More power to X‐rays: New developments in X‐ray spectroscopy

Recent developments in X‐ray spectroscopy in the last decade are reviewed. A specific emphasis is placed on displaying the strong natural connection between X‐ray spectroscopy and materials science. Brief explanations of several X‐ray spectroscopic methods are given. X‐ray spectroscopic instruments such as table‐top X‐ray sources are discussed in detail, whereas those employing synchrotron and other sources are briefly addressed. The spectroscopic methods and results from materials investigations are reviewed according to their positions in a 3D parameter space of time, length, and energy. New experimental measurements on atoms, molecules, nanomaterials, and bulk materials that include insulators, semiconductors, metals and magnetic materials using both static and time‐resolved methods are reviewed.     

Crystallographic and biophysical analysis of the fusion core from SARS-CoV-2 spike protein

Severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) is a newly emerging infectious pathogen causing coronavirus disease 2019 (COVID-19). The virus primarily infects cells via its spike glycoprotein, which is cleaved into S1 and S2 subunits to aid in cell attachment and membrane fusion, respectively. Heptad repeat 1 (HR1) and heptad repeat 2 (HR2) of the S2 subunit are essential for membrane fusion, culminating in an expected six-helix bundle termed fusion core. To better understand the structural and biophysical features of the SARS-CoV-2 fusion core, we designed, constructed, and bacterially produced a recombinant single-chain HR1-L6-HR2 protein and conducted a series of biochemical and biophysical experiments. Our findings demonstrate that the HR1-L6-HR2 protein spontaneously assembles into a highly stable trimeric complex, further confirmed by x-ray crystallographic analysis. The crystal structure of the fusion core reveals a trimeric coiled-coil structure of HR1 antiparallelly surrounded by three HR2 to form a six-helical bundle. Additionally, four residues of HR1 that contribute to binding with HR2 through the formation of hydrogen bonds and salt bridges were observed. These results indicate that the SARS-CoV-2 fusion core exhibits similar characteristics to other class I viral glycoproteins, suggesting potential for drug repurposing as an alternative strategy to combat COVID-19.     

Nonintegrability of the Painlevé IV equation in the Liouville–Arnold sense and Stokes phenomena

In this paper we study the integrability of the Hamiltonian system associated with the fourth Painlevé equation. We prove that one two-parametric family of this Hamiltonian system is not integrable in the sense of the Liouville–Arnold theorem. Computing explicitly the Stokes matrices and the formal invariants of the second variational equations, we deduce that the connected component of the unit element of the corresponding differential Galois group is not Abelian. Thus the Morales–Ramis–Simó theory leads to a nonintegrable result. Moreover, combining the new result with our previous one we establish that for all values of the parameters for which the $P_{IV}$ equation has a particular rational solution the corresponding Hamiltonian system is not integrable by meromorphic first integrals which are rational in t.