Dynamics of optical pulses in fiber optics

In this paper, we pay attention to the nonlinear dynamical behavior of ultra-short pulses in optical fiber. The new Hamiltonian amplitude equation is used as a governing model to analyze the pulses. We secure the ultra-short pulses in the forms of bright, dark, singular, combo and complex soliton solutions by the utilization of three of sound computational integration techniques that are protracted (or extended) Fan-sub equation method (PFSEM), the generalized exponential rational function method (GERFM), extended Sinh-Gordon equation expansion method (ShGEEM). Moreover, Jacobi’s elliptic, trigonometric, and hyperbolic functions solutions are also discussed as well as the constraint conditions of the achieved solutions are also presented. In addition, we discuss the different wave structures by the assistance of logarithmic transformation. The findings demonstrate that the examined equation theoretically contains a large number of soliton solution structures. By selecting appropriate criteria, the actual portrayal of certain obtained results is sorted out graphically in 3D and 2D profiles. The results suggest that the procedures used are concise, direct, and efficient, and that they can be applied to more complex phenomena. The resulting solutions are novel, intriguing, and potentially useful in understanding energy transit and diffusion processes in mathematical models of several disciplines of interest, including nonlinear optics. Our new results have been compared to these in the literature.

Solution Structures of Bacillus anthracis Protective Antigen Proteins Using Small Angle Neutron Scattering and Protective Antigen 63 Ion Channel Formation Kinetics

We are studying the structures of bacterial toxins that form ion channels and enable macromolecule transport across membranes. For example, the crystal structure of the Staphylococcus aureus α-hemolysin (α-HL) channel in its functional state was confirmed using neutron reflectometry (NR) with the protein reconstituted in membranes tethered to a solid support. This method, which provides sub-nanometer structural information, could also test putative structures of the Bacillus anthracis protective antigen 63 (PA63) channel, locate where B. anthracis lethal factor and edema factor toxins (LF and EF, respectively) bind to it, and determine how certain small molecules can inhibit the interaction of LF and EF with the channel. We report here the solution structures of channel-forming PA63 and its precursor PA83 (which does not form channels) obtained with small angle neutron scattering. At near neutral pH, PA83 is a monomer and PA63 a heptamer. The latter is compared to two cryo-electron microscopy structures. We also show that although the α-HL and PA63 channels have similar structural features, unlike α-HL, PA63 channel formation in lipid bilayer membranes ceases within minutes of protein addition, which currently precludes the use of NR for elucidating the interactions between PA63, LF, EF, and potential therapeutic agents.

Generalized variational principles of the Benney-Lin equation arising in fluid dynamics

Variational principle is important since it can not only reveal the possible solution structures of the equation but also provide the conservation laws in an energy form. Unfortunately, not all the differential equations can find their variational forms. In this work, the Benney-Lin equation is studied and its two different generalized variational principles are successfully established by using the semi-inverse method. The derivation process is given in detail. The finding in this work is expected to give a insight into the study of the nonlinear partial differential equations arising in fluid dynamics.

Effects of the Rare Earth Y on the Structural and Tensile Properties of Mg-based Alloy: A First-Principles Study

In order to investigate the effect of the rare earth element Y on the strengthening potency of magnesium alloys and its strengthening mechanism under tension. In this paper, the solid solution structures with Y atom content of 1.8 at.% and 3.7 at.% were built, respectively, and their cohesive energies and stress-strain curve were calculated in the strain range of 0–20%. The calculation results of the cohesive energies showed that the structure of element Y is more stable with the increase of strains. The calculation results of stress and strain showed that Y element can improve the yield strength and tensile strength of the Mg-based alloy, and the strengthening effect is better when the Y content is 3.7 at.%.

Structures of a deAMPylation complex rationalise the switch between antagonistic catalytic activities of FICD

The endoplasmic reticulum (ER) Hsp70 chaperone BiP is regulated by AMPylation, a reversible inactivating post-translational modification. Both BiP AMPylation and deAMPylation are catalysed by a single ER-localised enzyme, FICD. Here we present crystallographic and solution structures of a deAMPylation Michaelis complex formed between mammalian AMPylated BiP and FICD. The latter, via its tetratricopeptide repeat domain, binds a surface that is specific to ATP-state Hsp70 chaperones, explaining the exquisite selectivity of FICD for BiP’s ATP-bound conformation both when AMPylating and deAMPylating Thr518. The eukaryotic deAMPylation mechanism thus revealed, rationalises the role of the conserved Fic domain Glu234 as a gatekeeper residue that both inhibits AMPylation and facilitates hydrolytic deAMPylation catalysed by dimeric FICD. These findings point to a monomerisation-induced increase in Glu234 flexibility as the basis of an oligomeric state-dependent switch between FICD’s antagonistic activities, despite a similar mode of engagement of its two substrates — unmodified and AMPylated BiP.

Sliding of HIV-1 reverse transcriptase over DNA creates a transient P pocket – Targeting P-pocket by fragment screening

HIV-1 reverse transcriptase (RT) slides over an RNA/DNA or dsDNA substrate while copying the viral RNA to a proviral DNA. We report a crystal structure of RT/dsDNA complex in which RT overstepped the primer 3’-end of a dsDNA substrate and created a transient P-pocket at the priming site. We performed a high-throughput screening of 300 drug-like fragments by X-ray crystallography and identified binding of two to P-pocket, which is composed of structural elements from polymerase active site, primer grip, and template-primer that are resilient to drug-resistance mutations. Analogs of a fragment were synthesized of which two showed noticeable RT inhibition. An engineered RT/DNA aptamer complex trapped the transient P-pocket in solution. Structures of the RT/DNA complex were determined with a fragment and a synthesized analog bound at P-pocket by single-particle cryo-EM. Identification of P-pocket and the devised structure-based platform provide an opportunity for designing new types of polymerase inhibitors.

Variational principle of the one-dimensional convection–dispersion equation with fractal derivatives

The convection–dispersion equation has always been a classic equation for studying pollutant migration models. There are certain deviations in scientific research because of the existence of the impurity of the medium and the nonsmooth boundary. In this paper, we introduced the one-dimensional convection–dispersion equation with fractal derivatives in fractal space, and established the fractal variational formula of the equation through the semi-inverse method. The fractal variational formula we have obtained can provide the conservation laws in an energy form in the fractal space and possible solution structures of the given equation. An analytical solution is obtained through the two-scale transform method and Laplace transform.