1. In the name of GOD Classical Molecular Descriptors M.H. FATEMI Mazandaran University mhfatemi@umz.ac.ir

2. What is QSAR? • A QSAR is a mathematical relationship between a biological activity of a molecular system and its geometric and chemical characteristics. • QSAR attempts to find consistent relationship between biological activity and molecular properties, so that these “rules” can be used to evaluate the activity of new compounds.

3. Molecular Descriptors • Molecular descriptors are numerical values that characterize properties of molecules • The goal of a molecular descriptors is to provide a numerical representation of molecular structure • Examples: • Physicochemical properties (empirical) • Values from algorithms, such as 2D fingerprints • Vary in complexity of encoded information and in compute time

6. Molecular descriptors • Vary in complexity of encoded information and in compute time 1- Classification based on the representation of molecule 0D, 1D, 2D, 3D, others • 2- Classification based on the type of descriptors • Topological, Electronic, Geometrical, Physicochemical

7. 0D- Descriptors • Independent from molecular connectivity and conformations and can obtain from molecular formula C6H12O Such as atom , Molecular weights some of atomic properties Sum of atomic volumes, Mean of atomic polarizability,

8. 1D Functional group count Molecular descriptor based on the counting of functional group

9. 2D 1-Topological descriptors 2-Walk and path count 3-Connectivity indices 4-Information indices 5-2D autocorrelation 6-Edge adjacency indices 7- BCUT descriptors 8- Topological charge indices 9-Eigenvalue-based indices

10. 3D • 1-Geometrical descriptors • 2- Randic molecular profile • 3- RDF descriptors • 4- 3D MoRSE descriptors • 5- WHIM descriptors • 6- GETAWAY descriptors

11. Classical Types of Molecular Descriptors Topological 1&2-D structural formula Geometrical 3-D shape and structure Quantum Chemical Physico Chemichal Hybrid descriptors

13. Topological Geometrical Molecular Descriptors Electronic Physicochemical

14. Topological Geometrical Molecular Descriptors Electronic Physicochemical

17. Topological Constitutional Geometrical Connectivity Molecular Descriptors Electronic Sub structure Physicochemical Environmental

18. Constitutional descriptors • These simple descriptors reflect only the molecular composition of the compound without using the geometry or electronic structure of the molecule: • Very simple, can calculate from molecular formula such as: • Total number of atom • Absolute and relative number of atoms • Number of bonds (nBT) • Number of rings (nCIC) • Number of double bonds (nDB) • Number of aromatic bonds (nAB) • Number of 6-membered rings (nR06) • Number of benzene-like rings (nBnz)

19. Topological Constitutional Geometrical Connectivity Molecular Descriptors Electronic Subsctructure Physicochemical Environmental

20. Molecular Connectivity Descriptors Definition Molecular connectivity is a method of molecular structure quantitation in which weighted counts of substructure fragments are incorporated into numerical indices.

21. Molecular Connectivity Descriptors Molecular Connectivity indices obtained some information about: • The size and structure of molecule • Degree of branching • Connection of atoms in a molecule • Type of atoms in a molecule

22. Chemical graph A molecular graph represent the elements of a molecules and way that they connect to each other Some Explanations: 1. Each graph consist of some Vertices and Edges. 2. Edge connect the vertices to each other. 3. Each vertices (node) represent one atom 4. Each edge (line) represent a chemical bond

24. Chemical graph • Once the organic compounds are considered as graphs, the theorems of graph theory can then be applied to generating graph invariants, which in the context of chemistry are called topological descriptors.

25. Vertex-adjacency matrix Aij Aij= { 1 if i and j are adjacence } & 0 in other conditions A =

26. Vertex-adjacency matrix

27. Vertex-adjacency matrix

28. Vertex-adjacency matrix

29. Distance matrix Lij • D(G) =[Lij] Where Lij= lij if i≠j and Lij=0 in other conditions D(G) =

30. Distance matrix

31. Distance matrix

32. Some type of connectivity indices • 1-Wiener indices • 2-Balaban indices • 3-Randic and Kier & Hall connectivity indices • 4-Kier shape indices • 5-Information content indices

33. Wiener index • Introduced by Wiener in 1947 • Half of the sum of distance matrix elements • Encode degree of branching of molecule • Encode the compactness of molecule • Compact molecule has smaller Wiener number • Correlate to boiling point, surface tension, heat of formation, heat of vaporization and molar volume of alkanes

34. Wiener index w = ½ S S dij w = 46

35. Balaban index • It was introduced by Balaban in 1981 • Encode compacness of molecule • Calculate from the distance matrix • A.T. Balaban, Chem. Phys. Lett. 1981, 89, 399 • A.T. Balaban, Pure and Appl. Che. 1983, 55, 199

36. Methods • Di & DJ= sum of path between each atom and other atoms • (by summation of elements of each row in distance matrix) • J= M/ ( +1) ∑ (Di)(Di)]-1/2 • M= # of bonds in molecule • = cyclic number

37. How do they calculate?

38. How do they calculate?

39. Balaban index J= 0.868 J= 0.957 J= 0.500 J= 0.707

40. Randic and Kier & Hall connectivity indices • Was introduced in 1975 by Randic to encode the side chain in alkane •  = ∑[ (i). (j) ] -1/2 • where(j) = # of bond with adjacent ( non H ) atom • Modification by Kier & Hall in 1981 • L. B. Kier and L. H. Hall, Eur. J. Med. Chem., 12, 307 (1977). • L. B. Kier and L. H. Hall, J. Pharm. Sci., 70, 583 (1981).

41. How do they calculate? The calculation of the indices begins with the reduction of the molecule to the hydrogen-suppressed skeleton or graph. Each atom is assigned two atom descriptors based upon the count of sigma electrons or valence electrons present, other than those bonded to hydrogen atoms.

42. How do they calculate? • The sigma electron descriptor is =-h • where  is the count of electrons in orbital and h is the count of hydrogen atoms • This simple  value of an atom is equal to the number of neighboring atoms in the molecular skeleton ( as Randic indices)

43. How do they calculate? • The  values of each atom are subsequently used in calculating the simple molecular connectivity indices. • The valence electron descriptor (v) is given as v = Z v – h • where Z v is the count of the valence electrons. • The valence delta values are used in calculating the valence molecular connectivity indices.

44. How do they calculate? • The molecular connectivity indices or chi indices are symbolized mt • Ns m+1 • mt =∑ mCi where mCi =∏ (k) -0.5 • i=1 k=1

45. How do they calculate? Ns m+1 • mt =∑ mCi where mCi =∏ (k) -0.5 i=1 k=1 • m represent the type of interested sub-structure Sub-structures for a molecular skeleton are defined by the decomposition of the skeleton into fragments of: a)atoms (zero order, m = 0) 0p; b)one bond paths (first order, m = l) 1p ; c)two bond fragments (second order, m = 2) 2p ; d)three contiguous bond fragments (third order Path, m = 3, t = P) 3p ; and so forth.

46. How do they calculate? Other fragments: 1- Cluster (three atoms attached to a central atom, m = 3, t = C) 3c 2- Path/cluster (equivalent to the isopentane skeleton, m = 4, t = PC) 4pc 3- Chain fragment (cycles of 3, 4, 5 . . . atoms, m = 3, 4, 5. . ., t = CH) 4CH .

47. How do they calculate? How they calculate? • For each order and fragment type, a connectivity index may be calculated. • 1- The values for all non-H atoms were calculated  v

48. How do they calculate? 2-Then the calculation is continued by multiplying the  (or v ) values for each atom in a fragment within a molecule. 1p  v  v

49. How do they calculate? • This product is then converted to the reciprocal square root and called the connectivity sub graph term Ci. • Ci= ( 3)-1/2 = 0.577

50. How do they calculate? • These terms are then summed over all the subgraphs (of order m and type t) in the entire molecule, Ns, to calculate the molecular connectivity index mt of order m and type t. • 1p = (0.577) +(0.577)+(0.577)+(0.333)+(0.408) +(0.707) = 3.179