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Author: Anupa Bhattacharya
Density functional theory is one of the most popular quantum mechanical energy
minimization process used in physics, chemistry and materials science to investigate the
electronic structure of many-body systems. The name "density functional theory" comes from the use of functionals, i.e, function of functions, which in this case is spatially dependent
electron density.
For one-electron systems like the hydrogen atom, it is very easy to solve the Schrödinger
equation exactly, and calculate the possible energy states of the system by obtaining the
energy eigenvalue. The Schrödinger equation is represented as:
where H is the Hamiltonian operated on the wave-function (psi), and E is the energy eigenvalue.
However, the difficulty of the calculation increases with the dimension of the problem.
Therefore, it is very difficult to solve this equation for many-electron systems like polyatomic
molecules. DFT is nothing but a computational technique for achieving an approximate
solution to the Schrödinger equation for many-body systems [1]. The wave function of a N
electronic system is a function of 3N number of variables (coordinates of all the N atoms),
whereas taking electron density functional reduces the number of variables to 3 (x,y,z),
making the calculation easier. Also, it has been established by the Hohenburg-Kohn theorem
[2] that the electron density of any system determines all the ground state properties of that
system. By focusing on the electron density, it is possible to derive an effective one-electron
type Schrödinger equation for a many-electron system and get all possible energy states of
that system by solving it. Presently one of the most successful and promising approach
towards investigating the electronic structure, the applicability of DFT ranges from atoms,
molecules and solids to nuclei, quantum and classical fluids. It predicts a great variety of
molecular properties, structures, atomization energies, reaction pathways, etc.
It is an extraordinary tool in the in silico screening and design of active pharmaceutical
ingredients. A small work was done by me for my Master’s dissertation, which involved the in
silico screening of Non Steroidal Anti Inflammatory drugs using DFT and molecular
docking. Among the various properties that can be predicted from DFT, we had mainly
focused on the energy difference of the Highest Occupied Molecular Orbital (HOMO) and
Lowest Unoccupied Molecular Orbital (LUMO) of a molecule. It has been studied that the
inhibitory activity of a molecule is generally affected by its total energy, entropy, polarity and
electron transition probability. The electron transition probability is further dependent on the
HOMO-LUMO energy gap of a molecule. This energy gap, also gives us an idea about the
stability of a molecule, which follows a reverse order with electron transition probability.
Lower the HOMO-LUMO energy gap of a molecule, the more active and less stable is it, and
vice-versa. [3]. The DFT calculations were performed using DMOL 3 code [4, 5], under
Generalized Gradient Approximation (GGA) [6]. The density functional BLYP [7, 8] was
used along with the Double Numeric Plus polarization (DNP) basis set. The optimization was
carried out without any structural constraint and HOMO-LUMO energy gap was computed in
electron volts (eV).
Molecular docking is another popular aspect in structural molecular biology and computer-assisted drug design. It is used to predict the preferred orientation of one molecule to another when they are bound to form a stable complex [9], thus also giving an idea of binding affinity of one molecule to the other. Due to the ability of this technique to predict the binding conformation of a small molecule to its appropriate target (essentially macromolecules like proteins), molecular docking is found to have an extensive use in structure-based drug design.
Molecular docking mainly approaches towards achieving optimized conformations for both
the protein and ligand, and the relative orientation of the protein and ligand, so that the free
energy of the overall system is minimized. The ligand and the protein adjust their
conformation to achieve a “best-fit” conformationally as well as energetically [10]. The
mechanics of docking broadly involves two steps:
1. Search algorithms: Theoretically, a search space consists of all possible
conformations and orientations of the ligand bound to the protein. In actual practice, it
is not possible to explore the search space minutely, as molecules are dynamic and
exist as an ensemble of various conformational states. Therefore most docking
programs employ easier conformational search strategies. Among these, the most
widely used is the “genetic algorithm” which is used for evolving low energy
conformations, where the score of each bound conformation acts as the fitness
function to select molecules for the next iteration.
2. Scoring function: Among the potential protein-ligand conformations generated by a
docking program, some are rejected outright due to clashes. But the rest are evaluated
using a scoring function, representing a favorable binding interaction and ranking the
conformations relative to each other. The scoring function is generally represented as
a cumulative free energy for binding taking into account all other contributions
including solvent effects, conformational changes, etc.[11]. A lower (negative)
binding energy indicates a stable system and more likely binding interaction.
[Protein-ligand docking. http://biochemlabsolutions.com/Docking/screen.jpg.]
References
[1] Belaidi. S., Mellaoui. M., (2011), “Electronic Structure and Physical-Chemistry Property
Relationship for Oxazole Derivatives by Ab-Initio and DFT Methods”, Organic Chemistry
International, 2011, 7 pages.
[2] P. Hohenberg. P., Kohn. W., (1964),“Inhomogeneous Electron Gas”, Physical
Review, 136, B864.
[3] Ghosh. D.C. , Jana. J., (1999), “A study of correlation of the order of chemical reactivity
of a sequence of binary compounds of nitrogen and oxygen in terms of frontier orbital
theory”, Current Science, 76, 570-573.
[4] Bhattacharya. A. et al, (2010), “Crystal structure and electronic properties of two
nimesulide derivatives: A combined X-ray powder diffraction and quantum mechanical
study”, Chemical Physics Letters, 493, 151-157.
[5] Delley. B., (1998), “An all‐electron numerical method for solving the local density
functional for polyatomic molecules”, The Journal of Chemical Physics, 92, 508 (1990).
[6] Perdew. J.P. et al, (1996), “Generalized Gradient Approximation Made Simple”, Physical
Review Letters, 77 ,3865.
[7] Becke. A.D., (1988), “Density-functional exchange-energy approximation with correct
asymptotic behaviour”, Physical Review A, 38, 3098.
[8] Lee. A. C. et al, (1988), “Development of the Colle-Salvetti correlation-energy formula
into a functional of the electron density”, Physical Review B, 37, 785-789.
[9] Lengauer. T., Rarey. M., (1996), “Computational methods for biomolecular docking",
Current Opinion in Structural Biology, 6,402–406.
[10] Wei. B.Q et al, (2004). “Testing a flexible receptor docking algorithm in a model
binding site”, Journal of Molecular Biology”, 337, 1161–1182.
[11] Murcko. M.A., (1995). “Computational Methods to Predict Binding Free Energy in
Ligand Receptor Complexes”,Journal of Medicinal Chemistry. 38, 4953–4967.
About the Author
Anupa Bhattacharya is a 26 year old from West Bengal, India. She has completed her Master's in Applied Chemistry and has previously worked for two years as a high school chemistry teacher. She likes to describe herself as an avid reader, dreamer and science enthusiast, specifically in interdisciplinary research. Apart from that she is also highly interested in literature and performing arts.
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