Applications of Partial Supersymmetry

I examine quantum mechanical Hamiltonians with partial supersymmetry, and explore two main applications. First, I analyze a theory with a logarithmic spectrum, and show how to use partial supersymmetry to reveal the underlying structure of this theory. This method reveals an intriguing equivalence between two formulations of this theory, one of which is one-dimensional, and the other of which is infinite-dimensional. Second, I demonstrate the use of partial supersymmetry as a tool to obtain the asymptotic energy levels in non-relativistic quantum mechanics in an exceptionally easy way. In the end, I discuss possible extensions of this work, including the possible connections between partial supersymmetry and renormalization group arguments.Comment: 11 pages, harvmac, no figures; typo corrected in identifying info on title pag

The dynamics of chromosome organization and gene regulation

With the sequence of the human genome now complete, studies must focus on how the genome is functionally organized within the confines of the cell nucleus and the dynamic interplay between the genome and its regulatory factors to effectively control gene expression and silencing. In this review I describe our current state of knowledge with regard to the organization of chromosomes within the nucleus and the positioning of active versus inactive genes. In addition, I discuss studies on the dynamics of chromosomes and specific genetic loci within living cells and its relationship to gene activity and the cell cycle. Furthermore, our current understanding of the distribution and dynamics of RNA polymerase II transcription factors is discussed in relation to chromosomal loci and other nuclear domains

MALAT1 Long Non-Coding RNA: Functional Implications

The mammalian genome is pervasively transcribed and the functional significance of many long non-coding RNA (lncRNA) transcripts are gradually being elucidated. Metastasis Associated Lung Adenocarcinoma Transcript 1 (MALAT1) is one of the most well-studied lncRNAs. MALAT1 is a highly conserved nuclear retained lncRNA that is abundantly expressed in cells and tissues and has been shown to play a role in regulating genes at both the transcriptional and post-transcriptional levels in a context-dependent manner. However, Malat1 has been shown to be dispensable for normal development and viability in mice. Interestingly, accumulating evidence suggests that MALAT1 plays an important role in numerous diseases including cancer. Here, we discuss the current state-of-knowledge in regard to MALAT1 with respect to its function, role in diseases, and the potential therapeutic opportunities for targeting MALAT1 using antisense oligonucleotides and small molecules

A genetic locus targeted to the nuclear periphery in living cells maintains its transcriptional competence

The peripheral nuclear lamina, which is largely but not entirely associated with inactive chromatin, is considered to be an important determinant of nuclear structure and gene expression. We present here an inducible system to target a genetic locus to the nuclear lamina in living mammalian cells. Using three-dimensional time-lapse microscopy, we determined that targeting of the locus requires passage through mitosis. Once targeted, the locus remains anchored to the nuclear periphery in interphase as well as in daughter cells after passage through a subsequent mitosis. Upon transcriptional induction, components of the gene expression machinery are recruited to the targeted locus, and we visualized nascent transcripts at the nuclear periphery. The kinetics of transcriptional induction at the nuclear lamina is similar to that observed at an internal nuclear region. This new cell system provides a powerful approach to study the dynamics of gene function at the nuclear periphery in living cells

A BPS Interpretation of Shape Invariance

We show that shape invariance appears when a quantum mechanical model is invariant under a centrally extended superalgebra endowed with an additional symmetry generator, which we dub the shift operator. The familiar mathematical and physical results of shape invariance then arise from the BPS structure associated with this shift operator. The shift operator also ensures that there is a one-to-one correspondence between the energy levels of such a model and the energies of the BPS-saturating states. These findings thus provide a more comprehensive algebraic setting for understanding shape invariance.Comment: 15 pages, 2 figures, LaTe

Disassembly of interchromatin granule clusters alters the coordination of transcription and pre-mRNA splicing

To examine the involvement of interchromatin granule clusters (IGCs) in transcription and pre-mRNA splicing in mammalian cell nuclei, the serine-arginine (SR) protein kinase cdc2-like kinase (Clk)/STY was used as a tool to manipulate IGC integrity in vivo. Both immunofluorescence and transmission electron microscopy analyses of cells overexpressing Clk/STY indicate that IGC components are completely redistributed to a diffuse nuclear localization, leaving no residual structure. Conversely, overexpression of a catalytically inactive mutant, Clk/STY(K190R), causes retention of hypophosphorylated SR proteins in nuclear speckles. Our data suggest that the protein-protein interactions responsible for the clustering of interchromatin granules are disrupted when SR proteins are hyperphosphorylated and stabilized when SR proteins are hypophosphorylated. Interestingly, cells without intact IGCs continue to synthesize nascent transcripts. However, both the accumulation of splicing factors at sites of pre-mRNA synthesis as well as pre-mRNA splicing are dramatically reduced, demonstrating that IGC disassembly perturbs coordination between transcription and pre-mRNA splicing in mammalian cell nuclei