Conserved High Free Energy Sites in Human Coronavirus Spike Glycoprotein Backbones.

Methods previously developed by the author are applied to uncover several sites of interest in the spike glycoproteins of all known human coronaviruses (hCoVs), including SARS-CoV-2 that causes COVID-19. The sites comprise three-dimensional neighborhoods of peptides characterized by four key properties: (1) they pinpoint regions of high free energy in the backbone whose obstruction might interrupt function; (2) by their very definition, they occur rarely in the universe of all gene-encoded proteins that could obviate host response to compounds designed for their interference; (3) they are common to all known hCoV spikes, possibly retaining activity in light of inevitable viral mutation; and (4) they are exposed in the molecular surface of the glycoprotein. These peptides in SARS-CoV-2 are given by the triples of residues (131, 117, 134), (203, 227, 228), and (1058, 730, 731) in its spike.

Backbone Free Energy Estimator Applied to Viral Glycoproteins.

Earlier analysis of the Protein Data Bank derived the distribution of rotations from the plane of a protein hydrogen bond donor peptide group to the plane of its acceptor peptide group. The quasi Boltzmann formalism of Pohl-Finkelstein is employed to estimate free energies of protein elements with these hydrogen bonds, pinpointing residues with a high propensity for conformational change. This is applied to viral glycoproteins as well as capsids, where the 90th+ percentiles of free energies determine residues that correlate well with viral fusion peptides and other functional domains in known cases and thus provide a novel method for predicting these sites of importance as antiviral drug or vaccine targets in general. The method is implemented at https://bion-server.au.dk/hbonds/ from an uploaded Protein Data Bank file.

Hydrogen bond rotations as a uniform structural tool for analyzing protein architecture.

Proteins fold into three-dimensional structures, which determine their diverse functions. The conformation of the backbone of each structure is locally at each C(α) effectively described by conformational angles resulting in Ramachandran plots. These, however, do not describe the conformations around hydrogen bonds, which can be non-local along the backbone and are of major importance for protein structure. Here, we introduce the spatial rotation between hydrogen bonded peptide planes as a new descriptor for protein structure locally around a hydrogen bond. Strikingly, this rotational descriptor sampled over high-quality structures from the protein data base (PDB) concentrates into 30 localized clusters, some of which correlate to the common secondary structures and others to more special motifs, yet generally providing a unifying systematic classification of local structure around protein hydrogen bonds. It further provides a uniform vocabulary for comparison of protein structure near hydrogen bonds even between bonds in different proteins without alignment.

Enumeration of RNA complexes via random matrix theory.

In the present article, we review a derivation of the numbers of RNA complexes of an arbitrary topology. These numbers are encoded in the free energy of the Hermitian matrix model with potential V(x)=x2/2-stx/(1-tx), where s and t are respective generating parameters for the number of RNA molecules and hydrogen bonds in a given complex. The free energies of this matrix model are computed using the so-called topological recursion, which is a powerful new formalism arising from random matrix theory. These numbers of RNA complexes also have profound meaning in mathematics: they provide the number of chord diagrams of fixed genus with specified numbers of backbones and chords as well as the number of cells in Riemann's moduli spaces for bordered surfaces of fixed topological type.

Topology of RNA-RNA interaction structures.

The topological filtration of interacting RNA complexes is studied, and the role is analyzed of certain diagrams called irreducible shadows, which form suitable building blocks for more general structures. We prove that, for two interacting RNAs, called interaction structures, there exist for fixed genus only finitely many irreducible shadows. This implies that, for fixed genus, there are only finitely many classes of interaction structures. In particular, the simplest case of genus zero already provides the formalism for certain types of structures that occur in nature and are not covered by other filtrations. This case of genus zero interaction structures is already of practical interest, is studied here in detail, and is found to be expressed by a multiple context-free grammar that extends the usual one for RNA secondary structures. We show that, in O(n(6)) time and O(n(4)) space complexity, this grammar for genus zero interaction structures provides not only minimum free energy solutions but also the complete partition function and base pairing probabilities.

Topology and prediction of RNA pseudoknots.

MOTIVATION: Several dynamic programming algorithms for predicting RNA structures with pseudoknots have been proposed that differ dramatically from one another in the classes of structures considered. RESULTS: Here, we use the natural topological classification of RNA structures in terms of irreducible components that are embeddable in the surfaces of fixed genus. We add to the conventional secondary structures four building blocks of genus one in order to construct certain structures of arbitrarily high genus. A corresponding unambiguous multiple context-free grammar provides an efficient dynamic programming approach for energy minimization, partition function and stochastic sampling. It admits a topology-dependent parametrization of pseudoknot penalties that increases the sensitivity and positive predictive value of predicted base pairs by 10-20% compared with earlier approaches. More general models based on building blocks of higher genus are also discussed. AVAILABILITY: The source code of gfold is freely available at http://www.combinatorics.cn/cbpc/gfold.tar.gz. CONTACT: duck@santafe.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.