Alternativity and reciprocity in the Cayley-Dickson algebra

We calculate the eigenvalue \rho of the multiplication mapping R on the Cayley-Dickson algebra A_n. If the element in A_n is composed of a pair of alternative elements in A_{n-1}, half the eigenvectors of R in A_n are still eigenvectors in the subspace which is isomorphic to A_{n-1}. The invariant under the reciprocal transformation A_n \times A_{n} \ni (x,y) -> (-y,x) plays a fundamental role in simplifying the functional form of \rho. If some physical field can be identified with the eigenspace of R, with an injective map from the field to a scalar quantity (such as a mass) m, then there is a one-to-one map \pi: m \mapsto \rho. As an example, the electro-weak gauge field can be regarded as the eigenspace of R, where \pi implies that the W-boson mass is less than the Z-boson mass, as in the standard model.Comment: To be published in J. Phys. A: Mathematical and Genera

The Max b-HLH-LZ Can Transduce into Cells and Inhibit c-Myc Transcriptional Activities

The inhibition of the functions of c-Myc (endogenous and oncogenic) was recently shown to provide a spectacular therapeutic index in cancer mouse models, with complete tumor regression and minimal side-effects in normal tissues. This was achieved by the systemic and conditional expression of omomyc, the cDNA of a designed mutant of the b-HLH-LZ of c-Myc named Omomyc. The overall mode of action of Omomyc consists in the sequestration of Max and the concomitant competition of the Omomyc/Max complex with the endogenous c-Myc/Max heterodimer. This leads to the inhibition of the transactivation of Myc target genes involved in proliferation and metabolism. While this body of work has provided extraordinary insights to guide the future development of new cancer therapies that target c-Myc, Omomyc itself is not a therapeutic agent. In this context, we sought to exploit the use of a b-HLH-LZ to inhibit c-Myc in a cancer cell line in a more direct fashion. We demonstrate that the b-HLH-LZ domain of Max (Max*) behaves as a bona fide protein transduction domain (PTD) that can efficiently transduce across cellular membrane via through endocytosis and translocate to the nucleus. In addition, we show that the treatment of HeLa cells with Max* leads to a reduction of metabolism and proliferation rate. Accordingly, we observe a decrease of the population of HeLa cells in S phase, an accumulation in G1/G0 and the induction of apoptosis. In agreement with these phenotypic changes, we show by q-RT-PCR that the treatment of HeLa cells with Max* leads to the activation of the transcription c-Myc repressed genes as well as the repression of the expression of c-Myc activated genes. In addition to the novel discovery that the Max b-HLH-LZ is a PTD, our findings open up new avenues and strategies for the direct inhibition of c-Myc with b-HLH-LZ analogs

ULF Wave Transmission Across Collisionless Shocks : 2.5D Local Hybrid Simulations

We study the interaction of upstream ultralow frequency (ULF) waves with collisionless shocks by analyzing the outputs of 11 2D local hybrid simulation runs. Our simulated shocks have Alfvenic Mach numbers between 4.29 and 7.42 and their theta BN angles are 15 degrees, 30 degrees, 45 degrees, and 50 degrees. The ULF wave foreshocks develop upstream of all of them. The wavelength and the amplitude of the upstream waves exhibit a complex dependence on the shock's MA and theta BN. The wavelength positively correlates with both parameters, with the dependence on theta BN being much stronger. The amplitude of the ULF waves is proportional to the product of the reflected beam velocity and density, which also depend on MA and theta BN. The interaction of the ULF waves with the shock causes large-scale (several tens of upstream ion inertial lengths) shock rippling. The properties of the shock ripples are related to the ULF wave properties, namely their wavelength and amplitude. In turn, the ripples have a large impact on the ULF wave transmission across the shock because they change local shock properties (theta BN, strength), so that different sections of the same ULF wavefront encounter shock with different characteristics. Downstream fluctuations do not resemble the upstream waves in terms the wavefront extension, orientation or their wavelength. However, some features are conserved in the Fourier spectra of downstream compressive waves that present a bump or flattening at wavelengths approximately corresponding to those of the upstream ULF waves. In the transverse downstream spectra, these features are weaker.Peer reviewe

The Action Mechanism of the Myc Inhibitor Termed Omomyc May Give Clues on How to Target Myc for Cancer Therapy

Recent evidence points to Myc – a multifaceted bHLHZip transcription factor deregulated in the majority of human cancers – as a priority target for therapy. How to target Myc is less clear, given its involvement in a variety of key functions in healthy cells. Here we report on the action mechanism of the Myc interfering molecule termed Omomyc, which demonstrated astounding therapeutic efficacy in transgenic mouse cancer models in vivo. Omomyc action is different from the one that can be obtained by gene knockout or RNA interference, approaches designed to block all functions of a gene product. This molecule – instead – appears to cause an edge-specific perturbation that destroys some protein interactions of the Myc node and keeps others intact, with the result of reshaping the Myc transcriptome. Omomyc selectively targets Myc protein interactions: it binds c- and N-Myc, Max and Miz-1, but does not bind Mad or select HLH proteins. Specifically, it prevents Myc binding to promoter E-boxes and transactivation of target genes while retaining Miz-1 dependent binding to promoters and transrepression. This is accompanied by broad epigenetic changes such as decreased acetylation and increased methylation at H3 lysine 9. In the presence of Omomyc, the Myc interactome is channeled to repression and its activity appears to switch from a pro-oncogenic to a tumor suppressive one. Given the extraordinary therapeutic impact of Omomyc in animal models, these data suggest that successfully targeting Myc for cancer therapy might require a similar twofold action, in order to prevent Myc/Max binding to E-boxes and, at the same time, keep repressing genes that would be repressed by Myc

The Evolutionarily-conserved Polyadenosine RNA Binding Protein, Nab2, Cooperates with Splicing Machinery to Regulate the Fate of pre-mRNA

Numerous RNA binding proteins are deposited onto an mRNA transcript to modulate post-transcriptional processing events ensuring proper mRNA maturation. Defining the interplay between RNA binding proteins that couple mRNA biogenesis events is crucial for understanding how gene expression is regulated. To explore how RNA binding proteins control mRNA processing, we investigated a role for the evolutionarily conserved polyadenosine RNA binding protein, Nab2, in mRNA maturation within the nucleus. This work reveals that nab2 mutant cells accumulate intron-containing pre-mRNA in vivo. We extend this analysis to identify genetic interactions between mutant alleles of nab2 and genes encoding the splicing factor, MUD2, and the RNA exosome, RRP6, with in vivo consequences of altered pre-mRNA splicing and poly(A) tail length control. As further evidence linking Nab2 proteins to splicing, an unbiased proteomic analysis of vertebrate Nab2, ZC3H14, identifies physical interactions with numerous components of the spliceosome. We validated the interaction between ZC3H14 and U2AF2/U2AF^(65). Taking all the findings into consideration, we present a model where Nab2/ZC3H14 interacts with spliceosome components to allow proper coupling of splicing with subsequent mRNA processing steps contributing to a kinetic proofreading step that allows properly processed mRNA to exit the nucleus and escape Rrp6-dependent degradation

Molecular basis of FIR-mediated c-myc transcriptional control

The far upstream element (FUSE) regulatory system promotes a peak in the concentration of c-Myc during cell cycle. First, the FBP transcriptional activator binds to the FUSE DNA element upstream of the c-myc promoter. Then, FBP recruits its specific repressor (FIR), which acts as an on/off transcriptional switch. Here we describe the molecular basis of FIR recruitment, showing that the tandem RNA recognition motifs of FIR provide a platform for independent FUSE DNA and FBP protein binding and explaining the structural basis of the reversibility of the FBP-FIR interaction. We also show that the physical coupling between FBP and FIR is modulated by a flexible linker positioned sequentially to the recruiting element. Our data explain how the FUSE system precisely regulates c-myc transcription and suggest that a small change in FBP-FIR affinity leads to a substantial effect on c-Myc concentration.MRC Grant-in-aid U11757455