Lou Massa

The transition state for formation of the peptide bond in the ribosome

Using quantum mechanics and exploiting known crystallographic coordinates of tRNA substrate located in the ribosome peptidyl transferase center around the 2-fold axis, we have investigated the mechanism for peptide-bond formation. The calculation is based on a choice of 50 atoms assumed to be important in the mechanism. We used density functional theory to optimize the geometry and energy of the transition state (TS) for peptide-bond formation. The TS is formed simultaneously with the rotatory motion enabling the translocation of the A-site tRNA 3′ end into the P site, and we estimated the magnitude of rotation angle between the A-site starting position and the place at which the TS occurs. The calculated TS activation energy, Ea, is 35.5 kcal (1 kcal = 4.18 kJ)/mol, and the increase in hydrogen bonding between the rotating A-site tRNA and ribosome nucleotides as the TS forms appears to stabilize it to a value qualitatively estimated to be ≈18 kcal/mol. The optimized geometry corresponds to a structure in which the peptide bond is being formed as other bonds are being broken, in such a manner as to release the P-site tRNA so that it may exit as a free molecule and be replaced by the translocating A-site tRNA. At TS formation the 2′ OH group of the P-site tRNA A76 forms a hydrogen bond with the oxygen atom of the carboxyl group of the amino acid attached to the A-site tRNA, which may be indicative of its catalytic role, consistent with recent biochemical experiments.

The Kernel Energy Method: Application to a tRNA

The Kernel Energy Method (KEM) may be used to calculate quantum mechanical molecular energy by the use of several model chemistries. Simplification is obtained by mathematically breaking a large molecule into smaller parts, called kernels. The full molecule is reassembled from calculations carried out on the kernels. KEM is as yet untested for RNA, and such a test is the purpose here. The basic kernel for RNA is a nucleotide that in general may differ from those of DNA. RNA is a single strand rather than the double helix of DNA. KEM energy has been calculated for a tRNA, whose crystal structure is known, and which contains 2,565 atoms. The energy is calculated to be E = –108,995.1668 (a.u.), in the Hartree–Fock approximation, using a limited basis. Interaction energies are found to be consistent with the hydrogen-bonding scheme previously found. In this paper, the range of biochemical molecules, susceptible of quantum studies by means of the KEM, have been broadened to include RNA.

Kernel energy method applied to vesicular stomatitis virus nucleoprotein

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.

The kernel energy method of quantum mechanical approximation carried to fourth-order terms.

It is now possible to calculate the ab initio quantum mechanics of very large biological molecules. Two things lead to this perspective, namely, (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. The kernel energy method (KEM) carried to second order has been used to calculate the quantum mechanical ab initio molecular energy of peptides, protein (insulin and collagen), DNA, and RNA and the interaction of drugs with their biochemical molecular targets. The results were found to have good accuracy. In this article, the accuracy of the KEM is investigated up to an approximation including fourth-order interactions among kernels. Remarkable accuracy is achieved in the calculation of the energy of the ground state of the important biological molecule Leu1-zervamicin, whose crystal structure is known and used in the calculations.

Calculated interactions of a nitro group with aromatic rings of crystalline picryl bromide.

Several crystalline polymorphs have been discovered for picryl bromide. Among the several forces that control the formation of such polymorphs are the interactions among the nitro groups and phenyl rings of those crystals. Although there are >300 structures to be found in the Cambridge Structural Database displaying the nitro-phenyl interaction, nonetheless this interesting, and apparently important, interaction, seems not to have been discussed within any of the papers reporting the structures. In this article, quantum calculations are reported that assess the strength of these nitro-phenyl interactions within a crystal of picryl bromide. The rather flat molecules of picryl bromide are arranged in layered planes within the crystal, and we examine the attractive interactions that occur within a given plane, and between adjacent planes. Calculations of Hartree Fock and Møller Plesset perturbation theory carried to a second-order expansion are used. Both quantum mechanical approximations are implemented with 6–31G* basis functions.

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

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.

Quantum crystallography, a developing area of computational chemistry extending to macromolecules

We describe the concept of quantum crystallography (QCr) and present examples of its potential as a technique for facilitating computational chemistry, particularly, applications of quantum mechanics. Structural information has been used to facilitate quantum-mechanical calculations for several decades. Recent advances in theory and computational facilities have led to research opportunities that could be considered only in the past several years. We focus on the feasibility of applications of quantum mechanics to macromolecules. The approach used involves the concept of calculations based on fragments of molecules. The method for constructing fragments, their composition, and how they are assembled to form a projector matrix are discussed without the introduction of mathematical detail. Papers that provide the theoretical basis for QCr and our method for making fragment calculations are referenced, and some initial calculations are described here.

The localization-delocalization matrix and the electron-density-weighted connectivity matrix of a finite graphene nanoribbon reconstructed from kernel fragments.

Baders quantum theory of atoms in molecules (QTAIM) and chemical graph theory, merged in the localization-delocalization matrices (LDMs) and the electron-density-weighted connectivity matrices (EDWCM), are shown to benefit in computational speed from the kernel energy method (KEM). The LDM and EDWCM quantum chemical graph matrices of a 66-atom C46H20 hydrogen-terminated armchair graphene nanoribbon, in 14 (2×7) rings of C2v symmetry, are accurately reconstructed from kernel fragments. (This includes the full sets of electron densities at 84 bond critical points and 19 ring critical points, and the full sets of 66 localization and 4290 delocalization indices (LIs and DIs).) The average absolute deviations between KEM and directly calculated atomic electron populations, obtained from the sum of the LIs and half of the DIs of an atom, are 0.0012 ± 0.0018 e(-) (∼0.02 ± 0.03%) for carbon atoms and 0.0007 ± 0.0003 e(-) (∼0.01 ± 0.01%) for hydrogen atoms. The integration errors in the total electron population (296 electrons) are +0.0003 e(-) for the direct calculation (+0.0001%) and +0.0022 e(-) for KEM (+0.0007%). The accuracy of the KEM matrix elements is, thus, probably of the order of magnitude of the combined precision of the electronic structure calculation and the atomic integrations. KEM appears capable of delivering not only the total energies with chemical accuracy (which is well documented) but also local and nonlocal properties accurately, including the DIs between the fragments (crossing fragmentation lines). Matrices of the intact ribbon, the kernels, the KEM-reconstructed ribbon, and errors are available as Supporting Information .

Protoribosome by quantum kernel energy method

Significance The ribosome is essential to life as it functions as “the protein factory” that translates the genetic code into proteins. A universally conserved region around its major active site, where the nascent proteins are being created, was identified in all contemporary ribosomes. Thus, it seems to be a remnant of an entity from the prebiotic RNA world, hence called the “protoribosome.” Using quantum mechanics and crystal coordinates of this region, we aimed at answering the question of whether the putative protoribosome has properties essential to function as an evolutionary precursor to the modern ribosome. Our findings show that the necessary conditions that would characterize a practicable protoribosome, namely energetic structural stability and energetically stable attachment to substrates, are well satisfied. Experimental evidence suggests the existence of an RNA molecular prebiotic entity, called by us the “protoribosome,” which may have evolved in the RNA world before evolution of the genetic code and proteins. This vestige of the RNA world, which possesses all of the capabilities required for peptide bond formation, seems to be still functioning in the heart of all of the contemporary ribosome. Within the modern ribosome this remnant includes the peptidyl transferase center. Its highly conserved nucleotide sequence is suggestive of its robustness under diverse environmental conditions, and hence on its prebiotic origin. Its twofold pseudosymmetry suggests that this entity could have been a dimer of self-folding RNA units that formed a pocket within which two activated amino acids might be accommodated, similar to the binding mode of modern tRNA molecules that carry amino acids or peptidyl moieties. Using quantum mechanics and crystal coordinates, this work studies the question of whether the putative protoribosome has properties necessary to function as an evolutionary precursor to the modern ribosome. The quantum model used in the calculations is density functional theory–B3LYP/3–21G*, implemented using the kernel energy method to make the computations practical and efficient. It occurs that the necessary conditions that would characterize a practicable protoribosome—namely (i) energetic structural stability and (ii) energetically stable attachment to substrates—are both well satisfied.

Characterization of a Trihydrogen Bond on the Basis of the Topology of the Electron Density

Recent DFT calculations have predicted unexpected molecular structures for the ion induced dipole clusters H(n)(-) (3 ≤ n-odd ≤ 13). Analysis of these calculations suggests the definition of a new bond, called the trihydogen bond (THB). This is placed in context by a review and classification of multihydrogen interactions as usually discussed in the literature. The results of analysis related to the trihydrogen bond are presented. These include a series of linear relations exhibited by the H(n)(-) clusters involving the charge carried by the central H(-) ion, the binding energy of the clusters, and the relative stabilization of the central anion H(-) with respect to the energy of a free H(-) atom.