Quantitative Structure Activity Relationships are often used in the ligand structure-based drug design. The QSAR relates potency or toxicity of a set of similar drugs with a variety of molecular descriptors. Many descriptors can be calculated rapidly using empirical formulas based on the structure and the connectivity of atoms in the molecule. For example, descriptors such as the molecular weight and the number of H-bond acceptors are easy to determine. Some descriptors, such as logP and molecular polarizability can be approximated from atomic or group contributions. Descriptors that relate to electronic structure, such as the HOMO and LUMO energies, must be obtained from quantum chemical calculation. Oftentimes, descriptors of different nature and origin are mixed together. For example, the reactivity of a molecule can be described both in terms of its HOMO energy (a quantum-mechanical descriptor) and the bulk of the substituent (constitutional descriptor).
HOMO and LUMO refer to Highest Occupied Molecular Orbital and Lowest Unoccupied Molecular Orbital. According to the Frontier Orbital Theory, nucleophilic attack occurs by electron flow from a (HOMO of) nucleophile into the LUMO of the electrophile. In stable molecules, occupied electrons always reside on orbitals with negative energies and unoccupied orbitals have positive energies. The energies of HOMO and LUMO are related to the reactivity of the molecule: molecules with electrons at accessible (near-zero) HOMO levels tend to be good nucleophiles because it does not cost much to donate these electrons toward making a new bond. Similarly, molecules with low LUMO energies tend to be good electrophiles because it does not cost much to place an electron into such an orbital.
Polarizability characterizes how readily the atomic or molecular charge distribution is distorted by external static or oscillating electromagnetic fields. Static polarizability can be rigorously calculated as the first derivative of the dipole moment with respect to the electric field, or the second derivative of molecular energy with respect to electric field. Several computer programs can calculate this molecular property. Polarizability depends on the electronic structure of atoms and molecules. In general, large atoms in which electrons are far from the sphere of influence of the positively charged nucleus, are more polarizable that small atoms. For example, He is extremely non-polarizable while xenon is very polarizable.
The dynamic polarizability refers to the ability of a molecular charge distribution to respond to oscillating electromagnetic fields. This is important for the London dispersion forces, which arise from the coupling of fluctuating charge distributions in two interacting molecules. The accurate theory of London dispersion interactions is rather complicated, but to a good approximation, the binding energy between the two molecules is proportional to their static polarizabilities. Because the interaction energy is inversely proportional to the sixth power of the distance between interacting particles, the London dispersion force is only significant when the surfaces of the receptor and the ligand are in close proximity. In case of a receptor and multiple ligands that can fit to the receptor, the relative binding energy would thus depend on the polarizability of the ligand. All other things equal, a highly polarizable ligand (e.g. one with aromatic rings) is expected to bind stronger than a weakly polarizable ligand (e.g. one with cyclohexyl rings). Note that this simplified analysis neglects the London dispersion interaction between the solvent and the ligands.
MOLDEN serves as an interface to quantum chemistry programs such as Gaussian, Gamess, and MOPAC. Gaussian and Gamess are so-called ab initio codes because they allow quantum chemical calculations without any empirical molecule-specific parametrization. For larger molecules, ab initio quantum mechanical calculations may become time consuming, especially because QSAR studies require that calculations are carried out on many molecules. For example, it would be impractical to calculate properties such polarizabilities of barbiturates using accurate ab initio methods. Students who wish to try quantum chemistry calculations on their Windows or Linux PCs could download a free program Firefly (PC GAMESS). MOLDEN can create input files that (after some modification) are accepted by Firefly, and MOLDEN can read information from the Firefly output files.
MOPAC is a semi-empirical program. The semi-empirical approach uses experimental data to simplify its quantum-chemical model. Semi-empirical models are important because they allow calculation of structures and properties of large molecules that are of interest in biochemistry and drug design. They may be just accurate enough to give reasonably good descriptors for QSAR in a fraction of time.
Phenyl rings are common in many drugs, and they are often sites of drug metabolism. You will be studying the effect of a substituent on HOMO energy by comaring theoretical HOMO energies of toluene (methylbenzene) and fluorobenzene.
Hydrophobic analogs of barbituric acid act as central nervous system depressants. They were widely used before safer benzodiazepines were developed. It is believed that they act on GABAA receptors and potentiate the effect of GABA: they will keep the chloride channels open for a longer time. Experimental structure-activity studies of various barbiturates have been reported by Basak, Harriss, and Magnuson (PDF). Table VII in this paper provides activities and various molecular descriptors for 17 analogs. Your assignment involves re-analysis of this data, and evaluation of molecular polarizability as an additional molecular descriptor for the activity of barbiturates.
Calculations with MOPAC
You will calculate static polarizability of very analog using MOLDEN and MOPAC. First, obtain the structure of the ethyl analog of barbituric acid IV (pg. 434) using Online SMILES Translator by National Institutes of Health or MOLDEN. Save the structure (e.g. barbiturate_1.mol) in your directory as a 3D MOL file.