Blood Brain Barrier and Alzheimer’s Disease: Similarity and Dissimilarity of Molecular Alerts

Abstract

Background

Blood brain barrier and Alzheimer’s disease are interrelated. This interrelation is detected by physicochemical methods, pharmacological and electrophysiological analyses. Nature of the phenomenon is extremely complex. The description of this interrelation in mathematical terms is a very important task.

Objective

The systematization of facts, which are described in the literature and related to interaction between processes, which influence Alzheimer's disease and blood brain barrier is the subject of this work. In addition, establishing of correlations between molecular features and endpoints, which are related to the treatment of Alzheimer's disease and blood brain barrier using the CORAL software are subjects of this work.

Methods

The information on logically structured analysis is available in the literature and building up quantitative structure – activity relationships (QSARs) by the Monte Carlo method has been used to solve the task of systematization of facts related to the “treatment of Alzheimer's disease vs. blood brain barrier”.

Results

Comparison of agreements and disagreements of the available published papers together with the statistical quality of built up QSARs are results of this work.

Conclusion

The facts from published papers and technical details of QSAR built up in this study give possibility to formulate the following rules: (i) there are molecular alerts, which are promoters to increase blood brain barrier and therapeutic activity of anti-Alzheimer disease agents; (ii) there are molecular alerts, which contradict each other.

1. INTRODUCTION

Alzheimer’s disease is a disorder of the central nervous system accompanied by memory deterioration, and progressive impairment of daily life activities. Aging of an organism is a biochemical process. Therefore, the injection of chemicals can influence this process. The blood-brain barrier is a major factor hindering the development of neurotherapeutics. Experimental methods of Blood Brain Barrier permeation determination as well as experimental definition of many other biomedical endpoints are cumbersome and expensive. Under such circumstances, computational approaches for the prediction of biomedical endpoints, in general, and computational methods for prediction of Blood Brain Barrier permeation, in particular are attractive alternatives of the direct experiment. Currently, there is no cure for Alzheimer's disease [1].

Being the most common form of dementia, Alzheimer’s disease is currently affecting over 5.5 million people in the United States and more than 35 million worldwide [2, 3]. The hallmark of the disease is progressive cognitive decline that results in loss of language skills, difficulty in learning, loss of memory, and alterations in personality and mood [4-6].

There are some circumstances, which indicate the possible interrelation between processes related to Alzheimer’s disease and Blood Brain Barrier [7-9]. It has been noticed that breakdown of the Blood Brain Barrier is a particularly important development in Alzheimer’s disease progression [10-12].

According to the listed circumstances, the attractive paradigm to search agents versus Alzheimer’s disease can be represented by scheme illustrated in Fig. (1). It is important to note that there are logical implications and interrelation between all the mentioned components of the paradigm.

Fig. (1).

Possible scheme to design agents versus Alzheimer’s disease.

2. ONTOLOGY

The information about the interaction between the elements of phenomena represented in Fig. (1) is very complex and unclear owing to dynamical and combinatorial aspects. The methods to represent this information in a format, which is convenient for understanding, should be regarded as methods of critical importance. One of the possible ways to construct a method of the above mentioned quality is the analysis of molecular alerts (features) able to influence the blood brain barrier and likely able to suggest the perspective list of molecular features valuable from the point of view of drug discovery oriented to define a group of agents versus Alzheimer’s disease.

2.1. Task Definition: Interrelation Between Blood Brain Barrier and Alzheimer’s Disease

Much of the underlying biology leading to Alzheimer’s disease is unknown. Popular etiologic hypotheses have largely ignored the blood brain barrier as an important factor contributing to the pathologic hallmarks of this most common form of dementia. However, evidence identifying blood brain barrier dysfunction in Alzheimer’s disease continues to escalate [13].

Normal ageing and Alzheimer's disease have many common features. In many ways, both conditions only differ by quantitative criteria. A variety of genetic, medical and environmental factors modulate the ageing-related processes leading to Alzheimer’s disease. Thus, Alzheimer's disease is a metabolic disease [14]. The pathophysiological influence of microelements, including aluminum and iron, is highly controversial; at any rate, they may adversely affect of Alzheimer's disease progress [14].

The application of gene transfer (i.e. macromolecular sequences of amino acids) can also be used to augment existing or provide new functions to cells in the hope that this will be of therapeutic benefit [15].

The Blood Brain Barrier is a dynamic and complex interface between the blood and the central nervous system regulating brain homeostasis. Major functions of the Blood Brain Barrier include the transport of nutrients and protection of the brain from toxic compounds. The nutrition of the brain involves small molecules like sugars, amino acids, vitamins, and trace elements. Large biomolecules, lipoproteins, peptide and protein hormones cross the Blood Brain Barrier by receptor-mediated transport [16]. Dysfunction in the transport of nutrients at the Blood Brain Barrier is described in several neurological disorders and diseases. The Blood Brain Barrier penetration of neuroprotective nutrients, especially the potential protective effect of polyphenols and alkaloids, on brain endothelium is well-known [16, 17].

Thus, the search for molecular features (fragments, 3D-isomerism, intramolecular and intermolecular quantum mechanical conditions) with apparent influence to blood brain barrier and destructed fragments of neurons can be a perspective for drug discovery.

2.2. Molecular Features which Influence to Blood Brain Barrier

Mechanistic interpretation for QSAR related to blood brain barrier usually based on physicochemical conditions such as octanol/water partition coefficient, isolated atomic energy [18], H-bond donor surface area, H-acceptor surface area [19], Rotatable bonds count, Hydrogen bond acceptor count [20]. There is influence of the presence of heavy atoms on the blood brain barrier and central nervous system [17]. The binding energy predictions were highly correlated with r²=0.88, F=692.4, standard error of estimate =0.775, for selected blood brain barrier active/inactive compounds (n=93) [17].

Inhibition of efflux pumps present at the blood brain barrier by nutraceuticals and plant compounds can be carried out with a number of organic compounds such as Apigenin, Berbamine, Catechin, Chrysin, Rutin, etc. [16]. The rings are common attributes of these biologically active compounds [16]. Thus the six-membered rings are of molecular feature with influence on the blood brain barrier and central nervous system [16]. Presence of nitrogen in rings and size of linear molecular fragment connecting a couple of rings is also a molecular alert related to blood brain barrier [21].

2.3. Molecular Features which Influence the Alzheimer's Disease

Mechanistic interpretation for QSAR related to Alzheimer’s disease is usually based on physicochemical and biochemical conditions, such as molecular weight, total polar surface area hydrophilicity, absorption rate constants, etc., without molecular alerts [22]. However, modifiers of pharmacokinetics effects include molecular images such as 2-propan-water, acetone-water and the number of carbon atoms [22]. Chlorine and oxygen connected to six-membered rings, triple covalent bonds, as well as 3D-conformations can also be examined as structural alerts related to endpoints interrelated to Alzheimer’s disease [23]. Finally, groups of five-membered and six-membered rings involve oxygen and nitrogen respectively, aspotential agents for treating Alzheimer’s disease [24].

3. QSAR MODELS

3.1. Data

The binding affinity data (IC50 nM converted into negative decimal logarithm pIC50= -log₁₀IC50) of 233 gamma-secretase inhibitors (potential agents for treatment Alzheimer’s disease) are studied in the literature [25, 26]. The database for Blood brain barrier permeation (logBB) values for 291 substances is available from the literature [27].

3.2. Optimal Descriptor

A model for biological activity is building up as one-variable correlation

$$\mathit{Activity}=C_0+C_1\times \mathit{DCW}\left(T^{\text{∗}},N^{\text{∗}}\right)$$ (1)

The C₀ and C₁ are regression coefficients (intercept and slope) calculated with the Least squares method. “T” is threshold to define rare features extracted from SMILES. For instance, if T=3, all features which have prevalence less than 3 in the training set are considered as rare. The rare features are not used to build up a model (their correlation weights are zero). N is the number of epochs of the Monte Carlo optimization for correlation weights of molecular features involved in the modelling process. The T* and N* are values of the T and N which give the best statistical characteristics for model calculated with Eq. 1 for the calibration set.

The optimal descriptor of correlation weights (DCW) of different molecular features extracted from simplified molecular input-line entry system (SMILES) [28] and from molecular graph:

$$\mathit{DCW}\left(T^{\text{∗}},N^{\text{∗}}\right)=\mathit{DC}{W}_{\mathit{graph}}\left(T^{\text{∗}},N^{\text{∗}}\right)+\mathit{DC}{W}_{\mathit{SMILES}}\left(T^{\text{∗}},N^{\text{∗}}\right)$$ (2)

where

$$\mathit{DC}{W}_{\mathit{SMILES}}\left(T^{\text{∗}},N^{\text{∗}}\right)=\mathit{CW}\left(\mathit{HARD}\right)+\sum \mathit{CW}\left(S_k\right)+\sum \mathit{CW}\left(S{S}_k\right)$$ (3)

$$\mathit{DC}{W}_{\mathit{graph}}\left(T^{\text{∗}},N^{\text{∗}}\right)=\mathit{CW}\left(\mathit{C3}\right)+\mathit{CW}(\mathit{C4})+\mathit{CW}(\mathit{C5})+\mathit{CW}(\mathit{C6})+\mathit{CW}(\mathit{C7})$$ (4)

Twelve symbols for registration of molecular features extracted from SMILES are reserved in the program for possible modifications in the future.

Example of the molecular features extracted from SMILES and represented by twelve symbols is shown in Table 1. The C3 – C7 are situations in a molecular system related to the presence (absence) of three-membered, four-membered, five-membered, six-membered and seven-membered rings. Table 2 represents general scheme of the representation of different situations related to rings by twelve symbols.

Table 1.

Examples of representation of SMILES attributes by means of twelve symbols [SMILES = “NC(SCCF)=N” ].

ID	Comment	1	2	3	4	5	6	7	8	9	10	11	12
1	Representation of Sk	N	.	.	.	.	.	.	.	.	.	.	.
		C	.	.	.	.	.	.	.	.	.	.	.
		(*	.	.	.	.	.	.	.	.	.	.	.
		S	.	.	.	.	.	.	.	.	.	.	.
		C	.	.	.	.	.	.	.	.	.	.	.
		C	.	.	.	.	.	.	.	.	.	.	.
		F	.	.	.	.	.	.	.	.	.	.	.
		(	.	.	.	.	.	.	.	.	.	.	.
		=	.	.	.	.	.	.	.	.	.	.	.
		N	.	.	.	.	.	.	.	.	.	.	.
2	Representation of SSk	N	.	.	.	C	.	.	.	.	.	.	.
		C	.	.	.	(	.	.	.	.	.	.	.
		S	.	.	.	(	.	.	.	.	.	.	.
		S	.	.	.	C	.	.	.	.	.	.	.
		C	.	.	.	C	.	.	.	.	.	.	.
		F	.	.	.	C	.	.	.	.	.	.	.
		F	.	.	.	(	.	.	.	.	.	.	.
		=	.	.	.	(	.	.	.	.	.	.	.
		N	.	.	.	=	.	.	.	.	.	.	.
			=	#	@	N	O	S	P	F	Cl	Br	I
3	Definition of HARD attribute	$	1	0	0	1	0	1	0	1	0	0	0

^*)Brackets are the representation of molecular branching and used only “without”.

Table 2.

Definition of SMILES attributes related to the presence of rings.

	1	2	3	4	5	6	7	8	9	10	11	12
Ring status	C	x	.	.	.	a	h	.	y	.	.	.

The CW(x) is the correlation weights for a molecular feature x. The correlation weights are calculated with the Monte Carlo method optimization. The CORAL software is available for the calculations [29]. The optimal correlation weights give maximal correlation coefficient value between experimental and predicted activity for the training set. The predictive potential of the model should be checked up with external validation set [29]. The detailed description of the CORAL software is available on the Internet (http://www.insilico.eu/coral).

3.4. Predictive Models Built up with the CORAL Software

Three different splits into the training and validation set were studied for the binding affinity data on gamma-secretase inhibitors (pIC50), and were also studied for Blood brain barrier permeation (logBB). It is to be noted that the training set for the CORAL models is structured into training, invisible and calibration sets [30, 31].

Computational experiments have shown that efficacy of the “training” can be improved by means of special set which permanently checks the absence of overtraining. This set can be named as “passive training set” or “invisible training set”.

In other words, there are two ways to use a “total” training set to build up correlation “descriptor - endpoint”:

Traditional scheme: all compounds of the total training set are taken into the Monte Carlo optimization process. Result will be the maximal correlation coefficient between optimal descriptor and endpoint for all total training set.

Balance of correlations: The first half of the total training set is involved in the Monte Carlo optimization process. However, second half is not involved in the process. In this case, the result will be maximal correlation coefficient between the optimal descriptor and endpoint for the first half of compounds, whereas second half of compounds will give hint whether the correlation is objective or this correlation is preferable solely for the first active half of compounds.

Thus, the balance of correlation is building up a QSAR model with the following participants:

1. The training set is “builder of the model”;

2. The invisible training set is the “inspector of the model”; the inspector must detect and stop the process of the overtraining;

3. The calibration set is an expert; the expert must declare, “Model is ready”;

4. The validation set is the appraiser of real predictive potential of the model.

The advantage to this approach is the possibility of building up a model solely from 2D data on the molecular structure represented by SMILES with the interpretation of influence of different molecular features extracted from SMILES. However, there are some disadvantages of the approach. In particular, the Monte Carlo optimization is not a fast calculation especially for large datasets. In addition, some of the SMILES fragments do not have transparent physical meaning (e.g. symbols “[“, “@”, dots, etc.).

The x is the size of rings i.e. x=3, 4, 5, 6, 7; If there are aromatic rings then a=’A’, otherwise a=’.’; If there are heteroatoms in rings then h=’H’, otherwise h=‘.’; The y is the number of rings i.e. y=0, 1, 2, …

The models, which were built up with the balance of correlations, are as follows:

Binding Affinity of Gamma-secretase Inhibitors (Potential Agents for Treatment Alzheimer’s Disease)

Split 1

pIC₅₀ = 1.2942501 (± 0.0382248) + 0.1606057 (± 0.0009709) * DCW(1,15) (5)

n=62, r²=0.8258, RMSE=0.623, F=284 (training set)

n=71, r²=0.6856, RMSE=0.727 (invisible training set)

n=51, r²=0.6810, RMSE=0.751 (calibration set)

n=49, r²=0.7752, RMSE=0.733 (validation set)

Split 2

pIC₅₀ = 3.2737064 (± 0.0326601) + 0.1974723 (± 0.0013567) * DCW(1,15) (6)

n=66, r²=0.7711, RMSE=0.694, F=216 (training set)

n=67, r²=0.7702, RMSE=0.703 (invisible training set)

n=50, r²=0.7258, RMSE=0.718 (calibration set)

n=50, r²=0.7676, RMSE=0.645 (validation set)

Split 3

pIC₅₀ = 2.1408654 (± 0.0416128) + 0.1757965 (± 0.0012683) * DCW(1,15) (7)

n=61, r²=0.7725, RMSE=0.665, F=200 (training set)

n=63, r²=0.7724, RMSE=0.756 (invisible training set)

n=55, r²=0.7610, RMSE=1.11 (calibration set)

n=54, r²=0.7753, RMSE=0.882 (validation set)

Blood Brain Barrier Permeation (logBB)

Split 1

Log(BB) = -0.8609358 (± 0.0066439) + 0.0537248 (± 0.0003448) * DCW(1,15) (8)

n=101, r²=0.7438, RMSE=0.286, F=287 (training set)

n=104, r²=0.7540, RMSE=0.331 (invisible training set)

n=43, r²=0.9141, RMSE=0.198 (calibration set)

n=43, r²=0.8592, RMSE=0.240 (validation set)

Split 2

Log(BB) = -0.9164493 (± 0.0072757) + 0.0385240 (± 0.0002497) * DCW(1,10) (9)

n=103, r²=0.6830, RMSE=0.350, F=218 (training set)

n=107, r²=0.6828, RMSE=0.330 (invisible training set)

n=41, r²=0.8350, RMSE=0.229 (calibration set)

n=40, r²=0.8310, RMSE=0.319 (validation set)

Split 3

Log(BB) = -0.5038388 (± 0.0053701) + 0.0231569 (± 0.0001622) * DCW(1,10) (10)

n=104, r²=0.6388, RMSE=0.359, F=180 (training set)

n=105, r²=0.6477, RMSE=0.389 (invisible training set)

n=41, r²=0.8344, RMSE=0.275 (calibration set)

n=41, r²=0.7273, RMSE=0.274 (validation set)

3.5. Molecular Features which Influence the pIC50 and logBB Extracted from Coral-models

Table 3 contains correlation weights of different molecular features obtained in three runs of the Monte Carlo method

Table 3.

Lists of stable promoter of increase (all correlation weights are positive) or decrease (all correlation weights are negative) for pIC50 and logBB.

No.		Feature, F	CW(F) Run 1		CW(F) Run 2		CW(F) Run 3		Training Set		Invisible Training Set		Calibration Set
		pIC50, split 1
1		1...........	0.24936		0.81527		1.00426		62		71		51
2		O...(.......	1.81598		2.00425		2.94093		62		71		51
3		O...=.......	0.62907		0.75437		1.18718		62		71		51
4		C3......0...	1.74618		3.12552		2.49983		60		71		51
5		C4......0...	3.12573		4.43867		1.99580		60		71		51
6		C...(.......	0.68970		0.62551		0.25068		59		62		43
7		C...1.......	1.37112		1.12572		1.43837		59		61		43
8		c...(.......	1.25445		1.43762		1.37518		57		63		46
9		c...1.......	0.37510		0.68855		0.24748		55		65		47
10		N...(.......	0.43569		0.12723		0.12950		50		54		38
11		1...(.......	0.62013		0.37156		0.50154		41		46		28
12		N...C.......	0.74564		0.93512		0.62564		41		43		29
13		S...........	1.87883		1.44122		2.56649		40		43		33
14		[...C.......	2.87716		1.68980		1.75250		38		34		25
15		F...........	0.68765		0.74914		0.37233		37		38		28
16		C5......0...	4.87431		4.87313		3.87512		36		40		31
1		(...........	-0.50046		-0.62885		-0.05899		62		71		51
2		=...(.......	-0.37242		-0.24593		-0.56678		62		69		51
3		=...........	-2.24798		-1.12583		-2.05997		62		71		51
4		C...........	-0.56673		-0.56218		-0.50032		62		71		51
5		c...........	-0.06497		-0.18722		-0.31242		62		71		51
6		c...c.......	-0.56687		-0.49790		-0.81516		62		71		51
7		N...........	-0.68973		-1.12750		-0.68769		54		62		41
8		(...(.......	-0.74772		-1.12089		-1.81062		39		44		34
9		[...H.......	-1.56676		-1.25190		-0.31208		38		34		25
10		Cl..(.......	-0.24951		-0.56565		-0.62721		35		27		26
11		C...=.......	-2.37058		-2.74693		-3.44246		26		30		14
12		H...@@......	-1.06063		-0.37158		-1.43490		21		21		13
13		[...@.......	-2.31200		-2.81686		-1.50485		19		11		9
14		=...1.......	-1.31479		-1.74616		-1.00456		9		15		10
15		[...N.......	-0.43407		-2.19238		-1.93745		9		12		6
16		C6...AH.4...	-3.74966		-2.99712		-2.99987		8		6		5
No.	Feature, F			CW(F) Run 1		CW(F) Run 2		CW(F) Run 3		Training Set		Invisible Training Set	Calibration Set
	pIC50, split 2
1	1...........			0.37791		0.75136		0.50087		66		67	50
2	O...........			1.93510		2.31473		1.06252		66		67	50
3	C...(.......			0.06720		0.43483		0.62375		61		61	45
4	C...1.......			1.56744		1.62065		1.75150		61		58	43
5	c...(.......			1.56080		1.18804		1.75301		60		60	46
6	N...(.......			0.50498		0.62805		0.43364		54		49	36
7	C...C.......			0.37205		0.62336		0.37277		51		58	42
8	2...........			0.43523		0.56398		0.12820		45		51	32
9	C5......0...			6.00472		5.99545		6.25140		43		36	34
10	N...C.......			1.37968		1.68793		1.87623		39		41	27
11	[...C.......			0.12456		0.49768		1.80975		37		38	23
12	[...H.......			1.62581		0.69162		1.00379		37		38	23
13	c...2.......			0.99918		0.56194		1.12751		35		36	24
14	F...........			0.49877		0.44089		1.30846		34		37	28
15	F...(.......			0.62920		0.69236		0.37820		33		35	27
16	S...........			3.12476		2.87269		3.37296		33		43	31
1	(...........			-0.55900		-0.55795		-1.06147		66		67	50
2	=...........			-0.31255		-1.99752		-1.87560		66		67	50
3	C...........			-0.24649		-0.62194		-0.37101		66		67	50
4	C3......0...			-4.12984		-4.74520		-3.49783		66		66	49
5	c...........			-0.43299		-0.12822		-0.37044		66		67	50
6	c...c.......			-0.56748		-0.50425		-0.99606		66		67	50
7	N...........			-1.25121		-1.12588		-1.00118		57		60	39
8	H...........			-1.37596		-0.25167		-1.18672		37		38	23
9	c...C.......			-0.37586		-0.37213		-0.49682		37		38	25
10	[...(.......			-1.37164		-1.62892		-0.87345		35		35	22
11	(...(.......			-1.00341		-1.05836		-0.99682		32		44	32
12	C...=.......			-1.87617		-0.49606		-0.87942		26		28	23
13	C...@@......			-1.93993		-0.24818		-0.05935		23		21	15
14	[...1.......			-0.25399		-0.87790		-0.06226		22		25	17
15	$10011100100			-1.24578		-1.56069		-1.81534		13		10	7
16	C7...A..1...			-0.24768		-1.18849		-0.62114		11		21	10
	pIC50, split 3
1	1...........			0.80782		0.12046		1.00472		61		63	55
2	=...(.......			0.80859		0.43861		1.24558		61		63	53
3	O...(.......			2.81151		2.62129		2.31681		61		63	55
No.	Feature, F			CW(F) Run 1		CW(F) Run 2		CW(F) Run 3		Training Set		Invisible Training Set	Calibration Set
	pIC50, split 3
4	O...=.......			0.93514		1.43913		0.68355		61		63	55
5	c...........			0.06327		0.00247		0.12191		61		63	55
6	C...1.......			0.81487		1.06109		1.12812		58		60	46
7	c...(.......			0.68932		0.75280		0.93721		57		59	47
8	c...1.......			0.06090		0.30887		0.37182		53		58	51
9	N...(.......			0.37516		0.87510		1.68538		50		48	43
10	2...........			0.94011		1.18721		1.05999		48		43	36
11	[...C.......			1.18350		0.74643		1.12063		39		35	26
12	N...C.......			1.25462		1.31352		1.62911		37		42	33
13	S...........			1.24827		2.00081		0.93984		36		39	36
14	C5......0...			3.43701		5.50479		6.44186		35		37	34
15	F...(.......			1.12015		0.55846		1.12187		35		33	27
16	S...(.......			1.99622		1.55892		1.68773		33		37	34
1	(...........			-0.37339		-0.06365		-0.62191		61		63	55
2	=...........			-1.62730		-2.31258		-2.12289		61		63	55
3	C...........			-0.37397		-0.69070		-0.56000		61		63	55
4	c...c.......			-0.62350		-0.50475		-1.12573		61		63	55
5	N...........			-1.12086		-1.31212		-2.06263		54		53	48
6	C...C.......			-0.24581		-0.06071		-0.37304		48		47	46
7	[...H.......			-0.44110		-0.30958		-1.24568		39		35	26
8	@@..........			-0.87191		-0.19206		-0.62280		30		20	14
9	C...=.......			-1.75324		-1.80866		-1.87391		28		25	22
10	[...1.......			-0.12014		-0.56717		-0.31449		24		22	18
11	[...@.......			-2.05908		-1.00253		-0.12596		16		10	13
12	C7...A..1...			-1.06160		-1.43859		-0.62483		15		16	14
13	$10011100100			-0.62031		-0.25133		-2.50400		9		12	7
14	[...2.......			-1.31346		-1.43451		-0.75249		9		8	7
15	C6...AH.4...			-0.94103		-2.06365		-1.55992		8		7	7
16	S...C.......			-1.12210		-1.62776		-1.19212		8		1	1
	LogBB, split 1
1	C...........			0.69000		0.44177		0.44099		101		102	42
2	C4......0...			1.44233		1.93619		0.87009		100		104	43
3	C3......0...			9.24711		8.24931		6.37970		99		102	43
4	C...C.......			0.18958		0.24932		0.31713		90		88	41
5	C...(.......			1.06715		0.74746		1.24582		87		91	35
6	C...1.......			0.50407		0.68784		0.99825		80		76	26
No.	Feature, F			CW(F) Run 1		CW(F) Run 2		CW(F) Run 3		Training Set		Invisible Training Set	Calibration Set
	LogBB, split 1
7	C...=.......			1.06451		1.00467		0.93251		80		80	24
8	C5......0...			5.18616		4.87599		3.06013		66		70	32
9	N...C.......			1.06163		1.25062		1.05830		61		59	20
10	N...(.......			1.87440		1.80861		1.50002		50		50	16
11	O...=.......			3.74850		3.12144		3.50390		45		49	17
12	O...C.......			1.87390		1.62698		1.50087		42		35	10
13	=...2.......			1.31662		2.37411		1.93516		41		37	12
14	C...3.......			1.56423		0.24589		0.69105		36		43	10
15	$10011000000			3.49649		2.87644		4.06526		32		23	7
16	C5....H.1...			0.93855		0.49718		0.24570		29		28	11
1	=...........			-1.94237		-2.00425		-1.12592		89		86	30
2	(...........			-1.94146		-1.44173		-1.93644		88		91	35
3	N...........			-1.69081		-1.80786		-1.68985		74		69	22
4	O...........			-3.93612		-3.12302		-3.87867		66		69	27
5	=...(.......			-0.87699		-0.37408		-0.56436		62		58	23
6	C...2.......			-1.87318		-2.18807		-1.87392		60		59	16
7	O...(.......			-1.74592		-1.74659		-1.50041		43		49	19
8	2...(.......			-2.06074		-0.87009		-1.37681		36		35	10
9	N...=.......			-1.62360		-1.50313		-2.12455		30		35	11
10	=...3.......			-0.68502		-0.93424		-1.18858		26		29	8
11	N...2.......			-2.81032		-1.19035		-2.12915		24		19	6
12	[...........			-0.81319		-1.12785		-1.31036		10		8	3
13	=...4.......			-1.31236		-0.81692		-0.68350		9		19	5
14	N...H.......			-1.12172		-0.87838		-1.62984		7		6	3
15	[...C.......			-2.87947		-2.75490		-2.06543		7		5	3
16	Br..........			-0.49505		-0.49665		-1.94093		6		2	2
	LogBB, split 2
1	C3......0...			10.87070		9.99674		11.00131		103		103	41
2	C...........			0.12071		0.12533		0.37494		101		106	41
3	C...C.......			0.93320		0.87535		0.50239		89		96	37
4	C...(.......			1.19210		1.25322		0.62690		83		93	36
5	C...=.......			0.37918		1.37448		0.44201		80		86	24
6	1...........			1.49679		0.12476		1.06684		74		88	26
7	C...1.......			1.18368		1.49925		1.56002		74		88	26
8	C5......0...			4.25337		4.68880		4.12680		68		66	36
9	N...C.......			1.74585		1.50379		1.31711		61		68	19
No.		Feature, F	CW(F) Run 1		CW(F) Run 2		CW(F) Run 3		Training Set		Invisible Training Set		Calibration Set
		LogBB, split 2
10		2...........	1.37069		0.93599		0.87107		56		71		15
11		=...1.......	1.00094		1.00452		1.18761		48		61		19
12		N...(.......	2.00333		2.24552		1.81625		47		50		18
13		O...=.......	3.62311		3.49517		3.37670		42		52		19
14		=...2.......	1.18866		0.62164		0.18527		40		45		11
15		C...3.......	1.31047		0.87676		1.31327		38		47		9
16		O...C.......	2.12437		2.25455		1.81321		36		40		12
1		C4......0...	-0.49732		-0.50309		-0.50008		103		106		41
2		C7......0...	-3.50133		-3.24763		-2.87060		90		88		34
3		=...........	-1.12942		-2.24834		-1.31595		85		96		28
4		(...........	-1.62048		-1.81308		-1.18864		84		94		36
5		N...........	-2.49537		-2.68449		-2.25354		70		78		23
6		O...........	-3.62711		-4.25421		-3.56712		64		75		28
7		=...(.......	-2.18783		-0.74894		-1.93659		56		71		23
8		C...2.......	-2.49624		-2.30834		-1.81363		56		70		15
9		O...(.......	-2.12646		-1.87628		-2.00250		41		54		18
10		N...=.......	-1.12893		-0.99861		-0.99789		37		34		5
11		2...(.......	-1.75032		-0.75119		-0.49969		35		43		8
12		=...3.......	-1.00262		-0.62848		-0.25161		27		32		7
13		N...2.......	-2.00309		-0.24532		-0.87223		22		29		5
14		S...........	-0.80988		-2.37982		-1.12535		16		17		3
15		=...4.......	-2.24740		-0.99940		-1.12895		12		17		3
16		[...C.......	-3.81523		-3.37811		-2.81052		8		6		2
		LogBB, split 3
1		C...........	0.00132		0.19167		0.25322		103		104		40
2		C3......0...	9.74655		10.49769		9.50124		102		104		40
3		C...C.......	1.00004		1.25242		1.00283		92		97		33
4		C...(.......	0.50101		1.37191		1.00401		90		89		35
5		C...1.......	1.31706		1.00284		1.49553		77		83		27
6		C...=.......	0.55849		1.49910		0.06478		76		87		25
7		C5......0...	6.00291		4.74699		5.25173		71		66		32
8		N...C.......	1.24857		0.87346		1.62565		61		63		21
9		N...(.......	0.75396		1.37567		1.68298		58		43		17
10		O...=.......	1.50315		2.50127		1.49589		49		45		18
11		=...2.......	3.25269		1.68316		2.25396		38		45		12
12		3...........	1.62996		0.75194		0.74545		36		45		10
No.		Feature, F	CW(F) Run 1		CW(F) Run 2		CW(F) Run 3		Training Set		Invisible Training Set		Calibration Set
		LogBB, split 3
13		C...3.......	0.00153		0.25042		0.74564		36		45		10
14		1...(.......	1.87609		2.19099		3.00002		34		27		14
15		C6......0...	2.50113		4.75479		4.37791		33		27		16
16		O...C.......	0.62800		0.49543		0.74706		31		37		14
1		(...........	-0.50197		-1.74939		-1.25398		92		89		35
2		C7......0...	-3.00432		-2.24765		-2.50016		92		86		35
3		=...........	-1.74993		-2.19227		-0.93260		84		93		30
4		N...........	-1.50133		-2.62558		-3.30976		69		75		24
5		=...(.......	-0.37305		-0.00161		-0.68413		66		63		18
6		O...........	-3.49561		-3.49608		-3.05869		66		69		28
7		C...2.......	-1.25479		-1.19206		-1.56163		55		66		17
8		O...(.......	-1.62599		-1.87859		-2.25388		46		48		15
9		2...(.......	-1.25291		-1.75055		-2.00114		37		36		11
10		N...=.......	-3.00207		-2.49735		-2.24940		31		34		10
11		C5....H.1...	-0.31727		-0.62372		-0.06462		29		29		6
12		=...3.......	-1.25013		-2.25139		-0.31558		27		29		6
13		(...(.......	-1.49562		-1.56378		-2.00367		23		16		7
14		N...2.......	-2.18457		-2.87062		-2.50423		23		24		8
15		[...........	-0.44089		-0.31661		-0.31291		8		11		3
16		[...H.......	-0.75060		-0.74589		-0.12414		8		6		2

optimization procedure. These features are extracted according to the principles: (i) these have significant prevalence in training, invisible training and calibration sets; and (ii) these features have stable positive or stable negative correlation weights in all runs.

3.5. Molecular Features, which have Similar Effects for pIC50 and logBB

Table 4 contains lists of molecular features which are promoters of increase for both pIC50 and logBB together with features which are promoters of decrease for both pIC50 and logBB. In the first approximation, oxygen and nitrogen connected in rings and oxygen connected with carbon or nitrogen are promoters of increase for both pIC50 and logBB. Branching and the presence of double bonds as well as nitrogen itself are promoters of decrease for both pIC50 and logBB.

Table 4.

Molecular features which have the same effect for pIC50 (denoted 1) and logBB (denoted 2).

	1	1	1	2	2	2	TRN1*	iTRN1	CLB1	TRN2	iTRN2	CLB2
pIC50-split1-logBB-split1
O...=.......	+	+	+	+	+	+	62	71	51	45	49	17
C3......0...	+	+	+	+	+	+	60	71	51	99	102	43
C4......0...	+	+	+	+	+	+	60	71	51	100	104	43
C...(.......	+	+	+	+	+	+	59	62	43	87	91	35
C...1.......	+	+	+	+	+	+	59	61	43	80	76	26
N...(.......	+	+	+	+	+	+	50	54	38	50	50	16
1...(.......	+	+	+	+	+	+	41	46	28	25	29	14
N...C.......	+	+	+	+	+	+	41	43	29	61	59	20
C5......0...	+	+	+	+	+	+	36	40	31	66	70	32
N...1.......	+	+	+	+	+	+	36	33	22	23	23	6
O...C.......	+	+	+	+	+	+	22	23	20	42	35	10
(...........	-	-	-	-	-	-	62	71	51	88	91	35
=...(.......	-	-	-	-	-	-	62	69	51	62	58	23
=...........	-	-	-	-	-	-	62	71	51	89	86	30
N...........	-	-	-	-	-	-	54	62	41	74	69	22
pIC50-split1-logBB-split2
1...........	+	+	+	+	+	+	62	71	51	74	88	26
O...=.......	+	+	+	+	+	+	62	71	51	42	52	19
C3......0...	+	+	+	+	+	+	60	71	51	103	103	41
C...(.......	+	+	+	+	+	+	59	62	43	83	93	36
C...1.......	+	+	+	+	+	+	59	61	43	74	88	26
N...(.......	+	+	+	+	+	+	50	54	38	47	50	18
1...(.......	+	+	+	+	+	+	41	46	28	33	28	14
N...C.......	+	+	+	+	+	+	41	43	29	61	68	19
F...........	+	+	+	+	+	+	37	38	28	21	11	5
C5......0...	+	+	+	+	+	+	36	40	31	68	66	36
N...1.......	+	+	+	+	+	+	36	33	22	26	27	5
O...C.......	+	+	+	+	+	+	22	23	20	36	40	12
(...........	-	-	-	-	-	-	62	71	51	84	94	36
=...(.......	-	-	-	-	-	-	62	69	51	56	71	23
=...........	-	-	-	-	-	-	62	71	51	85	96	28
N...........	-	-	-	-	-	-	54	62	41	70	78	23
pIC50-split1-logBB-split3
O...=.......	+	+	+	+	+	+	62	71	51	49	45	18
C3......0...	+	+	+	+	+	+	60	71	51	102	104	40
	1	1	1	2	2	2	TRN1*	iTRN1	CLB1	TRN2	iTRN2	CLB2
pIC50-split1-logBB-split3
C...(.......	+	+	+	+	+	+	59	62	43	90	89	35
C...1.......	+	+	+	+	+	+	59	61	43	77	83	27
N...(.......	+	+	+	+	+	+	50	54	38	58	43	17
1...(.......	+	+	+	+	+	+	41	46	28	34	27	14
N...C.......	+	+	+	+	+	+	41	43	29	61	63	21
C5......0...	+	+	+	+	+	+	36	40	31	71	66	32
O...C.......	+	+	+	+	+	+	22	23	20	31	37	14
(...........	-	-	-	-	-	-	62	71	51	92	89	35
=...(.......	-	-	-	-	-	-	62	69	51	66	63	18
=...........	-	-	-	-	-	-	62	71	51	84	93	30
N...........	-	-	-	-	-	-	54	62	41	69	75	24
(...(.......	-	-	-	-	-	-	39	44	34	23	16	7
pIC50-split2-logBB-split1
C...(.......	+	+	+	+	+	+	61	61	45	87	91	35
C...1.......	+	+	+	+	+	+	61	58	43	80	76	26
N...(.......	+	+	+	+	+	+	54	49	36	50	50	16
C...C.......	+	+	+	+	+	+	51	58	42	90	88	41
C5......0...	+	+	+	+	+	+	43	36	34	66	70	32
N...C.......	+	+	+	+	+	+	39	41	27	61	59	20
O...C.......	+	+	+	+	+	+	22	18	19	42	35	10
(...........	-	-	-	-	-	-	66	67	50	88	91	35
=...........	-	-	-	-	-	-	66	67	50	89	86	30
N...........	-	-	-	-	-	-	57	60	39	74	69	22
pIC50-split2-logBB-split2
1...........	+	+	+	+	+	+	66	67	50	74	88	26
C...(.......	+	+	+	+	+	+	61	61	45	83	93	36
C...1.......	+	+	+	+	+	+	61	58	43	74	88	26
N...(.......	+	+	+	+	+	+	54	49	36	47	50	18
C...C.......	+	+	+	+	+	+	51	58	42	89	96	37
2...........	+	+	+	+	+	+	45	51	32	56	71	15
C5......0...	+	+	+	+	+	+	43	36	34	68	66	36
N...C.......	+	+	+	+	+	+	39	41	27	61	68	19
F...........	+	+	+	+	+	+	34	37	28	21	11	5
O...C.......	+	+	+	+	+	+	22	18	19	36	40	12
(...........	-	-	-	-	-	-	66	67	50	84	94	36
=...........	-	-	-	-	-	-	66	67	50	85	96	28
N...........	-	-	-	-	-	-	57	60	39	70	78	23
	1	1	1	2	2	2	TRN1*	iTRN1	CLB1	TRN2	iTRN2	CLB2
pIC50-split2-logBB-split3
C...(.......	+	+	+	+	+	+	61	61	45	90	89	35
C...1.......	+	+	+	+	+	+	61	58	43	77	83	27
N...(.......	+	+	+	+	+	+	54	49	36	58	43	17
C...C.......	+	+	+	+	+	+	51	58	42	92	97	33
C5......0...	+	+	+	+	+	+	43	36	34	71	66	32
N...C.......	+	+	+	+	+	+	39	41	27	61	63	21
O...C.......	+	+	+	+	+	+	22	18	19	31	37	14
(...........	-	-	-	-	-	-	66	67	50	92	89	35
=...........	-	-	-	-	-	-	66	67	50	84	93	30
N...........	-	-	-	-	-	-	57	60	39	69	75	24
(...(.......	-	-	-	-	-	-	32	44	32	23	16	7
pIC50-split3-logBB-split1
O...=.......	+	+	+	+	+	+	61	63	55	45	49	17
C...1.......	+	+	+	+	+	+	58	60	46	80	76	26
N...(.......	+	+	+	+	+	+	50	48	43	50	50	16
N...C.......	+	+	+	+	+	+	37	42	33	61	59	20
C5......0...	+	+	+	+	+	+	35	37	34	66	70	32
N...1.......	+	+	+	+	+	+	32	31	29	23	23	6
(...........	-	-	-	-	-	-	61	63	55	88	91	35
=...........	-	-	-	-	-	-	61	63	55	89	86	30
N...........	-	-	-	-	-	-	54	53	48	74	69	22
pIC50-split3-logBB-split2
1...........	+	+	+	+	+	+	61	63	55	74	88	26
O...=.......	+	+	+	+	+	+	61	63	55	42	52	19
C...1.......	+	+	+	+	+	+	58	60	46	74	88	26
N...(.......	+	+	+	+	+	+	50	48	43	47	50	18
2...........	+	+	+	+	+	+	48	43	36	56	71	15
N...C.......	+	+	+	+	+	+	37	42	33	61	68	19
C5......0...	+	+	+	+	+	+	35	37	34	68	66	36
N...1.......	+	+	+	+	+	+	32	31	29	26	27	5
(...........	-	-	-	-	-	-	61	63	55	84	94	36
=...........	-	-	-	-	-	-	61	63	55	85	96	28
N...........	-	-	-	-	-	-	54	53	48	70	78	23
pIC50-split3-logBB-split3
O...=.......	+	+	+	+	+	+	61	63	55	49	45	18
C...1.......	+	+	+	+	+	+	58	60	46	77	83	27
N...(.......	+	+	+	+	+	+	50	48	43	58	43	17
	1	1	1	2	2	2	TRN1*	iTRN1	CLB1	TRN2	iTRN2	CLB2
pIC50-split3-logBB-split3
N...C.......	+	+	+	+	+	+	37	42	33	61	63	21
C5......0...	+	+	+	+	+	+	35	37	34	71	66	32
(...........	-	-	-	-	-	-	61	63	55	92	89	35
=...........	-	-	-	-	-	-	61	63	55	84	93	30
N...........	-	-	-	-	-	-	54	53	48	69	75	24

^*)TRN1, iTRN1 and CLB1 are the numbers of a feature in the training, invisible training and calibration sets for endpoint 1; TRN2, iTRN2 and CLB2 mean the same for endpoint 2.

3.6. Molecular Features, which have Opposite Effects for pIC50 and logBB

Table 5 contains lists of molecular features, which have opposite effect on both pIC50 and for logBB. In the first approximation, presence of two rings and presence of carbon with double covalent bond have opposite effects on pIC50 and logBB.

Table 5.

Molecular features which have the opposite effect for pIC50 (denoted 1) and logBB (denoted 2).

	1	1	1	2	2	2	TRN1*	iTRN1	CLB1	TRN2	iTRN2	CLB2
pIC50-split1-logBB-split1
O...(.......	+	+	+	-	-	-	62	71	51	43	49	19
2...(.......	+	+	+	-	-	-	31	33	18	36	35	10
C...........	-	-	-	+	+	+	62	71	51	101	102	42
C...=.......	-	-	-	+	+	+	26	30	14	80	80	24
pIC50-split1-logBB-split2
O...(.......	+	+	+	-	-	-	62	71	51	41	54	18
C4......0...	+	+	+	-	-	-	60	71	51	103	106	41
2...(.......	+	+	+	-	-	-	31	33	18	35	43	8
C7......0...	+	+	+	-	-	-	28	21	22	90	88	34
C...........	-	-	-	+	+	+	62	71	51	101	106	41
C...=.......	-	-	-	+	+	+	26	30	14	80	86	24
pIC50-split1-logBB-split3
O...(.......	+	+	+	-	-	-	62	71	51	46	48	15
2...(.......	+	+	+	-	-	-	31	33	18	37	36	11
C7......0...	+	+	+	-	-	-	28	21	22	92	86	35
C...........	-	-	-	+	+	+	62	71	51	103	104	40
C...=.......	-	-	-	+	+	+	26	30	14	76	87	25
pIC50-split2-logBB-split1
O...........	+	+	+	-	-	-	66	67	50	66	69	27
2...(.......	+	+	+	-	-	-	31	30	25	36	35	10
C...........	-	-	-	+	+	+	66	67	50	101	102	42
C3......0...	-	-	-	+	+	+	66	66	49	99	102	43
C...=.......	-	-	-	+	+	+	26	28	23	80	80	24
pIC50-split2-logBB-split2
O...........	+	+	+	-	-	-	66	67	50	64	75	28
2...(.......	+	+	+	-	-	-	31	30	25	35	43	8
	1	1	1	2	2	2	TRN1*	iTRN1	CLB1	TRN2	iTRN2	CLB2
pIC50-split2-logBB-split2
C7......0...	+	+	+	-	-	-	27	23	21	90	88	34
C...........	-	-	-	+	+	+	66	67	50	101	106	41
C3......0...	-	-	-	+	+	+	66	66	49	103	103	41
C...=.......	-	-	-	+	+	+	26	28	23	80	86	24
pIC50-split2-logBB-split3
O...........	+	+	+	-	-	-	66	67	50	66	69	28
2...(.......	+	+	+	-	-	-	31	30	25	37	36	11
C7......0...	+	+	+	-	-	-	27	23	21	92	86	35
C...........	-	-	-	+	+	+	66	67	50	103	104	40
C3......0...	-	-	-	+	+	+	66	66	49	102	104	40
C...=.......	-	-	-	+	+	+	26	28	23	76	87	25
pIC50-split3-logBB-split1
=...(.......	+	+	+	-	-	-	61	63	53	62	58	23
O...(.......	+	+	+	-	-	-	61	63	55	43	49	19
C...........	-	-	-	+	+	+	61	63	55	101	102	42
C...C.......	-	-	-	+	+	+	48	47	46	90	88	41
C...=.......	-	-	-	+	+	+	28	25	22	80	80	24
pIC50-split3-logBB-split2
=...(.......	+	+	+	-	-	-	61	63	53	56	71	23
O...(.......	+	+	+	-	-	-	61	63	55	41	54	18
C7......0...	+	+	+	-	-	-	22	23	24	90	88	34
C...........	-	-	-	+	+	+	61	63	55	101	106	41
C...C.......	-	-	-	+	+	+	48	47	46	89	96	37
C...=.......	-	-	-	+	+	+	28	25	22	80	86	24
pIC50-split3-logBB-split3
=...(.......	+	+	+	-	-	-	61	63	53	66	63	18
O...(.......	+	+	+	-	-	-	61	63	55	46	48	15
C7......0...	+	+	+	-	-	-	22	23	24	92	86	35
C...........	-	-	-	+	+	+	61	63	55	103	104	40
C...C.......	-	-	-	+	+	+	48	47	46	92	97	33
C...=.......	-	-	-	+	+	+	28	25	22	76	87	25

^*)TRN1, iTRN1 and CLB1 are the numbers of feature in the training, invisible training and calibration sets for endpoint 1; TRN2, iTRN2, and CLB2 mean the same for endpoint 2.

It is to be noted that the number of features which have the same effect for pIC50 and logBB is larger than the number of features which have opposite effects for pIC50 and logBB. Consequently, the consideration of interrelations between these endpoints (maybe not only those) can be a perspective in the aspect of drug discovery.

Supplementary materials section contains SMILES and numerical data on examined endpoints.

CONCLUSION

There are arguments to consider the interrelation between gamma-secretase inhibitors activity (pIC50) and blood brain barrier permeation (logBB). The interrelation is described in the literature and confirmed in this work (Table 4). The interrelation can be detected and described in terms of molecular features extracted from SMILES and molecular graph which are involved in building up QSAR models for the pIC50 and logBB. The examination of equivalent and opposite effect of the presence of molecular features for other endpoint can be useful for other pairs of endpoints. From practical point of view, these can be (a) water solubility and octanol water partition coefficient; (b) water solubility and toxicity; (c) carcinogenicity and mutagenicity, etc.

LIST OF ABBREVIATIONS

QSAR

Quantitative structure – activity relationships

CWs

Correlation weights

BBB

Blood brain barrier

AD

Alzheimer's disease

SMILES

Simplified molecular input-line entry system

SUPPLEMENTARY MATERIAL

Supplementary material is available on the publisher’s web site along with the published article.

Consent for Publication

Not applicable.

Conflict of Interest

The authors declare no conflict of interest, financial or otherwise.