The Kernel Energy Method: Application to a tRNA

2009

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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...

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confidence: 76%

Kernel energy method applied to vesicular stomatitis virus nucleoprotein

2009

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“…The validity of the KEM, in the case of a variety of peptides (8), proteins (9), DNA (10), and RNA structures (12), has been shown in previous work. Of special relevance to this article, the KEM has been applied to the calculation of interaction energies between biological molecules and has been shown to be useful for that purpose (10,11).…”

Section: T He Topic Of Weak Interactions (Including Hydrogen Bonds) Ismentioning

confidence: 71%

“…We wish to calculate the interaction energy between full neighboring molecules, and having that value, to calculate the components of such interactions that are contributed by the various ''pieces'' of the molecules through their strong and weak hydrogen bonds. Thus, the relative importance of the weak and strong hydrogen bonds would be an outcome of the study.Since the molecules to be studied may be thought of as having a variety of pieces, each contributing to the various strong and weak interactions, a natural method of quantum calculation from 1995 is that of kernel density matrices (5-7), which has evolved more recently to the Kernel Energy Method (KEM) of Quantum Crystallography (8)(9)(10)(11)(12)(13)(14). In the KEM, the results of X-ray crystallography are combined with those of quantum mechanics.…”

mentioning

confidence: 99%

Calculation of strong and weak interactions in TDA1 and RangDP52 by the kernel energy method

et al. 2009

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Using the Kernel Energy Method we apply ab initio quantum mechanics to study the relative importance of weak and strong interactions (including hydrogen bonds) in the crystal structures of the title compounds TDA1 and RangDP52. Perhaps contrary to widespread belief, in these compounds the weak interaction energies, because of their large number and cooperativity, can be significant to the binding energetics of the crystal, and thus also to its other properties.CH-O bonds ͉ cooperativity of bonds ͉ cysteine macrocycles ͉ NH-CO bonds ͉ NH-S T he topic of weak interactions (including hydrogen bonds) is of increasing general interest because in large numbers and cooperativity they can be important to molecular properties. Desiraju and Steiner (1) discuss this aspect of weak hydrogen bonds and have published a collection of structures in which these bonds participate. The understanding of these weak interactions will likely be useful in future designs of complex selforganizing structures. It has been noted that cooperativity among weak interactions allows them to contribute effectively to tighten molecular packing in crystals to an extent beyond that associated with ordinary van der Waals forces. This can affect the thermal and electronic properties of molecules, including electron mobility, and physical properties such as hardness, melting point, and crystal stability (1-4). Because it is of increasing interest to recognize the significant and sometimes subtle effects on molecular properties caused by weak interactions, we have undertaken a quantum mechanical study of their energetics in crystals of 2 molecules that may stand as examples in addition to the compounds discussed by Desiraju and Steiner. These areIn the molecules to be studied the crystal structures and atomic coordinates are known (2, 3). This information is used to obtain the atomic coordinates of the near-neighbor molecules in the crystal to which they are related by operations of space group symmetry. In particular, it is the interaction energy between neighboring molecules of the crystal that is the object of our study. We wish to calculate the interaction energy between full neighboring molecules, and having that value, to calculate the components of such interactions that are contributed by the various ''pieces'' of the molecules through their strong and weak hydrogen bonds. Thus, the relative importance of the weak and strong hydrogen bonds would be an outcome of the study.Since the molecules to be studied may be thought of as having a variety of pieces, each contributing to the various strong and weak interactions, a natural method of quantum calculation from 1995 is that of kernel density matrices (5-7), which has evolved more recently to the Kernel Energy Method (KEM) of Quantum Crystallography (8)(9)(10)(11)(12)(13)(14). In the KEM, the results of X-ray crystallography are combined with those of quantum mechanics. It is assumed that the crystal structure is known for a molecule under study. With known atomic coordinates, the molecule is math...

“…The use of the single kernels and double kernels is an approximation that is made to obtain a simplification in the quantum calculation. The validity of this approximation, in the case of a variety of peptides, proteins, DNA, and RNA structures, has been shown in previous work (1,(3)(4)(5). In this article we depend on the known ab initio accuracy of the KEM to show how it may be used to obtain drug-RNA target interaction energies.…”

Section: Review Of the Kemmentioning

confidence: 90%

“…The examples used to make this point included peptides, protein (insulin), DNA, and RNA (1,(3)(4)(5). A great saving of computational time is associated with the KEM, and high accuracy is achieved.…”

Section: Discussionmentioning

confidence: 99%

Drug target interaction energies by the kernel energy method in aminoglycoside drugs and ribosomal A site RNA targets

2007

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It is possible to use the full power of ab initio quantum mechanics in application to the interaction of drugs and their molecular targets. This idea had barely been realized until recently, because of the well known growth in computational difficulty of the use of quantum mechanics, with the number of atoms in the molecule to be studied. Because the biochemical molecules of medicinal chemistry are so often large, containing thousands or even tens of thousands of atoms, the computational difficulty of the full quantum problem had been prohibitive. Two things have happened, however, that change this perspective: (i) the advances of parallel supercomputers, and (ii) the discovery of a quantum formalism called quantum crystallography and the use of quantum kernels, a method that is well suited for parallel computation. Such advances would allow the quantum mechanical ab initio calculation of the molecular energy of peptides, proteins, DNA, and RNA, obtaining results of high accuracy. In this approach the computational difficulty of representing a molecule increases only modestly with the number of atoms. The calculations are simplified by adopting an acceptable approximation that allows a full biological molecule to be represented by smaller ''kernels'' of atoms. These results suggest that problems of medicinal chemistry, such as the rational design of drugs, may be illuminated by quantum mechanical analysis. The general case is illustrated by specific examples, namely, the HF/STO-3G calculations of three aminoglycoside drugs that attach to ribosomal A-site RNA nucleotide targets.biological molecules ͉ Hartree-Fock ͉ quantum mechanics T his article combines structural crystallographic information with quantum-mechanical theory. One goal is to show that the kernel energy method (KEM) is of practical use in the calculation of drug-target interaction energies. In particular, this is a challenging problem for the common case of very large molecular targets involving proteins, DNA, or RNA. Another objective is to simplify computational chemistry calculations and enhance the information that may be derived from a crystallographic experiment. This article focuses on example calculations of the interaction energies of individual drug-ribosomal RNA targets.The KEM may be described as the determination of the quantum mechanical molecular energy by the use of the parts of a whole molecule, which are referred to as kernels. 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 has been simplified for biological molecules as large as the various configurations of RNA, combined with drugs studied in this article. The computational time is much reduced by using the KEM, and the accuracy obtained appears to be quite satisfactory, as shown in previous work.The first applications of ...