A comprehensive classification and nomenclature of carboxyl-carboxyl(ate) supramolecular motifs and related catemers: implications for biomolecular systems.:

Carboxyl and carboxylate groups form important supramolecular motifs (synthons). Besides carboxyl cyclic dimers, carboxyl and carboxylate groups can associate through a single hydrogen bond. Carboxylic groups can further form polymeric-like catemer chains within crystals. To date, no exhaustive classification of these motifs has been established. In this work, 17 association types were identified (13 carboxyl-carboxyl and 4 carboxyl-carboxylate motifs) by taking into account the syn and anti carboxyl conformers, as well as the syn and anti lone pairs of the O atoms. From these data, a simple rule was derived stating that only eight distinct catemer motifs involving repetitive combinations of syn and anti carboxyl groups can be formed. Examples extracted from the Cambridge Structural Database (CSD) for all identified dimers and catemers are presented, as well as statistical data related to their occurrence and conformational preferences. The inter-carboxyl(ate) and carboxyl(ate)-water hydrogen-bond properties are described, stressing the occurrence of very short (strong) hydrogen bonds. The precise characterization and classification of these supramolecular motifs should be of interest in crystal engineering, pharmaceutical and also biomolecular sciences, where similar motifs occur in the form of pairs of Asp/Glu amino acids or motifs involving ligands bearing carboxyl(ate) groups. Hence, we present data emphasizing how the analysis of hydrogen-containing small molecules of high resolution can help understand structural aspects of larger and more complex biomolecular systems of lower resolution

Spectral Statistics of Erd{\H o}s-R\'enyi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues

We consider the ensemble of adjacency matrices of Erd{\H o}s-R\'enyi random graphs, i.e.\ graphs on $N$ vertices where every edge is chosen independently and with probability $p \equiv p(N)$. We rescale the matrix so that its bulk eigenvalues are of order one. Under the assumption $p N \gg N^{2/3}$, we prove the universality of eigenvalue distributions both in the bulk and at the edge of the spectrum. More precisely, we prove (1) that the eigenvalue spacing of the Erd{\H o}s-R\'enyi graph in the bulk of the spectrum has the same distribution as that of the Gaussian orthogonal ensemble; and (2) that the second largest eigenvalue of the Erd{\H o}s-R\'enyi graph has the same distribution as the largest eigenvalue of the Gaussian orthogonal ensemble. As an application of our method, we prove the bulk universality of generalized Wigner matrices under the assumption that the matrix entries have at least $4 + \epsilon$ moments

Is the Riemann zeta function in a short interval a 1-RSB spin glass ?

Fyodorov, Hiary & Keating established an intriguing connection between the maxima of log-correlated processes and the ones of the Riemann zeta function on a short interval of the critical line. In particular, they suggest that the analogue of the free energy of the Riemann zeta function is identical to the one of the Random Energy Model in spin glasses. In this paper, the connection between spin glasses and the Riemann zeta function is explored further. We study a random model of the Riemann zeta function and show that its two-overlap distribution corresponds to the one of a one-step replica symmetry breaking (1-RSB) spin glass. This provides evidence that the local maxima of the zeta function are strongly clustered.Comment: 20 pages, 1 figure, Minor corrections, References update

Geometrical Insights for Implicit Generative Modeling

Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the Maximum Mean Discrepancy criterion. A careful look at the geometries induced by these distances on the space of probability measures reveals interesting differences. In particular, we can establish surprising approximate global convergence guarantees for the $1$-Wasserstein distance,even when the parametric generator has a nonconvex parametrization.Comment: this version fixes a typo in a definitio

The marginally stable Bethe lattice spin glass revisited

Bethe lattice spins glasses are supposed to be marginally stable, i.e. their equilibrium probability distribution changes discontinuously when we add an external perturbation. So far the problem of a spin glass on a Bethe lattice has been studied only using an approximation where marginally stability is not present, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a marginally stable solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non-perturbative approach to the Bethe lattice spin glass problem using approximations that should be hopeful consistent with marginal stability.Comment: 23 pages Revised version, hopefully clearer that the first one: six pages longe

Infrared Multiple Photon Dissociation Action Spectroscopy and Theoretical Studies of Diethyl Phosphate Complexes: Effects of Protonation and Sodium Cationization on Structure

The gas-phase structures of deprotonated, protonated, and sodium-cationized complexes of diethyl phosphate (DEP) including [DEP − H]−, [DEP + H]+, [DEP + Na]+, and [DEP − H + 2Na]+ are examined via infrared multiple photon dissociation (IRMPD) action spectroscopy using tunable IR radiation generated by a free electron laser, a Fourier transform ion cyclotron resonance mass spectrometer (FT-ICR MS) with an electrospray ionization (ESI) source, and theoretical electronic structure calculations. Measured IRMPD spectra are compared to linear IR spectra calculated at the B3LYP/6-31G(d,p) level of theory to identify the structures accessed in the experimental studies. For comparison, theoretical studies of neutral complexes are also performed. These experiments and calculations suggest that specific geometric changes occur upon the binding of protons and/or sodium cations, including changes correlating to nucleic acid backbone geometry, specifically P–O bond lengths and ∠OPO bond angles. Information from these observations may be used to gain insight into the structures of more complex systems, such as nucleotides and solvated nucleic acids

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field

The crystal structure of an ‘All Locked’ nucleic acid duplex

‘Locked nucleic acids’ (LNAs) are known to introduce enhanced bio- and thermostability into natural nucleic acids rendering them powerful tools for diagnostic and therapeutic applications. We present the 1.9 Å X-ray structure of an ‘all LNA’ duplex containing exclusively modified β-d-2′-O-4′C-methylene ribofuranose nucleotides. The helix illustrates a new type of nucleic acid geometry that contributes to the understanding of the enhanced thermostability of LNA duplexes. A notable decrease of several local and overall helical parameters like twist, roll and propeller twist influence the structure of the LNA helix and result in a widening of the major groove, a decrease in helical winding and an enlarged helical pitch. A detailed structural comparison to the previously solved RNA crystal structure with the corresponding base pair sequence underlines the differences in conformation. The surrounding water network of the RNA and the LNA helix shows a similar hydration pattern