Supersymmetry of 𝒫𝒯-symmetric tridiagonal Hamiltonians

We extend the study of supersymmetric tridiagonal Hamiltonians to the case of non-Hermitian Hamiltonians with real or complex conjugate eigenvalues. We find the relation between matrix elements of the non-Hermitian Hamiltonian [Formula: see text] and its supersymmetric partner [Formula: see text] in a given basis. Moreover, the orthogonal polynomials in the eigenstate expansion problem attached to [Formula: see text] can be recovered from those polynomials arising from the same problem for [Formula: see text] with the help of kernel polynomials. Besides its generality, the developed formalism in this work is a natural home for using the numerically powerful Gauss quadrature techniques in probing the nature of some physical quantities such as the energy spectrum of [Formula: see text]-symmetric complex potentials. Finally, we solve the shifted [Formula: see text]-symmetric Morse oscillator exactly in the tridiagonal representation.

A Fully Symmetrical High Performance Modular Milling Cutter

Milling cutters belong to a widely used category of cutting tools. In this category, modular milling cutters are a narrow niche, less studied, and developed. Usually, they are symmetrical cutting tools. A milling cutting tool that can be reconfigured due to its modularity and still keeps its symmetry becomes more interesting and useful for machining. The paper presents such a new concept in a computer aided design (CAD) model of a cutting tool based on some novel features. The tool itself is designed as a modular complex. The way the torque is transmitted from the shaft to the elementary cutters is an original one, as they are joined together based on a profiled assembling. The profile is one formed of filleted circular sectors and segments. The reaming of the elementary cutters has two sections each of them assuming a task: transmitting the torque, and precisely centring, respectively. The cooling system, which is a component of the tool, provides the cutting area with coolant both on the front and side face of the cutting tool. Some nozzles placed around the cutting tool send jets or curtains of coolant towards the side surface of the cutter, instead of parallel, as some existing solutions do. The source of the coolant supply is the inner cooling system of the machine tool. This provides the tool with coolant having proper features: high enough flow and pressure. The output of the research is a CAD-based model of the modular milling cutter with a high performance cooling system. All of this model’s elements were designed taking into account the design for manufacturing principles, so it will be possible to easily manufacture this tool. Several variants of milling cutters obtained by reconfiguring the complex tool are presented. Even if the tool is usually a symmetric complex, it can process asymmetric parts. Symmetry is intensively used to add some advantages to the modular cutting tool: balanced forces in the cutting process, the possibility of controlling the direction of the axial cutting force, and a good machinability of the grooves used to assemble the main parts of the cutting tool.

Biochemical and Biophysical Characterization of the dsDNA Packaging Motor from the Lactococcus lactis Bacteriophage Asccphi28

Double-stranded DNA viruses package their genomes into pre-assembled protein procapsids. This process is driven by macromolecular motors that transiently assemble at a unique vertex of the procapsid and utilize homomeric ring ATPases to couple genome encapsidation to ATP hydrolysis. Here, we describe the biochemical and biophysical characterization of the packaging ATPase from Lactococcus lactis phage asccφ28. Size-exclusion chromatography (SEC), analytical ultracentrifugation (AUC), small angle X-ray scattering (SAXS), and negative stain transmission electron microscopy (TEM) indicate that the ~45 kDa protein formed a 443 kDa cylindrical assembly with a maximum dimension of ~155 Å and radius of gyration of ~54 Å. Together with the dimensions of the crystallographic asymmetric unit from preliminary X-ray diffraction experiments, these results indicate that gp11 forms a decameric D5-symmetric complex consisting of two pentameric rings related by 2-fold symmetry. Additional kinetic analysis shows that recombinantly expressed gp11 has ATPase activity comparable to that of functional ATPase rings assembled on procapsids in other genome packaging systems. Hence, gp11 forms rings in solution that likely reflect the fully assembled ATPases in active virus-bound motor complexes. Whereas ATPase functionality in other double-stranded DNA (dsDNA) phage packaging systems requires assembly on viral capsids, the ability to form functional rings in solution imparts gp11 with significant advantages for high-resolution structural studies and rigorous biophysical/biochemical analysis.

Biochemical and Biophysical Characterization of the dsDNA packaging motor from the Lactococcus lactis bacteriophage asccphi28

Double-stranded DNA viruses package their genomes into pre-assembled protein procapsids. This process is driven by macromolecular motors that transiently assemble at a unique vertex of the procapsid and utilize homomeric ring ATPases to couple genome encapsidation to ATP hydrolysis. Here we describe biochemical and biophysical characterization of the packaging ATPase from Lactococcus lactis phage asccφ28. Size-exclusion chromatography, analytical ultracentrifugation, small angle x-ray scattering, and negative stain TEM indicate that the ~45 kDa protein formed a 443 kDa cylindrical assembly with a maximum dimension of ~155 Å and radius of gyration of ~54 Å. Together with the dimensions of the crystallographic asymmetric unit from preliminary X-ray diffraction experiments, these results indicate that gp11 forms a decameric D5-symmetric complex consisting of two pentameric rings related by 2-fold symmetry. Additional kinetic analysis shows that recombinantly expressed gp11 has ATPase activity comparable to that of functional ATPase rings assembled on procapsids in other genome packaging systems. Hence, gp11 forms rings in solution that likely reflect the fully assembled ATPases in active virus-bound motor complexes. Whereas ATPase functionality in other dsDNA phage packaging systems requires assembly on viral capsids, the ability to form functional rings in solution imparts gp11 with significant advantages for high resolution structural studies and rigorous biophysical/biochemical analysis.

Highly potent bispecific sybodies neutralize SARS-CoV-2

ABSTRACTThe COVID-19 pandemic has resulted in a global crisis. Here, we report the generation of synthetic nanobodies, known as sybodies, against the receptor-binding domain (RBD) of SARS-CoV-2 spike protein. We identified a sybody pair (Sb#15 and Sb#68) that can bind simultaneously to the RBD, and block ACE2 binding, thereby neutralizing pseudotyped and live SARS-CoV-2 viruses. Cryo-EM analyses of the spike protein in complex with both sybodies revealed symmetrical and asymmetrical conformational states. In the symmetric complex each of the three RBDs were bound by both sybodies, and adopted the up conformation. The asymmetric conformation, with three Sb#15 and two Sb#68 bound, contained one down RBD, one up-out RBD and one up RBD. Bispecific fusions of the sybodies increased the neutralization potency 100-fold, as compared to the single binders. Our work demonstrates that linking two binders that recognize spatially-discrete binding sites result in highly potent SARS-CoV-2 inhibitors for potential therapeutic applications.

Mirror world and planetary orbit distribution in the solar system（Geometric derivation and physical significance of the distribution law of the orbits of the solar and solar-like planets）

There are different opinions on the distribution formula of the distance between Titius-Bode's planets [1,-5] Some people use this theory to prove that exoplanet systems have the same regularity [4] , But the emergence of the Hot Jupiter has made many people less convinced of the empirical formula Titius-Bode law. The explanation of the Titius-Bode law in our past theory is not convincing because of the incorporation of too many traditional theories and concepts, and almost all the papers that explain the distribution of planets are in the present theoretical framework [2-5] To explain. In fact, the distribution law of the distance of planets is related to the cause of gravitation. I dont know the cause of the gravitation and the process of action. The "planetary distance distribution rule" cannot be interpreted correctly. To use "six-level multidimensional symmetric complex geometry" [7] to understand the genesis of the derivation of the solar system's orbit, the actual application is a simple and easy-to-understand explanation of the "gravity of six-level multidimensional symmetric complex geometry" [8] , so understanding this article requires understanding" Six-level symmetry theory of gravity' [7, 8] .