Extracting Quantitative Information at Quantum Mechanical Level from Noncovalent Interaction Index Analyses

Abstract

The noncovalent interaction (NCI) index is nowadays a well-known strategy to detect NCIs in molecular systems. Even though it initially provided only qualitative descriptions, the technique has been recently extended to also extract quantitative information. To accomplish this task, integrals of powers of the electron distribution were considered, with the requirement that the overall electron density can be clearly decomposed as sum of distinct fragment contributions to enable the definition of the (noncovalent) integration region. So far, this was done by only exploiting approximate promolecular electron densities, which are given by the sum of spherically averaged atomic electron distributions and thus represent too crude approximations. Therefore, to obtain more quantum mechanically (QM) rigorous results from NCI index analyses, in this work, we propose to use electron densities obtained through the transfer of extremely localized molecular orbitals (ELMOs) or through the recently developed QM/ELMO embedding technique. Although still approximate, the electron distributions resulting from the abovementioned methods are fully QM and, above all, are again partitionable into subunit contributions, which makes them completely suitable for the NCI integral approach. Therefore, we benchmarked the integrals resulting from NCI index analyses (both those based on the promolecular densities and those based on ELMO electron distributions) against interaction energies computed at a high quantum chemical level (in particular, at the coupled cluster level). The performed test calculations have indicated that the NCI integrals based on ELMO electron densities outperform the promolecular ones. Furthermore, it was observed that the novel quantitative NCI−(QM/)ELMO approach can be also profitably exploited both to characterize and evaluate the strength of specific interactions between ligand subunits and protein residues in protein−ligand complexes and to follow the evolution of NCIs along trajectories of molecular dynamics simulations. Although further methodological improvements are still possible, the new quantitative ELMO-based technique could be already exploited in situations in which fast and reliable assessments of NCIs are crucial, such as in computational high-throughput screenings for drug discovery.

Current developments and trends in quantum crystallography

“…Among many, it is worth highlighting: (i) its extension through the NCI-Milano version to also consider experimental electron densities resulting from multipole model or maximum entropy refinements (Saleh et al, 2012(Saleh et al, , 2013; (ii) the coupling with the ELMO libraries to perform NCI-index analyses based on quantum mechanically rigorous electron density distributions also in the case of large biomolecular systems (Arias-Olivares et al, 2019); (iii) the introduction of more advanced variants of the approach to also obtain quantitative results from the NCIindex computations (see Fig. 10) (Peccati, 2020;Boto et al, 2020;Wieduwilt et al, 2023); (iv) and the creation of a userfriendly webserver to facilitate the analyses of noncovalent interactions in large systems of biological interest (Novoa et al, 2023). Based on the current state-of-the-art, today the NCI-index approach can be considered as a quite mature technique and more and more applications to quantum crystallographic problems are expected in the next years.…”

The NCIWEB Server: A Novel Implementation of the Noncovalent Interactions Index for Biomolecular Systems

“…Nevertheless, charged residues lead to stronger interactions, which are reflected on the distances and hence on the densities . This functionality is to be extended in the future through the use of localized molecular orbitals derived from charged fragments. , …”

“…It does not require any a priori parametrization or definition of particular NCIs (i.e., it does not require any notion of what types of interactions are present). Although the NCI index does not provide interaction energies, it has been shown that the integral of the density in the NCI regions are proportional to the strength of the interactions. ,, Thus, it can provide complementary information for the visualization, identification and monitoring of NCIs in such systems. Hence, they have also been included in NCIWEB (see the section entitled “The NCIWEB Server”).…”

“…Most generally, the NCI index relies on a general approach derived from density functional theory for the visualization and analysis of NCIs. ,, While a rigorous description of the theoretical framework of this approach can be found elsewhere and is beyond the scope of this work, ,− the gist of the NCI index is to use the electron density of the system ρ­( r ) to identify noncovalent interactions as the regions where (i) the reduced density gradient s ( s ( r ) = 1/(2­(3π2) 1/3 |∇ρ­( r )|/ρ­( r ) 4/3 ) nearly vanishes, and (ii) ρ­( r ) is lower than that of a covalent interaction. Since the NCI index exclusively relies on the electron density, which can be reconstructed from atomic densities without complex sets of parameters to adjust empirically (Figure a), ,− it has been used in systems ranging from small molecules, , to solid-state chemistry, − to biomolecules, − for diverse applications including the understanding of reactivity, − cofactor and active site activity in biomolecules, , and performance of chemotherapy carriers …”

“…20 This functionality is to be extended in the future through the use of localized molecular orbitals derived from charged fragments. 36,37 Overall, the NCI index provides an intermediate accuracy option: distances are taken into account just as in the case of radii, but environments reveal their influence (since all atomic densities contribute). Since these atomic densities are approximate, quantum mechanical calculations are not involved, thus providing an efficient approach for the analysis of NCIs in biosystems.…”