Some substrates of P-glycoprotein targeting β-amyloid clearance by quantitative structure-activity relationship ( QSAR ) / membrane-interaction ( MI )-QSAR analysis

The pathogenesis of Alzheimer’s disease (AD) putatively involves a compromised blood-brain barrier (BBB). In particular, the importance of brain-to-blood transport of brain-derived metabolites across the BBB has gained increasing attention as a potential mechanism in the pathogenesis of neurodegenerative disorders such as AD, which is characterized by the aberrant polymerization and accumulation of specific misfolded proteins, particularly β-amyloid (Aβ), a neuropathological hallmark of AD. P-glycoprotein (P-gp), a major component of the BBB, plays a role in the etiology of AD through Aβ clearance from the brain. Our QSAR models on a series of purine-type and propafenone-type substrates of P-gp showed that the interaction between P-gp and its modulators depended on Molar Refractivity, LogP, and Shape Attribute of drugs it transports. Meanwhile, another model on BBB partitioning of some compounds revealed that BBB partitioning relied upon the polar surface area, LogP, Balaban Index, the strength of a molecule combined with the membrane-water complex, and the changeability of the structure of a solute-membranewater complex. The predictive model on BBB partitioning contributes to the discovery of some molecules through BBB as potential AD therapeutic drugs. Moreover, the interaction model of P-gp and modulators for treatment of multidrug resistance (MDR) indicates the discovery of some molecules to increase Aβ clearance from the brain and reduce Aβ brain accumulation by regulating BBB P-gp in the early stages of AD. The mechanism provides a new insight into the therapeutic strategy for AD.


INTRODUCTION
Therapy for central nervous system (CNS) diseases requires drugs that can cross the blood-brain barrier (BBB) [1].BBB not only maintains the homeostasis of the CNS, but also refuses many potentially important diagnostic and therapeutic agents from entering into the brain [2].The pathological hallmarks of Alzheimer's disease (AD) are progressive brain atrophy and the accumulation of cortical senile plaques, formed by the aggregation of amyloid beta peptide (Aβ) [3], and neurofibrillary tangles (NFT), namely the self-assembly of hyperphosphorylated forms of the microtubule associated protein tau into fibers termed "paired helical filaments (PHFs)" [4,5].The pathogenesis of AD's senile plaque and NFT lesions putatively involves a compromised BBB [6], which protects the brain against endogenous and exogenous compounds and plays an important part in the maintenance of the microenvironment of the brain [7].The ability of drug permeating across BBB becomes critical in the development of new medicines, especially in the design of new drugs active in brain tissue.In particular, the importance of brain-to-blood transport of brain-derived metabolites across the BBB has gained increasing attention as a potential mechanism in the pathogenesis of neurodegenerative disorders such as Parkinson's disease (PD) [8] and AD characterized by the aberrant polymerization and accumulation of specific misfolded proteins, particularly Aβ.P-glycoprotein (P-gp or MDR1/ABCB1) is a 170-kDa transmembrane (TM) protein widely expressed from the epithelial cells of the intestine, liver, kidney, placenta, uterus, and testis to endothelial cells of the BBB [9].It belongs to the ABC (ATP-binding cassette) transporter family and serves to pump exogenous substances out of the cells.The domain topology of P-gp consists of two homologous halves each consisting a TM domain preceding a cytosolic nucleotide binding domain.Each TM domain is composed of six TM α-helix segments involved in efflux as well as in drug binding [10].The ABC transport protein P-gp, a major component of the BBB, mediates the efflux of Aβ from the brain as well as is a major factor in mediating resistance to brain entry by numerous exogenous chemicals, including therapeutic pharmaceuticals [11].P-gp plays a role in the etiology of AD through the clearance of Aβ from the brain.Some drugs, such as rifampicin, dexamethasone, caffeine, verapamil, hyperforin, β-estradiol and pentylenetetrazole, were able to improve the efflux of Aβ from the cells via P-gp upregulation [12].Meanwhile, some compounds have been shown to reverse the P-gp mediated multidrug resistance (MDR), including verapamil, adriamycin, cyclosporin, and dexverapamil [13].Hartz et al. have shown that upregulating P-gp in the early stages of AD has the potential to increase Aβ clearance from the brain and reduce Aβ brain accumulation by a transgenic mouse model of AD (hAPP-overexpressing mice) [14].Abuznait et al. have also elucidated the impact of P-gp up-regulation on the clearance of Aβ [12], which indicated that targeting Aβ clearance via P-gp up-regulation was effective in slowing or halting the progression of AD and there was the possibility of P-gp as a potential therapeutic target for AD.
P-gp at the BBB functions as an active efflux pump by extruding a substrate from the brain, which is important for maintaining loco-regional homeostasis in the brain and protection against toxic compounds [8].P-gp is also discovered in various resistant tumor cells and expressed widely in many normal tissues and plays a very important role in drug ADME-Tox (absorption, distribution, metabolism, excretion, and toxicity).MDR is a matter of growing concern in chemotherapy.Cells which express the MDR phenotype can over-express efflux transporters after exposure to a single agent.As a result, these cells become resistant to the selective agent and cross-resistant to a broad spectrum of structurally and functionally dissimilar drugs.The drug efflux pump P-gp has been shown to promote MDR in tumors as well as to influence ADME properties of drug candidates [15].P-gp is expressed at the BBB, the blood-cerebrospinal fluid barrier, and the intestinal barrier, thus modulating the absorption and excretion of xenobiotics across these barriers.P-gp and its ligands (substrates and inhibitors) are therefore extensively studied both with respect to reversing MDR in tumors and for modifying ADME-Tox properties of drug candidates, such as CNS active agents [15].P-gp possesses broad substrate specificity and the substrates include members of many clinically important therapeutic drug classes, including anti-HIV protease inhibitors, calcium channel blockers used in the treatment of angina, hypertension, antibiotics and cancer chemotherapeutics [16].In this active efflux process, energy originating from ATP hydrolysis is directly consumed.Because of such a wide distribution of P-gp, if a drug such as quinidine or verapamil inhibits the function of P-gp, it will also inhibit the excretion of digoxin by P-gp's leading to increased plasma levels and toxicity due to digoxin.It is believed to be an important protective mechanism against environmental toxins.Since the function of P-gp always results in the lack of intracellular levels of the drug necessary for effective therapy, the overexpression of P-gp in certain malignant cells is always associated with MDR phenotype [17].Although a low resolution structure of P-gp is obtained, its physiological function and mechanisms of MDR modulation are still not very clear [18].It is well known that a large number of structurally and functionally diverse compounds act as substrates or modulators of P-gp, including calcium and sodium channel blockers, calmodulin antagonists and structural analogues, protein kinase C inhibitors, steroidal and structurally related compounds, indole alkaloids, cyclic peptides and macrolide compounds, flayanoids and miscellaneous compounds [19], which mostly share common structural features, such as aromatic ring structures and high lipophilicity.Some of them possess MDR reversing activity while only a small number of them have entered clinical study.Classification of candidate drugs as substrates or inhibitors of the carrier protein is crucial in drug development [20].
On the other hand, the prerequisite to cure neurological disorders is that the drug distribution in CNS can reach effectively therapeutic concentrations [2].Usually, the high BBB penetration is needed for drugs that activate in brain.The molecule negotiating the BBB must go through cellular membranes comprised of a lipid bilayer.Until now, it is widely accepted that interaction of compounds with P-gp is a complex process and at this time the details of its mechanism of action are still the subject of hot debate.Although the experimental analysis of drug permeability is essential, the procedure of experiment is time consuming and complicated, a theoretical model of drug permeability is effective to give predictions.Membrane-interaction (MI)-QSAR (quantitative structure-activity relationship) method is a structure-based design methodology combined with classic intramolecular QSAR analysis to model chemically and structurally diverse compounds interacting with cellular membranes.Our modified MI-QSAR method that combines QSAR with solute-membrane-water complex simulating the BBB environment is more close to the body condition than MI-QSAR and possesses higher ability to predict organic compounds across BBB [21].There are several critical assumptions considered that can influence validity and correctness of any QSAR study as follows: the same mechanism of action of all studied analogs; a comparable manner of their binding to the receptor; correlation of binding to the interaction energies; correlation of measured biological activities to the binding affinities [22].
All the accuracy answer and research based on the above questions above may guarantee that proper and reliable relationships are obtained.However, different mechanisms and different binding sites may be involved in the case of MDR modulators.Several screening assays can help in the identification of substrates and inhibitors although they have both advantages and drawbacks, such as cytotoxity assays [23], inhibition of efflux assays [16], P-gp-ATPase activation assays, and drug transport assays [24].
The goal of a QSAR study is to find a means of predicting the activity of a new compound.If possible, a desirable goal is the understanding of the biology and chemistry that give rise to that activity and the consequential possibility of reengineering the compound to remove or enhance that activity.One successful example is the transformation of nalidixic acid with the help of QSAR into an important family of drug: the quinolone carboxylates, such as norfloxacin, fleroxacin, ciprofloxacin, and levofloxacin [25].Since the method was established in the 1960s, QSAR equations have been used to describe the biological activities of thousands of different drugs and drug candidates [26].The method definitely provides a more accurate way to synthesize or filtrate the new chemical compounds.At last, the final destination is to degrade the cost of research and manufacture.To date, so many methods have been used in QSAR study and some of them have got successful results.There are general methods used in the literatures these years, such as multiple linear regression (MLR) method, partial least square regression (PLSR) [18], MI-QSAR analysis [21], 3D QSAR [27], and artificial neural network (ANN) [28].In order to get more accurate results and QSAR models, we have used two different analyses: MLR and PLSR.Moreover, we focus on constructing theoretical models of the interaction between organic compounds and P-gp as well as the predictive models of BBB partitioning of organic compounds on the basis of QSAR analysis and MI-QSAR analysis.

P-Glycoprotein Ligands
Building of some compounds.36 purine derivatives were selected and used in QSAR analysis (Table 1) [29].These compounds were divided into two sets: the training set and the test set.The study of the MDR-reversing properties of these derivatives was carried out in vitro on P388/VCR-20 cells, a murine leukemia cell line whose resistance was induced by vincristine (VCR), and KB-A1 cells, a human epidermoid carcinoma cell line whose resistance was induced by adriamycin (ADR).The compounds were tested at four concentrations (0.5 -5 μM) in association with VCR (P388/VCR-20 cells) or ADR (KB-A1 cells).In this test, MDR ratio in P388/VDR-20 and KB-A1 in vitro was used as biological activity for the whole dataset, namely Here "CD" is the abbreviation for cytotoxic drug (such as VCR and ADR) in cytotoxity assays, and "mod" means modulators.It is defined as ratio between the IC 50 values (concentration that inhibits the growth of MDR cells by 50%) of the cytotoxic agent in absence and presence of relatively nontoxic concentration of the modifier [23].
Most often the IC 50 for several concentration of a cytotoxic drug is evaluated in the presence and absence of a nontoxic concentration of a P-gp modifier.In this assay modulators that interacted with P-gp and thus reduced the efflux of the cytotoxic compounds would increase the apparent toxicity of the cytotoxic compound [16].The IC 50 data were based on a general assessment of cytotoxicity and thus might account for more then one acting mechanism in the resistant cells used [16].Furthermore, it is well known that the MDR ratio for any given compound can vary greatly depending on the cell type used for the assay as well as the intrinsic cytotoxicity of the compounds used.The data is also dependent on the concentration of the P-gp substrates or modulators used in the studies [30].
Similarly, another 21 propafenone analogs were selected from the literature of Diethart Schmid et al. and used in QSAR analysis (Table 2) [31].In this test Ka of P-gp ATPase in the adriamycin-resistant subline CCRF ADR5000 was used as biological activity for the whole dataset [31].The assays were performed based on the colorimetric determination of inorganic phosphate released by the hydrolysis of ATP.Table 2 shows all the structures and the experimental biological activity value.
Finally, all two-dimensional (2D) structures of these compounds mentioned above were constructed using the chemical drawing software ChemDraw 8.0 and prepared for the next calculation.
Calculation of some descriptors.Molecular descriptors are "numbers that characterize a specific aspect of the molecular structure" [32].There are some molecular descriptors used in QSAR studies as follows: physicochemical properties (i.e.hydrophobicity, aqueous solubility, molecular electronegativity, and molecular refractivity), quantum chemical parameters (e.g.atomic charges, energies of HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital)) [33], topological indexes (such as molecular connectivity indexes) [34], and other 3D descriptors.Molecular descriptors were mostly calculated by the commercial soft-   Index (WI)), thermodynamic parameters, including Henry's Law Constant (H), Hydration Energy (E hyd ), Logarithm of partition coefficient in n-octanol/water (LogP), Molar Refractivity (MR), and molecular polar surface area (PSA) that defined as the surface area (Å 2 ) occupied by polar atoms, usually oxygen, nitrogen and hydrogen attached to them, which will restrict molecule penetration into the membranes [2].The other properties involved in number of hydrogen bond acceptor (NBA) and number of hydrogen bond donor (NBD).

In vitro reversal fold reversion (MDR
The energy parameters root in the results of molecular mechanism and molecular dynamics.The total energy of a system expressed as follows [35]: E total = E valence + E crossterm + E nonbone .Here, the valence interactions includes bond stretching (bond), valence angle bending (angle), dihedral angle torsion (torsion), and inversion, also called out-of-plane interactions (oop) terms, which are part of nearly all forcefields for covalent systems.A Urey-Bradley term (UB) may be used to account for interactions between atom pairs involved in 1 -3 configurations (i.e., atoms bound to a common atom): E valence = E bond + E angle + E torsion + E oop + E UP .Modern (second-generation) forcefields generally achieve higher accuracy by including cross terms to account for such factors as bond or angle distortions caused by nearby atoms.Crossterms can include the following terms: stretch-stretch, stretch-bendstretch, bend-bend, torsion-stretch, torsion-bend-bend, bend-torsion-bend, stretch-torsion-stretch.The interaction energy between non-bonded atoms is accounted by van der Waals (VDW), electrostatic (Coulomb), and hydrogen bond (hbond) terms in some older forcefields.E non-bond = E VDW + E Coulomb + E hbond .Restraints that can be added to an energy expression include distance, angle, torsion, and inversion restraints.Restraints are useful for information on restraints and their implementation and use if you are interested in only part of a structure, and so is the documentation for the particular simulation engine.
These descriptors were calculated using Chemoffice Chem3D Ultra 8.0 and Hyperchem 7.5 as follows: 1) the structures of the compounds were drawn in ChemDraw 8.0 and sequentially changed to 3D structures by Chem3D; 2) the chosen compounds were minimized by molecular mechanism using MM2 force field with RMS (root mean square) gradient of 0.100; and 3) under the menu of Analyze-compute properties, the properties were selected to calculate and finally every descriptor value of each compound was gotten.
QSAR models.QSAR models of some purine derivatives (Table 1) were achieved by partial sum of squares for regression with software SPSS 10.0.A training set of 26 structurally diverse purine derivatives are measured is used to construct QSAR models.The QSAR models are optimized using MLR fitting and stepwise method (Eqs.1-5).A test set of five compounds is evaluated using the QSAR models as part of a validation process.Take MDR ratio in vitro in P388/VDR cell lines as dependent variable and molecule descriptors as independent variable.With the aid of Virtual Computational Chemistry Laboratory software [20], QSAR modeling was constructed by PLSR (Eq.6).
Similarly, a training set of 18 structurally diverse propafenone analogs (Table 2) are measured is used to construct QSAR models.The QSAR models are optimized using MLR fitting and stepwise method (Eqs.7-11).Another QSAR modeling was constructed by PLSR (Eq.12).A test set of five compounds is evaluated using the QSAR models as part of a validation process.

Blood-Brain-Barrier
Data. 37 organic compounds [36,37] were elected to compose a train set while another 8 organic compounds were acted as a test set (Table 3).The dependent variable is the logarithm of the BBB partition coefficient, log BB = log(C brain /C blood ), where C brain is the concentration of the test compound in the brain, and C blood is the concentration of the test compound in blood.Experimental values of logBB published to date lie approximately between −2.00 to +1.04.Compounds with logBB values of >0.30 are readily distributed to the brain whereas compounds with values <−1.00 are poorly distributed to the brain.Building of all these compounds was performed using the Build modules of Hyperchem 7.5.The geometry of these compounds was opitimized using the Amber 94 force field in gas state and sequentially placed at a periodic solvent box with a volume of 16 × 10 × 18 Å 3 , which included 96 water molecules.Here, temperature is 300˚K and pressure is 1 standard atmosphere.Then, the compounds in water were minimized by the above method and simulated by Monte Carlo method.
Molecular modeling of a dimyristoylphosphatidylcholine (DMPC) monolayer membrane complex with a layer of water.A model of DMPC monolayer membrane composed of 25 DMPC molecules (5 × 5 × 1) was constructed using Material Studio and minimized for 200 steps with the smart minimizer.Here, the parameter of the single crystal of DMPC with a = 8 Å, b = 8 Å, and γ = 96.0˚resulted in each lipid molecule with an average area of 64Å 2 similar to Stouch's research results [38].Moreover, a layer of water (40 × 40 × 10 Å 3 ) including 529 water molecules was added to the polar side of the DMPC monolayer membrane (Figure 1).
Molecular dynamic simulation of compound-DMPCwater complex models.A compound displaced a DMPC molecule in the DMPC monolayer membrane at three different positions (upper, center or lower) to form each solute-membrane-water complex.Molecular dynamic

RESULTS
simulation of the complex was performed for 1000 steps by Discover module with Materials Studios, using Compass force field.Here, the 3D volume was restricted to a border of X = 40 Å, Y = 40 Å, Z = 91.76Å, and γ = 96.0˚.

QSAR Analysis Based on MDR Ratio in P388/VDR-20 and KB-A1 in Vitro
MDR ratio of compounds in vitro in KB-A1/ADR cell lines was taken as the dependent variable.A training set of 26 compounds (Table 4) was used to construct QSAR models.The QSAR models were optimized using MLR fitting and stepwise method by SPSS (Eqs.1-5).A test set of 5 compounds (A27-A31) was evaluated using the models as part of a validation process (Figure 2 upper, Table 5).
QSAR model of BBB partitioning of some compounds.MI-QSAR model of a training set of 37 compounds through BBB were achieved by partial sum of squares for regression with SPSS.Molecular dynamics simulations were used to determine the explicit interaction of each compound with a model of DMPC monolayer membrane complexed with a layer of water.An additional set of intramolecular solute descriptors were computed and considered in the trial pool of descriptors for building MI-QSAR models.The MI-QSAR models were optimized using multidimensional linear regression fitting and stepwise method.The MI-QSAR models were then evaluated by a test set of 8 compounds.
Similarly, MDR ratio of compounds in vitro in P388/ VDR cell lines acted as the dependent variable.With the aid of Virtual Computational Chemistry Laboratory software (http://vcclab.org)[20], some QSAR models were constructed by PLSR (Eq.6, Figure 2 down).Table 6 shows the calculated descriptors mentioned above and

Predictive values of MDR ratio Predictive values of MDR ratio
No.

QSAR Analysis Based on Ka of ATPase in CCRF ADR5000 Cell Lines
On the other hand, 37 organic compounds of training set and 8 compounds of test set were built and minimized, dissolved in liquid, and optimized by Monte Carlo method.Molecular modeling of the compound-membrane-water complex model revealed that the energy of an organic compound inserted at the middle position in the DMPC model with a layer of water was lower than that of the other two positions.Molecular descriptors of compounds in a training set and a test set are listed in Table 9. Six QSAR equations were constructed based on Table 9 and were listed as follows.
Meanwhile, took Ka of ATPase of compounds in CCRF ADR5000 cell lines as dependent variable.Some QSAR models of a training set of 16 compounds were built using MLD method (Eqs.7-11) and PLSR method (Eq.12) (see Figure 3).All the molecular descriptors were listed in Table 7.A test set of 2 compounds was evaluated using the models as part of a validation process.Table 8 displays the comparison of the experiment Ka and prediction Ka values of ATPase.Note: a E total and E torsion mean the total energy and the torsion energy of the compound-DMPC-water complex; b ΔE total and ΔE torsion are the residues between the compound-DMPC-water complex and the DMPC-water complex.

OPEN ACCESS
and the torsion energy of the membrane-water complex are −340.7589and −1724.4164(Kcal/mol), respectively.ΔE total is the change in the total potential energy of the solute-membrane-water complex comparing with that of the membrane-water model and so is ΔE torsion .
With the increase of the independent variable, the relativity of QSAR model was also improved and its predictive ability was enhanced.The most significant Eq.18 displayed that the capability of a compound through BBB was directly proportional to ClogP and ΔE total , but inversely proportional to PSA, BI, E stretch , and ΔE torsion .Figure 4 showed the comparison of the experimental logBB with the corresponding predicted logBB of the molecules in the training set based on Eqs.17 and 18 models (see Table 10).Compound B18 was predicted with a higher logBB than observed, supported by the result of Iyer et al. [35].
The test set of 8 compounds to span almost the entire range in BBB partitioning was selected for validation of the QSAR models mentioned above.The observed and predicted logBB values for this test set were given in Table 10 and plotted in Figure 4 (right).It seemed to suggest that Eqs.17 and 18 models could predict logBB for other compounds in drug design.

DISCUSSION
Some predictive models of MDR, Ka and BBB partitioning of organic compounds were built by simulating the interaction between modulators or drugs and P-gp and/or the interreaction of the organic compound with the phospholipide-rich regions of cellular membranes.We have constructed theoretical models of the interaction between organic compounds and P-gp and compounds with the affinity for and simulation of the P-gp ATPase.On one hand, the interaction between compounds and P-gp (P-gp binding or MDR-reversal activity of compounds) is found to depend on LogP, LogMR, and ShA of compounds it transports, which proportional to Log MR whereas inversely proportional to LogP and ShA (see Eqs.1-5).Moreover, modulators or drugs interacting with P-gp and thus reducing the efflux of the cytotoxic compounds would increase the apparent toxicity of the cytotoxic compounds, which might account for more than one mechanism of action in the resistant cells used.There were many uncertainty factors in the MDR ratio assay method which was convinced by our linear  regression models.Our research results using two different statistic methods, MLR and PLSR, have revealed that the QSAR equation was also improved and the predictive ability of the models was enhanced with the increase of the variable.Eq.5 was built on KB-A1 cell line with a cytotoxic compound of 2.5 μM ADR while Eq.6 was based on P388/VDR-20 cell line with 1.5 μM VCR.Here, most of the models gave satisfactory cross-validated Q 2 above 0.500, conventional R above 0.800 and less SE values, indicating their proper predictive ability.Significant differences between values were examined using two-tailed paired T test provided by SPSS.All the results were considered not significant if P < 0.05.Eq.5 model was the most significant and indicated that the potential of P-gp modulators interacted with P-gp depended upon MR, BI, E hyd , ShA, and LogP.The former three displayed positive contributions to the MDR activity of P-gp, suggesting that the MDR activity increased accordingly with the increase of MR.The latter two displayed negative contribution to the MDR activity of P-gp.
On the other hand, our built models for Ka of ATPase based on the analogies of purine and propafenone analogs suggested that the enzyme hydrolysis of these compounds largely depended on LogP, MR, ShA, MW and E HOMO , especially positive related to MR but negative to LogP and ShA (see Eqs.7 to 11).Both models, Eq.11 by MLR and Eq.12 by PLSR, pointed out that E HOMO, positive related with the activity of P-gp ATPase, was an important parameter for the compound stimulated AT-Pase activity with high affinity, whereas another LogP was negative related with the activity of P-gp ATPase.Figure 3 showed that molecular A39 and A42 with higher Ka value of ATPase were depart from other compounds.This may be because they have lower lipophilicity, which is supported by the research results of Diethart Schmid et al. [31].The results above showed that the P-gp binding capacity of these compounds shares common characteristics with their ATPase hydrolysis, namely their hydrophobic parameters (such as logP) and steric parameters (e.g.MW, ShA, and MR).
In another aspect, our MI-QSAR models indicated that the distribution of organic molecules through BBB was not only influenced by organic solutes themselves, but also related to the properties of the solute-membranewater complex, namely interactions of the molecule with the phospholipide-rich regions of cellular membranes.The QSAR model, especially Eq.18 most significant, revealed that the capability of BBB partitioning of an organic compound focused on six significant features.Obviously, two descriptors, ClogP and ΔE total , had positive regression coefficients and the other four descriptors, PSA, BI, E stretch , and ΔE torsion , had negative regression coefficients.Moreover, PSA descriptor was found as a dominant descriptor in these QSAR models, which was related to the aqueous solubility of the solute compound along with a direct lipophilicity descriptor.When the value of PSA of a molecule lessened within the range from 0 to 108.80 Å 2 , its value of LogBB would increase.This was consistent with the experimental results that the more polarity it possessed, the more difficultly a molecule entered the hydrophobic environment of BBB [38].BI as the connective index of molecular average total distance pertained to the volume parameter.Our research result showed that a molecule more and more difficultly acrossed through BBB by diffusion with the addition of its bulk.However, the value of LogBB of a molecule increased with the increase of ClogP.It meaned that the hydrophobic molecule could pass through BBB more easily than the hydrophilic molecule does.The presence of E stretch descriptor suggested that with the decrease of the stretch-bend energy of a molecule, its value of LogBB increased.Two of the descriptors, ΔE total and ΔE torsion , found in the logBB QSAR models (Eqs.17 and 18), reflected the behavior of the solutes in the membrane and the entire membrane-solute complex.Along with the meaning mentioned, ΔE total was equivalent to the change in the average total potential energy between the ternary complex of solute-membrane-water and the binary complex of membrane-water.Similarly, ΔE torsion was the difference between the dihedral torsion energy of the ternary complex and that of the binary complex.Here, the more the change value of ΔE total was, the more its value of LogBB increased.This may be because small molecules across BBB membrane could lead to the change of the complex structure.The more changeability of the structure resulted in greater change of the total potential energy, while the addition of the energy change could be the important cause of the increase of the capability of a small molecule through BBB.On the contrary, the less the difference of the torsion energy was, the larger its LogBB value was.It displayed that a small molecule tight combined with the membrane-water complex could lead to the increase of its LogBB.Moreover, the relationship would suggest that the solute became more flexible within the membrane-water complex, which would possess the greater logBB value, in agreement with the research results of Iyer M et al. [35].Furthermore, BBB partitioning was mainly found to depend upon two parameters, namely PSA and ClogP, where the ability of organic molecules permeating across BBB was directly proportional to LogP but inversely proportional to PSA (see Eqs.13-18), which was consistent with the research results of Chen and co-worker [2], namely the increasing PSA decreased LogBB rapidly while LogP was positively related to LogBB.It indicated that molecules with higher lipophilic would be partitioned into the lipid bilayer more easily with more chances to penetrate BBB, sup-ported by the research result of Wang et al., namely a large number of structurally and functionally diverse compounds as substrates or modulators of P-gp mostly sharing common structural features, such as aromatic ring structures and high lipophilicity [19].PSA of CNS active drug should be lower than 90 Å 2 [2], while the penetration through the BBB is optimal for LogP value in the range 1.5 -2.7 (Norinder & Haeberlein, 2002).
In addition, several non-MI-QSAR computational models to describe and predict BBB partitioning have been reported that includes other descriptors besides PSA and ClogP [39].An alternative, complementary approach to BBB partitioning prediction uses MI-QSAR analysis developed by Iyer M et al. [35].Their research results showed that BBB partitioning of an organic compound depended upon PSA, CLogP, and the conformational flexibility of the compounds as well as the strength of their "binding" to the model biologic membrane.The MI-QSAR models indicated that BBB partitioning process could be reliably described for structurally diverse molecules and provided interactions of the molecule with the phospholipide-rich regions of cellular membranes.An extension of these approaches that combined QSAR with solute-membrane-water complex had been developed by us, which was addition of a layer of water on the hydrophilic side of DMPC monolayer membrane in order to simulate the truth BBB environment.Our results revealed that the distribution of organic molecules through BBB was not only influenced by the properties of organic solutes, but also related to the property of the solute-membrane-water complex.The former involved the polarity, hydrophobic, size, and conformational freedom degree of organic molecules, while the latter dealt with the strength of an organic molecule combined with BBB membrane and the structural changeability of a solutemembrane-water complex.Furthermore, the capability of a small molecule across BBB was mainly related to four physicochemical factors, which depended on the relative polarity of a small molecule (namely PSA and ClogP), the molecular volume (i.e.BI), the strength of a small molecule combined with DMPC-water model (viz.ΔE torsion ), and the changeability of the structure of a solute-membrane-water complex (scilicent ΔE total ).The QSAR model showed that the less polarity and more hydrophobic molecules relatively easily passed through BBB and entered brain to cure.The reason for the change of the total energy was that small molecules across BBB membrane caused the structural change of the solute-membrane-water complex.The more the changeability of the complex structure was, the more the change value of its total energy was, and the more easily a small molecule penetrated BBB.
In particular, cerebral clearance of Aβ was considered to occur via elimination across BBB, as well as prote-olytic degradation.Attenuation of its elimination was likely to result in the increase of cerebral Aβ deposition, which may facilitate progression of AD [40].P-gp detoxified cells by exporting hundreds of chemically unrelated toxins but had been implicated in MDR in the treatment of cancers.Substrate promiscuity was a hallmark of P-gp activity, thus a structural description of poly-specific drug-binding was important for the rational design of anti-amyloid accumulation drugs, anticancer drugs and MDR inhibitors.The x-ray structure of apo P-gp at 3.8 angstroms revealed an internal cavity of approximately 6000 Å 3 with a 30 Å separation of the two nucleotide-binding domains.Two additional P-gp structures with cyclic peptide inhibitors demonstrated distinct drug-binding sites in the internal cavity capable of stereoselectivity that was based on hydrophobic and aromatic interactions.Apo and drug-bound P-gp structures had portals open to the cytoplasm and the inner leaflet of the lipid bilayer for drug entry.The inward-facing conformation represented an initial stage of the transport cycle that was competent for drug binding [41].Currently, P-gp was identificated as an energy-dependent pump, whereas ATPase activity as an assay in itself was possibly problematical because the assay was based upon one assumption that drug-induced ATP hydrolysis reflects transport by the transporter [16].There may be many ways in which this activity could be altered, including direct action on the ATP binding domain.Scientists once observed some compounds such as daunomycin and vinblastine inhibit ATPase activity, but increase in others, suggesting that modulation of ATPase activity was highly dependent on experimental conditions and may not correlate well with the ability of P-gp to transport the drug [42][43][44].The work of Litman et al. was one of the few studies suggesting that affinity between drugs and ATPase activity has no correlation to LogP, but Surface Area [45].Because of the less comparability of molecular structures in a training set, our QSAR model possessed more universal significance.However, the precision of the QSAR models was so low that there was still a distance to its application.So a series of organic compounds with similar structures are chosen and consist of a training set, thus the precision of QSAR simulation will be largely increased, while the prediction of the analogues through BBB will be greatly improved.

CONCLUSIONS
The pathogenesis of AD is characterized by the aggregation of Aβ into neurotoxic plaques.P-gp is involved in MDR and in neurodegenerative disorders such as PD, AD and epilepsy.P-gp mediates the efflux of Aβ from the brain as well as mediates MDR, while P-gp transports neutral or positively-charged hydrophobic sub-strates with consuming energy from ATP hydrolysis.In comparison with the ability of organic molecules permeating across BBB, P-gp binding or MDR-reversal activity of compounds has a negative correlation with LogP.Moreover, P-gp binding or MDR-reversal activity of compounds is mainly proportional to LogMR (Eqs.1 to 5) but inversely proportional to LogP (Eqs.4 and 5).Similarly, ATPase activity of these compounds was largely negatively related to LogP (Eqs.7 to 12) but positively related to MR (Eqs.9 to 11), where most compounds are with logP value more than 2.7.This showed that the P-gp binding capacity of these compounds shared common characteristics with their ATPase hydrolysis, namely their hydrophobic parameters (i.e.logP) and steric parameters (e.g.MR).Additionally, the distribution of organic molecules through BBB was not only influenced by organic solutes themselves, but also related to the properties of the solute-membrane water complex, namely interactions of the molecule with the phospholipide-rich regions of cellular membranes.The ability of organic molecules permeating across BBB was mostly proportional to LogP (Eqs.14 to 18) but inversely proportional to PSA (Eqs.13 to 18), which is consistent with the research results of Chen and co-workers [2], namely the increasing PSA decreased LogBB rapidly while LogP positively related to LogBB.Chen et al. have indicated that the optimum logP for designing CNS active drug was about 2.9 and the compound with LogP lower than 2.9 had a positive correlation with logBB, but the compound with logP bigger than 2.9 made an unfavorable contribution [2].It is disclosed that molecules with higher lipophilic would be partitioned into the lipid bilayer more easily with more chances to penetrate BBB, supported by the research result of Wang et al., namely a large number of structurally and functionally diverse compounds as substrates or modulators of P-gp mostly share common structural features, such as aromatic ring structures and high lipophilicity [19].The LogP not only offered opportunity to penetrate the lipid bilayer, but also gave favorable contribution to binding with P-gp or P450.There may be two reasons for this phenomenon.Firstly, the compounds with higher liposolubility are more vulnerable to cytochrome P450 metabolism, leading to faster clearance [46].P450 enzymes catalyze the metabolism of a wide variety of endogenous and exogenous compounds including xenobiotics, drugs, environmental toxins, steroids, and fatty acids.Aminated thioxanthones have recently been reported as P-gp inhibitors as well as its interaction with cytochrome P450 3A4 (CYP3A4), as many substrates of P-gp and CYP3A4 are common [47], which could be a major cause of P-gp binding or MDRreversal activity of compounds inversely proportional to LogP.The second reason was related to the mechanism of P-gp action.According to the model proposed by Higgins and Gottesman [48], after entering into the phospholipid bilayer, compound may interact with P-gp in the inner leaflet of the lipid bilayer.Upon interaction with P-gp, the compound was flipped from the inner leaflet to the outer leaflet of the lipid bilayer.The lipophilic compounds with high LogP entered into cellular membrane easily and intended to retain there, so its opportunity to interact with P-gp increased and then its opportunity to be pumped out of cells enhanced.
In conclusion, the predictive model of BBB partitioning of organic compounds contributed to the discovery of potential AD therapeutic drugs.Moreover, the interaction model of P-gp and modulators for the treatment of multidrug resistance indicates the discovery of some molecules to increase Aβ clearance from the brain and reduce Aβ brain accumulation by regulating BBB P-gp in the early stages of AD.Because P-gp is a transporter whose ligands are almost exclusively small molecules, it is not surprising that the pump itself is unable to transport Aβ.Nazer and co-worker have indicated the nonproteolytic clearance of Aβ via receptor-mediated transport across the BBB and investigated P-gp and the lowdensity lipoprotein receptor-related protein (LRP) involving Aβ efflux across the BBB [49].Nevertheless, LRP or P-gp alone was insufficient for non-proteolytic transcytosis of intact Aβ.LRP in transcytosing intact Aβ across the BBB may require a co-transporter, such as P-gp [49].Elucidation of the molecular mechanisms of the potential of LRP and P-gp to efflux cortical Aβ across BBB should help to promote rational therapeutic strategy in AD.

Figure 1 .
Figure 1.Compound B1 colored by atom-type in water and the solvent box defined in Monte Carlo simulation.

Figure 2 .
Figure 2. Comparison of the experimental MDR values with the corresponding predicted MDR values.Upper: MDR value in KB-A1/ADR cell lines (blue rhombic dots); MDR as predicted by Eq.4 MLR model (red square dots) and by Eq.5 MLR model (yellow triangle dots) for all the molecules of the training and test set.Down: MDR value in P388/VDR cell lines (blue rhombic dots); MDR as predicted by the method of PLSR (Eq.6) (red square dots) for all the molecules of the training and test set.The rhombic dots represented the experimental values (P388) and the predicted values of MDR, respectively.

Figure 3 .
Figure 3.Comparison of the experimental Ka value (blue rhombic dots) with the corresponding predicted Ka as predicted by Eq.11 MLR model (red square dats) and by Eq.12 PLSR model (yellow triangle dots) for all the molecules of the training and test.

Figure 4 .
Figure 4. Comparison of the experimental logBB values (blue rhombic dots) for all the molecules of the training sets (upper) or the test set (down) to the corresponding predicted logBB as predicted by Eq.17 MI-QSAR model (red square dots) and by Eq.18 MI-QSAR model (yellow triangle dots).

Table 1 .
The structures and MDR ratios of 35 purine derivatives in the training/test sets.

Table 2 .
The structures and Ka values and LogP of 18 propafenone analogs in the training/test sets.

Table 3 .
The structures and LogBB values of some compounds in the training/test sets.

Table 4 .
The molecular descriptors of some compounds related to MDR ratios in the training/test sets.

Table 5 .
The experimental values and the predictive values of MDR ratio of these compounds.

Table 6 .
Comparison of experimental value of MDR ratio with predicted value of MDR ratio by PLSR.

Table 7 .
The molecular descriptors of some compounds related to ATPase in the training/test sets.

Table 8 .
Comparison the experimental values with the predictive values of Ka of these compounds.

Table 9 .
The molecular descriptors of the compounds related to BBB in the training/test sets.

Table 10 .
The experimental values and the predictive values of Log BB of these compounds.