The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

NMR chemical shifts in proteins depend strongly on local structure. The program TALOS establishes an empirical relation between 13C, 15N and 1H chemical shifts and backbone torsion angles ϕ and ψ (Cornilescu et al. J Biomol NMR 13 289–302, 1999). Extension of the original 20-protein database to 200 proteins increased the fraction of residues for which backbone angles could be predicted from 65 to 74%, while reducing the error rate from 3 to 2.5%. Addition of a two-layer neural network filter to the database fragment selection process forms the basis for a new program, TALOS+, which further enhances the prediction rate to 88.5%, without increasing the error rate. Excluding the 2.5% of residues for which TALOS+ makes predictions that strongly differ from those observed in the crystalline state, the accuracy of predicted ϕ and ψ angles, equals ±13°. Large discrepancies between predictions and crystal structures are primarily limited to loop regions, and for the few cases where multiple X-ray structures are available such residues are often found in different states in the different structures. The TALOS+ output includes predictions for individual residues with missing chemical shifts, and the neural network component of the program also predicts secondary structure with good accuracy.

/pdf/talos-a-hybrid-method-for-predicting-protein-backbone-4t5z8ivciv.pdf

TALOS+: a hybrid method for predicting protein backbone torsion angles from NMR chemical shifts.

INTRODUCTION. ELEMENTS OF GRAPH THEORY. The Definition of a Graph. Isomorphic Graphs and Graph Automorphism. Walks, Trails, Paths, Distances and Valencies in Graphs. Subgraphs. Regular Graphs. Trees. Planar Graphs. The Story of the Koenigsberg Bridge Problem and Eulerian Graphs. Hamiltonian Graphs. Line Graphs. Vertex Coloring of a Graph. CHEMICAL GRAPHS. The Concept of a Chemical Graph. Molecular Topology. Huckel Graphs. Polyhexes and Benzenoid Graphs. Weighted Graphs. GRAPH-THEORETICAL MATRICES. The Adjacency Matrix. The Distance Matrix. THE CHARACTERISTIC POLYNOMIAL OF A GRAPH. The Definition of the Characteristic Polynomial. The Method of Sachs for Computing the Characteristic Polynomial. The Characteristic Polynomials of Some Classes of Simple Graphs. The Le Verrier-Faddeev-Frame Method for Computing the Characteristic Polynomial. TOPOLOGICAL ASPECTS OF HUECKEL THEORY. Elements of Huckel Theory. Isomorphism of Huckel Theory and Graph Spectral Theory. The Huckel Spectrum. Charge Densities and Bond Orders in Conjugated Systems. The Two-Color Problem in Huckel Theory. Eigenvalues of Linear Polyenes. Eigenvalues of Annulenes. Eigenvalues of Moebius Annulenes. A Classification Scheme for Monocyclic Systems. Total p-Electron Energy. TOPOLOGICAL RESONANCE ENERGY. Huckel Resonance Energy. Dewar Resonance Energy. The Concept of Topological Resonance Energy. Computation of the Acyclic Polynomial. Applications of the TRE Model. ENUMERATION OF KEKULE VALENCE STRUCTURES. The Role of Kekule Valence Structures in Chemistry. The Identification of Kekule Systems. Methods for the Enumeration of Kekule Structures. The Concept of Parity of Kekule Structures. THE CONJUGATED-CIRCUIT MODEL. The Concept of Conjugated Circuits. The p-Resonance Energy Expression. Selection of the Parameters. Computational Procedure. Applications of the Conjugated-Circuit Model. Parity of Conjugated Circuits. TOPOLOGICAL INDICES. Definitions of Topological Indices. The Three-Dimensional Wiener Number. ISOMER ENUMERATION. The Cayley Generation Functions. The Henze-Blair Approach. The Polya Enumeration Method. The Enumeration Method Based on the N-Tuple Code.

Chemical Graph Theory

Big is beautiful--"aromaticity" revisited from the viewpoint of macromolecular and supramolecular benzene chemistry.

Anisotropy of the Induced Current Density (ACID), a General Method To Quantify and Visualize Electronic Delocalization

Accepting a commission to review progress in the subject embodied in our title is, perhaps, to take up something of a ‘poisoned chalice’. One of us, contributing on this same topic more than 20 years ago at the 1979 International Symposium on Aromaticity in Dubrovnik, wrote1 “A cynic would say that there are actually only two difficulties in discussing the subject of ‘aromaticity’ and ‘ring currents’sdeciding what is meant by ‘ring current’, and assigning a meaning to the term ‘aromaticity’!” That comment, though ostensibly facetious, had serious intent: it did encapsulate, with only a modicum of exaggeration, the problems that inherently beset any assessment such as the one attempted at Dubrovnik1 and in the present review. At the heart of the matter lies the undeniable fact that neither ring currents nor aromaticity are physical observables. Nevertheless, the intervening period has seen the ring-current idea, at least, become generally less controversial and more accepted than it once was. At the time of our opening quotation, one of us and Haigh had just published an exhaustive review2 of the ring-current concept covering the period up to about 1980sthe end of what might now be regarded as the era of semiempirical calculations in this field.2 This review2 (1979/1980) concluded that “the ‘ring current’ picture has proved itself ... to have great power in rationalising, at least qualitatively, the magnetic properties of π-electron systems. It is so pictorial that one can almost feel what is happening when a [conjugated] molecule is subjected to a magnetic field. Whatever advances the future may bring, it may be that the favourite habitat of the ‘ring current’ will be that in which it was born and brought up, namely, that of semi-empirical π-electron theory”. In other words, these authors were sanguine that, at the time (ca. 1980), the ring-current idea was gently coming to the end of its natural, useful life. However, as recently as 1997, when reviewing progress concerning the status of the ring-current model during the decade and a half or so after 1980s a period in this field that we have dubbed3 ‘the ab initio era’sthe present authors3 were initially somewhat surprised to find themselves concluding that “the ‘ring-current’ idea has well survived the first 15 years of the ab initio era.” Lazzeretti’s subsequent magnum opus4 on ring currents has more than confirmed this. By contrast, the sheer fact that in 2001sthe very first year of the 21st centurysthe American Chemical Society has seen fit to run this particular issue of Chemical Reviews shows that the concept of Aromaticity is as elusive as it ever was (see section II). There are three reasons for our not feeling obliged or inclined to present, in this review, an exhaustive, systematic, or historical critique of the ring-current concept itself. First, as we have just claimed, the idea of a ring current seems more secure now than it was 20 years ago, and it would appear that less apology or justification is needed for invoking it. Second, we ourselves have, in any case, only recently updated 1349 Chem. Rev. 2001, 101, 1349−1383

https://www.fc.up.pt/pessoas/jfgomes/documentos/ArtigosPDF/ChemRev,%20101,%201349-83(2001).pdf

Aromaticity and ring currents.

Ring current theories in nuclear magnetic resonance

A new theory6 for ‘ring current’ effects on the chemical shifts of protons in or out of the plane of a benzene ring is summarized, and pictorially compared with the predictions of the earlier semi-classical theory of Johnson and Bovey.1 In the Appendix are presented extensive numerical tables of the predicted shieldings.

New tables of ‘ring current’ shielding in proton magnetic resonance

Hückel theory for organic chemists

The McWeeny ‘ring current’ theory is tested critically against a set of consistent, accurate experimental chemical shifts for 85 protons in 16 planar unsubstituted condensed benzenoid hydrocarbons, and a regression equation is derived relating quantities calculated from the theory to experimental τ values for the non-hindered protons Systematic deviations of different types of protons from this line are discussed, as also are sigma-bond anisotropy effects and discrepancies observed for overcrowded protons Some of the assumptions about the geometry of planar benzenoid hydrocarbons normally made in these calculations are relaxed The McWeeny theory gives a good account of the chemical shifts of non-hindered protons in planar molecules, and the predictions of the theory are not significantly altered if the calculations are based on experimental x-ray geometry Sigma-bond anisotropy effects are unimportant for non-hindered protons, and, at most, make only a partial contribution to the down-field shifts of h

R. B. Mallion

Papers

Aromaticity and ring currents.

Ring current theories in nuclear magnetic resonance

New tables of ‘ring current’ shielding in proton magnetic resonance

Hückel theory for organic chemists

Proton magnetic resonance of non-planar condensed benzenoid hydrocarbons