^{1}

^{2}

^{3}

Prediction of antagonistic activity of
*β*-carboline and its thirteen derivatives has been made using topological descriptors viz, connectivity index, and kappa shape index of different orders. For evaluation of values of descriptor, molecular modeling and geometry optimization of all the compounds were carried out with CAChe Pro software by opting semiempirical PM3 method using MOPAC 2002. For prediction of activity multiple linear regression analysis (MLR) was performed. MLR analysis has been made by Project Leader Software associated with CAChe by using the above descriptors as independent variables and biological activity as dependent variables. We were performed leave-one-out methods and the result reflected a direct relationship between biological activity and connectivity index of zero order, while indirect relationship with connectivity index of second order and thus connectivity index is a reliable descriptor to predict the biological activity of
*β*-carboline and its various derivatives.

In our previous publications, we have studied 1) PM3 based QSAR study of β-carbolines using electronegativity and absolute hardness as reactive parameters [^{0}χ_{t}); 2) connectivity index of first order (^{1}χ_{t}); 3) connectivity index of second order (^{2}χ_{t}); 4) valence connectivity index of zero ( χ 0 t v ); 5) valence connectivity index of first order ( χ 1 t v ); 6) valence connectivity index of second order ( χ 2 t v ); 7) kappa shape indix for first order (^{1}K); 8) kappa shape indix for second order (^{2}K); and 9) kappa shape indix for third order (^{3}K) [

The evaluation of the above topological parameters is given below. The molecular connectivity indices are symbolized by χ m t [

χ m t = ∑ i = 1 N s C m i (1)

and C m i is given by Equation (2):

C m i = ∏ k = 1 m + 1 ( δ k ) − 0.5 (2)

where m = 1 for first order, m = 2 for second order and m = 3 for third order. Similarly the valence connectivity index is given by Equation (3):

χ m t V = ∑ i = 1 N s C m i V (3)

and C m i V is given by Equation (4):

C m i V = ∏ k = 1 m + 1 ( δ k V ) − 0.5 (4)

where m = 1 for first order, m = 2 for second order and m = 3 for third order.

Kappa shape indices are also a method of molecular structure quantization in which attributes of molecular shape are encoded into kappa values (^{1}K for first order, ^{2}K for second order, ^{3}K for third order) [

K 1 = A ( A − 1 ) 2 ( P 1 i ) 2 (5)

K 2 = ( A − 1 ) ( A − 2 ) 2 ( P 2 i ) 2 (6)

K 3 = ( A − 1 ) ( A − 3 ) 2 ( P 3 i ) 2 if A is odd (7)

K 3 = ( A − 3 ) ( A − 2 ) 2 ( P 3 i ) 2 if A is even (8)

where P_{i} is the length of paths of bond length “i” in the hydrogen suppressed molecule and “A” is the number of non-hydrogen atoms in the molecule.

The study materials of this work are β-carboline and its thirteen derivatives as listed in _{50} antagonistic activity, and IC_{50} binding affinities to displace 50% of [3H]flunitrazepam on benzodiazepines receptor [_{50} antagonistic activity for the study. For prediction of antagonistic activity molecular modeling and geometry optimization [^{2}) and cross validation coefficient ( r C V 2 ) [

Benzodiazepines (BDZs) are the drugs of choice in the pharmacotherapy of anxiety and related emotional disorders, sleep disorders, status epilepticus, and other convulsive states; they are used as centrally acting muscle relaxants, for premedication, and as inducing agents in anesthesiology [_{A}) family [_{50} antagonistic activity binding to the benzodiazepine receptor. β-Carbolines posssess a broad spectrum of pharmacological actions (as muscle relaxants) mediated via occupation of BzR in the central nervous system [

_{50} antagonistic activity of β-Carboline and its thirteen derivative binding to benzodiazepines receptor [

For prediction of antagonistic activity multiple regression analysis has been performed using topological descriptors used as independent variables and biological activity as dependent variable. Through leave-out-one method a number of MLR equations have been developed using topological descriptors not more than three.

when k = 1 then the reliable modal is:

PBA = 0. 256 × χ 0 t v + 4 . 225 (9)

r C V 2 = 0.308

r 2 = 0.571

when k = 2 then the reliable model obtained by different combination of descriptors is:

PBA = 2.389 × χ 0 t − 3.847 × χ 2 t + 7.486 (10)

r C V 2 = 0.648

r 2 = 0.736

when k = 3 then the reliable model obtained by different combination of descriptors is:

PBA = 1.869 × K 1 − 0.246 × K 2 − 3.724 × K 3 + 5.645 (11)

r C V 2 = 0.583

r 2 = 0.736

Among the above MLR equations Equation (10) is best model as clear from the correlation coefficient (r^{2}) and cross validation coefficient ( r C V 2 ) values. Predicted activity as obtained from this model is also tabulated in

S.No. | Descriptors | OBA | PA | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

^{0}χ_{t} | ^{1}χ_{t} | ^{2}χ_{t} | χ 0 t v | χ 1 t v | χ 2 t v | ^{1}K | ^{2}K | ^{3}K | |||

1 | 8.673 | 6.449 | 5.652 | 6.989 | 4.254 | 3.092 | 8.32 | 3.293 | 1.333 | 5.79 | 6.462 |

2 | 9.544 | 6.843 | 6.286 | 7.359 | 4.399 | 3.259 | 9.242 | 3.539 | 1.547 | 5.40 | 6.103 |

3 | 10.251 | 7.381 | 6.455 | 8.32 | 4.788 | 3.443 | 10.173 | 4.108 | 1.744 | 6.91 | 7.142 |

4 | 10.958 | 7.881 | 6.836 | 9.027 | 5.375 | 3.672 | 11.111 | 4.704 | 2.08 | 7.62 | 7.368 |

5 | 11.665 | 8.381 | 7.189 | 9.734 | 5.875 | 4.087 | 12.055 | 5.325 | 2.42 | 7.96 | 7.697 |

6 | 9.544 | 6.843 | 6.286 | 8.045 | 4.742 | 3.61 | 9.242 | 3.539 | 1.547 | 7.35 | 6.103 |

7 | 11.121 | 7.754 | 7.185 | 8.175 | 4.764 | 3.516 | 11.111 | 4.349 | 1.966 | 6.90 | 6.413 |

8 | 9.544 | 6.843 | 6.286 | 7.489 | 4.464 | 3.325 | 9.242 | 3.539 | 1.547 | 4.60 | 6.103 |

9 | 10.958 | 7.881 | 6.836 | 9.083 | 5.235 | 3.644 | 11.111 | 4.704 | 2.08 | 8.10 | 7.368 |

10 | 11.828 | 8.292 | 7.327 | 9.228 | 5.242 | 3.777 | 12.055 | 4.938 | 2.172 | 8.30 | 7.558 |

11 | 15.69 | 10.651 | 9.375 | 12.343 | 6.937 | 4.882 | 16.844 | 7.266 | 3.299 | 9.05 | 8.905 |

12 | 16.397 | 11.189 | 9.544 | 13.304 | 7.325 | 5.064 | 17.811 | 7.92 | 3.52 | 9.30 | 9.944 |

^{a}13^{ } | 17.104 | 11.689 | 9.925 | 14.011 | 7.913 | 5.293 | 18.781 | 8.59 | 3.908 | 8.64 | 10.169 |

14 | 20.924 | 14.707 | 12.571 | 17.105 | 9.97 | 6.944 | 23.168 | 11.228 | 5.507 | 9.00 | 9.116 |

^{a}data point not used in deriving the equation. Where ^{0}χ_{t} = connectivity index of zero order, ^{1}χ_{t} = connectivity index of first order, ^{2}χ_{t} = connectivity index of second order, χ 0 t v = valence connectivity index of zero, χ 1 t v = valence connectivity index of first order, χ 2 t v = valence connectivity index of second order, ^{1}K = kappa shape indix for first order, ^{2}K = kappa shape indix for second order, ^{3}K = kappa shape indix for third order, OBA = observed biological activity in term of IC_{50} antagonistic activity and PBA = predicted biological activity.

The study concluded that the connectivity indexes of zero-order and connectivity second order are reliable descriptors to predict the biological activity of β-carboline and its various derivatives. The study also reflected a direct relationship between biological activity and connectivity index of zero-order (positive value of descriptor coefficient), while the indirect relationship with connectivity index of second order (negative value of descriptor coefficient).

The authors are thankful to Principal, Maharani Lal Kunwari Post Graduate College, Balrampur for laboratory facilities and to respected Dr. P. P. Singh for valuable discussion and suggestions.

The authors declare no conflicts of interest regarding the publication of this paper.

Soni, A.K., Singh, G.P. and Sahu, V.K. (2021) Prediction of Antagonistic Activity of β-Carboline and Its Derivatives Using Topological Descriptors. Open Journal of Applied Sciences, 11, 577-584. https://doi.org/10.4236/ojapps.2021.115041