Topological Analysis of Electron Density in Large Biomolecular Systems

A great step toward describing the structure of the molecular electron was made in the era of quantum chemical methods. Methods play a very important role in the prediction of molecular properties and in the description of the reactivity of compounds, which cannot be overestimated. There are many works, books, and articles on quantum methods, their applications, and comparisons. At the same time, quantum methods of a high level of theory, which give the most accurate results, are time-consuming, which makes them almost impossible to describe large complex molecular systems, such as macromolecules, enzymes, supramolecular compounds, crystal fragments, and so on.

To propose an approach that allows real-time estimation of electron density in large systems, such as macromolecules, nanosystems, proteins.

AlteQ approach was applied to the tolopogical analysis of electron density for "substrate - cytochrome" complexes. The approach is based on the use of Slater's type atomic contributions. Parameters of the atomic contributions were found using high resolution X-ray diffraction data for organic and inorganic molecules. Relationships of the parameters with atomic number, ionization potentials and electronegativities were determined. The sufficient quality of the molecular electron structure representation was shown under comparison of AlteQ predicted and observed electron densities. AlteQ algorithm was applied for evaluation of electron structure of "CYP3A4 - substrate" complexes modeled using BiS/MC restricted docking procedure. Topological analysis (similar to Atoms In Molecules (AIM) theory suggested by Richard F.W. Bader) of the AlteQ molecular electron density was carried out for each complex. The determination of (3,-1) bond, (3,+1) ring, (3,+3) cage critical points of electron density in the intermolecular "CYP3A4 - substrate" space was performed.

Different characteristics such as electron density, Laplacian eigen values, etc. at the critical points were computed. Relationship of pKM (KM is Michaelis constant) with the maximal value of the second Laplacian eigen value of electron density at the critical points and energy of complex formation computed using MM3 force field was determined.

It was shown that significant number of (3,-1) bond critical points are located in the intermolecular space between the enzyme site and groups of substrate atoms eliminating during metabolism processes.