We derive the stabiliser group of the four-vector, also known as Wigner’s little group, in case of massless particle states, as the maximal solvable subgroup of the proper orthochronous Lorentz group of dimension four, known as the Borel subgroup. In the absence of mass, particle states are disentangled into left and right handed chiral states, governed by the maximal solvable subgroups sol2± of order two. Induced Lorentz transformations are constructed and applied to general representations of particle states. Finally, it is argued how the spin-flip contribution is closely related to the occurrence of nonphysical spin operators.

We study the existence or absence of non-Shannon inequalities for variables that are related by functional dependencies. Although the power-set on four variables is the smallest Boolean lattice with non-Shannon inequalities there exist lattices with many more variables without non-Shannon inequalities. We search for conditions that excludes the existence of non-Shannon inequalities. It is demonstrated that planar modular lattices cannot have non-Shannon inequalities. The existence of non-Shannon inequalities is related to the question of whether a lattice is isomorphic to a lattice of subgroups of a group.

Avian metapneumovirus subgroup C (aMPV/C) causes respiratory diseases and egg dropping in chickens and turkeys, resulting in severe economic losses to the poultry industry worldwide. Integrin β1 (ITGB1), a transmembrane cell adhesion molecule, is present in various cells and mediates numerous viral infections. Herein, we demonstrate that ITGB1 is essential for aMPV/C infection in cultured DF-1 cells, as evidenced by the inhibition of viral binding by EDTA blockade, Arg-Ser-Asp (RSD) peptide, monoclonal antibody against ITGB1, and ITGB1 short interfering (si) RNA knockdown in cultured DF-1 cells. Simulation of the binding process between the aMPV/C fusion (F) protein and avian-derived ITGB1 using molecular dynamics showed that ITGB1 may be a host-factor for benefiting aMPV/C attachment or internalization. Transient expression of avian ITGB1 rendered porcine and feline non-permissive cells (DQ cells and CRFK cells, respectively) susceptible to aMPV/C infection. Replication kinetic of aMPV/C in siRNA-knockdown cells revealed that ITGB1 plays an important role in aMPV/C infection at the early stage (attachment and internalization). aMPV/C was also able to infect efficiently human non-small cell lung cancer (A549) cells. This may be due to a consequence of the similar structures of both metapneumovirus F protein-specific motifs (RSD for aMPV/C and RGD for human metapneumovirus) recognized by ITGB1. Overexpression of avian-derived ITGB1 and human-derived ITGB1 in A549 cells enhanced aMPV/C infectivity. Taken together, this study demonstrated that ITGB1 acts as an essential receptor for aMPV/C attachment and internalization into host cells in which facilitates aMPV/C infection.

The receptor-type protein tyrosine phosphatases (RPTPs) are involved in a wide variety of physiological functions which are mediated via their diverse extracellular regions. They play key roles in cell-cell contacts, bind various ligands and are regulated by dimerization and other processes. Depending on the subgroup they have been described as everything from ‘rigid rods’ to ‘floppy tentacles’. Here we review current experimental structural knowledge on the extracellular region of RPTPs and draw on AlphaFold structural predictions to provide further insights into structure and function of these cellular signalling molecules.