Kernel energy method applied to vesicular stomatitis virus nucleoprotein

Abstract

The kernel energy method (KEM) is applied to the vesicular stomatitis virus (VSV) nucleoprotein (PDB ID code 2QVJ). The calculations employ atomic coordinates from the crystal structure at 2.8-Å resolution, except for the hydrogen atoms, whose positions were modeled by using the computer program HYPERCHEM. The calculated KEM ab initio limited basis Hartree-Fock energy for the full 33,175 atom molecule (including hydrogen atoms) is obtained. In the KEM, a full biological molecule is represented by smaller ''kernels'' of atoms, greatly simplifying the calculations. Collections of kernels are well suited for parallel computation. VSV consists of five similar chains, and we obtain the energy of each chain. Interchain hydrogen bonds contribute to the interaction energy between the chains. These hydrogen bond energies are calculated in Hartree-Fock (HF) and Møller-Plesset perturbation theory to second order (MP2) approximations by using 6 -31G** basis orbitals. The correlation energy, included in MP2, is a significant factor in the interchain hydrogen bond energies.Hartree-Fock ͉ KEM ͉ Møller-Plesset ͉ quantum mechanics T he kernel energy method (KEM) combines structural crystallographic information with quantum-mechanical theory, and is of practical use in the calculation of molecular interaction energies, which is otherwise a challenging problem for large molecular targets such as the vesicular stomatitis virus (VSV) nucleoprotein. This article focuses on calculations of total energy for the entire molecule and the hydrogen bond interaction energies between the chains of VSV which make up the full nucleoprotein, whose PDB ID code is 2QVJ (1).The KEM here used determines the quantum mechanical molecular energy by the use of parts of a whole molecule, which are referred to as kernels, as in supporting information (SI) Fig. S1. Because the kernels are much smaller than a full biological molecule, the calculations of kernels and double kernels are practicable. Subsequently, kernel contributions are summed in a manner affording an estimate of the energy for the whole molecule. Thus, the task of obtaining a quantum mechanical energy is simplified for large biological molecules. The computational time is much reduced by using the KEM, and the accuracy obtained appears to be quite satisfactory, as shown in previous work (2-8).As the crystal structure is known for 2QVJ under study, the molecule may be mathematically broken into the tractable pieces called kernels. The kernels are chosen such that each atom occurs in only one kernel. Only kernels and double kernels are used for all quantum calculations. The total molecular energy is reconstructed there from, by summation over the contributions of the double kernels reduced by those of any single kernels that have been over counted.If all double kernels are included, the total energy is,where E ij ϭ energy of a double kernel of name ij, E i ϭ energy of a single kernel of name i, i, j ϭ running indices, and n ϭ number of single kernels.In this article we obtain the total molec...

Protoribosome by quantum kernel energy method

“…The symbols i and j are running indices and n is the number of single kernels. The validity of this has been shown in previous works (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24). In this article we use the reliable accuracy of KEM to calculate the interaction energies associated with putative protoribosome molecules.…”

“…As an example of the large size of systems that can be studied with ab initio KEM, we have applied the method to a HartreeFock (HF) calculation of a 33,000-atom protein (16). It is entirely feasible to treat even larger molecules within the context of KEM capabilities.…”

The Kernel energy method: Application to graphene and extended aromatics

“…Although the graphene flake chosen for a demonstration calculation in this article is relatively small, containing a total of 104 atoms, we envision no difficulty in applying the KEM to finite graphenes of great extension. We have applied the KEM, for example, to a protein made of more than 33K atoms [40]. Thus, the KEM will be applicable to finite aperiodic graphenes containing very large numbers of atoms.…”

“…It has been used to calculate, what is perhaps at present the largest molecule in the literature of ab initio calculations [40]. To the point of this article, however, KEM has not been applied to graphenes and extended aromatic molecules.…”

Subsystem Quantum Mechanics and In Silico Medicinal and Biological Chemistry

“…A method particularly suited to obtaining an excellent approximation to the total and binding energies (and energy derivatives) of macromolecules at a very high level of quantum mechanical theory is termed the kernel energy method (KEM) [25][26][27][28][29][30][31]. The macromolecule is broken into single and double kernels (subsystems), capped with hydrogen atoms, then the energy of the full system is obtained by recombining the energies of the pieces in a manner that accounts, to a very good approximation, for the 'self' energies of each kernel, in addition to its interactions with all other kernels in the full molecule.…”