Induction Hierarchy Research Articles

Soliton curves in three-dimensional space forms

The localized induction hierarchy is the integrable hierarchy for the localized induction equation, a geometric evolution equation for space curves modeled on the motion of vortex filaments. A solution of the n th stationary equation associated to the localized induction hierarchy is called an n th soliton curve. In this paper, we consider soliton curves in simply-connected three-dimensional space forms. In particular, we give explicit expressions of n th soliton curves in terms of the natural curvatures.

Abstract 2320: Heme oxygenase-1 mediates ferroptosis

Abstract Ferroptosis is a form of oxidative cell death and has become a chemotherapeutic target for cancer treatment. BAY 11-7085 (BAY), which is a well-known IκBα inhibitor, suppressed viability in cancer cells via induction of ferroptotic death in an NF-κB-independent manner. This study was aimed to characterize the underlying mechanism by BAY and demonstrate its potential chemotherapeutic targets for cancer treatment. Reactive oxygen species scavenging, relief of lipid peroxidation, replenishment of glutathione and thiol-containing agents, as well as iron chelation, rescued BAY-induced cell death in human breast cancer cells (MDA-MB-231 and MDA-MB-468) and glioblastoma cells (DBTRG-05MG). The results from quantitative real-time PCR and western blotting analysis showed that BAY upregulated a variety of nuclear factor-E2-related factor 2 (Nrf2) target genes related to redox regulation, particularly heme oxygenase-1 (HO-1) and solute carrier family 7 membrane 1 (SLC7A11). Studies with pharmacological inhibitors and shRNA interventions suggested that the hierarchy of induction is Nrf2-SLC7A11-HO-1. The ferroptotic process induced by hHO-1 overexpression further indicated that HO-1 is a key mediator of BAY-induced ferroptosis that operates through cellular redox regulation and iron accumulation. Our study discovered that BAY induced ferroptosis via Nrf2-SLC7A11-HO-1 pathway and provided new insights to understand the mechanism of HO-1-induced ferroptosis, suggesting HO-1 as a new chemotherapeutic target for cancer treatment. Citation Format: Shih-Kai Chiang, Shuen-Ei Chen, Ling-Chu Chang. Heme oxygenase-1 mediates ferroptosis [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 2320.

Heme oxygenase-1 mediates BAY 11–7085 induced ferroptosis

Ferroptosis is a form of oxidative cell death and has become a chemotherapeutic target for cancer treatment. BAY 11–7085 (BAY), which is a well-known IκBα inhibitor, suppressed viability in cancer cells via induction of ferroptotic death in an NF-κB-independent manner. Reactive oxygen species scavenging, relief of lipid peroxidation, replenishment of glutathione and thiol-containing agents, as well as iron chelation, rescued BAY-induced cell death. BAY upregulated a variety of Nrf2 target genes related to redox regulation, particularly heme oxygenase-1 (HO-1). Studies with specific inhibitors and shRNA interventions suggested that the hierarchy of induction is Nrf2−SLC7A11−HO-1. SLC7A11 inhibition by erastin, sulfasalazine, or shRNA interference sensitizes BAY-induced cell death. Overexperession of SLC7A11 attenuated BAY-inhibited cell viability. The ferroptotic process induced by hHO-1 overexpression further indicated that HO-1 is a key mediator of BAY-induced ferroptosis that operates through cellular redox regulation and iron accumulation. BAY causes compartmentalization of HO-1 into the nucleus and mitochondrion, and followed mitochondrial dysfunctions, leading to lysosome targeting for mitophagy. In this study, we first discovered that BAY induced ferroptosis via Nrf2−SLC7A11−HO-1 pathway and HO-1 is a key mediator by responding to the cellular redox status.

CONGRUENCE SOLUTIONS TO THE LOCALIZED INDUCTION HIERARCHY IN THREE-DIMENSIONAL SPACE FORMS

The localized induction hierarchy in three-dimensional space forms is studied. In particular, we determine all the generating curves of congruence solutions to each evolution equation belonging to the localized induction hierarchy. Here, a congruence solution means a solution moving without changing shape. Also, we give the characterization of some low-order soliton curves.

Inhibition of neural crest formation by Kctd15 involves regulation of transcription factor AP-2

The neural crest develops in vertebrate embryos within a discrete domain at the neural plate boundary and eventually gives rise to a migrating population of cells that differentiate into a multitude of derivatives. We have shown that the broad-complex, tramtrack and bric a brac (BTB) domain-containing factor potassium channel tetramerization domain containing 15 (Kctd15) inhibits neural crest formation, and we proposed that its function is to delimit the neural crest domain. Here we report that Kctd15 is a highly effective inhibitor of transcription factor activating enhancer binding protein 2 (AP-2) in zebrafish embryos and in human cells; AP-2 is known to be critical for several steps of neural crest development. Kctd15 interacts with AP-2α but does not interfere with its nuclear localization or binding to cognate sites in the genome. Kctd15 binds specifically to the activation domain of AP-2α and efficiently inhibits transcriptional activation by a hybrid protein composed of the regulatory protein Gal4 DNA binding and AP-2α activation domains. Mutation of one proline residue in the activation domain to an alanine (P59A) yields a protein that is highly active but largely insensitive to Kctd15. These results indicate that Kctd15 acts in the embryo at least in part by specifically binding to the activation domain of AP-2α, thereby blocking the function of this critical factor in the neural crest induction hierarchy.

The Crc global regulator binds to an unpaired A-rich motif at the Pseudomonas putida alkS mRNA coding sequence and inhibits translation initiation

Crc is a key global translational regulator in Pseudomonads that orchestrates the hierarchy of induction of several catabolic pathways for amino acids, sugars, hydrocarbons or aromatic compounds. In the presence of amino acids, which are preferred carbon sources, Crc inhibits translation of the Pseudomonas putida alkS and benR mRNAs, which code for transcriptional regulators of genes required to assimilate alkanes (hydrocarbons) and benzoate (an aromatic compound), respectively. Crc binds to the 5′-end of these mRNAs, but the sequence and/or structure recognized, and the way in which it inhibits translation, were unknown. We have determined the secondary structure of the alkS mRNA 5′-end through its sensitivity to several ribonucleases and chemical reagents. Footprinting and band-shift assays using variant alkS mRNAs have shown that Crc specifically binds to a short unpaired A-rich sequence located adjacent to the alkS AUG start codon. This interaction is stable enough to prevent formation of the translational initiation complex. A similar Crc-binding site was localized at benR mRNA, upstream of the Shine–Dalgarno sequence. This allowed predicting binding sites at other Crc-regulated genes, deriving a consensus sequence that will help to validate new Crc targets and to discriminate between direct and indirect effects of this regulator.

Analogy between a vortex-jet filament and the Kirchhoff elastic rod

Motion of a vortex filament with axial flow in the core, i.e. a vortex-jet filament, is governed, in the localized induction approximation, by the first two terms of the localized induction hierarchy. It is shown that permanent form of a steadily translating vortex-jet filament is identical with equilibrium form of an inextensible elastic rod of circular cross-section. A variational principle is presented for the statics of an elastic rod with respect to the director field, which manifests the origin of this analogy.

Fused Hierarchy Produced by mKdV Hierarchy and Sine-Gordon Hierarchy

By using the inverse problem, we have found a system with two hierarchies, that is, the localized induction hierarchy and the hierarchy including the dispersionless equation. Recently, with the same system, we have found a fused hierarchy which is produced by fusing two hierarchies with help of the recursion formulae. In this short note, we would like to show that the mKdV hierarchy and the sine-Gordon hierarchy produce another fused hierarchy. It is recognized that the recursion operators of the mKdV hierarchy and the sine-Gordon hierarchy is the inverse operator in each other. However, it has been misunderstood that two hierarchies are not connected since the boundary conditions have not been carefully considered. If each member of equations in the mKdV hierarchy is written by tðx; tÞ nðx; tÞ 1⁄4 0; ðn 1⁄4 1; 2; . . .Þ ð1Þ

Three-dimensional motion of a vortex filament and its relation to the localized induction hierarchy

Three-dimensional motion of a slender vortex tube, embedded in an inviscid incompressible fluid, is investigated under the localized induction approximation for the Euler equations. Using the method of matched asymptotic expansions in a small parameter e, the ratio of core radius to curvature radius, the velocity of a vortex filament is derived to O(e3), whereby the influence of elliptical deformation of the core due to the self-induced strain is taken into account. It is found that there is an integrable line in the core whose evolution obeys a summation of the first and third terms of the localized induction hierarchy.

Recursion formulae for IKK system with two hierarchies

In a previous paper an inverse system with two hierarchies for a given symmetry was proposed. The scheme was found to have so constructive structure that relation between members of the hierarchies was systematically determined. In this Letter, with the proposed system we find simply and directly recursion formulae for two hierarchies for the su(2) algebra, i.e., the localized induction hierarchy and the hierarchy with the dispersionless equation. We show that, as a special case, the recursion formulae reduce to those of the modified Korteweg–de Vries hierarchy and the sine–Gordon hierarchy.

Straightening soliton curves

A canonical straightening process is described for soliton curves associated with the localized induction hierarchy. Following computer animated examples, the present topic is placed in the context of a larger theme: the soliton class is a natural setting for representation of diverse topological and geometrical behavior of curves and their motions.

The relationship between the dispersionless equation and the localized induction hierarchy through the Pohlmeyer-Lund-Regge equation

Fukumoto and Miyajima (Fukumoto Y and Miyajima M 1996 J. Phys. A: Math. Gen. 29 8025) have discussed that an evolution equation obtained by summing up an infinite number of equations of the localized induction hierarchy (LIH) is equivalent to the Pohlmeyer-Lund-Regge equation (PLRE). On the other hand, the dispersionless equation (DLE) is also shown to be equivalent to the PLRE, so we investigate a link between the equation derived from the LIH and the DLE through the PLRE. We find that their result is not correct. However, we show that there is a special case where a solution of the LIH satisfies the PLRE.

The localized induction hierarchy and the Lund - Regge equation

An evolution equation of a curve is constructed by summing up the infinite sequence of commuting vector fields of the integrable hierarchy for the localized induction equation (LIE). It is shown to be equivalent to the Lund - Regge equation. The intrinsic equations governing the curvature and torsion are deduced in the form of integrodifferential evolution equations. A class of exact solutions which correspond to the permanent forms of a curve evolving by a steady rigid motion are presented. The analysis of the solutions reveals that, given the shape, there are two speeds of motion, one of which has no counterpart in the case of the LIE.

Localized induction hierarchy and Weingarten systems

We describe a method of constructing Weingarten systems of triply orthogonal coordinates, related to the localized induction equation hierarchy of integrable geometric evolution equations.