Physics Explains Biology -
van der Waals Dispersion Forces in Drug Discovery
Carfilzomib, a United States Food and Drug Administration (FDA) approved anti-cancer drug, is an inhibitor of cellular proteasome. Carfilzomib is a tetrapeptide with four side chains (P1-4). Its specificity for the catalytic subunit beta5 of the 20S proteasome core particle is determined by van der Waals interactions of its hydrophobic P1 leucyl group in the S1 pocket. The side chains of amino acid residues Ala20, Val31, Met45 and Ala49 are involved in these interactions.
Three types of intermolecular interaction, all electrostatic in nature, are collectively called van der Waals interactions – permanent dipole-permanent dipole, permanent dipole-induced dipole and induced dipole-induced dipole.
Molecular dipole: Most molecules carry no net charge, but many possesses an electric dipole. In some molecules, such as Cl2, the bonding pair of electrons are equally attracted by the two atoms and, therefore, placed exactly halfway between them. The electron cloud is uniform and the centers of positive and negative charges are not separated. The bond is purely covalent or nonpolar. There are also examples of nonpolar functional groups such as methyl.
On the other hand, hydrogen (H) and chlorine (Cl) combine to form HCl by sharing a pair of electrons. However, due to the difference in electronegativity (that is, the ability of an atom to attract a bonding pair of electrons), the electron density is greater towards the Cl – end which, consequently, becomes slightly negative (δ-). Simultaneously, the H-end becomes δ+. The bond is polar covalent or, simply, polar and the molecule is a dipole. Similarly, a number if functional groups, such as hydroxyl, are polar in nature.
In a molecular dipole, the electron cloud is not uniform but denser towards one end. Consequently, the centers of positive and negative charges are separated by a finite distance. Dipole-dipole interactions, as the term suggests, occur between two permanent molecular dipoles
Nevertheless, some of the nonpolar molecules (or functional groups) are fairly polarizable, that is, their charges are displaced by an electric field. If, for example, a positively charge ion (cation) approaches a polarizable nonpolar molecule, some electrons move towards the cation-proximal end while the distal end becomes deficient in electrons.
Similarly, a permanent molecular dipole can induce a dipole moment in a nonpolar molecule. Evidently, the dipole-induced dipole interaction is dependent on the polarizability of the nonpolar molecule.
Based on what has been discussed so far, it may appear that the interaction between two nonpolar molecules, where one cannot induce a dipole moment in the other, is very unlikely. However, it is to be noted that the electron distribution within a molecule, polar or nonpolar, is not static. The uniformity of the electron cloud that is attributed to the characteristic of a nonpolar molecule (or functional group) is only a time-average. Continuous movement of the electrons results in an instantaneous dipole. The instantaneous dipole, in turn, induces an instantaneous dipole in its neighboring molecules generating induced dipole-induced dipole forces. These forces, between all atoms and molecules including the totally neutral ones, are called dispersion forces, London forces or electrodynamic forces
When the molecules are close to each other, say, for a cluster of molecules (within a range of a few angstroms), the polarities fluctuate in synchronization, so that there will always be attraction between them.
The P1 leucyl group of carfilzomib, as well as the side chains of interacting amino acid residues Ala20, Val31, Met45 and Ala49, are all nonpolar. Nevertheless, the electron cloud corresponding to each of these functional groups is dynamic. Their polarities fluctuate in synchronization, each influencing and being influenced by the others. As a result, the binding of carfilzomib to b5 subunit is established.
Computer simulations at the atomistic level have been very useful in studying the binding of a small molecule (ligand) to its (receptor) protein. It is known that molecules are quantum mechanical entities. Hence, the dynamic behavior of a molecule is best described by the quantum mechanical equation of motion. However, this equation is extremely difficult to solve for a large molecule.
For this reason, atomic motions of the molecules are studied by molecular dynamics (MD) which is based on classical mechanics and utilizes Newton’s equation of motion. MD plays an important role in drug discovery. Along with other forces, van der Waals interactions receives major considerations in MD simulations.
References:
Harshbarger, W. et al. 2015. Crystal structure of the human 20S proteasome in complex with carfilzomib. Structure 23:418-424.
* For the basic concept of van der Waals interactions the readers are referred to Fundamentals of Molecular Structural Biology (Chapter 4, Elsevier publication, 2019)