hundreds, if not thousands, of molecules of pharmaceutical interest in a handful of hours. While the organic synthesis throughput has expanded so noticeably in recent years, screening methodologies are still lagging behind, instead [2]. Indeed, most of the testing still requires animal models that have the undeniable advantage of mirroring more closely the complexity of human beings than cells. However, animal models are facing criticism from the public since they often require the sacrifice of vertebrates [3] and heavily impact the environment due to the huge number of carcasses to dispose of. The assessment of the ability of a drug to cross the biological membranes in the early stages of its http://dx.doi.org/10.5599/admet.1034 https://doi.org/10.5599/admet.1034 http://www.pub.iapchem.org/ojs/index.php/admet/index mailto:G.Russo@napier.ac.uk http://creativecommons.org/licenses/by/4.0/ Grumetto and Russo ADMET & DMPK 9(4) (2021) 267-281 268 development plays a pivotal role in pharmaceutical industrial research. Notably, the development of drugs acting toward the central nervous system (CNS) has poorer success rates and requires longer times than non-CNS drugs [4]. This occurs due to the complexity of the blood-brain barrier (BBB). In fact, in a healthy brain, the BBB plays a crucial role in protecting normal brain functions from potentially harmful compounds occurring in the bloodstream [5]. Strategies for brain drug delivery have developed in the last decades, and various techniques are available to study the BBB's role in drug uptake. These include in vivo, in vitro [6] and in situ techniques [7]. Separation science offers valuable alternatives to animal testing that can provide effectiveness in the drug discovery/drug development pipeline as biomimetic liquid chromatography [8-11], performed employing stationary phases emulating biological components or using mobile phase ingredients simulating physiological environments. A consistent branch of this is represented by liquid chromatography (LC) conducted on stationary phases based on immobilized artificial membranes (IAM). IAM phases are based on membrane phospholipid analogs covalently bound to aminopropyl silica [7,12,13]. Some of these phases are available commercially as IAM.PC.MG and IAM.PC.DD2. Both these support phosphatidylcholine analogs (PC), but they differ from each other in the end-capping of the free aminopropyl moieties, which is performed with methyl glycolate (MG) or with C3 or C10 anhydrides (DD2). In recent years, we parameterized the excess of the polar/electrostatic interactions occurring between drugs and biological membranes as Δlog kw IAM [14-19]. Δlog kw IAM is obtained by combining n-octanol/water lipophilicity with phospholipophilicity, i.e., the affinity of the compound for the IAM phases measured as a retention factor extrapolated at 100 % of aqueous phase (kw IAM ) [20]. This represents the difference between the logarithm of the chromatographic retention factor (log kw IAM ) measured for each analyte, i.e., the experimentally determined phospholipophilicity, and the value expected for a neutral isolipophilic molecule that is estimated by correlative equations. Δlog kw IAM values were inversely related to the drug passage of complex biological barriers, such as the BBB and the intestinal wall [13,17,18]. The increasing need for high-throughput drug discovery methods has provided several in silico models of BBB permeation based on in vivo log BB values [21,22]. Log BB is generally measured on murine models and is still nowadays considered as a solid indication for BBB delivery [23]. Log BB is defined as (Eq. 1): log BB = log 𝐶Brain 𝐶Blood (1) in which CBrain is the concentration that the analyte realizes in the brain tissues, and CBlood is the concentration that it achieves in the blood. The in silico models bring the advantages of being much faster to perform and applicable to molecules that are not yet synthesized and/or not easily detectable. Back in 2017, we developed some statistical models to predict the phospholipophilicity of small molecules based on more than 200 individual measurements performed in our laboratories. This also materialized in an online service, namely log kw IAM.MG/DD2 calculator, offering the opportunity to predict the phospholipophilicity of all compounds included in PubChem collection as log kw IAM on both MG and DD2 chromatographic columns [24]. In the present study, we aim at applying these statistical models to calculate the phospholipophilicity of a dataset of compounds whose log BB is known from the scientific literature and from there to estimate Δlog kw IAM , based either on experimentally determined or calculated lipophilicity values. Our goal is to evaluate whether these parameters calculated in silico, therefore called from here on cΔlog kw IAM , can offer effectiveness in screening libraries of compounds for their potential to reach the brain. If so, we will look at ways to implement these procedures in the drug discovery/development industrial programs. ADMET & DMPK 9(4) (2021) 267-281 BBB passage based on in silico phospholipophilicity doi: http://dx.doi.org/10.5599/admet.1034 269 Experimental Data collection Experimental lipophilicity values were collected from the scientific literature. Specifically, all the log P values were taken from PubChem but those of nevirapine and thioxolone, which were taken from the literature [25]. Calculated log P values were obtained by either ALOGPS [26] or by MarvinSketch [27]. For acidic compounds, whose ’log kw IAM but not their log kw IAM were previously found related to log BB, log D 7.4 values were again calculated by MarvinSketch software [27]. Log BB values were taken from the literature [28]. c/’log kw IAM values calculation c/’log kw IAM values were calculated from phospholipophilicity values estimated in silico according to a procedure we developed in 2017 [24]. In brief, the best relationships were found to be: log kw IAM.MG = -0.1405 (0.1282) + 0.4401(0.0297)miLogP + 0.0536 (0.0057)Heavy Atoms - 0.0833 (0.0201)HLBM - 0.0435(0.0144)Rotatable bonds (2) n=204 r 2 = 0.81 q 2 = 0.80 SE = 0.438 F4,199 = 213.92 P<1.0 10 -8 PC = 39.403 and log kw IAM.DD2 = -2.3989 (0.2812) + 0.4936(0.0379)miLogP + 0.4354 (0.0470)Volume Diameter - 0.0640 (0.0226)HLBPSA - 0.0497(0.0173)Rotatable bonds (3) n=160 r 2 = 0.85 q 2 = 0.84 SE = 0.459 F4,155 = 212.94 P<1.0 10 -8 PC = 33.974 A detailed explanation of the main descriptors, along with relevant references, is reported in supporting information (Table S1). In these equations, n is the number of data considered to derive the regression equation, r 2 is the square of the correlation coefficient, SE is the standard error of the estimate, F (the subscripts are the degrees of freedom and the number of variables) is the Fisher statistic of the regression, P is the observed significance level, i.e., the probability of obtaining a result equal to or “more extreme” than what was observed, and PC is the Amemiya predictive criterion of the regression. The hydrophilic-lipophilic balance (HLB) can be taken into account by the methods by Griffin [29] (HLBG), Davies [30] (HLBD), and taking into account the steric effects (HLBPSA), not considered by the two approaches. HLBPSA is defined as follows: HLBPSA=20⋅PSA/Surface where PSA is the polar surface area and Surface is the total surface. HLB (HLBM) is the mean resulting from the values by all three methods. miLogP is the octanol-water partition coefficient predicted by the online program for the calculation of molecular properties and bioactivity prediction [31]. The calculations were made completely automated and easily accessible to anyone via a user-friend tool to predict log kw IAM.MG and log kw IAM.DD2 , a Web service and a set of scripts for VEGA ZZ program [24]. This is available at https://www.ddl.unimi.it/vegaol/logkwiam.htm and offers a calculation of log k IAM.MG/DD2 of any molecule included in the PubChem collection as implemented in the script version. log kw IAM values were calculated as the difference between the log kw IAM computed from equations (2) and (3) and the log kw IAM expected for neutral isolipophilic molecules. Indeed, as reported in our previous studies [14,15], IAM retention data on both IAM phases relate unambiguously with log P values of http://dx.doi.org/10.5599/admet.1034 https://www.ddl.unimi.it/vegaol/logkwiam.htm Grumetto and Russo ADMET & DMPK 9(4) (2021) 267-281 270 structurally non-related neutral compounds, in the log P range 1.0–4.8. These relationships are expressed by the following equations: log kw IAM.MG = 0.792 (±0.038) log P - 0.732(±0.105) (4) n = 36 r 2 = 0.926 s = 0.248 F1, 34 = 422.40 F1, 34 α,0.001 = 12.90 log kw IAM.DD2 = 0.934 (±0.038) log P - 0.883(±0.104) (5) n = 36 r 2 = 0.946 s = 0.246 F1, 34 = 595.74 F1, 34 α,0.001 = 12.90 For acidic compounds, analogously to what was reported in our previous study [15], log D 7.4 rather than log P N was used for the computation of delta values in equations (4) and (5). Their values were therefore named ’log kw IAM values to avoid any ambiguity. Molecular modeling An ample array (> 1,600) of physico-chemical descriptors, subdivided into 20 logical blocks (atom type, functional group, fragment counts, topological and geometrical descriptors), were calculated by the web service E-DRAGON 1.0 [32]. In brief, the molecules were input as SMILES code in a text document and converted by the integrated applet CORINA in 3D before all the indices were computed. The Quantitative structure-property relationship (QSPR) models were obtained by the automatic stepwise approach implemented in the “automatic linear regression” script of VEGA ZZ software [33], calculating regression models, including from one to five independent variables. The predictive strength of the best equation was evaluated by leave-one-out (LOO) cross-validation. The regression coefficients were calculated to evaluate the set in terms of the standard deviation of errors (SE), regression coefficients (r 2 is the square of the correlation coefficient, q 2 is the square of the correlation coefficient after cross-validation), intercept, Fisher statistic for the regression (F), probability (P) and Amemiya prediction criterion (PC). Descriptors with too low regression coefficient (r 2 < 0.1) were excluded, and collinear descriptors were detected by evaluating the variance inflation factor (VIF) whose threshold value was set to 5. Data handling Data were input in a spreadsheet and data points were plotted from Microsoft Excel, part of the Microsoft Office 365 suite of programs. Results and Discussion c/’log kw IAM : simple linear regression In our previous studies [14-19, 34], /’log kw IAM values were found inversely related to the passage of complex biological barriers, such as the BBB and the intestinal wall. The calculation of /’log kw IAM parameters are based on two physico-chemical properties, i.e., n-octanol/water lipophilicity either of the neutral species (giving log kw IAM ) or of the mixture of the species at the physiological pH, i.e., 7.4 (giving ’log kw IAM ) and the affinity of the compound for IAM phases. Indeed, in our previous studies [14-16], we verified that for acidic compounds, significant relationships vs. log BB data could only be obtained when delta parameters were calculated by using the lipophilicity of the mixture of the species present in solution at the experimental pH, i.e., log D 7.4 , rather than that of the neutral species, i.e., log P N . For neutrals, bases and ampholytes, delta parameters were estimated by using log P N values instead. For consistency, we extended the same approach to delta values surrogated in silico (c/’log kw IAM ). However, while there are plenty of tools available to surrogate log P values [35], to the best of our knowledge, the in silico platform we developed is the only service that predicts phospholipophilicity. Table ADMET & DMPK 9(4) (2021) 267-281 BBB passage based on in silico phospholipophilicity doi: http://dx.doi.org/10.5599/admet.1034 271 1 lists names, chemical nature (A= acid, B=basic, BB= bibasic, N= neutral), calculated log kw IAM.MG and log kw IAM.DD2 , exp log P N , clog P N and calculated log D 7.4 (for acids only) values for the dataset considered. c/’log kw IAM values are reported in Table 2 along with the experimental log BB values. Table 1. Names, chemical nature (A= acid, B=basic, BB= bibasic, N= neutral), calculated log kw IAM.MG and log kw IAM.DD2 , exp log P N , clog P N values for the dataset considered. molecule nature clog kw IAM.MG clog kw IAM.DD2 exp log P N [36] clog P N (1) [26] clog P N (2) [37] clog D 7.4 [37] 1,1,1-trichloroethane N 1.063 1.247 2.49 2.45 2.04 1,2-dimethylbenzene N 1.400 1.635 3.12 3.16 2.98 1,4-dimethylbenzene N 1.421 1.599 3.15 3.15 2.98 1,7-dimethylxanthine A -0.073 -0.001 -0.22 -0.63 0.09 0.09 1-chloro-2,2,2- trifluoroethane N 0.811 0.774 1.82 1.86 1-hydroxymidazolam N 1.839 2.043 3.09 2.9 2,2-dimethylbutane N 1.283 1.578 3.82 3.74 2.85 2-methylpentane N 1.388 1.706 3.21 3.66 2.82 3-methylhexane N 1.561 1.949 4.18 3.21 3-methylpentane N 1.292 1.599 3.60 3.98 2.82 4-hydroxymidazolam N 1.950 2.191 3.05 3.35 acetaminophen N 0.184 0.302 0.91 0.51 1.09 acetone N -0.247 -0.359 -0.24 -0.29 0.38 aminopyrine N 1.045 1.349 1.00 0.94 1.60 amobarbital A 0.899 1.181 2.07 1.87 1.86 1.60 antipyrine N 0.901 1.139 0.56 1.18 1.61 bretazenil N 2.103 2.447 3.05 2.29 cyclohexane N 1.476 1.671 3.44 2.38 cyclopropane N 0.284 0.105 1.72 1.56 1.19 Desmonomethyl- promazine B 2.287 2.703 4.28 3.68 didanosine A -0.404 -0.294 -1.24 -1.26 -0.50 -1.06 diethylene glycol divinyl ether N -0.127 0.200 0.87 1.26 0.87 enflurane N 1.075 1.203 2.10 2.24 2.42 ethanol N -0.534 -0.683 -0.31 -0.40 -0.22 ethyl ether N 0.162 0.308 0.89 1.12 0.70 ethylbenzene N 1.398 1.616 3.15 3.27 2.91 flunitrazepam N 1.621 1.739 2.06 2.20 2.58 fluroxene N 0.570 0.637 1.70 1.58 halothane N 1.165 1.300 2.30 2.50 1.97 indinavir BB 2.864 2.745 2.90 3.26 2.39 isobutyl alcohol N 0.045 0.169 0.76 0.60 0.65 isoflurane N 1.074 1.207 2.30 2.48 http://dx.doi.org/10.5599/admet.1034 Grumetto and Russo ADMET & DMPK 9(4) (2021) 267-281 272 Table 1. Continued… molecule nature clog kw IAM.MG clog kw IAM.DD2 exp log P N [36] clog P N (1) [26] clog P N (2) [37] clog D 7.4 [37] isopropyl alcohol N -0.241 -0.243 0.05 0.04 0.19 mesoridazine B 2.640 3.027 3.90 3.83 3.41 methoxyflurane N 0.864 1.070 2.21 2.01 1.91 methyl cyclopentane N 1.140 1.347 3.37 3.15 2.31 methyl ethyl ketone N 0.047 0.057 0.29 0.41 1.01 mirtazapine B 1.969 2.287 2.90 3.38 m-xylene N 1.410 1.641 3.20 3.15 2.98 nevirapine N 1.152 1.332 2.50 [25] 1.75 2.19 n-heptane N 1.791 2.189 3.28 n-hexane N 1.545 1.861 2.88 nordazepam N 1.838 2.055 2.79 3.24 northioridazine B 3.120 3.607 5.29 5.1 n-pentane N 1.299 1.529 2.49 quinidine B 2.016 2.394 3.44 2.82 2.32 sulforidazine B 2.684 3.057 4.45 4.32 3.6 teflurane N 1.029 1.066 2.07 1.63 thioridazine B 3.318 3.816 5.90 5.93 5.48 thioxolone N 2.414 2.834 3.90 2.69 2.93 tiotidine B 0.186 0.375 0.68 0.59 1.18 triazolam N 2.102 2.365 2.42 2.94 3.31 trichloroethylene N 0.837 0.944 2.45 2.17 trifluoperazine BB 3.305 3.651 5.03 4.87 4.72 valproic acid A 1.135 1.542 2.75 2.54 2.61 0.37 zidovudine A -0.063 0.094 0.05 -0.1 -0.22 -0.28 Figure 1 illustrates the relationships between log BB and the c/’log kw IAM values on the MG (A) and DD2 (B) stationary phases and a clear descending trend is visible in both plots. These values, calculated by considering exp log D 7.4 values for acids and log P N values for all the other molecules, are reported in Table 2 along with the experimental log BB values. The dataset was divided according to the molecules’ ionization in neutrals (N), bases supporting one (B) or two (BB) basic groups and acidic (A) compounds. This was set to evaluate whether any specific trend was visible in each subgroup. Three of the assayed molecules markedly deviate from the pattern identified by the main distribution of points are triazolam, trifluoperazine and valproic acid. The chromatographic behaviorur of small molecules on IAM phases has been characterized by many research groups for more than three decades [38,39]. Trifluoperazine is a highly lipophilic base, and it is well ascertained [14] that these interact with phospholipids weaker than isolipophilic neutral compounds, especially on the IAM.PC.DD2 phase. As to triazolam and valproic acid, the reasons for these deviating from the main distribution of points do not seem that straightforward to spot. Triazolam is a benzodiazepine derivative featuring a structure of three condensed rings covalently bound to one chlorobenzene moiety sharing the same plane. It has been again already characterized [39] that those planar structures tend to interact with IAM phases stronger than the extent expected based on their lipophilicity, but it is hard to assess whether this played a role in this instance. For its being an acid, the calculation of cΔ’log kw IAM of valproic acid was based on log D 7.4 rather than log P N . However, since we could not retrieve the ADMET & DMPK 9(4) (2021) 267-281 BBB passage based on in silico phospholipophilicity doi: http://dx.doi.org/10.5599/admet.1034 273 experimental value from literature sources, we had to rely on the calculated value, whose closeness to the actual value cannot be reasonably taken for granted. Interestingly, a descending trend is visible for neutral compounds between the c/’log kw IAM and log BB values ranging from +1 to 0 but the distribution flattens for log BB < 0. Figure 1. Relationships between log BB values and c/’log kw IAM.MG (A) and c/’log kw IAM.DD2 values (B). Table 2. c/’log kw IAM.MG , c/’log kw IAM.DD2 values and experimental log BB values for the dataset considered. molecule cΔ/Δ’log kw IAM.MG cΔ/Δ’log kw IAM.DD2 log BB 1,1,1-trichloroethane -0.177 -0.196 0.40 1,2-dimethylbenzene -0.339 -0.396 0.37 1,4-dimethylbenzene -0.342 -0.460 0.31 1,7-dimethylxanthine 0.588 0.798 0.06 1-chloro-2,2,2-trifluoroethane 0.070 -0.080 0.08 1-hydroxymidazolam 0.274 0.217 -0.07 2,2-dimethylbutane -1.010 -1.107 1.04 2-methylpentane -0.422 -0.409 0.97 3-methylhexane -0.249 -0.166 0.90 3-methylpentane -0.827 -0.880 1.01 4-hydroxymidazolam 0.029 -0.055 -0.30 acetaminophen 0.195 0.335 -0.31 acetone 0.675 0.748 -0.15 aminopyrine 0.985 1.298 0.00 amobarbital 0.364 0.570 0.04 antipyrine 1.189 1.499 -0.10 bretazenil 1.021 1.191 -0.09 cyclohexane -0.516 -0.659 0.92 cyclopropane -0.346 -0.618 0.00 desmonomethylpromazine 0.104 0.149 0.59 didanosine 1.168 1.579 -1.30 diethylene glycol divinyl ether -0.084 0.270 0.11 http://dx.doi.org/10.5599/admet.1034 Grumetto and Russo ADMET & DMPK 9(4) (2021) 267-281 274 Table 2. Continued… molecule cΔ/Δ’log kw IAM.MG cΔ/Δ’log kw IAM.DD2 log BB Enflurane 0.144 0.125 0.24 ethanol 0.444 0.490 -0.16 ethyl ether 0.189 0.360 0.00 ethylbenzene -0.365 -0.443 0.20 flunitrazepam 0.721 0.698 0.06 fluroxene 0.051 0.044 0.13 halothane 0.075 0.035 0.35 indinavir 1.299 0.919 -0.74 isobutyl alcohol 0.175 0.342 -0.17 Isoflurane 0.174 0.166 0.42 isopropyl alcohol 0.451 0.593 -0.15 mesoridazine 0.283 0.267 -0.36 methoxyflurane -0.154 -0.111 0.25 methyl cyclopentane -0.797 -0.918 0.93 methyl ethyl ketone 0.549 0.669 -0.08 mirtazapine 0.404 0.461 0.53 m-xylene -0.392 -0.465 0.29 nevirapine -0.096 -0.120 0.00 n-heptane -0.075 0.008 0.81 n-hexane -0.004 0.054 0.80 nordazepam 0.004 -0.088 0.50 northioridazine -0.187 -0.273 0.75 n-pentane 0.059 0.086 0.76 quinidine 0.024 0.064 -0.46 sulforidazine -0.108 -0.216 0.18 teflurane 0.470 0.427 0.27 thioridazine -0.623 -0.812 0.24 thioxolone 0.057 0.074 0.40 tiotidine 0.379 0.623 -0.82 triazolam 0.917 0.988 0.74 trichloroethylene -0.150 -0.200 0.34 trifluoperazine 0.053 -0.164 1.44 valproic acid 1.574 2.079 -0.22 zidovudine 0.891 1.239 -0.72 Figure 2 instead displays the relationship occurring between the data of permeation through the BBB and experimental n-octanol/water lipophilicity values. The experimental log P values for 1-chloro-2,2,2- trifluoroethane, 1-hydroxymidazolam, 3-methylhexane, 4-hydroxymidazolam, bretazenil, desmonomethyl- promazine, fluroxene, isoflurane, n-heptane, n-hexane, nordiazepam, northioridazine, n-pentane, teflurane and trichloroethylene were not available and, therefore, calculated values were used instead. Clearly, log P represents an index of paramount importance in pharmaceutical discovery and development [40]. The assumption is that lead compounds should lie in a specific range of lipophilicity to be considered for further ADMET & DMPK 9(4) (2021) 267-281 BBB passage based on in silico phospholipophilicity doi: http://dx.doi.org/10.5599/admet.1034 275 implementations. The expectation is that lipophilicity should be positively related with data of drugs’ passage through complex barriers, including the BBB [40]. However, the extremely scattered data points of Figure 2 evidence that no relationship between log P and log BB values can be observed. Likewise, no trend is visible between the two considered variables if all the compounds are considered. However, an ascending trend is visible for acidic compounds, albeit their number is limited. Figure 2. Relationships between log BB values and log P values. Conversely, the situation changes noticeably when considering only the lowest range of log BB (< -0.20). Indeed, as Figure 3 displays, the relationship between log BB and cΔ/Δ’log kw IAM becomes inverse linear for this subset with a rather solid r 2 value, i.e., > 0.59, with a superior accuracy afforded by delta values on the DD2 phase. This is analogous to what we achieved using delta values obtained from experimentally determined log kw IAM values [14-19,34] instead of the calculated ones. We subsequently compared the performance in predicting log BB values of delta descriptors again vs. experimentally determined log P N values (detailed in Figure 4). Although a direct linear relationship is observable between log BB (< -0.20) and log P N values, its accuracy as assessed from r 2 is inferior to that of the relationship developed from cΔ/Δ’log kw IAM.DD2 values. If cΔ/Δ’log kw IAM are calculated from in silico rather than experimental log P data, the relationship between log BB (< -0.20) and cΔ/Δ’log kw IAM values weaken, although not much, especially on the DD2 phase (r 2 = 0.68 by using clogP values calculated by MarvinSketch, data not shown). Although the size of our dataset is relatively limited (n = 56), we can extract some interesting information from the results achieved. Specifically, the method for predicting cΔ/Δ’log kw IAM cannot yet be used alone in the discovery phase. However, this can be run as complementary along with other assays for profiling the ADME potential of drug candidates as it can provide additional information that is not afforded by other early assessments, e.g., lipophilicity. Moreover, the method hereby reported seems to be more selective in the identification of the candidates with the slimmest chances to gain access to the brain. This is advantageous, especially if the potency of the candidates that are screened is high enough to be effective, even if the amounts that are successfully delivered to the brain are low. http://dx.doi.org/10.5599/admet.1034 Grumetto and Russo ADMET & DMPK 9(4) (2021) 267-281 276 Figure 3. Relationships beween log BB values (<0.20) and c/’log kw IAM.MG (A) and c/’log kw IAM.DD2 values (B). Figure 4. Relationships beween log BB (<0.20) and log P values. These considerations would support the implementation of this method as a filter in the discovery phase to filter out the compounds intended to act toward the brain, with substandard potential to partition in the CNS. The method seems to work better if the estimation of cΔ/Δ’log kw IAM relies on experimental lipophilicity data rather than calculated ones. This is not an obstacle since many high throughput platforms for log P assessments are now available on the market [41] or being described [42] and for sure log kw IAM measurements are more demanding since they require samples to be run over (at least) three organic modifier concentrations. A further consideration concerns the models used to calculate phospholipophilicity. These are already rather good but could be improved by analysing more and more chemically diverse solutes to broaden their applicability space. c/’log kw IAM : multiple linear regression The passage of therapeutics through the BBB is unanimously recognized as an extremely complex ADMET & DMPK 9(4) (2021) 267-281 BBB passage based on in silico phospholipophilicity doi: http://dx.doi.org/10.5599/admet.1034 277 phenomenon, which results from an interplay of various passage patterns, including transcellular passive, transcellular active and paracellular passage pathways [43]. Therefore, it is rather unlikely that a sole descriptor can encode all the interactions taking place in BBB uptake. For this reason, we calculated an ample array (> 1,600) of physico-chemical descriptors by the software E-DRAGON 1.0 and studied them in (i) simple linear regression and (ii) multiple linear regression vs. log BB values. Task (i) was done to establish how c/’log kw IAM indexes compared to other physico-chemical descriptors in terms of predictive strength, while task (ii) was accomplished to study whether using multiple variables to model the BBB passage of the dataset could yield some useful statistic models. The results of the simple linear regression analysis are listed in Table 3, along with the relevant statistics. An analysis of the data suggests that all regression coefficients are significant at the 99 % level. Among all the E-DRAGON descriptors, c/’log kw IAM.DD2 and c/’log kw IAM.MG ranked fourth and fifth, respectively and their r 2 values were exceeded only by parameters referring to polarity (TPSA(NO)), molecular lipophilicity (AlogPS), and the number of oxygen atoms (nO). A detailed explanation of these and relevant references is reported in supporting information (Table S1). The aspect that both the topological surface area and the number of oxygen atoms relate to a fair extent with the BBB passage of the molecules in the dataset may suggest that H-bonding may act by preventing the uptake of these chemicals through the BBB. This agrees well with the observations made by Diamond and co-workers [44] and other research groups [45]. Subsequently, the incorporation of c/’log kw IAM descriptors was attempted in multiple linear regression reported below: log BB = 0.0668 + 0.1548 ALOGPS_logP - 0.0779 cΔ/Δ’log kw IAM.MG - 0.0046 TPSA(Tot) - 0.3464 nROH (6) r 2 = 0.73 q 2 = 0.67 SE= 0.280 F = 34.45 P=6.26e-14 PC=4.450 and after LOO: log BB = 0.0425 + 0.1657 ALOGPS_logP - 0.0609 cΔ/Δ’log kw IAM.MG - 0.0043 TPSA(Tot) - 0.3709 nROH (7) r 2 = 0.76 SE= 0.266 F = 38.79 P=9.35e-15 PC=3.93 Exc: mesoridazine Table 3. Variable considered and r 2 vs log BB values. A detailed description of the descriptors is offered in supporting information (Table S1). The statistics of the each regressor is reported in 2.3. The statistics of the equations has been detailed in 2.3, while Exc identifies the compound that was excluded from the regression. According to both equations (6) and (7), the BBB diffusion of chemicals seems to be promoted by molecular lipophilicity and hindered for molecules featuring high c/’log kw IAM.MG , which is an index accounting for the excess of the polar/electrostatic interaction forces realized in the interplay between the chemical species and membrane phospholipids. Again, according to the models presented above, the BBB uptake of molecules is less efficient for those supporting many polar atoms (and specifically many hydroxyl groups). An r 2 (n-1) value equal to 0.76 suggests that the statistic model is robust and reliable. A plot experimental vs. predicted (according to Eq. (7)) log BB values is presented in Figure 5. The value of each descriptor is reported in supporting information (Table S2). Variable r 2 q 2 SE F P PC TPSA(NO) 0.46 0.42 0.385 46.08 9.08e-09 7.985 ALOGPS_logP 0.42 0.37 0.398 39.36 6.19e-08 8.561 nO 0.38 0.33 0.411 33.46 3.77e-07 9.138 cΔ/Δ’log kw IAM.DD2 0.38 0.32 0.413 32.82 5.36e-07 9.205 cΔ/Δ’log kw IAM.MG 0.37 0.32 0.414 32.36 5.36e07 9.255 http://dx.doi.org/10.5599/admet.1034 Grumetto and Russo ADMET & DMPK 9(4) (2021) 267-281 278 Figure 5. Experimental vs predicted log BB values calculated according to Eq. (7). Conclusions The present study proposes a method to streamline the drug discovery/development process and filter out solutes whose BBB permeation is envisaged to be substandard. Even if the dataset is limited in size and the method is not mature enough for broad implementation alone, it may be applied, along with other methodologies by pharmaceutical companies and research institutes, to focus only on candidates that tend to concentrate on the brain. This way, all the others can be neglected, thus saving time and money resources. 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