INTRODUCTION:

Molecular descriptors are quantum mechanically derived mathematical depictions of a chemical structure, obtained using a specific algorithm. Also, molecular descriptor is the ultimate conversion of an information encoded in a chemical structure into a numerical value, which directly correlates the structure to its biological property or to its physicochemical property¹. Molecular descriptors are based on the principles of quantum-chemistry, mechanistic organic chemistry, and graph theory etc. Molecular descriptors are categorized into two important categories, the first being experimentally derived descriptors and second category is theoretically derived descriptors.

The important examples of experimentally derived descriptors are; Logp (lipophilicity descriptors), polar surface area, dielectric constant etc. The theoretically derived descriptors involves various distance connectivity matrices, topological descriptors etc. Theoretical descriptors have low statistical error owing to the absence of experimental noise. Theoretical descriptors from physico-chemical analysis and theory show slight degree of overlap with respect to experimental measurements. Experimental counterpart descriptors include surface areas, volume descriptors and quantum chemical descriptors. The main advantage of theoretical descriptors compared to experimental descriptors include less time requirement and cost effectiveness.

Until the 1970s, mathematically linked relationships in experimentally measured quantities was the core of molecular modeling. The trend now, however, has shifted towards relationships between property that is measured and descriptors which are capable in capturing structural chemical data. The advent of these descriptors have not just opened a new window in exploring new mathematical models, but has paved way to ignite a compounding change in the research interest in this area. The present scenario has allowed to understand the co-relation between experimental basis and theoretical data from molecular structure. Simple kind of molecular descriptors could be attained just by counting type of atom or fragments present in the molecule, through physico-chemical and properties such as number donors or acceptors of of hydrogen bond, molecular weight as well as number of hydroxyl groups to name a few. 2D-descriptors are generated through algorithms which are used on a topological representation. Other molecular descriptors known as geometrical or 3D-descriptors are obtained through spatial coordinates (x, y, z) of the particular molecule. 4D-descriptors are obtained from the energy generation that occur between molecules which are imbedded into grid and probe. Higher information content is present in 3D- or 4D-descriptors compared to simple ones. Thus, it is logical to think of using the most reliable descriptors in all kind of modeling procedures. This thought process is however not proper as the most suitable descriptors are the ones in which the information content can be compared with the response for which the model is sought. Thus, having abundant information in the independent variables in terms of response is considered as noise giving rise to an unstable or unpredictive model. In general, molecular descriptors should be able to satisfy the basic necessities besides trivial invariance properties. It can thus be mentioned that the most reliable descriptor which is effective for all the issues does not exist.

Stepwise process for the generation and interpretation of a molecular descriptor:

Representation of chemical structures: Molecular representation is one of the important preparative step before the generation of a chemical descriptor. The kind of representation is based primarily on extent of chemical input that is transferred to a molecule^{2, 3}. The most common molecular representation is through chemical or molecular formula. This can be illustrated with the example of 4-bromo toluene, C₇H₇Br, which indicates the presence of 8 atoms in the molecule excluding the hydrogens, where N_C =7(number of carbon atoms), N_H=7(number of hydrogen atoms) and N_Br=1(number of bromine atoms). This molecular representation do not give any idea of the actual molecular structure, hence molecular descriptors generated solely based on chemical formula are known as 0 dimensional descriptors.

Atoms in a molecule are usually characterized based on their atomic properties which also explain about chemical information of a molecular structure. Vander Waals radii, atomic mass, charge, electronegativities as well as atomic polarizabilities are the usual atomic properties for calculation of molecular descriptor. Local vertex invariants (LOVIs) that can be generated through graph theory is also used to characterize atoms. A one-dimensional depiction of a molecule includes list of fragments of a molecule and substructure representation list falls under it. 1D-molecular descriptors are the descriptors obtained from such representation and they are bit-strings and/or holographic vectors. 0D as well as 1D descriptors can be calculated easily. As the method does not need optimization of molecular structure they can easily be interpreted.

The basic frame in two-dimensional representation include connecting of atoms in a molecular complex and the nature of chemical bonds. Topological form of representation is basically when a molecule is represented through molecular graph. Such graphs, give information on the connection of atoms in a molecule not taking into account the parameters such as torsion angle, bond angles and nuclei distance.

In 3D representation, a molecule is considered as geometrical object which is rigid in space demonstrating the nature and atoms that are connected, as well as total configuration and is referred as geometrical representation. Such representation defines a molecule by type of atom comprising a molecule as well as the set coordinates x,y and z that are linked to every atom.

Molecules represented through lattice are linked to properties obtained through electron distribution and interaction of such molecules with a given probe describing the space surrounding them which is characteristic of QSAR techniques based on grid. At this junction, descriptors can be regarded as 4D-molecular descriptors that are channelized by scalar field, that are linked with 3D molecular geometry.

Generation and application of some important descriptors used in molecular design

a) Topological indexes:

Distance present among atoms and calculated by the number of intervening bonds form the basis of topological indexes and are regarded as through-bond indexes^4,5. The result of topological index non uniqueness is that they do not let re-construction of a molecule. Kier shape descriptors, path counts, Hosoya Z index, self-returning walk counts and path/walk shape indexes^[^6,7,8,9,10] are some of the specific graph elements in simple TIs that include count. Wiener operator is the half-sum of the matrix elements which is among the most common TI is obtained by using graph operators to graph–theoretical matrixes including Harary indexes, Wiener index and spectral indexes ^[11,12,13]. In the past, efforts have been made to come out with algorithms with respect to molecular graph.^14.

b) Graph theoretical matrices¹⁵:

Structural information of molecules are commonly encoded by mathematical tool such as molecular matrixes. Graph–theoretical matrixes can be vertex matrixes or edge matrices. Vertex matrixes are the ones if the column and rows indicate graph vertexes (atoms) or matrix elements encode properties of pairs of vertexes whereas edge matrixes are the ones when rows and columns refer to graph edges (bonds) and matrix elements encode properties of pairs of edges. Edge and Vertex matrixes are square shaped with dimensions of B×B, B and A× A, A respectively. Vital graph–theoretical matrixes include incidence matrixes that are utilized to describe a molecular graph.

c) Auto correlation descriptors:

The molecular descriptors, which are purely based on autocorrelation function AC_l

Autocorrelation¹⁶ measures the strength of correlation between observations as a direct function of space and time separated between them, where f(x) corresponds to a time dependent function.

d) Moreau-Broto autocorrelation¹⁷:

The most applied autocorrelation descriptor applied on a molecular graph.

e) Nucleophilic superdelocalizability:

Sum overall of the unoccupied molecular orbitals (NMONOCC)

Measure of availability for additional electron density on the a^th atom. If the transition states are controlled by the frontier orbital, the nucleophilic super delocalizability is calculated on the lowest unoccupied molecular orbital (LUMO).

f) Composite nuclear potential:

The descriptors defines the composite nuclear potential¹⁸for a respective configuration of a molecule. It is expressed as

Where, Z_a is the nuclear charge at a position defined as R_a

g) Quantum chemical descriptors:

These descriptors are mainly based on Schrodinger equation.

Where H corresponds to a Hamiltonian operator, E_icorresponds to electronic energy state of i^th atom and remaining one corresponds to the wave function. The spectrum of electronic molecular energy levels are themselves are characterized molecular descriptors.

h) Bertz-Herndon relative complexity index (C_BH): The structural complexity of a molecule is assessed by descriptors based on the molecular graph¹⁹in comparison with its parent molecular graph

K is the total number of interconnected sub graphs in G and K (G).

i) Minoli complexity index:

The descriptor measures the complexity of a molecular graph²⁰ based on the incremental addition of edges and vertices.

Where A represents number of vertices and B represents number of edges. And L is the length of the longest path in the graph.

j) Maximum nuclear repulsion C-H bond index: The descriptors corresponds to the nuclear repulsion energy between a carbon and its bonded hydrogen.²¹

Where Z corresponds to the atomic numbers, r_CHstands for C-H bond length and k is the pairs of bonded carbon and protons.

k) ALPHA descriptor:

A vector based molecular descriptor²² calculated from the trajectories got through molecular dynamic simulations by utilizing Gaussian smoothing. Alpha descriptor is expressed as

In the above equation, a and s are the mean and standard deviation of the Gaussian functions.

l) Amphiphilic moments:

The difference between free energies of transfer between aqueous phases to the aqueous: air phase is known as amphiphilicity. It is quantified by the relative surface tension measurements^.23

Where d stands for the distance

m) Atomic solvation parameter:

Solvation free energy of chemical species is calculated using an empirical molecular descriptor.²⁴

Where SA stands for solvent accessible surface area.

n) Molecular electronegativity edge vector:

Is a modified version of the Moreau-broto autocorrelation defined by applying the reciprocal of topological distances in conjunction with atom electronegativities. The auto correlation for kth lag is calculated as

Where d_ij refers to the topological distance between i^th and j^th atoms.

o) Balaban like indices:

In such indices, the distance connectivity descriptors calculated by applying the distance connectivity indices J.²⁵.

p) Bio descriptors:

Numerical quantities which encode information about biochemical systems and complex biological macromolecules. They give clear link between graph theories, topological parameters with molecular biology.

q) Amino acid descriptors:

Due to the wide importance and complexity of proteins, some descriptors were defined to represent amino acid side chains, these being responsible for the packing of the regular elements of secondary structure and then for the tertiary structure of a protein. As a consequence, the structure of a protein can be expressed quantitatively by means of side chain amino acid properties. Starting from the pioneering work of Sneath, who described peptide sequences by semi quantitative experimental parameters of the 20 coded amino acids.²⁶, several amino acid descriptors have been proposed that contain information about properties of side chains of amino acids.

r) Pharmacological indices:

Minimal dose that produces the desired effect of a drug is known as the effective dose (ED), often determined based on analyzing the dose–response relationship specific to the drug. The dosage which is able to produce a desired effect in half the test population is referred to as the median effective dose ED₅₀,

s) Therapeutic index:

Comparison of the amount of a therapeutic agent that causes the therapeutic effect to the amount that causes toxic effects. Quantitatively, it is the ratio of the dose required to produce the toxic effect over the therapeutic dose. A commonly used measure of therapeutic index is the lethal dose of a drug for 50% of the population (LD50) divided by the effective dose for 50% of the population (ED50)

t) Median Inhibitory Concentration (IC₅₀):

Measure of concentration that is required for producing 50% inhibition of a biological activity (i.e., an enzyme reaction, cell growth, reproduction, etc.). In simpler terms, it measures how much of a particular substance/molecule is needed to inhibit some biological process by 50%. IC50 is commonly used as a measure of drug-receptor binding affinity

CONCLUSION:

The present day researchers are showing deeper level of interest in the field of QSAR. In the process of solving QSAR problems, many of the chemoinformatics methods were specifically conceived. This has enabled to answer the demand to know in depth the chemical systems and their relationships with biological systems. As the likelihood of dealing with various biological systems described by peptide/protein or DNA sequences, to describe proteomics maps, or to give effective answers to ecological and health problems have increased, in the present scenario, it has promoted new borders where in mathematics orientation, statistics analysis, chemistry basis and biology together with their inter-relationships may produce new effective useful knowledge. In the recent years, several molecular descriptors have been proposed underlining the great interest the present generation scientific community has shown in theoretical approach to gather information about chemical compounds as well as the need for more specialized and sophisticated molecular descriptors useful for the development of predictive QSAR/QSPR models.

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Received on 17.06.2017 Modified on 14.07.2017

Research J. Pharm. and Tech. 2017; 10(9): 3237-3241.

DOI: 10.5958/0974-360X.2017.00574.1